,a ,,class ,,room ,,logic ,,deductive ,,and ,,inductive ,,with ,,special ,,application ,,to ,,the ,,science ,,and ,,art ,,of ,,teaching ,,by ,,george ,,hastings ,mc,n,a,i,r1 ,,ph4 ,d4 ,,head ,,of ,,department ,,of ,,logic ,,and ,,mathematics1 ,,city ,,training ,,school ,,for ,,teachers4 ,,jamaica4 ,,new ,,york ,,city ,,the ,,ethlas ,,press ,,five ,,north ,,broadway4 ,,nyack4 ,,new ,,york ,,copyright1 #aiad1 ,,by ,,george ,,hastings ,mc,n,a,i,r ,to ,,my ,,wife4 ,transcriber's ,notes ,punctuation has been standardized4 ,characters in small caps have been replaced by all caps4 ,non-printable characteristics have been given the following transliteration3 ,italic text3 -- text bold text3 -- text4 ,this book was written in a period when many words had not become standardized in their spelling4 ,words may have multiple spelling variations or inconsistent hyphenation in the text4 ,these have been left unchanged unless indicated with a ,transcriber's ,note4 ,the symbol #8' indicates the description in parenthesis has been added to an illustration4 ,this may be needed if there is no caption or if the caption does not describe the image adequately4 ,index references have not been checked for accuracy4 ,footnotes are identified in the text with a number in brackets #b and have been accumulated in a single section at the end of the text4 ,transcriber's ,notes are used when making corrections to the text or to provide additional information for the modern reader4 ,these notes are not identified in the text1 but have been accumulated in a single section at the end of the book4 ,,preface4 ,this treatise is an outgrowth of our class room work in logic4 ,it has been published in the hope of removing some of the difficulties which handicap the average student4 ,we trust that the language is simple and definite and that the illustrative exercises and diagrams may be helpful in making clear some of the more abstruse topics4 ,if a speedy review for examination is necessary1 it is recommended that the briefer course as outlined on page #dic be followed and that the summaries closing each chapter be carefully read4 ,only the fundamentals of deductive and inductive logic have received attention4 ,moreover emphasis has been given to those phases which appear to commend themselves because of their practical value4 ,further than this we trust that the book may fulfill in some small way the larger mission of inspiring better thinking and1 in consequence1 of leading to a more serviceable citizenship4 ,surely as civilization advances it is with the expectation of giving greater significance to the assumption 8that man is a rational animal40 ,i am indebted to a number of writers on logic1 notably to ,mill1 ,lotze1 ,keynes1 ,hibben1 ,fowler1 ,aikins1 ,hyslop1 ,creighton and ,jevons4 ,i am likewise under obligation to that large body of students who1 by frankly revealing their difficulties1 have given me a different point of view4 ,for constructive criticism and definite encouragement ,i owe a personal debt of gratitude to ,prof4 ,charles ,gray ,shaw of ,new ,york ,university1 to ,prof4 ,frank ,d4 ,blodgett of the ,oneonta ,normal ,school and to ,prin4 ,a4 ,c4 ,mac,lachlan of the ,jamaica ,training ,school for ,teachers4 ,g4 ,h4 ,mc,n4 ,city ,training ,school for ,teachers1 ,jamaica1 ,n4 ,y4 ,city4 ,october #c1 #aiad4 ,,table ,,of ,,contents ,,chapter #a4,,the ,,scope ,,and ,,nature ,,of ,,logic4 #a4 ,the ,mind4 #b4 ,logic ,related to ,other ,subjects4 #c4 ,logic ,defined4 #d4 ,the ,value of ,logic to the ,student4 #e4 ,outline4 #f4 ,summary4 #g4 ,review ,questions4 #h4 ,questions for ,original ,thought and ,investigation4 ,,chapter #b4,,thought ,,and ,,its ,,operation4 #a4 ,the ,knowing ,mind ,compared with the ,thinking ,mind4 #b4 ,knowing by ,intuition4 #c4 ,the ,thinking ,process4 #d4 ,notions1 ,individual and ,general4 #e4 ,knowledge and ,idea as ,related to the ,notion4 #f4 ,the ,logic of the ,psychological ,terms ,involved in the ,notion4 #g4 ,thought in the ,sensation and ,percept4 #h4 ,evolution and the ,thinking ,mind4 #i4 ,the ,concept as a ,thought ,product4 #aj4 ,the ,judgment as a ,thought ,product4 #aa4 ,inference as a ,thought ,product4 #ab4 ,thinking and ,apprehension4 #ac4 ,stages in ,thinking4 #ad4 ,outline4 #ae4 ,summary4 #af4 ,review ,questions4 #ag4 ,questions for ,original ,thought and ,investigation4 ,,chapter #c4,,the ,,primary ,,laws ,,of ,,thought4 #a4 ,two ,fundamental ,laws4 #b4 ,the ,law of ,identity4 #c4 ,the ,law of ,contradiction4 #d4 ,the ,law of ,excluded ,middle4 #e4 ,the ,law of ,sufficient ,reason4 #f4 ,unity of ,primary ,laws of ,thought4 #g4 ,outline4 #h4 ,summary4 #i4 ,illustrative ,exercises4 #aj4 ,review ,questions4 #aa4 ,questions for ,original ,thought and ,investigation4 ,,chapter #d4,,logical ,,terms4 #a4 ,logical ,thought and ,language ,inseparable4 #b4 ,meaning of ,term4 #c4 ,categorematic and ,syncategorematic ,words4 #d4 ,singular ,terms4 #e4 ,general ,terms4 #f4 ,collective and ,distributive ,terms4 #g4 ,concrete and ,abstract ,terms4 #h4 ,connotative and ,non-connotative ,terms4 #i4 ,positive and ,negative ,terms4 #aj4 ,contradictory and ,opposite ,terms4 #aa4 ,privative and ,nego-positive ,terms4 #ab4 ,absolute and ,relative ,terms4 #ac4 ,outline4 #ad4 ,summary4 #ae4 ,illustrative ,exercises4 #af4 ,review ,questions4 #ag4 ,questions for ,original ,thought and ,investigation4 ,,chapter #e4,,the ,,extension ,,and ,,intension ,,of ,,terms4 #a4 ,two-fold ,function of ,connotative ,terms4 #b4 ,extension and ,intension ,defined4 #c4 ,extended ,comparison of ,extension and ,intension4 #d4 ,a ,list of ,connotative ,terms ,used in ,extension and ,intension4 #e4 ,other ,forms of ,expression for ,extension and ,intension4 #f4 ,law of ,variation in ,extension and ,intension4 #f;a4 ,important ,facts in ,law of ,variation4 #f;b4 ,law of ,variation ,diagrammatically ,illustrated4 #g4 ,outline4 #h4 ,summary4 #i4 ,illustrative ,exercises4 #aj4 ,review ,questions4 #aa4 ,questions for ,original ,thought and ,investigation4 ,,chapter #f4;,,definition4 #a4 ,importance4 #b4 ,the ,predicables4 #c4 ,the ,nature of a ,definition4 #d4 ,definition and ,division ,compared4 #e4 ,the ,kinds of ,definitions4 #f4 ,when the ,three ,kinds of ,definitions are ,serviceable4 #g4 ,the ,rules of ,logical ,definition4 #h4 ,terms ,which ,cannot be ,defined ,logically4 #i4 ,definitions of ,common ,educational ,terms4 #aj4 ,outline4 #aa4 ,summary4 #ab4 ,illustrative ,exercises4 #ac4 ,review ,questions4 #ad4 ,questions for ,original ,thought and ,investigation4 ,,chapter #g4,,logical ,,division ,,and ,,classification4 #a4 ,nature of ,logical ,division4 #b4 ,logical ,division ,distinguished from ,enumeration4 #c4 ,logical ,division as ,partition4 #d4 ,four ,rules of ,logical ,division4 #e4 ,dichotomy4 #f4 ,classification ,compared with ,division4 #g4 ,kinds of ,classification4 #h4 ,two ,rules of ,classification4 #i4 ,use of ,division and ,classification4 #aj4 ,outline4 #aa4 ,summary4 #ab4 ,review ,questions4 #ac4 ,questions for ,original ,thought and ,investigation4 ,,chapter #h4,,logical ,,propositions4 #a4 ,the ,nature of ,logical ,propositions4 #b4 ,kinds of ,logical ,propositions4 #c4 ,the ,four ,elements of a ,categorical ,proposition4 #d4 ,logical and ,grammatical ,subject and ,predicate ,distinguished4 #e4 ,the ,four ,kinds of ,categorical ,propositions4 #f4 ,propositions which do not ,conform to ,logical ,type4 #g4 ,propositions not ,necessarily ,illogical4 #h4 ,the ,relation between ,subject and ,predicate4 #i4 ,outline4 #aj4 ,summary4 #aa4 ,illustrative ,exercises4 #ab4 ,review ,questions4 #ac4 ,questions for ,original ,thought and ,investigation4 ,,chapter #i4;,,immediate ,,inference,,opposition4 #a4 ,the ,nature of ,inference4 #b4 ,immediate and ,mediate ,inference4 #c4 ,the ,forms of ,immediate ,inference4 7#a7 ,opposition4 ,,chapter #aj4;,,immediate ,,inference 7,continued74 7#b7 ,immediate ,inference by ,obversion4 7#c7 ,immediate ,inference by ,conversion4 7#d7 ,immediate ,inference by ,contraversion4 #d4 ,epitome of the ,four ,processes of ,immediate ,inference4 ,inference by ,inversion4 #e4 ,outline4 #f4 ,summary4 #g4 ,illustrative ,exercises4 #h4 ,review ,questions4 #i4 ,problems for ,original ,thought and ,investigation4 ,,chapter #aa4,,mediate ,,inference,,the ,,syllogism4 #a4 ,inference and ,reasoning4 #b4 ,the ,syllogism4 #c4 ,the ,rules of the ,syllogism4 #d4 ,rules of ,syllogism ,explained4 #e4 ,aristotle's ,dictum4 #f4 ,canons of the ,syllogism4 #g4 ,mathematical ,axioms4 #h4 ,outline4 #i4 ,summary4 #aj4 ,illustrative ,exercises4 #aa4 ,review ,questions4 #ab4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ab4;,,figures ,,and ,,moods ,,of ,,the ,,syllogism4 #a4 ,the ,four ,figures of the ,syllogism4 #b4 ,the ,moods of the ,syllogism4 #c4 ,testing the ,validity of the ,moods4 #d4 ,special ,canons of the ,four ,figures4 #e4 ,special ,canons ,related4 #f4 ,mnemonic ,lines4 #g4 ,relative ,value of the ,four ,figures4 #h4 ,outline4 #i4 ,summary4 #aj4 ,illustrative ,exercises4 #aa4 ,review ,questions4 #ab4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ac4;,,incomplete ,,syllogisms ,,and ,,irregular ,,arguments4 #a4 ,enthymeme4 #b4 ,epicheirema4 #c4 ,polysyllogisms4 ,prosyllogism,episyllogism4 #d4 ,sorites4 #e4 ,irregular ,arguments4 #f4 ,outline4 #g4 ,summary4 #h4 ,review ,questions4 #i4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ad4;,,categorical ,,arguments ,,tested ,,according ,,to ,,form4 #a4 ,arguments of ,form and ,matter4 #b4 ,order of ,procedure in a ,formal ,testing of ,arguments4 #c4 ,illustrative ,exercise in ,testing ,arguments which are ,complete and whose ,premises are ,logical4 #d4 ,illustrative ,exercise in ,testing ,completed ,arguments1 one or both of whose ,premises are ,illogical4 #e4 ,incomplete and ,irregular ,arguments4 #f4 ,common ,mistakes of the ,student4 #g4 ,outline4 #h4 ,summary4 #i4 ,review ,questions4 #aj4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ae4;,,hypothetical ,,and ,,disjunctive ,,arguments ,,including ,,the ,,dilemma4 #a4 ,three ,kinds of ,arguments4 #b4 ,hypothetical ,arguments4 #c4 ,antecedent and ,consequent4 #d4 ,two ,kinds of ,hypothetical ,arguments4 #e4 ,rule and ,two ,fallacies of ,hypothetical ,argument4 #f4 ,hypothetical ,arguments ,reduced to ,categorical ,form4 #g4 ,illustrative ,exercises ,testing ,hypothetical ,arguments of ,all ,kinds4 #h4 ,disjunctive ,arguments4 #i4 ,two ,kinds of ,disjunctive ,arguments4 #aj4 ,first ,disjunctive ,rule4 #aa4 ,second ,disjunctive ,rule4 #ab4 ,reduction of ,disjunctive ,argument4 #ac4 ,the ,dilemma4 #ad4 ,four ,forms of ,dilemmatic ,arguments4 #ae4 ,the ,rule of ,dilemma4 #af4 ,illustrative ,exercises ,testing ,disjunctive and ,dilemmatic ,argument4 #ag4 ,ordinary ,experiences ,related to ,disjunctive ,proposition and ,hypothetical ,argument4 #ah4 ,outline4 #ai4 ,summary4 #bj4 ,review ,questions4 #ba4 ,questions for ,original ,thought and ,investigation4 ,,chapter #af4,,the ,,logical ,,fallacies ,,of ,,deductive ,,reasoning4 #a4 ,a ,negative ,aspect4 #b4 ,paralogism and ,sophism4 #c4 ,a ,division of the ,deductive ,fallacies4 #d4 ,general ,divisions ,explained4 #e4 ,fallacies of ,immediate ,inference4 #f4 ,fallacies in ,language 7,equivocation74 #g4 ,fallacies in ,thought 7,assumption74 #h4 ,outline4 #i4 ,summary4 #aj4 ,illustrative ,exercises in ,testing ,arguments in ,both ,form and ,meaning4 #aa4 ,review ,questions4 #ab4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ag4;,,inductive ,,reasoning4 #a4 ,inductive and ,deductive ,reasoning ,distinguished4 #b4 ,the 8,inductive ,hazard40 #c4 ,complexity of the ,problem of ,induction4 #d4 ,various ,conceptions of ,induction4 #e4 ,induction and ,deduction ,contiguous ,processes4 #f4 ,induction an ,assumption4 #g4 ,universal ,causation4 #h4 ,uniformity of ,nature4 #i4 ,inductive ,assumptions ,justified4 #aj4 ,three ,forms of ,inductive ,research4 #aa4 ,induction by ,simple ,enumeration4 #ab4 ,induction by ,analogy4 #ac4 ,induction by ,analysis4 #ad4 ,perfect ,induction4 #ae4 ,traduction4 #af4 ,outline4 #ag4 ,summary4 #ah4 ,review ,questions4 #ai4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ah4,,mill',s ,,five ,,special ,,methods ,,of ,,observation ,,and ,,experiment4 #a4 ,aim of ,five ,methods4 #b4 ,method of ,agreement4 #c4 ,method of ,difference4 #d4 ,the ,joint ,method of ,agreement and ,difference4 #e4 ,the ,method of ,concomitant ,variations4 #f4 ,the ,method of ,residues4 #g4 ,general ,purpose and ,unity of ,five ,methods4 #h4 ,outline4 #i4 ,summary4 #aj4 ,review ,questions4 #aa4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ai4;,,auxiliary ,,elements ,,in ,,induction4 ,,observation,,experiment,,hypothesis4 #a4 ,foundation of ,inductive ,generalizations4 #b4 ,observation4 #c4 ,experiment4 #d4 ,rules for ,logical ,observation and ,experiment4 #e4 ,common ,errors of ,observation and ,experiment4 #f4 ,the ,hypothesis4 #g4 ,induction and ,hypothesis ,distinguished4 #h4 ,hypothesis and ,theory ,distinguished4 #i4 ,the ,requirements of a ,permissible ,hypothesis4 #aj4 ,uses of ,hypothesis4 #aa4 ,characteristics ,needed by ,scientific ,investigators4 #ab4 ,outline4 #ac4 ,summary4 #ad4 ,review ,questions4 #ae4 ,questions for ,original ,thought and ,investigation4 ,,chapter #bj4,,logic ,,in ,,the ,,class ,,room4 #a4 ,thought is ,king4 #b4 ,special ,functions of ,induction and ,deduction4 #c4 ,two ,types of ,minds4 #d4 ,conservatism in ,school4 #e4 ,the ,method of the ,discoverer4 #f4 ,real ,inductive ,method not in ,vogue in ,class ,room ,work4 #g4 ,as a ,method of ,instruction1 ,deduction ,superior4 #h4 ,conquest1 not ,knowledge1 the ,desideratum4 #i4 ,motivation as ,related to ,spirit of ,discovery4 #aj4 ,discoverer's ,method ,adapted to ,class ,room ,work4 #aa4 ,question and ,answer ,method not ,necessarily ,one of ,discovery4 #ab4 ,outline4 #ac4 ,summary4 #ad4 ,review ,questions4 #ae4 ,questions for ,original ,thought and ,investigation4 ,,chapter #ba4,,logic ,,and ,,life4 #a4 ,logic ,given a ,place in a ,secondary ,course4 #b4 ,man's ,supremacy ,due to ,power of ,thought4 #c4 ,importance of ,progressive ,thinking4 #d4 ,necessity of ,right ,thinking4 #e4 ,indifferent and ,careless ,thought4 #f4 ,the ,rationalization of the ,world of ,chance4 #g4 ,the ,rationalization of ,business and ,political ,sophistries4 #h4 ,the ,rationalization of the ,spirit of ,progress4 #i4 ,a ,rationalization of the ,attitude ,toward ,work4 #aj4 ,the ,logic of ,success4 #aa4 ,outline4 #ab4 ,summary4 #ac4 ,review ,questions4 #ad4 ,questions for ,original ,thought and ,investigation4 ,,general ,,exercises ,,in ,,testing ,,categorical ,,arguments4 ,,general ,,exercises ,,in ,,testing ,,hypothetical1 ,,disjunctive ,,and ,,dilemmatic ,,arguments4 ,,examination ,,questions ,,for ,,training ,,schools ,,and ,,colleges4 ,,bibliography4 ,,outline ,,of ,,briefer ,,course4 ,,index4 ,,chapter #a4 ,,the ,,scope ,,and ,,nature ,,of ,,logic4 #a4 ,,the ,,mind4 ,as to the true conception of matter the world is ignorant4 ,yet when asked1 8,what does matter do80 the reply is1 8,matter moves1 matter vibrates40 ,moreover1 relative to the exact nature of mind1 the world is likewise ignorant4 ,but to the question1 8,what does mind do80 the response comes1 8,the ,mind knows1 the mind feels1 the mind wills40 ,the mind has ever manifested itself in these three ways4 ,because of this three-fold function it is easy to think of the mind as being separated into distinct compartments1 each constituting an independent activity4 ,this is erroneous4 ,the mind is a living unit having three sides but never acting one side at a time4 ,when the mind knows it also feels in some way and wills to some extent4 ,to illustrate3 ,music is heard and one knows it to be ,rubinstein's ,melody in ,f4 ,the execution being good one feels pleasure4 ,that the pleasurable state may be augmented one wills a listening attitude4 ,for analytical purposes the psychologists have a way of naming the state of mind from the predominating manifestation4 #b4 ,,logic ,,related ,,to ,,other ,,subjects4 ,what the mind is may in time be answered satisfactorily by philosophy2 what the mind does is described by psychology2 what the mind knows is treated by logic4 ,again3 the mind as a whole furnishes the subject matter for psychology1 whereas logic is concerned with the mind knowing1 aesthetics with the mind feeling1 and ethics with the mind willing4 ,ethics attempts to answer the question1 8,what is right80 aesthetics1 8,what is beautiful80 and logic1 8,what is true80 ,though both psychology and logic treat of the knowing aspect of the mind1 yet the fields are not identical4 ,the former deals with the process of the knowing mind as a whole1 while the latter is concerned mainly with the product of the knowing mind when it thinks4 ,to be specific3 ,the mind knows when it becomes aware of anything1 moreover1 this condition of awareness appears in two ways3 first1 immediately or by intuition2 second1 after deliberation or by thinking4 ,for example1 one may know immediately or by intuition that the object in the hand is a lead pencil1 but when requested to state the length of the pencil there is deliberation involving a comparison of the unknown length with a definite measure4 ,it may now finally be asserted that the pencil is six inches long4 ,when we know without hesitation the process involved is intuition1 whereas when the knowledge comes after some sort of comparison the mental act is called thinking4 ,it1 therefore1 becomes the business of psychology to deal with both intuition and thinking while logic devotes its attention to thinking only1 and even in this field the work of logic is more or less indirect4 ,the specific scope of logic is the product of thinking or thought4#a ,what are the forms of thought8 ,what are the laws of thought8 ,are the several thoughts true8 ,these are the questions which logic is supposed to answer4 ,for the logician thought has two sources1 his own mind and the mind of others4 ,in the latter case thought becomes accessible through the medium of language4 ,there is in consequence a close connection between logic1 the science of thought1 and grammar1 the science of language4 ,because of this near relation logic is sometimes called the 8grammar of thought40 ,to study any science properly one must have thoughts and since logic is the science of all thought the subject may be regarded as the science of sciences4 #c4 ,,logic ,,defined4 8,logic is the science of thought40 ,this definition commonly given is too brief to be helpful4 ,should not a definition of any subject represent a working basis upon which one may build with some knowledge of what the structure is to be8 ,the following1 a little out of the ordinary1 seems to supply this condition3 ,logic as a science makes known the laws and forms of thought and as an art suggests conditions which must be fulfilled to think rightly4 ,in justification of the latter definition it may be argued that it covers the topics usually treated by logicians4 ,it is said that a science teaches us to know while an art teaches us to do4 ,as a science logic teaches us to know certain laws which underlie right thinking4 ,for example1 the law of identity which makes possible all affirmative judgments1 such as 8,some men are wise10 8,all metals are elements10 etc4 ,likewise as a science logic acquaints us with certain universal forms to which thought shapes itself1 such as definitions1 classifications1 inductions1 deductions4 ,further1 logic lays down definite rules which lead to right thinking4 ,to wit3 ,because it is true of a part of a class it should not be assumed that it is true of the whole of that class3 or1 in short1 do not distribute an undistributed term4 ,a possible profit to the student may result from a study of certain authentic definitions herewith subjoined3 7#a7 8,logic is the science of the laws of thought40 ,jevons4 7#b7 8,logic is the science which investigates the process of thinking40 ,creighton4 7#c7 8,logic as a science aims to ascertain what are the laws of thought2 as an art it aims to apply these laws to the detection of fallacies or for the determination of correct reasoning40 ,hyslop4 7#d7 8,logic is the art of thinking40 ,watts4 7#e7 8,logic is the science and also the art of thinking40 ,whateley4 7#f7 8,logic is the science of the formal and necessary laws of thought40 ,hamilton4 7#g7 8,logic is the science of the regulative laws of the human understanding40 ,ueberweg4 7#h7 8,logic treats of the nature and of the laws of thought40 ,hibben4 7#i7 8,logic may be defined as the science of the conditions on which correct thoughts depend1 and the art of attaining to correct and avoiding incorrect thoughts40 ,fowler4 7#aj7 8,logic is the science of the operations of the understanding which are subservient to the estimation of evidence40 ,mill4 7#aa7 8,logic may be briefly described as a body of doctrines and rules having reference to truth40 ,bain4 ,it would seem as if there were as many different definitions as there are books on the subject4 ,this is due partly to the disposition of the older logicians to ignore the art of logic and partly to the difficulty of giving in a few words a satisfactory description of a broad subject4 ,in the fundamentals of logical doctrine present-day authorities virtually agree4 #d4 ,,the ,,value ,,of ,,logic ,,to ,,the ,,student4 ,logic is rapidly coming into favor as a major subject in institutions devoted to educational theory4 ,some of the reasons for this change of attitude are herewith subjoined3 7#a7 ,logic should stimulate the thought powers4 ,this is the age of the survival of the thinker4 ,the fact that the man who thinks best is the man who thinks much and carefully will be accepted by those who believe that practice makes perfect4 8,one needs only to observe the average commuter to conclude that a large percent4 of our business men read too much and think too little40 8,much readee and no thinkee0 was the reply of a ,chinaman when asked his opinion of the doings of the average ,american4 8,we as a people are newspaper mad1 reading for entertainment1 seldom for mental improvement40 7#b7 ,logic aims to secure correct thought4 ,are not many of the sins and most of the failures in this world due to incorrect thinking8 7#c7 ,logic should train to clear thinking4 ,it would be difficult to estimate the loss of energy to the brain worker because he has not the power to think clearly4 ,maximum efficiency is impossible with a befogged brain4 ,how discouraging it is to the student to attempt to get from the paragraph the thought of the author1 who in trying to be profound succeeds in being profoundly abstruse4 ,there is a probable need for broad1 deep thoughts1 but these when placed in a text book should be sharpened to a point4 7#d7 ,logic should aid one to estimate aright the statements and arguments of others4 ,this is of especial value to the teacher who is constrained to teach largely from text books4 ,because it is found in a book is not proof positive that it is true4 ,why should we assume that the book is infallible when we know that the man behind the book is fallible8 7#e7 ,logic insists on definite1 systematic procedure4 ,to be logical is to be businesslike4 ,a study of logic would1 no doubt1 benefit our churches and parliamentary orders as well as our schools4 7#f7 ,logic demands lucid1 pointed1 accurate expression4 ,how we would increase our working efficiency could we but express our thoughts in an attractive and interesting manner4 ,to listen to the speeches of some of our great and good men who are concerned in directing the 8ship of state0 is sufficient argument that the ,american schools need more logic4 7#g7 ,logic is especially adapted to a general mental training4 ,despite the swing of the pendulum of public opinion toward the bread-and-butter side of life1 there are many of high repute who claim that for the sake of that mental acumen which distinguished the ,greek from his contemporaries we cannot afford to sacrifice everything on the altar of commercialism4 7#h7 ,logic worships at the shrine of truth and adds to our store of knowledge4 ,what has aided the world more in its march onward than this deep-seated passion for truth and what has impeded it more than that vain and wanton indifference to truth which brought to the world its darkest age8 #e4 ,,outline ,,the ,,scope ,,and ,,nature ,,of ,,logic4 7#a7 ,the ,mind4 ,three aspects4 ,unity of4 7#b7 ,logic ,related to ,other ,subjects4 ,mental philosophy1 psychology1 logic4 ,psychology1 logic1 aesthetics1 ethics4 ,two ways of knowing4 ,special province of logic4 ,logic and language4 ,a science of sciences4 7#c7 ,logic ,defined4 ,a general definition4 ,a more satisfactory definition4 ,a list of authentic definitions4 7#d7 ,the ,value of ,logic to the ,student4 ,eight reasons for its study4 #f4 ,,summary4 7#a7 ,the aspects of the mind are knowing1 feeling and willing4 ,the mind is a living unit and never knows without feeling in some way and willing to some extent4 7#b7 ,what the mind is must be answered by philosophy2 what the mind does by psychology and what the mind knows by logic4 ,psychology treats of the mind as a whole1 logic of the mind knowing1 aesthetics of the mind feeling and ethics of the mind willing4 ,ethics answers the question1 ,what is right8 ,aesthetics1 ,what is beautiful8 ,logic1 ,what is true8 ,the standpoint of logic is not identical with any particular portion of psychology4 ,the mind knows in two ways3 7a7 by intuition1 7b7 by thinking4 ,thinking is a processthought a product4 ,logic deals indirectly with the former and directly with the latter4 ,generally speaking1 logic is a systematic study of thought4 ,for the logician thought has two sources3 7a7 his own mind and 7b7 spoken or written language4 ,because of the ambiguity of language logic has much to do with it as a faulty vehicle of thought4 7#c7 ,logic as a science makes known the laws and forms of thought and as an art suggests conditions which must be fulfilled to think rightly4 ,author4 8,logic may be defined as the science of the conditions on which correct thoughts depend1 and the art of attaining to correct and avoiding incorrect thoughts40 ,fowler4 ,in the fundamentals of logical doctrine present day logicians virtually agree4 7#d7 ,logic should stimulate the thought powers2 secure correct and clear thinking2 aid in the estimation of arguments2 inspire definite1 systematic procedure2 demand lucid1 pointed1 accurate expression and be especially adapted to general mental discipline4 ,logic adds to our store of knowledge and develops a passion for the truth4 #g4 ,,review ,,questions4 7#a7 ,explain and illustrate the three ways in which the mind may manifest itself4 7#b7 ,illustrate the fact that the mind acts in unity4 7#c7 ,show briefly how logic is related to mental philosophy1 psychology1 aesthetics1 ethics and grammar4 7#d7 ,illustrate the two ways of knowing4 7#e7 ,distinguish between thinking and thought4 7#f7 ,give a general definition of logic4 ,why is this definition unsatisfactory8 7#g7 ,what are the two sources of thought8 7#h7 ,why are logic and language so closely related8 7#i7 ,give that definition of logic which best satisfies you4 7#aj7 ,summarize the benefits which you hope to derive from your study of logic4 7#aa7 ,why should teachers be clear thinkers8 7#ab7 ,why should teachers be especially on guard against incorrect statements of all kinds8 7#ac7 ,show how logic might be of assistance to the business man4 #h4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,prove that there is nothing real in the world save the mind itself4 7#b7 8,logic is concerned primarily with how we ought to think and only in a secondary way with how we actually think40 ,explain this quotation4 7#c7 ,prove that there is no such thing as intuitive knowing4 7#d7 ,is there any difference between knowledge and thoughts8 ,illustrate4 7#e7 ,show by illustrations that the ,english language is ambiguous4 7#f7 ,prove by concrete illustration that this is the age of the survival of the thinker4 7#g7 ,which is the more harmful3 falsehood mixed with truth or unadulterated falsehood8 ,give reasons4 7#h7 ,give a concrete example of incorrect thinking4 7#i7 ,show that wrong thinking leads to wrong doing4 7#aj7 ,to be worth while must every subject have a practical value8 7#aa7 8,the #bjth century virtue is a passion for truth40 ,prove the truth of this4 ,,chapter #b4 ,,thought ,,and ,,its ,,operation4 #a4 ,,the ,,knowing ,,mind ,,compared ,,with ,,the ,,thinking ,,mind4 ,in the preceding chapter we were told that the mind may know in two ways 7#a7 by intuition and 7#b7 by thinking4 ,it is thus implied that the knowing mind includes the thinking mind plus intuition4 ,thinking always involves knowing1 but knowing need not involve thinking1 and when some logicians maintain that to know a thing one must think it1 there is danger of being misled4 ,they mean by this that in order to know anything in a permanent and highly serviceable way one must think it4 ,all animals know1 even such a stupid one as the oyster1 and yet one would hardly give an oyster credit for thinking4 ,only the higher orders of animal life think4 ,some argue that the power is confined exclusively to the human family4 ,this opinion is debatable4 ,if the claimant means by thinking1 reasoning then his ground is well taken4 ,but if he is willing to give to thinking a broader content1 then he has little defense for his stand4 ,however1 attach as broad a meaning to thinking as the derivation of the word will permit and even then it is a narrower term than knowing4 ,thinking plus intuition equals knowing1 and in intuition there is probably no thinking4 #b4 ,,knowing ,,by ,,intuition4 ,it has been affirmed that intuition is the process involved when the mind knows instantly4#b ,,illustrations3 7#a7 ,as ,i raise my eyes a figure comes to view4 ,my mind knows instantly that it is the figure three4 7#b7 ,the ear catches immediately a tune which is being sung in the room below4 ,without deliberation the mind recognizes the tune as ,america4 ,the mind may thus know by intuition through any one of the five senses4 ,these are the wires of connection between the outer world and the mind within and transmission over these wires may be instantaneous or intuitive4 ,this is not all4 7#c7 ,my mind may center its attention on itself and may recognize there a mental picture or image of a pet dog4 ,since this activity is without any apparent deliberation the process must be intuitive4 ,to define intuitive knowledge as that which comes to the mind through the senses only is incorrect1 as it leaves out altogether the knowledge the mind may obtain of its own activity as in illustration 87#c740 ,knowledge is anything known4 ,intuitive knowledge is knowledge which comes to the mind immediately by direct observation4 ,the field for intuitive knowledge may be the external world or the internal world though1 of course1 the former is the more common ground4 ,it is here that the mind by intuition secures the most of its raw material which1 through the process of thinking1 is worked over into a connected1 unified system of lasting value4 ,the intuitions are the beginning and the basis of all knowledge1 and knowledge gained by intuition is the basis of all thinking4 #c4 ,,the ,,thinking ,,process4 ,it is claimed that think comes from the same root as thick4 ,from this one would conclude that the process of thinking is virtually a process of thickening4 ,surely as one thinks he enriches or thickens his knowledge4 ,as one thinks percepts into concepts and concepts into judgments he makes richer in meaning the various notions concerned4 ,thinking is largely a matter of pressing many into one3 of linking together the disconnected fragments of the conscious field4 ,,definition3 ,thinking is the deliberative process of affirming or denying connections4 ,the same idea may be expressed in a variety of ways as the following indicate4 7#a7 8,thinking is the conscious adjustment of a means to an end in problematic situations40 ,miller4 7#b7 8,to think is to designate an object through a mark or attribute or what is the same thing1 to determine a subject through a predicate40 ,bowen4 7#c7 8,thought is the comprehension of a thing under a general notion or attribute40 ,wm4 ,hamilton4 7#d7 8,to think is to make clear through concepts the perceived objects40 ,dressler4 ,in the foregoing definitions it is implied that thinking is a connecting or thickening process4 ,in all forms of thinking from the simplest to the most complex the knowing mind hunts for some basis of connection and having found it thinks the relationship into a unified whole4 ,the thinking process is the digestive process of the mind4 ,much as the digestive organs assimilate the food stuff of the physical world1 so the thinking organ assimilates the food stuff of the mental world4 ,,illustrations ,,of ,,the ,,thinking ,,process3 7#a7 ,the child is unable to explain the meaning of 8hocus-pocus0 as it occurs in the question1 8,what hocus-pocus is this80 ,the child mind is unable to establish any connection between the word and its real meaning4 ,in short1 is unable to think into it a meaning2 it therefore becomes necessary for the teacher to establish some basis of connection and this he does by suggesting nonsense as a synonym4 7#b7 ,the teacher holds before the class an ,egyptian house god and asks1 8,what is it80 ,after a moment of hesitation some child who has seen pictures of 8his satanic majesty0 avers that the object is a 8little devil40 ,thus has a connection been established between the idol and pictures of satan4 7#c7 ,john is unable to solve the following problem as he can discern no connection between the data given and the data required4 ,problem4 #c_/d of my salary is #ijj1 what is my salary8 ,data4 ,given3 #c_/d of salary #ijj4 ,required3 #d_/d of salary 8 ,in order that ,john may think a solution the teacher must lead him to see some connection between #c_/d and #d_/d4 ,with this in mind the form of the data is changed to ,given3 #c-;fourths #ijj ,required3 #d-;fourths 8 or ,given3 #c parts #ijj ,required3 #d parts 8 ,john now notes that #d parts is #d_/c times #c parts and consequently writes #d_/c of #ijj1 which is #a1bjj as the answer4 ,or he may find the value of #a part and then of #d parts4 #d4 ,,notions1 ,,individual ,,and ,,general4 ,a notion is any product of the knowing mindanything which the mind notes or becomes aware of4 ,but the mind knows in two ways1 by intuition and by thinking4 ,in consequence the mind has two kinds of notions1 those which are intuitive or individual notions and those which originally result from thinking or general notions4 ,an individual notion is a notion of one thing4 ,a general notion is a notion of a class of things4 ,note4 ,here it is necessary to distinguish between a thing and an object4 ,an object is a thing which occupies space such as a pencil or a book4 8,thing0 is1 therefore1 a broader term than 8object40 8,a thing is that which has individual existence40 ,from the viewpoint of logic 8thing0 includes objects1 qualities1 relations1 spiritual entities4 ,gravitation is a thing but not an object4 ,a tree is both an object and a thing4 ,,illustrations ,,of ,,notions4 ,my notion of the pencil with which ,i am writing is an individual notion1 but my notion of pencil as a class name is general4 ,my yellow dog1 the honesty of ,lincoln1 ,albert ,white1 ,new ,york ,city1 are individual notions1 while dog1 honesty1 man1 city1 are general notions4 ,a sure way to determine whether the notion is individual or general is to attempt to divide it into its kinds4 ,only general notions may be subdivided4 #e4 ,,knowledge ,,and ,,idea ,,as ,,related ,,to ,,the ,,notion4 ,knowledge is anything known1 while anything of which the mind becomes aware is a notion4 ,notions are always bits of knowledge1 but knowledge is not always a notion4 ,notions are mental products belonging to the mind which thinks them1 while knowledge1 though it must first be a mental product of someone's mind1 may not necessarily be a product of yours or mine4 ,notions are always found in the mind1 while knowledge may be found in books1 but not necessarily in some individual mind4 ,knowledge stands for everything known1 the notion1 for everything noted4 ,the ,egyptians may have possessed much knowledge of which we may never become aware4 ,much of their knowledge may never become notions of the ,american people4 ,a notion is an existing state of consciousness4 ,said notion may be committed to paper1 and then it may give way to another notion4 ,it now ceases to be your notion1 but remains on the printed page1 as a bit of knowledge4 8,idea10 because of its ambiguity1 really has no place in logic4 ,the term is frequently restricted to a reproduced percept4 ,to illustrate3 ,when the pencil is before me the mental product is a percept1 but when the pencil is withdrawn and ,i try to think of it1 then have ,i an idea of 8pencil40 ,probably idea is most commonly associated with meaning and belief4 ,to illustrate3 ,what is your idea as to the meaning of homogeny8 or ,what are your ideas on the tariff8 #f4 ,,the ,,logic ,,of ,,the ,,psychological ,,terms ,,involved ,,in ,,the ,,notion4 ,concerning the knowing mind the psychologist classifies its activities and their products as follows3 ,activity ,product 7#a7 ,presentative 7#a7 ,sensation ,sensation 7#b7 ,perception ,percept 7#b7 ,representative 7#a7 ,imagination ,image 7#b7 ,memory 7#c7 ,thinking 7#a7 ,conception ,concept 7#b7 ,judging ,judgment 7#c7 ,reasoning ,inference ,the notion as any product of the knowing mind includes the six products as indicated by the psychologist4 ,the individual notion which is intuitive includes the sensation1 percept and image2 the general notion which is a thought product stands for the concept1 judgment and inference4 ,to put it mathematically sensation ,individual notion percept intuitive products image notion concept ,general notion judgment thought products inference ,as we shall have occasion frequently to refer to these psychological terms it may be well to define them4 ,psychological ,definition4 ,logical ,definition4 ,a sensation is the first and ,a sensation is a vague1 simplest mental result of the unlocalized mental product of stimulation of an incarrying the knowing mind4 nerve4 ,a percept is a mental ,a percept is a consciously product which results from a localized group of sensations4 consciousness of particular material things present to the sense4 ,an image is a mental product ,an image is a reproduced which results from particular percept4 material things not present to the sense4 ,a concept is a representation ,a concept is a mental product in our minds answering to a arising from thinking many general name4 notions into one class4 ,a judgment is the result of ,a judgment is the mental asserting an agreement or product arising from conjoining disagreement between two ideas4 or disjoining notions4 ,an inference is a judgment ,an inference is a judgment derived from perceiving derived from antecedent relations between other judgments4 judgments4 ,it is seen that the sensations furnish the raw material4 ,ignoring the few exceptions we may then say that a percept is a made-over group of sensations2 a concept a thought-made group of percepts2 a judgment a thought-made group of concepts2 an inference a judgment derived from other judgments4 ,developed thinking is first found in the concept1 and as we study the thought products1 8concept10 8judgment0 and 8inference10 the truth is forced upon us that thinking as a process aims to group the many into one4 ,from many percepts is built the one concept1 from two concepts is built the one judgment and from two judgments is built the one inference4#c ,speaking figuratively1 thinking is a matter of picking up the fragments along the shore of consciousness and tying them into bundles4 #g4 ,,thought ,,in ,,the ,,sensation ,,and ,,percept4 ,so far in this discussion it has been assumed that there is no thinking involved in the sensation or the percept4 ,there are good authorities1 however1 who insist on dignifying the sensation1 even with a crude form of thinking4 ,to illustrate3 ,one may be reading an interesting novel4 ,the mind is being entertained and ignores the activities of the objective world1 yet we cannot say that the mind is dead to the world outside4 ,there is a dim consciousness of certain noises without4 ,these unlocalized sounds are sensations2 but how is the mind able to recognize them as sounds or noises8 ,to interpret the noises is it not necessary for the mind to affirm a connection between them and some past mental experience8 ,is it possible for the mind to know anything without establishing some kind of connection between the outside occurrence and an inner situation8 ,if this is granted then in sensation there must be implicit thinking4 ,as the percept is a localized group of sensations then there must be involved in perception a more complex form of thinking1 since in grouping sensations there is a recognition of connections4 ,if there is thinking in the sensation which is the simplest and lowest form of the knowing-mind then thinking conditions all knowledge and really is the basic elemental cell of all knowing4 ,on the other hand there are those who maintain that the sensation and percept are mere reflections of consciousness2 the sensation being a reflected quality and the percept a reflected object4 ,these mental situations come into being instantlythere is no time for thought and we all know that thought requires time4 78,as quick as thought0 is misleading1 since light travels more rapidly by many times than the agencies of thought47 ,it will probably never be settled to the satisfaction of all just when thinking commences4 ,the question is as difficult as some others which have never been solved4 ,for example3 ,where does life commence8 ,when does the plant merge into the animal8 ,which was first the egg or the hen8 ,does the objective world really exist or is it only a mental interpretation of vibrations8 etc4 ,logically considered the question is immaterial4 ,all will agree that developed thought is involved in the concept1 judgment and inference1 while1 if it appears at all in the percept and sensation1 it is more or less undeveloped and consequently lies quite without the province of the logical field4 #h4 ,,evolution ,,and ,,the ,,thinking ,,mind4 ,speaking in general terms evolution is a development from a lower to a higher state4 ,thus have come the various species of the vegetable and animal world4 ,the lower orders of life are simple in structure and function4 ,in the one-celled animate form a single organ performs all of the work needed to maintain life and perpetuate the species4 ,if these simple life-forms are cut in two1 life continues in the two parts as if nothing had happened4 ,aside from their simplicity there is little of interdependence of function and little of co-ordination of organs in the lowest life-forms4 ,in short there is no division of labor2 8each cell is a world unto itself40 ,an analogous development is seen in the thinking mind4 ,the little child thinks in lumps1 and these lumps are only faultily linked together1 but the adult thinks in terms of the grains of the lump1 each grain having its place1 which it must occupy for the sake of all the other grains as well as the entire lump4 ,the child's thinking is vague1 general and inaccurate1 while the adult's thinking should be definite1 specialized and accurate4 ,thinking in the lump means little discrimination and very faulty integration or unity1 while thinking in terms of the grains means detailed discrimination and perfect integration4 ,to illustrate3 ,the child sees a dog trotting along the side walk which1 according to the suggestion of his mother1 he learns to call 8bow-wow40 ,later he observes a cat and at once says 8bow-wow10 because all that the child notes is that something with legs1 ears and a tail is trotting along the side walk4 ,anything which fits these general marks is a 8bow-wow40 ,similarly when a child first observes a robin perched on a gate post he fails to distinguish between the twoit is all bird from the top of the robin's head to the bottom of the gate post4 ,progress in thinking is measured by progress in discrimination4 ,the skilled thinker divides the large unit into very small units1 compares these with each other and then reunites them into a more perfect and unified whole4 ,first there is an analysis and then a synthesis4 ,like a shuttle the power of thought works in and out2 it goes in to separate1 it comes out to unify4 ,there is another aspect in the analogy between the life of the physical and mental worlds4 ,somewhere in the order of progress there is a connecting link between the mineral and vegetable kingdoms1 likewise between the vegetable and animal kingdoms4 ,the sensation is as much a state of feeling as an act of knowing and consequently is the connecting link between the feeling mind and the knowing mind4 ,if the percept is the result of thinking as well as intuition then it may stand for the dividing line between the knowing#d mind and the thinking mind4 #i4 ,,the ,,concept ,,as ,a ,,thought ,,product4 ,conception is the process of thinking many notions into one class4 ,the product of such a process is called a concept4 7#a7 ,the concept may stand for a group of concrete general notionsas the concept man1 which stands for the five general notions3 ,caucasian1 ,mongolian1 ,ethiopian1 ,malay and ,american ,indian4 7#b7 ,the concept may stand for a group of concrete individual notions4 ,for example1 the same concept man represents all of the individual men of the world4 7#c7 ,the concept may stand for a group of abstract general notions4 ,to wit3 ,virtue represents such general notions as honesty1 justice1 industry1 purity1 etc4 7,these are general notions because they admit of a subdivision into kinds4 ,industry1 for instance1 may be divided into two kinds3 mental industry and physical industry47 7#d7 ,the concept may stand for a group of abstract individual notions4 ,to illustrate3 ,blueness stands for the various shades of blue1 as sky blue1 bird's egg blue1 navy blue1 etc4 ,thus does the concept stand for a group of all kinds of notions1 individual and general1 abstract and concrete4 ,,the ,,process ,,of ,,conception ,,illustrated4 ,i see for the first time in my life a pencil4 ,in other words ,i become conscious of a localized group of sensationsthis is a percept4 ,i am told that the name of that which ,i see is pencil4 ,i note that this particular pencil has a thread of black lead encased in a cylindrical strip of wood which is brown in color4 ,a second object is presented which ,i recognize as a pencil though the shape is prismatic rather than cylindrical and the color green rather than brown4 ,but ,i call it a pencil because it has a thread of black lead encased in a strip of wood4 ,the notion which ,i now have in mind stands for two pencils and is therefore represented by a class name4 ,as ,i observe other pencils of various shapes1 made of wood and paper with threads of different colored lead1 my notion of pencil broadens till finally it stands for all pencils4 ,this is the process of conception according to the definition1 namely3 8,the process of thinking many notions into one class40 ,in this case the notions are individual4 ,an examination of conception makes evident two distinct characteristics4 ,first1 ,i may be able to recognize each individual pencil because of the two common qualities1 a thread of lead and an encasement of some kind4 ,this process of the knowing mind whereby it recognizes and affirms connections is called thinking as we have already learned4 ,here is the thinking aspect of conception4 ,second1 as the instances of the observed objects are multiplied1 my notion of pencil is broadened4 ,it is a building process where many are cemented into one2 like the blocks of a cement wall4 ,here we find the characteristic which enables us to call the process conception4 ,this is the mark which distinguishes conception from all the other thought processes4 #aj4 ,,the ,,judgment ,,as ,a ,,thought ,,product4 ,judging is the process of conjoining and disjoining notions4 ,the product of judging is the judgment and all judgments are expressed by means of propositions4 ,a proposition consists of one subject and one predicate connected by some form of the verb be or its equivalent4 7#a7 ,a judgment may conjoin or disjoin two individual notions4 ,to wit3 ,conjoined,this pencil belongs to ,albert ,white4 ,disjoined,this pencil does not belong to ,mary ,smith4 7#b7 ,a judgment may conjoin or disjoin two general notions4 ,conjoined,some men are virtuous4 ,disjoined,some men are not virtuous4 7#c7 ,a judgment may conjoin or disjoin a general and an individual notion4 ,conjoined,abraham ,lincoln was virtuous4 ,disjoined,edgar ,allen ,poe was not temperate4 ,in order that the knowing mind may conjoin notions it must recognize some mark of similarity or connection4 ,this is the thinking aspect of the judgment4 ,it is likewise to a certain degree the judging aspect as the latter is simply a matter of affirming or denying connections between notions4 ,but thinking is a broader term than judging4 ,there may be connections established between a name and a notion4 ,for example in the case of the dog which the child sees trotting along the sidewalk and which the mother refers to as a 8bow-wow02 the term 8bow-wow0 is not a percept and has no meaning independent of its association with the dog1 hence it is not a notion1 yet some connection has been made in the child's mind between 8bow-wow0 and his notion of dog4 ,this is a simple form of thinking1 but not of judging1 as the latter affirms or denies connections between notions only4 ,the fact that judging and thinking so closely resemble each other has given just cause for some logicians to designate judging as the most fundamental element in all thinking4 8,the simplest form of thinking10 says ,creighton1 8is judging40 ,in order to think many notions into one class it is necessary to conjoin notions4 ,to illustrate3 ,the child who has a general notion of man sees for the first time a negro4 ,if he recognizes the negro as a colored man he must conjoin his general notion of man with this individual notion4 ,in short1 a concept is built by means of a series of judgments4 ,it may be said further that an inference is simply a made-over judgment4 ,it is thus evident that judging appears in both the thought processes of conception and inference and1 therefore1 as a final conclusion it may be affirmed that judging1 though perhaps not the simplest form of thinking1 is the basic element of developed thought4 #aa4 ,,inference ,,as ,a ,,thought ,,product4 ,reasoning is the process of deriving a new judgment from a consideration of other judgments4 ,the product of any reasoning process may be called an inference1 although1 as will appear in a later chapter1 inference is commonly used as indicating the process as well as the product4 ,often reasoning may assume a syllogistic form with the inference as its conclusion4 ,a syllogism is an arrangement of three propositions using three different terms4 ,the following are syllogisms3 7#a7 ,all children should play4 ,mary is a child4 ,hence1 ,mary should play4 7#b7 ,no teacher should judge hastily4 ,you are a teacher4 ,hence1 you should not judge hastily4 ,in the second syllogism the inference1 8you should not judge hastily10 is derived from the other two judgments by merely eliminating the common term teacher and disjoining the remaining two terms4 ,the inference is consequently a new judgment4 ,therefore1 reasoning is only a matter of judging carried to a more complex stage4 ,to summarizeconception is largely a matter of conjoining a general notion with an individual notion1 judging of conjoining and disjoining all kinds of notions and inference of conjoining and disjoining judgments4 ,all three processes go to form the larger process of thinking4 ,the concept1 the judgment and the inference are products arising from conjoining and disjoining notions4 #ab4 ,,thinking ,,and ,,apprehension4 ,says ,jevons3 8,simple apprehension is the act of the mind by which we merely become aware of something1 or have an idea or impression of it brought into the mind20 while ,hyslop states that 8,the process of knowledge which gives us percepts is apprehension40 ,it is obvious that the idea of the latter is that apprehension yields individual notions only1 while ,jevons1 in citing the term iron as an illustration of his definition1 would infer that the general notion is the product of apprehension4 ,the term is strikingly ambiguous and will not be referred to often in this treatise4 ,if the student desires a definition this will cover the concensus of opinion on the meaning of apprehension4 ,apprehension is that process of the knowing mind which yields the percept and concept4 ,some logicians give to the thinking mind the three aspects of apprehension1 judging and reasoning4 #ac4 ,,stages ,,in ,,thinking4 ,in all thinking there are three steps or stages which may be termed discrimination1 comparison1 integration4 ,in the case of the two pencils held in the hand1 it is noted that one is longer than the other4 ,let us analyze the process which made possible this conclusion4 ,step one,attention is given first to one pencil and then to the other4 ,in each case the pencils are distinguished from the hand and the other surrounding objects4 ,this is discrimination4 ,step two,the pencils are compared in length4 ,step three,the two notions are united in the judgment1 8,pencil number one is longer than pencil number two40 ,this is integration4 ,another illustration4 ,the child is requested to solve this problem3 ,if #h tons of hay cost #afe1 what will #af tons cost8 ,statement3 ,given3 #h tons cost #afe4 ,required3 #af tons cost8 ,discrimination4 ,the child notes that #h tons cost #afe and at this rate he is required to find the cost of #af tons4 ,comparison4 ,the child perceives that #af tons is twice #h tons4 ,integration4 ,the child concludes that the cost of #af tons will be twice the cost of #h tons or #ccj4 ,when we think1 we first tear to pieces that we may become acquainted with every part4 ,this may be called analysis4 ,then we put the related pieces together again4 ,this may be called synthesis4 ,before1 however1 the parts are re-united a certain amount of comparison is necessary4 ,the three stages of thought might thus be denominated3 7#a7 analysis1 7#b7 comparison1 7#c7 synthesis4 ,after the synthesis or integration it is necessary to name the result1 consequently a fourth step is sometimes given1 namely denomination4 #ad4 ,,outline4 ,,thought ,,and ,,its ,,operation4 7#a7 ,the ,knowing ,mind ,compared with the ,thinking ,mind4 7#b7 ,knowing by ,intuition4 7#c7 ,the ,thinking ,process4 ,defined4 ,other definitions4 7#d7 ,notions4 ,individual4 ,general4 ,thing and object distinguished4 7#e7 ,knowledge and ,idea as ,related to the ,notion4 7#f7 ,the ,logic of ,psychological ,terms ,involved in the ,notion4 ,the sensation ,the percept ,individual notions4 ,the image ,the concept ,the judgment ,general notions4 ,the inference ,terms defined4 7#g7 ,thought and the ,sensation and ,percept4 7#h7 ,evolution and the ,thinking ,mind4 7#i7 ,the ,concept as a ,thought ,product4 7#aj7 ,the ,judgment as a ,thought ,product4 ,the simplest form of thinking4 7#aa7 ,inference as a ,thought ,product4 7#ab7 ,thinking and ,apprehension4 7#ac7 ,stages in ,thinking4 ,discrimination4 ,comparison4 ,integration4 7,denomination47 #ae4 ,,summary4 7#a7 ,knowing is a broader term than thinking as the former equals the latter plus intuition4 7#b7 ,intuitive knowledge is that which comes to the mind immediately by direct observation4 ,although intuitive knowledge comes to the mind without thought1 yet such knowledge is essential to all thinking4 ,intuitive knowledge is the foundation upon which the thinking mind builds4 7#c7 ,thinking is the deliberative process of affirming and denying connections4 ,thinking is a 8thickening process10 the smaller units being pressed together to make a larger4 ,thinking is chiefly a matter of reducing plurality to unity4 7#d7 ,a notion is any product of the knowing mind4 ,an individual notion is the notion of one thing4 ,a general notion is a notion of a class of things4 ,a thing includes objects1 qualities1 relations or any existing entity4 ,a thing is that which has individual existence4 7#e7 ,a bit of knowledge must have been a notion of some one's mind1 but may not necessarily be a notion of your mind4 ,knowledge may be found in books1 but a notion is a mental product found only in the mind4 ,idea is ambiguous1 though its meaning is usually restricted to an image1 a meaning or a belief4 7#f7 ,the products of the knowing mind are the sensation1 the image1 percept1 concept1 judgment1 inference4 ,the sensation1 image and percept are individual notions1 while the concept1 judgment and inference are general notions4 ,a sensation is a vague1 unlocalized product of the knowing mind4 ,a percept is a consciously localized group of sensations4 ,an image is a reproduced percept4 ,a concept is a mental product arising from thinking many notions into one class4 ,a judgment is a mental product arising from conjoining and disjoining notions4 ,an inference is a judgment derived from antecedent judgments4 ,the developed thought processes are the concept1 the judgment and the inference4 7#g7 ,just where the simplest form of thinking appears in the various activities of the knowing mind is still an undecided question4 ,it is agreed that thinking in its developed and more complex form is found in conception1 judging and reasoning4 7#h7 ,thinking evolves from the simple to the more complex1 just as life has evolved4 ,the child thinks in vague1 indefinite wholes1 while the adult thinks in clear1 definite parts4 ,the child discriminates very imperfectly while the adult discriminates accurately4 ,the sensation seems to be the connecting link between the feeling mind and the knowing mind1 while the percept links together the knowing mind and the thinking mind4 7#i7 ,conception is the process of thinking many notions into one class4 ,the product of such a process is a concept4 ,the concept stands for groups of all kinds of objects4 ,conception has the two aspects of affirming connections and of building many into one4 ,the first is the thinking side of the process and the second is the mark which distinguishes conception from the other thought processes4 7#aj7 ,judging is the process of conjoining or disjoining notions4 ,judgment is the product of judging4 ,judgments conjoin and disjoin all kinds of notions4 ,judging and thinking1 though they closely resemble each other1 are not synonomous terms4 ,thinking is a broader term in that connections may be established between a notion and a name for that notion4 ,judging is the most fundamental of all thinking1 as the concept is built from a series of judgments and an inference is simply a made-over judgment4 7#aa7 ,inference4 ,reasoning is the process of deriving a new judgment from a consideration of antecedent judgments4 ,this derived judgment may be called an inference4 ,sometimes the term inference denotes the process of reasoning as well as the product4 ,reasoning often takes the form of a syllogism4 ,the concept1 the judgment and the inference are products arising from conjoining and disjoining notions4 7#ab7 ,some give to the thinking mind the three aspects1 apprehension1 judging and reasoning4 ,apprehension is another word for the two processes1 perception and conception4 7#ac7 ,the three important stages in thinking are discrimination1 comparison1 integration2 or analysis1 comparison and synthesis4 #af4 ,,review ,,questions4 7#a7 ,show the difference between the knowing mind and the thinking mind4 7#b7 ,describe the process known as intuition4 7#c7 ,what is intuitive knowledge8 7#d7 ,is the assumption that think comes from the same root as thick a feasible one8 ,explain4 7#e7 ,define thinking in at least two ways4 7#f7 8,inability to think is due to inability to note connections40 ,show this by making use of some problem in arithmetic4 7#g7 ,distinguish between individual and general notions4 7#h7 ,which is the broader term1 object or thing8 ,explain4 7#i7 ,what kind of notions only admit of subdivisions8 ,illustrate4 7#aj7 ,what is the difference between knowledge and notions8 ,explain4 7#aa7 ,explain and illustrate the meaning of idea4 7#ab7 ,classify the various activities of the knowing mind and define each4 7#ac7 ,explain by definition and illustration the products of the knowing mind4 7#ad7 ,relate the general notion to the psychological products of the knowing mind4 7#ae7 8,the thinking mind is a unit40 ,explain fully4 7#af7 ,trace the analogy between the evolution of the physical world and the evolution of thought4 7#ag7 ,show that the sensation and the percept may be regarded as connecting links between lower and higher states4 7#ah7 ,define and illustrate conception4 7#ai7 ,show that the concept stands for all kinds of notions4 7#bj7 ,point out the thinking aspect of conception as distinguished from the activity which gives the process its name4 7#ba7 ,define the judgment4 ,illustrate two kinds4 7#bb7 ,show that the concept is built by means of a series of judgments4 7#bc7 ,show that judging is the fundamental element in the thought products4 7#bd7 ,define and illustrate reasoning4 7#be7 ,describe the syllogism4 7#bf7 ,explain the use of apprehension4 7#bg7 ,what are the stages in thinking8 ,illustrate fully4 7#bh7 ,show that thinking is a matter of analysis and synthesis4 #ag4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,give your argument in favor of the statement1 8,dogs think1 but do not reason40 7#b7 ,show by illustration that thinking would be impossible without intuition4 7#c7 8,thinking is the conscious adjustment of a means to an end in problematic situations40 ,illustrate this4 7#d7 ,the class is unable to solve the following problem3 8,i sell my house for #ab1jjj1 which is a gain of #be on the cost4 ,find the cost40 ,what is the trouble8 ,state the problem so that some connection is apparent4 7#e7 8,two-thirds of my salary is #b1djj4 ,what is my salary80 ,a child solves this by dividing #b1djj by two and multiplying this result by three4 ,illustrate a plan for establishing right connections4 7#f7 ,may a judgment express a general notion8 ,illustrate4 7#g7 ,is a thought a thing8 ,illustrate4 7#h7 ,show the illogic of dividing notions into individual1 general and abstract4 7#i7 ,show that goodness is a general notion4 7#aj7 ,is the concept an idea8 ,explain4 7#aa7 ,prove that a mental image is always an individual notion4 7#ab7 8,in sensation is there implicit thinking80 ,argue both sides of the question4 7#ac7 ,show that the concept1 the judgment and the inference are products of the thinking mind4 7#ad7 ,show by illustration where perception ceases and conception begins4 7#ae7 ,is there actually any difference between thinking and judging8 ,illustrate4 7#af7 8,reasoning is controlled thought40 ,explain4 7#ag7 ,of the three stages in thinking which one most concerns the teacher8 ,illustrate4 ,,chapter #c4 ,,the ,,primary ,,laws ,,of ,,thought4 #a4 ,,two ,,fundamental ,,laws4 ,the elemental form of evolved thought is the judgment4 ,the laws or axioms of thought may1 therefore1 be discovered by studying the judgment4 ,judging is the process of conjoining and disjoining notions4 ,when these notions are conjoined the judgment is affirmative2 when disjoined the judgment is negative4 ,to illustrate3 8,some men are wise10 is an affirmative judgment1 while 8,some men are not wise10 is a negative judgment4 ,all judgments are either affirmative or negative and this suggests that there may be but two fundamental laws or axioms underlying judging or all forms of developed thinking4 ,one law would condition the affirmative judgment2 the other the negative4 ,such is actually the case4 ,the law which permits the affirmative judgment is called the law of identity1 while the law which allows a negative judgment is known as the law of contradiction4 ,there is a third law termed the law of excluded middle1 which is in reality a combination of the other two4 #b4 ,,the ,,law ,,of ,,identity4 ,in general the law of identity implies a certain permanency throughout the material world4 ,that door is a door and always will be a door till the conditions change4 ,if it were not for this law1 that everything is permanently identical with itself1 it would be impossible to think at all4 ,for example3 ,take away the notion of permanency from the door and thought becomes at once ridiculous4 ,suppose that while we are asserting that the object is a door1 it changes to a tree1 and while we insist that the object is now a tree1 it changes to a cow1 etc4 ,we can readily see that it would hardly be worth while to think at all4 ,the law of identity may be stated in three ways3 7#a7 ,whatever is1 is2 7#b7 ,everything remains identical with itself2 7#c7 ,the same is the same4 ,,absolute ,,identity,,complete ,,and ,,incomplete4 ,applying the law of identity to the affirmative judgment expressed in the form of a proposition1 we find two kinds of identity1 absolute and relative4 ,in the propositions1 8,socrates is ,socrates10 8dogs are dogs10 8honesty is honesty10 the subject is absolutely identical with the predicatethe same in form and meaning4 ,if we were to illustrate the subject and predicate by two circles they would be of the same size and shape1 the one coinciding with the other point to point4 ,this kind of absolute identity which makes possible all truisms we may term1 for want of a better name1 complete absolute identity4 ,this would imply that there is an incomplete absolute identity and such seems to be the case4 ,examining the definition1 8,a man is a rational animal10 we observe that the notion man has the same content or meaning as the notion rational animal4 ,in meaning1 then1 the two notions are absolutely identical4 ,the one includes just as many objects or qualities as the other1 and if we were to draw two circles representing them1 they would be of the same size4 ,in form1 in mode of expression1 however1 the notions differ and the circles1 though coinciding1 would need to differ in form1 the boundary of one might be a solid line1 the other a dotted4 ,this we may call incomplete absolute identity4 ,all logical definitions illustrate identities of this kind4 ,,relative ,,identity4 ,relative identity is best understood by thinking of it as partial identity1 just as we may think of absolute identity as total identity4 ,in relative identity the whole of one notion may be affirmed of a part of another notion2 or a part of one notion may be affirmed of a part of another notion4 ,to illustrate3 7#a7 ,all men are mortal2 7#b7 ,some men are wise4 ,these and their like are made possible because of the law of relative identity4 ,in the first proposition all of the 8men0 class is identical with a part of the 8mortal0 class4 ,if we were to represent this relation by circles1 the 8men0 circle would be made smaller than the 8mortal0 circle and placed inside it1 as in ,fig4 #a4 ,illustration3 ,fig4 #a4 ,be it remembered that circles are surfaces1 and in ,fig4 #a the men circle is identical with that portion of the mortal circle which is immediately underneath it4 ,the same relation may be indicated by a small pad being placed on top of a larger pad4 ,then the whole of the smaller pad could be thought of as being identical with that part of the larger pad which is immediately underneath4 ,in the case of the second proposition a part of the 8men0 class is identical with a portion of the 8wise0 class4 ,the two circles indicating this relation must intersect each other so that a portion of each may be common ground1 as in ,fig4 #b where the shaded part represents the identity4 ,illustration3 ,fig4 #b4 ,thus we see that the law of identity underlies all affirmative propositions4 ,absolute identity making possible the truism and definition1 and relative identity conditioning all the universal and particular affirmative propositions which are neither truisms nor definitions4 ,the three forms may be symbolized as follows3 7#a7 ,a is ,a,absolute complete 7#b7 ,a is ,a,absolute incomplete 7#c7 ,a is ,b,relative4 ,the student will note that the 8,a's0 of absolute incomplete differ in form4 #c4 ,,law ,,of ,,contradiction4 ,the law of contradiction underlies all negative propositions4 ,it is the mission of this law to tear down or to be destructive in nature2 while the law of identity builds up or is constructive in nature4 ,the law of contradiction may be stated in this way3 ,it is impossible for the same thing to be and not to be at the same time and in the same place4 ,or better1 it is impossible for the same thing to be itself and its contradictory at the same time4 ,bringing out a further aspect1 no thing can have and not have the same attributes at the same time4 ,the little word not bisects the universe4 ,all the people in the world are either honest or not honest1 virtuous or not virtuous4 ,these are contradictory statements and what is comprehended by the one cannot be comprehended by the other at the same time1 any more than a man can shake his head and nod his head at the same time4 ,if we assert the identity between two notions then we cannot in the same breath deny their identity4 ,,illustrations3 7#a7 ,a red flower cannot be a red flower and not a red flower at the same time4 7#b7 ,no man can be guilty and not guilty at the same time4 7#c7 ,a boy cannot be working and not working at the same time4 ,if ,i assert that the flower is red1 then ,i cannot affirm in the same breath that the flower is not red4 ,,two ,,uses ,,of ,,not4 ,the word not when used with the copula of a given proposition makes that proposition negative1 as 7#a7 8,some men are not wise40 ,but when not is attached to the predicate by a hyphen1 the predicate is made negative1 not the proposition1 as 7#b7 8,some men are not-wise40 ,here the predicate not-wise is negative1 but the proposition in which it appears is affirmative4 ,it is obvious that the proposition 8,some men are not wise0 illustrates the law of contradiction1 since the some men referred to are contradicted of all which is wise4 ,whereas the proposition 8,some men are not-wise0 illustrates relative identity1 since the subject 8some men0 is affirmed of a part of the predicate 8not-wise40 ,the student may be led to see these relations by drawing circles1 the one to represent the subject1 the other the predicate4 7,see page #ada47 ,,further ,,illustrations3 ,some teachers are wise ,some teachers are not-wise ,illustrate the law of identity4 ,some teachers are unwise ,some teachers are not wise ,some teachers are not not-wise ,illustrate the law of contradiction4 ,some teachers are not unwise ,the student must understand that a term and its contradictory destroy each other4 ,if we affirm something of the one1 then we must deny it of the other1 or we undermine the integrity of both4 ,if it is affirmed of teachers ,a1 ,b and ,c that they are wise1 then it must be denied that they are not-wise4 ,,illustrations3 ,a1 ,b and ,c are wise4 ,these are mutually ,a1 ,b and ,c are not-wise4 destructive4 ,a1 ,b and ,c are wise4 ,these are not mutually destructive1 ,a1 ,b and ,c are not not-wise4 but virtually mean the same thing4 ,,symbolization ,,of ,,the ,,law ,,of ,,contradiction4 ,a is not not-,a4 ,a is not ,b4 7,as ,a is always ,a it would or or be absurd to say that ,a is ,a is not not-,b4 not ,a47 ,,contradictory ,,and ,,opposite ,,terms4 ,it is easy to use opposite terms in a contradictory sense4 ,this leads to serious error4 8,not-guilty0 is the contradictory of 8guilty10 while 8innocent0 is the opposite of 8guilty40 ,we could hardly say that the water must either be cold or hot1 as it might be warm4 8,not-hot0 is the only term which contradicts 8hot40 ,the law of contradiction has nothing to do with opposites4 ,further1 it is dangerous to regard words with the negative prefix as being contradictory of the affirmative form4 ,for example3 ,valuable and invaluable are not contradictory4 ,there is likewise some doubt as to the contradictory nature of such words as agreeable and disagreeable1 though we are sure that agreeable and not-agreeable contradict each other4 ,to use the 8not0 with a hyphen is safer than to depend upon some prefix which is supposed to mean 8not40 ,,illustrations ,,of ,,contradictory ,,and ,,opposite ,,terms4 ,opposite4 ,contradictory4 bad good bad not-bad soft hard soft not-soft cold hot cold not-cold rough smooth rough not-rough good evil good not-good warm cool warm not-warm weak strong weak not-weak #d4 ,,the ,,law ,,of ,,excluded ,,middle4 ,the law of excluded middle may be considered as a combination of identity and contradiction4 ,identity gives the proposition1 8,john ,doe is honest40 ,contradiction1 8,john ,doe is not honest40 ,combine the two using either and or and we have the excluded middle proposition1 8,either ,john ,doe is honest or he is not honest40 ,excluded middle explains itself4 ,of the two contradictory notions it must be either the one or the other4 ,there is no 8go-between0 notion4 ,the law may be stated in many ways1 as will be seen by the following3 7#a7 ,everything must either be or not be4 7#b7 ,either a given judgment is true or its contradictory is true2 there is no middle ground4 7#c7 ,of two contradictory judgments one must be true4 7#d7 ,every predicate may be affirmed or denied of every subject4 ,,illustrations3 7#a7 ,a man is either mortal or he is not mortal4 7#b7 ,john ,doe is either honest or not-honest4 7#c7 ,either you are going or you are not going4 ,,symbolization ,,of ,,excluded ,,middle4 ,a is either ,a or not-,a or ,a is either ,b or not-,b4 #e4 ,,the ,,law ,,of ,,sufficient ,,reason4 ,the law may be stated in this wise4 ,every phenomenon1 event or relation must have a sufficient reason for being what it is4 ,to illustrate3 7#a7 ,if ,venus is the evening star1 there must be a sufficient reason4 7#b7 ,if the ground is wet1 there must be a cause4 ,many logicians argue that this law has no place in logic1 its field being that of the physical sciences4 ,the laws of identity1 contradiction and excluded middle are1 however1 universally regarded as the ,primary ,laws of thought4 #f4 ,,unity ,,of ,,primary ,,laws ,,of ,,thought ,,illustrated ,,by ,,symbols4 7#a7 ,absolute ,symbols ,relative ,symbols4 ,excluded middle4 ,a is either ,a or not-,a4 ,a is either ,b or not-,b4 ,contradiction4 ,a is not not-,a4 ,a is not ,b or ,a is not not-,b4 ,identity4 ,a is ,a4 ,a is not-,b or ,a is ,b4 7#b7 ,propositions made to fit symbols4 ,excluded middle4 ,a man is either a man or ,a man is either honest or a not-man4 not-honest4 ,contradiction4 ,a man is not a not-man4 ,a man is not honest1 or a man is not not-honest4 ,identity4 ,a man is a man4 ,a man is not-honest1 or a man is honest4 ,the 8excluded middle0 propositions of the foregoing express alternatives which are mutually contradictory4 ,there is no middle ground4 ,the 8contradictory propositions0 contradict the identity of the subject with one alternative1 while the 8identity0 propositions affirm the identity of the subject with the other alternative4 ,this is made possible because of the principle1 8,of two mutually contradictory terms1 if one is true the other must be false40 ,the foregoing scheme shows how closely 8contradictory0 and 8identity0 propositions are related to 8excluded middle0 propositions4 ,expressed mathematically3 excluded middle contradiction identity4 #g4 ,,outline4 ,,primary ,,laws ,,of ,,thought4 7#a7 ,two fundamental laws4 ,identity1 contradiction4 7#b7 ,law of identity4 ,absolutecomplete1 incomplete4 ,relative4 7#c7 ,law of contradiction4 ,two uses of not4 ,contradictory and opposite terms4 7#d7 ,law of excluded middle4 7#e7 ,law of sufficient reason4 7#f7 ,unity of primary laws of thought4 #h4 ,,summary4 7#a7 ,the elemental forms of evolved thought are the affirmative and negative judgments4 ,this suggests two fundamental laws of thought1 the law of identity and the law of contradiction4 ,the former conditions the affirmative judgment1 the latter the negative4 7#b7 ,the law of identity implies a permanency of being4 8,everything remains identical with itself10 is a statement of identity4 ,absolute identity may be divided into complete and incomplete identity4 ,in complete absolute identity the subject is the same as the predicate in both form and meaning4 ,truisms illustrate this4 ,in incomplete absolute identity the subject is identical with the predicate in meaning only4 ,illustrated by definitions4 ,in relative identity the whole of the subject may be affirmed of a part of the predicate or a part of the subject may be affirmed of a part of the predicate4 7#c7 8,it is impossible for the same thing to be itself and its contradictory at the same time10 is a statement of the law of contradiction4 ,identity is constructive while contradiction is destructive in nature4 ,to make the proposition negative the word not must be used with the copula4 8,not0 attached to the predicate with a hyphen makes the predicate negative1 but not the proposition4 ,to use opposite terms in a contradictory sense leads to serious error4 ,the safest way of making a positive term a contradictory negative term is to prefix 8not0 with a hyphen or use 8non40 7#d7 ,the law of excluded middle is virtually a combination of identity and contradiction4 ,it may be stated as follows3 8,a thing must either be itself or its contradictory40 7#e7 8,every condition must have a sufficient reason for its existence10 is the law of sufficient reason4 ,its distinct province is physical science rather than logic4 7#f7 ,the laws may be expressed mathematically3 excluded middle identity contradiction4 ,,schematic ,,statement ,,of ,,primary ,,laws4 ,name ,stated ,symbolized ,illustrated ,absolute ,whatever is1 is ,a is ,a ,work is work identity ,relative ,the whole is ,all ,a is ,b ,work is a blessing identity identical with ,some ,a is ,b ,some play is a a part or a part blessing is identical with a part ,contra- ,nothing can both ,a is not not-,a ,work is not diction be and not be at or not-work the same time ,a is not ,b ,john is not honest or ,albert is not ,a is not not-,b not-honest ,excluded ,everything must ,a is either ,a ,fair play is middle either be or not or not-,a either fair play be or or not-fair play ,a is either ,b ,this man is either or not-,b educated or not-educated #i4 ,,illustrative ,,exercises4 7#a;a7 ,each of the following propositions is made possible because of the existence of which law of thought8 ,in answering this question ,i summarize in my mind the meaning of each law of thought4 ,viz43 7#a7 ,in complete absolute identity the subject and predicate are the same in form and meaning4 7#b7 ,in incomplete absolute identity the subject and predicate are the same in meaning1 but not in form4 7#c7 ,in relative identity either the whole or a part of the subject is identical with a part of the predicate4 7#d7 ,the law of contradiction always denies the identity between subject and predicate4 7#e7 ,excluded middle conditions all alternative expressions4 ,,the ,,propositions4 7#a7 8,a thief is a thief40 ,complete absolute identity4 7#b7 8,thinking is the process of affirming or denying connections40 ,incomplete absolute identity4 7#c7 8,all good men are wise40 ,relative identity4 7#d7 8,no triangle has interior angles whose sum is greater than two right angles40 ,contradiction4 7#e7 8,a stitch in time saves nine40 ,relative identity4 7#f7 8,judging is the process of conjoining and disjoining notions40 ,incomplete absolute identity4 7#g7 8,you are either a voter in this district or you are not a voter in this district40 ,excluded middle4 7#h7 8,some people do not know how to live40 ,contradiction4 7#i7 8,all is well that ends well40 ,incomplete absolute identity4 7#aj7 8,some men teach school40 ,relative identity4 7#aa7 8,none of the planets are as large as the sun40 ,contradictory4 7#ab7 8,all the trees in this grove are maple40 ,relative identity4 7#a;b7 ,indicate the law which conditions each of the following propositions3 7#a7 8,he who laughs last laughs best40 7#b7 8,perfect is perfect40 7#c7 8,he is a wolf in sheep's clothing40 7#d7 8,either your memory is poor or you are telling a deliberate falsehood40 7#e7 8,some of our greatest teachers thought they were failures40 7#f7 8,no man of sense would ever try to get something for nothing40 7#g7 8,failure is not to try40 7#h7 8,success is the right man in the right place doing his best40 7#i7 8,every man is insane on some topic40 7#aj7 8,some pupils are not industrious40 7#aa7 8,you are either a genius or a successful fakir40 7#ab7 8,honesty is the best policy40 #aj4 ,,review ,,questions4 7#a7 ,how many kinds of judgments are there8 ,illustrate4 7#b7 ,name the fundamental laws of thought and explain how they are related to the kinds of judgments4 7#c7 ,show that it would be impossible to think at all were it not for the law of identity4 7#d7 ,state the law of identity in three ways4 7#e7 ,explain the kinds of absolute identity4 ,illustrate by propositions and by circles4 7#f7 ,explain by word and by diagrammatical illustration relative identity4 7#g7 ,symbolize the three forms of identity4 ,fit words to these symbols4 7#h7 ,state in three ways the law of contradiction4 7#i7 ,show by illustration that not bisects the world4 7#aj7 ,explain the uses of not4 7#aa7 ,prove that 8,john ,doe is not-honest10 illustrates identity and not contradiction4 7#ab7 ,symbolize in three ways contradiction4 ,fit words to these symbols4 7#ac7 ,illustrate contradictory and opposite terms4 7#ad7 ,show that words with negative prefixes are not necessarily the contradictory of the corresponding affirmative forms4 7#ae7 ,state and explain the law of excluded middle4 7#af7 ,symbolize the law of excluded middle4 7#ag7 ,state the law of sufficient reason4 ,illustrate4 7#ah7 ,illustrate the unity of the three primary laws of thought4 #aa4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,prove that the judgment is the elemental form of evolved thought4 7#b7 ,what is meant by evolved thought8 7#c7 ,show that 8,whatever is1 is0 is a statement of complete absolute identity only4 7#d7 ,state incomplete absolute identity4 7#e7 ,by means of one proposition state relative identity4 7#f7 ,show that incomplete absolute identity is a term more or less illogical4 7#g7 ,show that these statements are exact expressions of relative identity3 ,all men are some wise4 ,some men are some wise4 7#h7 ,why is the law of contradiction so named8 7#i7 ,show that space may be bisected by drawing a circle upon the black board4 7#aj7 ,show that there is a difference in meaning between 8,you are not honest0 and 8,you are not-honest40 7#aa7 ,is there any difference in meaning between disagreeable and not agreeable8 7#ab7 ,which is the stronger term not-just or unjust8 ,why8 7#ac7 ,give a list of words in which the contradictory forms are expressed by the ordinary prefixes4 7#ad7 ,illustrate by circles the law of excluded middle4 7#ae7 ,illustrate by a line-diagram the difference between contradictory and opposite terms4 7#af7 ,show that the province of the law of sufficient reason is physical science4 ,,chapter #d4 ,,logical ,,terms4 #a4 ,,logical ,,thought ,,and ,,language ,,inseparable4 ,any impression upon the mind tends to manifest itself in some form of expression4 ,impression which arouses thought tends to expression in the form of symbols4 ,thought and symbol go hand in hand4 ,expression1 taking the form of word-symbols1 constitutes a word-language4 ,it is commonly supposed that language is serviceable mainly in communicating one's thoughts to others1 but language does service in another way which is quite as important4 ,it tends to clarify and make definite all thought4 ,without a word-language thinking would lack continuity2 would be vague1 loose1 illogical4 ,the right use of a word-language1 therefore1 is a necessary adjunct to logical thought4 ,the basic element of a word-language is the logical term4 #b4 ,,meaning ,,of ,,logical ,,term4 ,a notion has been referred to as any product of the knowing mind4 ,when we express these notions in words such expressions may be called logical terms4 ,definition4 ,a logical term is a word or a group of words denoting a definite notion4 ,illustrations3 ,honesty1 ,chicago1 tree1 walking1 the man who was ill1 beautiful roses4 ,this is a list of logical terms1 because each word or group of words denotes a notion of some kind4 ,it is now evident that any subject or predicate with its modifiers constitutes a logical term4 ,in the proposition1 8,the beautiful red house on the hill1 owned by ,mr4 ,jones1 has burned10 the term used as the subject consists of eleven words4 ,the reader must not confuse logical terms with grammatical parts of speech4 8,of0 is a preposition but not a logical term1 as no definite notion is indicated4 #c4 ,,categorematic ,,and ,,syncategorematic ,,words4 ,there are some words which1 when used alone1 denote definite notions1 such as man1 tree1 dog1 justice4 ,on the other hand there are other words which1 when used alone1 do not stand for a definite notion1 such as up1 beautifully1 a1 and4 ,words like those in the first list are called categorematic words1 while those in the second list illustrate syncategorematic words4 ,,definition4 ,a categorematic word is one which forms a logical term unaided by other words4 ,a syncategorematic word is one which must be used with other words to form a logical term4 ,any word or group of words which can be used as either subject or predicate of a proposition is a logical term4 ,if the one word in question can be used as either subject or predicate of a proposition then it must be a categorematic word4 ,if it is impossible to use the one word as either subject or predicate of a proposition then this is a sure indication that such a word is syncategorematic4 ,for example1 there is no sense in the expressions1 8,and is honest10 8,of is not true02 hence and and of are syncategorematic4 ,we may conclude from this that nouns1 descriptive adjectives and verbs may be categorematic words1 while adverbs1 prepositions and conjunctions are syncategorematic words4 #d4 ,,singular ,,terms4 ,a singular term is a term which denotes one object or one attribute4 ,proper nouns1 when they stand for individuals1 are singular terms1 such as ,john ,adams1 ,mississippi ,river1 ,socrates4 ,some proper names stand for a class of objects1 as the ,caesars1 the ,mephistopheles1 the ,napoleons4 ,but when thus used they lose their character as proper names4 ,such names1 therefore1 are general terms1 not singular4 ,common nouns may be made singular by some modifying word1 as the first man1 the pole star1 the highest good1 my pet dog1 etc4 ,certain attributes which imply a oneness or a distinct individuality are singular1 such as absolute justice1 birds-egg blue1 perfect happiness1 etc4 ,some claim that terms like water1 air1 salt1 etc41 are singular1 as they stand for one thing4 ,this1 however1 cannot be if such terms admit the possibility of classification as3 hard water1 soft water1 mineral water4 #e4 ,,general ,,terms4 ,a general term is one which denotes an indefinite number of objects or attributes4 ,class-names are general terms1 such as men1 chair1 tree1 army1 nation4 ,words like redness1 sweetness1 justice1 are probably general in that they denote a combination of qualities or may be subdivided into kinds4 ,the way the term is employed in the proposition should determine its singular or general nature4 #f4 ,,collective ,,and ,,distributive ,,terms4 ,a collective term is a general term which indicates an indefinite number of objects as one whole4 ,such words as class1 crowd1 army1 forest1 nation1 are collective4 ,a distributive term is a general term which indicates an indefinite number of objects as a whole1 and also may be used to refer to each one of the group separately4 ,such as man1 pupil1 tree1 book4 ,it is easy to distinguish collective from distributive terms when we attempt to use them in the designation of individuals4 ,pointing to a body of troops1 one may remark1 8,there is the regiment40 ,but when pointing to one man in the regiment1 he could hardly say1 8,there is the regiment40 8,regiment0 is therefore collective because it may be used with reference to the whole body of troops but cannot be used in connection with any individual of that body4 ,on the other hand in the sentence1 8,man is mortal10 8man0 refers to the whole family of men4 ,it also indicates any one of them4 ,as1 8,this man1 ,john ,doe1 is mortal40 ,thus 8man0 is distributive4 ,the distributive term1 therefore1 can be used in a two-fold sense2 namely1 to denote the whole or to denote each4 ,it must be noted that1 viewed from a different standpoint1 some collective terms become distributive in nature4 ,as for example in the proposition1 8,the army of the world is composed of able bodied men10 army is used with reference to all armies4 ,while it may be used to designate some particular army1 as ,the ,american army4 ,collective terms have been classified as general terms4 ,it must be borne in mind1 however1 that such may be made singular by some modifying word4 ,for example1 people is a general term1 but ,american people is a singular term in that it refers to one people1 being thus limited by the word ,american4 #g4 ,,concrete ,,and ,,abstract ,,terms4 ,a concrete term is a term which denotes a thing2 e4 g41 this man1 that tree1 ,john ,doe1 denote in each case a thing4 ,man and tree1 denote many things4 ,all are concrete4 ,an abstract term is a term which denotes an attribute of a thing2 e4 g41 whiteness1 patience1 squareness1 are abstract terms4 ,such words as red1 honest1 just1 are concrete2 while redness1 honesty1 justice1 are abstract4 ,on first thought it might be inferred that 8red0 is the name of an attribute just as much as 8redness40 ,this is a mistaken thought1 however1 as when we use the word red we mean red somethingan object which is red in color1 not the color itself4 ,for example1 in saying the house is red1 we refer to the thing that is red1 not to the color redness4 ,descriptive adjectives1 because they describe things1 are concrete4 ,they do not alone name qualities of things1 hence they are not abstract4 #h4 ,,connotative ,,and ,,non-,,connotative ,,terms4 ,a connotative term is one which denotes a subject and at the same time implies an attribute4 7,a subject is anything which possesses attributes47 ,all concrete general terms are connotative because they denote subjects and at the same time stand for certain attributes2 e4 g41 8man0 denotes many subjects2 in fact1 it stands for all the men in the world2 it also implies rationality1 the power of speech1 power of locomotion1 etc4 8,triangle0 stands for all plane figures of three sides2 it likewise stands for the qualities1 three-sided1 three-cornered1 etc4 ,both 8man0 and 8triangle0 are connotative4 ,a non-connotative term is one which denotes a subject only1 or implies an attribute only4 ,such words as ,boston1 ,columbus1 ,the ,elizabeth ,white1 denote a subject only4 8,blueness10 8justice10 8width10 imply an attribute only4 ,all these terms are non-connotative4 ,the words blue1 just1 wide1 are connotative4 8,blue10 for example1 denotes all blue things1 as the blue sky1 the blue sea2 at the same time 8blue0 implies that something possesses the quality1 blueness4 ,generally speaking1 proper and abstract nouns are non-connotative2 though such proper nouns as ,mount ,washington1 ,mississippi ,river1 are1 no doubt1 connotative1 as they denote an object and imply at least one attribute4 ,in the case of ,mount ,washington an object is surely denoted1 and the attribute mountainous is implied4 ,any proper noun which conveys definite information is connotative4 ,it may be claimed that all proper nouns give information4 ,for example1 to many ,boston indicates not only an object1 but the qualities common to a city4 ,in reply it may be said that 8,boston0 might indicate a boat1 or a dog1 or almost any individual object4 #i4 ,,positive ,,and ,,negative ,,terms4 ,a positive term is one which signifies the possession of certain attributes2 e4 g41 metal1 man1 teacher1 happy1 honest4 ,a negative term is one which signifies the absence of certain attributes2 e4 g41 inorganic1 unhappy1 non-metallic4 ,terms which have the prefix not1 non1 un1 in1 dis1 etc41 or the affix less1 are usually considered negative4 ,the fact that there are some exceptions to this must not be overlooked4 ,for example1 unloosed1 invaluable1 are positive terms4 ,in theory every positive term has its corresponding negative2 as pure1 impure2 organic1 inorganic2 metal1 non-metal2 good1 not-good4 ,in some instances the language does not supply the word with the negative prefix because no need of it has been felt4 ,the only way to express the negative of such words as good1 table1 etc41 is to prefix 8not0 or 8non40 #aj4 ,,contradictory ,,and ,,opposite ,,terms4 7,see page #ch74 ,positive terms with their negatives have contradictory meanings and therefore are referred to as contradictory terms4 ,for example1 honest and not-honest1 metallic and non-metallic1 perfect and imperfect1 are contradictory terms4 ,such terms are mutually destructive4 ,when we assert the truth of one we also imply the falsity of the other4 ,if1 for example1 we assert that ,abraham ,lincoln was honest1 we carry with this assertion the implication that ,lincoln was not not-honest1 or that any statement to the effect that he was not honest is false4 ,contradictory terms1 when used in a sentence1 illustrate the law of excluded middle1 as in the statements3 8,john's recitation is either perfect or imperfect40 8,this teacher is either just or not-just40 ,there is no middle ground in such propositions4 ,when contradictory terms are used in classification the whole is divided into but two classes2 e4 g43 honest not-honest agreeable not-agreeable metallic non-metallic perfect imperfect pure impure organic inorganic ,all the men in the world are either honest or not-honest4 ,all the substances in existence are either organic or inorganic1 etc4 ,it will also be seen from this list that the contradictory of the positive form is not always indicated by using the prefix4 ,honest and dishonest1 or agreeable and disagreeable1 are not contradictory terms4 ,in the case of agreeable and disagreeable1 there seems to be the middle ground of absolute indifference4 ,for example3 the music of the orchestra is agreeable while the humming of the enthusiast back of me is decidedly disagreeable2 but as to the noise upon the street1 it is neither agreeable nor disagreeable as long practice has made me indifferent to it4 ,when there is any doubt as to the terms being contradictory1 the safest plan is to prefix 8not0 or 8non0 to the positive form4 ,terms which oppose each other but do not contradict are said to be opposite or contrary terms4 ,the following list illustrate opposite terms3 hot cold cool warm less greater wise foolish bitter sweet soft hard tall short agreeable disagreeable ,all these terms admit of a medium4 ,in the case of hot or cold1 for example1 a substance need not necessarily be either4 ,it may be warm or cool4 ,terms seem to be contradictory when it is a matter of quality1 but opposite when it is a question of quantity or degree4 #aa4 ,,privative ,,and ,,nego-,,positive ,,terms4 ,a privative term is one which is positive in form but negative in meaning4 ,such words as blind1 deaf1 dumb1 dead1 maimed1 orphaned1 are privative terms1 in that there is no negative prefix or suffix and yet they denote the absence of certain qualities4 8,blind10 for example1 is positive in form1 but denotes absence of sight4 ,a nego-positive term is one which is negative in form but positive in meaning4 ,such terms as invaluable1 unloosed1 immoral1 indwell1 are nego-positive because1 though they have negative prefixes1 yet they possess a certain positive meaning4 8,invaluable10 for instance1 does not mean not-valuable1 but very valuable4 #ab4 ,,absolute ,,and ,,relative ,,terms4 ,an absolute term is one whose meaning becomes intelligible without reference to other terms4 ,automobile1 water1 tree1 house1 book1 are absolute terms4 ,any of them may be made clear to a child or a foreigner without special reference to other terms4 ,for example1 the child will recognize from certain common marks the automobile every time he sees it4 ,the marks of tree1 house1 flower1 are apparent to every one4 ,a relative term is one which derives its meaning from its relation to some other term4 ,parent1 teacher1 shepherd1 monarch1 eldest1 cause1 commander1 are relative terms4 ,for example1 in explaining the meaning of 8parent0 to a foreigner1 reference must be made to 8child40 ,the pairs of terms thus associated are spoken of as correlatives4 ,parent and child1 teacher and pupil1 shepherd and flock1 monarch and subject1 eldest and youngest1 cause and effect1 commander and army1 are correlative terms4 ,either one of each pair is the correlate to the other1 and every relative term needs its correlate to make its meaning clear4 ,to say that a relative term denotes an object which cannot be thought of without reference to some other object1 is confusing1 as it is quite impossible to think of any object without calling to mind some other object or notion4 ,fire calls to mind water2 tree suggests shade1 etc4 #ac4 ,,outline4 ,,logical ,,terms4 7#a7 ,meaning of term4 7#b7 ,categorematic and syncategorematic words4 7#c7 ,kinds of terms4 ,singular terms4 ,general terms4 7a7 ,collective terms4 7b7 ,distributive terms4 ,concrete and abstract terms4 ,connotative and non-connotative terms4 ,positive and negative terms4 ,contradictory and opposite terms4 ,privative and nego-positive terms4 ,absolute and relative terms4 #ad4 ,,summary4 ,a logical term is a word or group of words denoting a definite notion4 ,a singular term is a term which denotes one object or one attribute4 ,a general term is a term which denotes an indefinite number of objects or attributes4 ,general terms are collective or distributive4 ,a collective term is a general term which indicates an indefinite number of objects considered as one whole4 ,a distributive term is a general term which indicates an indefinite number of objects as a whole and also may be used to refer to each one of the group separately4 ,a concrete term is a term which denotes a thing4 ,an abstract term is a term which denotes the attribute of a thing4 ,a connotative term is one which denotes a subject and at the same time implies an attribute4 ,a non-connotative term is one which denotes a subject only or implies an attribute only4 ,a positive term is one which signifies the possession of certain attributes4 ,a negative term is one which signifies the absence of certain attributes4 ,in theory every positive term has its negative4 ,as related to each other positive and negative terms are said to be contradictory4 ,if one denotes a true notion then the other denotes a false notion4 ,some terms oppose each other but do not flatly contradict4 ,as related to each other such terms are said to be opposite4 ,a privative term is one which is positive in form but negative in meaning4 ,a nego-positive term is one which is negative in form but positive in meaning4 ,an absolute term is one whose meaning becomes intelligible without reference to other terms4 ,a relative term is one which derives its meaning from its relation to some other term4 #ae4 ,,illustrative ,,exercises4 7#a;a7 ,the words in italics are categorematic4 7#a7 8,honesty is the best policy40 7#b7 8,a wise teacher never scolds40 7#c7 8,the woodcock has a long bill and eyes high up on the head40 ,,note,if there is any doubt as to such words as never1 on1 etc41 being syncategorematic1 attempt to use them as subject or predicate of a proposition2 e4 g41 ,john is never4 7#a;b7 ,underscore the categorematic words in the following3 7#a7 8,socrates was the greatest teacher of pagan times40 7#b7 8,play is nature's way of teaching a child how to work40 7#c7 8,a man may be what he chooses if he is willing to pay the price40 7#b;a7 ,in the following1 words enclosed in parentheses are logical terms3 7#a7 78,all men7 are 7mortal407 7#b7 78,the law of identity7 is 7one of the primary laws of thought407 7#c7 78,judging7 is 7the process of conjoining and disjoining notions407 7#b;b7 ,indicate the logical terms in the sentences under #a;b4 7#c;a7 ,the logical characteristics of the term teacher are 7#a7 general term1 7#b7 distributive term1 7#c7 concrete term1 7#d7 connotative term1 7#e7 positive term1 7#f7 relative term4 7#c;b7 ,the logical characteristics of other terms are as follows3 7#a7 ,goodnessgeneral1 abstract1 non-connotative1 positive1 abstract4 7#b7 ,softgeneral1 concrete1 non-connotative1 positive1 8hard0 is its opposite1 8not-soft0 is its contradictory1 absolute4 7#c7 ,disagreeablegeneral1 concrete1 non-connotative1 8agreeable0 is its opposite1 8not-disagreeable0 is its contradictory1 nego-positive1 absolute4 7#d7 ,aristotlesingular1 concrete1 non-connotative1 positive1 absolute4 7#e7 ,classgeneral1 collective1 concrete1 connotative1 positive1 relative4 7#c;c7 ,give the logical characteristics of the following terms3 justice1 ,abraham ,lincoln1 tree1 library1 ,america1 president1 principle1 sympathy1 dumb1 nation4 #af4 ,,review ,,questions4 7#a7 ,what is the connection between logical thinking and language8 7#b7 ,why is man a categorematic word8 7#c7 ,why is beautifully syncategorematic8 7#d7 ,distinguish between singular and general terms4 7#e7 ,show how a collective term may be used in a distributive sense4 7#f7 ,why are the words tree and book distributive8 7#g7 ,distinguish between concrete and abstract terms4 7#h7 ,define and illustrate a non-connotative term4 7#i7 ,why are concrete general terms connotative8 7#aj7 ,distinguish between positive and privative terms4 7#aa7 ,why is not the word immoral negative8 7#ab7 ,give the opposite of 8hot40 ,what is the contradictory of 8hot08 7#ac7 ,distinguish by definition and illustration between relative and absolute terms4 7#ad7 ,what is the correlate of the word effect8 #ag4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,is it possible to think independent of language8 7#b7 ,may words be spoken or written without thought8 ,illustrate4 7#c7 ,are categorematic words always logical terms8 7#d7 ,must all the words of a logical term be categorematic8 7#e7 ,are pronouns and auxiliary verbs categorematic8 7#f7 ,indicate the logical connection between the terms of a proposition and the termini of a railroad4 7#g7 ,show that attribute is a broader term than quality4 7#h7 ,is the word ,washington general or singular8 ,give reasons4 7#i7 ,make the word dog a singular term4 7#aj7 ,give an illustration where the word class would not be collective4 7#aa7 8,all the members of the baseball team are star players40 ,how has the term star players been used1 collectively or distributively8 7#ab7 ,why may the term ,new ,york ,city be connotative to a ,new ,yorker and non-connotative to a ,patagonian8 7#ac7 ,so far as your present knowledge of the martyred president ,abraham ,lincoln is concerned1 is the term ,abraham ,lincoln connotative or non-connotative8 7#ad7 ,are non-connotative terms always singular8 ,illustrate4 7#ae7 ,are singular terms always non-connotative8 7#af7 ,what is the difference in meaning between immoral and unmoral1 disagreeable and not-agreeable8 7#ag7 ,why is immoral a nego-positive term while unmoral is negative8 7#ah7 ,what is the contradictory of the opposite of wise8 7#ai7 ,show that there is some ground for believing all terms to be relative4 7#bj7 ,is army a relative term8 ,if 8army0 were used so as to be distributive in nature would it then be general or collective8 7#ba7 ,why should the pronoun be ignored by the logician8 7#bb7 ,show the difference between thing and subject4 7#bc7 ,argue to the effect that no term can be non-connotative4 ,,chapter #e4 ,,the ,,extension ,,and ,,intension ,,of ,,terms4 #a4 ,,two-,,fold ,,function ,,of ,,connotative ,,terms4 7,see page #eb47 ,it has been indicated that a connotative term is one which possesses the double function of signifying a subject as well as an attribute4 ,it may be observed here that an attribute of a notion is any mark1 property or characteristic of that notion4 ,attribute1 then1 represents quality1 relation or quantity4 ,by a subject is meant anything which possesses attributes4 ,most subjects stand for objects and most attributes are qualities2 consequently1 for the sake of simplicity1 we may use subject and object interchangeably2 likewise1 attribute and quality4 ,a connotative term1 therefore1 denotes an object at the same time it implies a quality4 ,to illustrate3 ,the symbol man stands for the various individual men of the world1 such as ,lincoln1 ,washington1 ,alfred the ,great1 etc41 or for certain qualities like rationality1 power of speech and power of locomotion4 ,the connotative term teacher may be used to denote ,socrates1 ,pestalozzi1 ,thomas ,arnold1 or connote such qualities as ability to instruct1 sympathy1 and scholarship4 ,the term planet stands for such objects as ,venus1 ,earth1 and ,mars1 and for such qualities as rotation upon axis1 revolution about sun1 and opaque or semi-opaque bodies4 ,in each of the three illustrations the term is employed in the two-fold sense of denoting objects and of implying qualities4 #b4 ,,extension ,,and ,,intension ,,defined4 ,this double function of connotative terms furnishes an important topic for the student of logicthe ,extension and ,intension of ,terms4 ,in short1 some authorities claim that to master the extension and intension of terms is virtually to master the entire subject of logic4 ,though this position may be an exaggerated one1 yet it tends to emphasize the importance of the topic4 ,a term is used in extension when it is employed with reference to the objects for which the term stands4 ,when the term triangle is used to refer to the objects isosceles triangle1 scalene triangle1 right triangle1 it is employed in extension4 ,a term is used in intension when it is employed with reference to the attributes for which the term stands4 ,the term triangle is employed in intension when we use it to refer to the qualities1 three sided and three angled4 #c4 ,,extended ,,comparison ,,of ,,extension ,,and ,,intension4 ,a connotative term seems to be two dimensionalit has extent or length and intent or depth4 8,extension consists of the things to which the term applies10 while 8intension consists of the properties which the term implies40 ,extension is quantitative1 while intension is qualitative4 ,an extensional use means to point out or number objects1 while an intensional use means to describe by naming qualities4 ,to name is to use a term in extensionto describe is to use a term in intension4 ,to divide a term into its kinds we must regard it in an extensional sense2 e4 g41 the term man may be divided into ,caucasian1 ,mongolian1 ,malay1 ,ethiopian1 ,american ,indian4 ,to define a term we must regard it in an intensional sense2 e4 g41 man is a rational animal4 ,etymologically considered extension means to stretch out1 intension1 to stretch within4 ,to use a term extensionally one must look out4 ,to use a term intensionally one must look in4 ,in attempting to use a term in extension we may ask ourselves the question1 8,what are the kinds80 or 8,to what objects may the term be applied80 ,while if we would use a term in intension the question should be1 8,what does it mean80 or 8,what are the qualities80 ,let us1 for example1 use the term metal in the two senses1 first in extension1 second in intension4 ,question3 ,to what objects may the term metal be applied8 ,answer3 ,metal may be applied to the objects silver1 gold and iron4 ,thus has metal been employed in extension4 ,question3 ,what are the qualities of metal8 ,answer3 ,the qualities are element1 metallic lustre1 good conductor of heat and electricity4 ,thus has metal been used in intension4 ,,note4 ,since an attribute is anything which belongs to a subject1 then the parts of a subject must be classed as attributes4 ,hence1 a term is used intensionally when reference is made to its parts4 #d4 ,a ,,list ,,of ,,connotative ,,terms ,,used ,,in ,,extension ,,and ,,intension4 ,the ,term4 ,extensional ,use4 ,intensional ,use4 roots1 branches1 trunk4 tree4 maple1 oak1 beech4 or woody-fiber1 sap1 bark4 house4 stone1 brick1 cement4 foundation1 frame-work1 roof4 dog4 shepherd1 fox terrier1 carnivorous1 quadruped1 bull4 propensity to bark4 book4 textbook1 dictionary1 cover1 leaves1 binding4 encyclopaedia4 quadrilateral4 trapezium1 trapezoid1 four sides1 four angles1 parallelogram4 limited plane4 logic4 theoretical logic1 science of thinking1 art of applied logic1 right thinking1 treats of educational logic4 laws of thought4 star4 ,sirius1 ,arcturus1 ,vega4 heavenly body1 gives light and heat1 twinkles4 force4 gravitation1 molecular1 produces motion atomic4 changes motion destroys motion4 term4 general1 singular1 word or group of words1 non-connotative4 definite idea4 government4 monarchy1 aristocracy1 body of people1 democracy4 established form of law1 banded together for mutual protection4 bird4 crow1 robin1 pigeon4 biped1 feathered1 winged4 #e4 ,,other ,,forms ,,of ,,expression ,,for ,,extension ,,and ,,intension4 ,extension4 ,intension4 comprehension content extent intent breadth depth denotation connotation application implication ,formerly the words extension and intension were applied to concepts while denotation and connotation were applied to terms representing the concepts1 but now the words are interchangeable4 ,denotation1 the noun1 and denote1 the verb1 signify1 etymologically1 a marking off4 ,to denote is to mark off or indicate the objects or classes of objects for which the term stands4 ,connotation1 the noun1 and connote1 the verb1 signify to mark along with4 ,to connote is to mark along with the object1 its attributes4 ,the terms which should be remembered are extension intension or and or denotation connotation #f4 ,,law ,,of ,,variation ,,in ,,extension ,,and ,,intension4 ,it has been noted that the intension of a term has reference to its qualities while extension considers its application to various objects4 ,it may be wise to experiment with the extension and the intension of certain terms as types with a view of ascertaining how the two ideas are related to each other4 ,for the sake of definiteness let us make use of the following scheme3 ,i4 ,intensional ,extensional 7#a7 four sides 7#b7 parallel sides common qualities of 7#a7 squares 7#c7 equal sides 7#d7 right angles 7#a7 four sides 7#b7 parallel sides common qualities of 7#a7 squares 7#c7 equal sides 7#b7 rhombs 7#a7 squares 7#a7 four sides common qualities of 7#b7 rhombs 7#b7 parallel sides 7#c7 rectangles 7#d7 rhomboids 7#a7 squares 7#b7 rhombs 7#a7 four sides common qualities of 7#c7 rectangles 7#d7 rhomboids 7#e7 trapezoids 7#f7 trapeziums ,,ii4 7#a7 nebulae 7#b7 fixed stars 7#a7 heavenly body common qualities of 7#c7 sun 7#d7 comets 7#e7 meteors 7#f7 moon 7#a7 nebulae 7#a7 heavenly body common qualities of 7#b7 fixed stars 7#b7 self-luminous 7#c7 sun 7#d7 comets 7#a7 heavenly body 7#a7 nebulae 7#b7 self-luminous common qualities of 7#b7 fixed stars 7#c7 fixed 7#c7 sun 7#a7 heavenly body 7#b7 self-luminous common qualities of 7#a7 nebulae 7#c7 fixed 7#b7 fixed stars 7#d7 twinkle 7#a7 heavenly body 7#b7 self-luminous 7#c7 fixed common qualities of 7#a7 nebulae 7#d7 twinkle 7#e7 foggy ,in considering the first illustration we observe that as the number of qualities is decreased1 the number of objects increases4 ,while in the second example as the qualities are increased1 the number of objects decreases4 ,it would appear from this that the intension and extension of a term are inversely related to each other4 ,as the one increases the other decreases and vice versa4 ,it is customary to state this relation in the form of a law known as the law of variation4 8,as the intension of a term is increased its extension is decreased and vice versa10 or the extension and intension of a term vary in an inverse ratio to each other4 ,to further illustrate3 this book refers to a large number of objects2 add to the qualities of book those of text book and the application is much reduced4 ,in other words as we increase the intension1 the extension is diminished4 ,increase the intension further by adding the quality ,english text book and the extension becomes still less4 #f;a4 ,,two ,,important ,,facts ,,in ,,the ,,law ,,of ,,variation4 ,in studying the law of variation two facts are especially evident4 7#a7 ,the law applies only to a series of terms representing notions of the same family4 ,the extension and intension of 8text book10 for example1 could not be compared with the extension and intension of 8house0 as they belong to a different class of words1 the genus of text book being book1 while the genus of house is building4 ,to illustrate the law of variation1 determine upon any class name1 then think of its proximate genus 7the next higher-up class to which it belongs74 ,continue this till the series is sufficiently complete to illustrate the law4 ,or proceed in the opposite direction4 ,that is1 after selecting the class name think of the next lower term in the class and thus continue till series is complete4 ,illustration3 ,the class name man is determined upon2 the proximate genus of man is biped1 the proximate genus of biped is animal1 and so on4 ,or thinking downward3 a proximate species of man is white man1 of white man4 ,european1 etc4 ,thus the series3 animal biped man white man ,european 7#b7 ,as a second fact3 the increase and decrease is not a mathematical one4 ,that is1 by doubling the extension the intension is not halved4 ,or if the intension is decreased by one quality the extension is not necessarily increased by one object4 ,thus 8man0 stands for one billion seven hundred million beings or objects4 ,decrease the intension of 8man0 by the one quality of rationality and the extension would include all bipedsmany billion objects4 #f;b4 ,,the ,,law ,,of ,,variation ,,diagrammatically ,,illustrated4 ,in a general way lines may be used to represent the variation in extension and intension4 ,for example3 we may let a line an inch long represent the extension of man1 one two inches long represent the extension of biped1 three inches long represent the extension of animal1 etc4 ,while on the other hand1 if a line an inch long represents the intension of man1 a line one-half inch long may be used to represent the intension of biped1 one a quarter of an inch long to represent the intension of animal1 etc4 ,the following illustrates this scheme in connection with another series of words3 ,extension ,intension barn building structure object ,in the foregoing scheme building refers to a greater number of objects than barn1 hence the line under extension representing building should be longer than the line for barn4 ,likewise structure1 referring to a greater number of objects than building1 is represented by a longer line4 ,thus when the series is viewed from top to bottom a gradual increase in extension is noted4 ,giving attention to the intensional use of the series we note that building has fewer qualities than barn1 structure fewer than building and object fewer than structure4 ,therefore1 from top to bottom1 the intension of the terms gradually decreases4 ,the variation may be made still more apparent if triangles are used1 one triangle being placed upon the other1 vertex to base1 like the following3 ,illustration3 7 ,intension and ,extension 7 8,biped0 is written near the base or in the broadest part of the extension triangle because it denotes the greatest number of objects1 and is1 therefore1 broadest in extension4 8,man0 occupies a narrower part of the extension triangle because it refers to fewer objects or is narrower in extension than 8biped40 8,arnold0 occupies the narrowest part of the extension triangle because it is the narrowest in extension4 ,on the other hand 8,arnold0 occupies the broadest part of the intension triangle because intensionally it possesses more qualities than the others1 while 8biped10 having the least depth in intension or possessing the fewest qualities1 occupies the narrowest portion of the intension triangle4 #g4 ,,outline4 ,,the ,,extension ,,and ,,intension ,,of ,,terms4 #a4 ,two-fold ,function of ,connotative ,terms4 #b4 ,extension and ,intension ,defined4 #c4 ,extended ,comparison of ,extension and ,intension4 #d4 ,a ,list of ,connotative ,terms used in ,extension and ,intension4 #e4 ,other ,forms of ,expression for ,extension and ,intension4 #f4 ,law of ,variation in ,extension and ,intension4 #f;a4 ,two ,important ,facts in the ,law of ,variation4 #f;b4 ,the ,law of ,variation ,diagrammatically ,illustrated4 #h4 ,,summary4 #a4 ,connotative terms are used in a two-fold sense3 first1 to denote objects2 second1 to imply qualities4 #b4 ,a term is used in extension when it is employed with reference to the objects for which the term stands4 ,a term is used in intension when it is employed with reference to the qualities for which the term stands4 #c4 ,the answer to either of the following questions will lead one to use any term in extension3 ,first1 what are the kinds8 or second1 to what objects may the term be applied8 ,the answer to either of the following questions will lead to the use of any term in intension3 ,first1 what does it mean8 or second1 what are the qualities8 #d4 ,to illustrate extension and intension it is best to use the class-names in every day speech4 #e4 ,the word denotation is commonly used for extension and connotation for intension4 #f4 8,as the intension of a term is increased its extension is decreased and vice versa10 is a statement of the ,law of ,variation in the extension and intension of terms4 #f;a4 ,the law of variation applies only to a series of terms representing notions of the same class or family1 the words being arranged in a species-genus order4 ,the increase and decrease of the extension and intension of a series is not proportional4 #f;b4 ,the law of variation is best explained by using two triangles1 one super-imposed upon the other vertex to base and base to vertex4 #i4 ,,illustrative ,,exercises4 #a;a4 ,employ the following terms in extension,european1 flower1 term1 truth4 ,russian ,european ,englishman ,scotchman lily flower rose pansy singular term distributive collective ,truth has no extension4 truth ,since it refers to a quality only1 it is non-connotative4 #a;b4 ,employ the following in extensiongrain1 rock1 soil1 precious stone4 #b;a4 ,use intensionally bird1 quadruped1 letter1 ,john4 two feet bird ability to fly feathers four feet quadruped back bone hairy covering heading letter body complimentary close ,john has no intension4 ,john ,since it refers to an object only1 it is non-connotative4 #b;b4 ,use the following in intensionword1 table1 purity1 government4 #c;a4 ,the use of a term in extension follows when attempting to answer two questions3 ,first1 what are the kinds8 ,second1 to what objects may the term be applied8 ,make application of this with reference to the term man4 #a4 ,what are the kinds of men8 ,caucasian1 ,malay1 ,mongolian1 ,ethiopian1 ,redman4 #b4 ,to what objects does the term man refer8 ,george ,washington1 ,chas4 ,hughes1 ,john ,smith4 ,in both #a and #b the word man is used to denote objects1 hence it is employed in extension4 #c;b4 ,use the term vegetable in extension by answering the two questions in #c;a4 #d;a4 ,decrease one by one the qualities of some common object with a view of noting how when the intension is decreased the extension is increased4 ,intension ,extension binding leaves cover school arithmetic printed matter designed for instruction instruction in arithmetic binding leaves school arithmetic cover school grammar printed matter school speller1 etc4 designed for instruction binding school arithmetic leaves school grammar cover school speller1 etc4 printed matter encyclopaedia novel school arithmetic binding school grammar leaves school speller1 etc4 cover encyclopaedia novel note book #d;b4 ,with a view of noting how when the intension is decreased the extension is increased1 decrease one by one the common qualities of peach tree4 #e;a4 ,in the following series what word could be substituted for 8mammal0 and why8 ,being1 organized being1 animal1 vertebrate1 mammal4 ,answer3 ,fish1 reptile1 or bird2 because there are at least seven classes of animals which belong to the vertebrate family1 any one of which could be used to complete the series4 #e;b4 ,form a series of which 8,baldwin apple0 has the narrowest extension4 ,what terms may be substituted for 8,baldwin apple80 #f;a4 ,in a series of which 8pupil0 is a member show that the increase and decrease is not proportional4 ,the series3 logic pupil1 pupil1 youth1 human being1 being4 ,in decreasing the intension of 8logic pupil0 by dropping the one quality1 logic1 the extension is made larger by many more than one1 as 8pupil0 represents many more objects than 8logic pupil40 ,therefore1 the increase is not in proportion to the decrease4 #f;b4 ,in a series in which 8ruler0 appears1 show that the increase and decrease is not proportional4 #g4 ,from the following list select the proper words of the series2 arrange them2 draw and name the triangles3 ,caesar1 brute1 man1 ,roman1 ,american1 biped1 sensuous being1 animal1 individual4 #aj4 ,,review ,,questions4 #a4 ,what is a connotative term8 ,illustrate4 #b4 ,which is the broader term1 quality or attribute8 ,why8 #c4 ,when is a term used in extension8 #d4 ,use the term triangle in intension4 #e4 ,as an aid to using a term in extension or intension what questions may one ask himself8 #f4 ,by asking these questions use the term clock in both extension and intension4 #g4 ,by experimenting with the qualities of a rectangle show that as the intension is decreased the extension is increased4 #h4 ,write a list of five connotative terms4 ,prove that they are connotative by illustrating their extension and intension4 #i4 ,the term metal denotes such qualities as element1 metallic connotes lustre1 conductor of heat and electricity4 ,in the foregoing which of the two words following the brace should be used8 ,give reasons4 #aj4 ,state the law of variation in two ways4 #aa4 ,as one studies the law of variation what two facts are especially evident8 ,explain fully4 #ab4 ,for the purpose of illustrating the law of variation form a series of which desk is a member4 ,draw and name the triangles4 #aa4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 #a4 ,which is the broader term1 subject or object8 ,prove it4 #b4 ,if a term like ,caesar is given extension does it become a general term8 ,why8 #c4 ,using 8man0 as a member of each1 arrange at least three different series4 #d4 ,why may it be said that a connotative term is two dimensional8 #e4 ,is there a word which has a broader extension than 8being08 ,why8 #f4 ,prove that youth has less intension than human being4 #g4 ,devise a series of words in which the variation is proportional4 #h4 ,advance arguments supporting the hypothesis that the term ,john has neither extension nor intension4 #i4 ,suggest arguments to prove that 8,george ,washington0 has both extension and intension4 ,,chapter #f4 ,,definition4 #a4 ,,importance4 ,to be clear1 cogent1 concise and consistent is to be logical4 ,reference has been made to a striking tendency on the part of writers and speakers to use words loosely4 ,it is a noticeable fact that scholars generally aim to be profound rather than clear1 philosophical rather than pointed4 ,in the use of text books more or less pedagogical these are the common complaints3 8,i don't understand what he means0 or 8,you have to read so much to get so little40 ,this condition gives to the topic of definition a prominence which cannot be overlooked by those who are seeking the truth2 because the definition is the clearest1 briefest and altogether the most satisfactory way of describing an idea4 ,likewise the habit of defining any doubtful term reduces to a minimum the possibility of misunderstanding4 ,the subject must appeal strongly to the instructor1 as he1 above all others1 should make his work stand for clearness1 pointedness and continuity4 #b4 ,,the ,,predicables4 ,a predicable is a term which can be affirmed or predicated of any subject4 ,in the proposition1 8,a man is a rational animal10 the term 8rational animal0 is a predicable1 because it can be affirmed of the subject man4 ,to gain a clear knowledge of the definition it is quite necessary to understand the five predicables which we shall consider in the following order3 #a4 ,genus4 #b4 ,species4 #c4 ,differentia 7difference74 #d4 ,property4 #e4 ,accident4 7#a7 ,genus and 7#b7 ,species4 ,genus and species are relative terms and can best be defined together4 ,a genus is a term which stands for two or more subordinate classes4 ,a species is a term which represents one of the subordinate classes4 ,the genus may be subdivided into species2 the species together form the genus4 ,to illustrate3 ,the term man stands for five subordinate classes or species1 as white1 black1 brown1 yellow and red4 8,man0 is1 therefore1 a genus1 while 8white man0 and 8black man10 etc41 are species4 ,the term 8polygon0 is a genus with reference to 8trigon10 8tetragon10 8pentagon10 etc41 while 8trigon0 is a species of 8polygon40 ,any given genus may be a species of some higher class4 ,that is1 8man10 which is a genus with reference to the kinds of men1 is a species of the higher class 8biped10 while 8biped0 is a species of 8animal10 8animal0 a species of 8organized being10 8organized being0 of 8material being10 8material being0 of 8being40 ,but here we stop1 as there is no higher grade to which 8being0 can be referred4 ,this highest genus takes the name of summum genus4 ,similarly any given species may be a genus of some lower class4 8,white man10 for example1 which is a species of 8man10 is a genus of 8,american10 8,englishman10 8,german10 8,frenchman10 etc4 8,american0 is a genus of 8,new ,yorker10 8,californian10 etc41 while 8,new ,yorker0 is a genus of 8,smith of ,jamaica40 ,this last term is an individual and cannot be subdivided4 ,it represents the lowest possible species and is referred to in logic as infima species4 ,it is obvious that the highest genus cannot become a species1 neither can the lowest species become a genus4 ,,proximate ,,genus4 ,the proximate genus is the next class above4 ,to illustrate3 8,animal0 is a genus of 8man10 but 8biped0 is the proximate genus of 8man40 8,quadrilateral0 is the genus of 8square10 but 8rectangle0 is the proximate genus4 ,the next class above 8trigon0 is polygon not figure4 ,hence 8polygon0 is the proximate genus of 8trigon40 ,,genus ,,and ,,species ,,of ,,natural ,,history4 ,in natural history the following terms are used to denote the various grades of kinship in any scheme of classification3 7#a7 kingdom1 7#b7 class1 7#c7 order1 7#d7 family1 7#e7 genus1 7#f7 species1 7#g7 variety1 7#h7 the individual thing4 ,here 8genus0 and 8species0 are absolute not relative and occupy a fixed place in the scheme1 while from a logical viewpoint any of the grades indicated between the lowest and highest would be the species of the next higher grade or a genus of the next lower2 e4 g41 order is a species of 8class10 while it is the genus of 8family40 ,,genus1 ,a ,,double ,,meaning4 ,we recall that any class name or genus has a double use1 extensional and intensional4 ,when considered from the standpoint of its extension1 a genus represents a group of objects or is mathematical in its application1 but when used in an intensional sense it represents a group of qualities or is logical in its application4 ,considered extensionally the genus refers to a larger number of objects than the species4 ,but when viewed intensionally the species refers to more qualities than the genus4 ,this was made clear when discussing the law of variation in the extension and intension of terms4 7#c7 ,differentia4 ,the differentia of a term is that attribute which distinguishes a given species from all the other species of the genus4 ,it has been observed that the species refers to more qualities than the genus4 ,in fact1 it represents all the attributes of the genus plus those which distinguish the particular species from the other species of the genus4 ,these additional qualities are the differenti of the particular species4 ,,to ,,illustrate3 ,the attribute which distinguishes man from the other bipeds of the world is his rationality4 ,that which distinguishes the rectangle from the other parallelograms is its four right angles4 ,the attributes rationality and right angles are differentiae4 7#d7 ,property4 ,a property of a term is any attribute which helps to make the term what it is4 ,thus 8consciousness0 is a property of man1 8binding0 a property of book1 8angles0 a property of triangle4 ,deprive the terms of these attributes and their true nature is altered4 ,a differentia is a property according to the foregoing definition4 ,however1 ,jevons defines 8property0 as 8,any quality which is common to the whole of a class1 but is not necessary to mark out the class from other classes40 ,this viewpoint excludes 8differentia0 from the notion of property4 ,the difference in opinion is of slight importance4 7#e7 ,accident4 ,an accident of a term is any attribute which does not help to make the term what it is4 ,it may indifferently belong or not belong to the term4 ,deprive a term of an accident and the nature of the term remains unchanged4 ,thus1 a teacher's position1 a man's watch1 the fact that the angle is one of #hj are all accidents4 ,it is obvious that a property is a constant attribute while an accident is variable4 ,this gives to the former a universal validity while the latter is more or less shifting and uncertain4 ,all triangles must have three angles 7property7 while the value of each angle in degrees 7accident7 admits of unlimited variation4 ,some logicians divide accidents into separable and inseparable4 ,a man's hat would be a separable accident while his birthplace would be an inseparable accident4 ,,five ,,predicables ,,illustrated4 ,in the following brief descriptions the five predicables are designated3 7species7 7genus7 7differentia7 7#a7 ,this is a with rectangle parallelogram four right angles 7accident7 its longer sides being 4 ten inches 7species7 7differentia7 7prox4 genus7 7#b7 ,this is a with the man rational biped 7property7 7accident7 and a 4 power of locomotion ruddy complexion 7species7 7genus7 7differentia7 7property7 7#c7 ,a is a of and 1 trigon polygon three sides three angles 7accident7 4 the sum of the angles being equal to two right angles #c4 ,,the ,,nature ,,of ,a ,,definition4 ,it will be remembered that an individual notion is a notion of a single thing or attribute1 while a general notion is a notion of a class of things or a group of attributes4 ,a term which represents an individual notion is known as a singular term1 while a term which stands for a general notion is referred to as a general term4 ,one may explain the meaning of a singular term which stands for one thing by enumerating its various attributes4 ,for example1 such attributes as a piercing bark1 a yellow color1 intelligent1 companionable1 a strong liking for sweetmeats1 explain the meaning of the singular term 8,fido40 ,likewise we may explain the meaning of a general term by enumerating its attributes4 ,to illustrate3 power of speech1 rationality1 ability to laugh1 etc41 explain the meaning of the general term man4 ,the explanation of the singular term fits only ,fido4 ,there is probably no other dog in the world just like ,fido4 ,but the explanation of the general term man may be applied to all men4 ,a brief enumeration of attributes which may be applied to a class of things often takes the form of a definition4 ,the word definition comes from the word definire1 meaning to limit or fix the bounds of4 ,a definition1 then1 consists of the enumeration of such attributes as distinguish a term from all other terms4 ,in this sense it would seem that the singular term ,fido1 as well as the general term man1 admits of definition1 but it is usual for logicians to confine definition to the general term4 ,singular terms may be described2 general terms1 defined4 ,a ,,definition ,,of ,,definition4 ,a definition of a term is a statement of its meaning by enumerating its characteristic attributes4 ,that the enumeration must be in terms of its distinguishing or characteristic attributes is implied in the derivation of the term definition4 ,the attributes must establish limits or bounds1 just as a line fence limits a land owner's possessions4 ,to indicate that man is a creature possessing the power of locomotion1 sense of sight and ability to eat1 is surely not a definition1 as the marks are not characteristic of men only4 ,these attributes set no boundary between man and horse1 consequently the statement is a faulty description of man1 not a definition4 ,but when the enumeration includes such attributes as power of speech1 rationality and ability to laugh1 then does the description become a definition4 ,to put it differently3 ,a definition is a description of a term by means of its distinguishing attributes4 ,this statement may be considered a definition of man1 though somewhat faulty3 8,a man is a creature who is rational and who possesses the power of speech and ability to laugh40 #d4 ,,definition ,,and ,,division ,,compared4 ,we have learned that general terms when connotative may be used extensionally or intensionally4 ,a definition indicates the intensional nature of a term1 while a statement which points out the extensional nature of a term is known as logical division4 ,more briefly3 ,a definition is an intensional statement of the nature of the term1 while logical division is an extensional statement of the nature of the term4 ,to illustrate3 ,the following statements are definitions3 7#a7 ,a dog is a domesticated quadruped of the genus canis and given to barking4 7#b7 ,a quadrilateral is a rectilinear figure of four sides4 7#c7 ,soil is a substance composed of pulverized rock and decayed vegetable matter in which plants will grow4 ,the following represent ,logical ,division3 7#a7 ,dogs are divided into hounds1 terriers1 bull1 etc4 7#b7 ,the kinds of quadrilaterals are trapeziums1 trapezoids and parallelograms4 7#c7 ,the various soils are loam1 sand1 clay1 muck1 etc4 #e4 ,,the ,,kinds ,,of ,,definitions4 ,generally speaking there are three kinds of definitions1 namely1 7#a7 ,etymological1 7#b7 ,descriptive1 7#c7 ,logical4#e 7#a7 ,an etymological definition is one based upon the derivation of the term4 ,this kind of a definition1 which gives merely the meaning of the symbol1 is sometimes called a nominal or verbal definition2 while a real definition is regarded as one which gives the meaning of the notion for which the symbol stands4 ,the modern logician is inclined to ignore this classification on the argument that to make a distinction between a symbol and the notion it symbolizes is simply to misunderstand the relation which exists between them4 ,if the definition does not agree with the thing then it cannot correctly explain the term which represents the thing4 ,define correctly the term and one has defined correctly the notion signified by the term4 ,the attributes of a term may be separated into three classes3 differentia1 property and accident4 ,it would appear possible1 therefore1 to define a term by enumerating the accidents only or by enumerating the properties1 or1 finally1 by stating the differentiae4 ,but if the enumeration is confined to accidents the chances are that the statement will be a description1 not a definition1 as accidents are seldom sufficiently characteristic to determine the boundaries of a term4 ,this leaves open two distinct ways of defining a term3 ,first1 by naming the properties or properties and accidents only2 second1 by stating the differenti only4 ,the former kind is the so-called descriptive definition1 while the latter is the logical4 7#b7 ,a descriptive definition of a term is a description of its nature by means of its properties and accidents4 7#c7 ,a logical definition of a term is a description of its nature by means of its differenti4 ,,the ,,three ,,kinds ,,of ,,definitions ,,illustrated ,,and ,,compared4 ,etymological ,definition of ,trigon4 ,a trigon is a figure of three corners4 ,descriptive3 ,a trigon is a figure which has three sides and three angles1 the sum of the latter being equal to two right angles4 ,logical3 ,a trigon is a polygon of three angles4 ,it is seen that an etymological definition is simply a root-word analysis4 ,in the case of trigon1 the prefix comes from the ,greek1 meaning three1 while the root-word comes from the ,greek meaning corner4 ,the descriptive definition of trigon names the properties1 8three sides and three angles0 7differenti7 and the accident1 8the sum of the angles of which equals two right angles40 ,the logical definition of trigon simply states the proximate genus1 8polygon10 and the differentia1 8three angles40 #f4 ,,when ,,the ,,three ,,kinds ,,of ,,definitions ,,are ,,serviceable4 ,the etymological definition is helpful in furnishing a cue for remembering the descriptive and logical definitions4 ,it also leads to precision of expressionthe right word in the right place4 ,here is where the knowledge of a foreign language1 particularly ,latin1 is helpful4 ,the descriptive definition is best adapted to the child-mind4 ,children think in the large2 are not given to hair-splitting discriminations1 and1 therefore1 many characteristic marks must be mentioned in order to insure a mastery of the content4 ,with children the logical definition is often too brief to be clear4 ,for example1 it is easy to see which of the following definitions would be better adapted to the child-mind4 ,logical3 ,a square is an equilateral rectangle4 ,descriptive3 ,a square is a figure of four equal sides and four right angles4 ,the logical definition may be introduced to the student of the secondary school4 ,few exercises are better adapted to the development of powers of discrimination and precision than practice in defining logically the common terms of every-day life4 ,for example3 8,a book is a pack of paper-sheets bound together40 8,a chair is a piece of furniture with back and seat1 designed for the seating of one person40 8,a lead pencil is a cylindrical writing implement with lead through the center40 8,a door is an obstacle designed to swing in and out to open and close an entrance40 8,an eraser is an implement made to rub out written or printed characters40 ,these definitions1 coming from training school students1 are not above criticism1 yet they illustrate the point in hand4 #g4 ,,the ,,rules ,,of ,,logical ,,definition4 ,five rules summarize the requirements to which a logical definition must conform4 ,,first ,,rule4 ,a logical definition should state the essential attributes of the species defined4 ,this means that a logical definition should contain the species1 the proximate genus and the differentia4 ,as the terms species1 genus and differentia have been explained1 it will be sufficient to briefly illustrate this rule4 ,logical ,according to the ,first ,rule4 species genus differentia 7#a7 ,a is a with 4 bird biped feathers species genus differentia 7#b7 ,a is a 4 mascot person supposed to bring good luck species genus differentia 7#c7 is a of 4 ,religion system faith and worship species genus differentia 7#d7 ,a is a 4 moonbeam ray of light from the moon ,illogical ,according to the ,first ,rule4 7#a7 ,a man is a rational animal4 78,biped0 is the proximate genus1 not 8animal407 7#b7 ,a ,connotative term always denotes both an object and an attribute4 7,no genus47 7#c7 ,a trigon is a polygon4 7,no differentia47 7#d7 ,it is a term which denotes an indefinite number of objects or attributes4 7,no species47 ,the ,foregoing ,illogical ,definitions ,made ,logical4 7#a7 ,a man is a rational biped4 7#b7 ,a ,connotative term is a term which denotes both an object and an attribute4 7#c7 ,a trigon is a polygon of three angles4 7#d7 ,a general term is a term which denotes an indefinite number of objects or attributes4 ,,second ,,rule4 ,a logical definition should be exactly equivalent to the species defined4 ,this means that the species must equal the genus plus the differentia or the subject and predicate of the definition must be co-extensiveof the same bigness4 ,the subject must refer to the same number of objects as the predicate4 ,a man upon the witness stand makes the declaration that he will testify to the truth1 the whole truth and nothing but the truth4 ,a logical definition must contain the species1 the whole species and nothing but the species4 ,if the definition does not include all the species1 it is too narrow2 while on the other hand1 if it includes other species of the genus it is too broad4 ,an excellent test of this second requirement is to interchange subject and predicate4 ,if the interchanged proposition means the same as the original then the conditions have been met4 ,to illustrate3 ,original,a trigon is a polygon of three angles4 ,interchanged,a polygon of three angles is a trigon4 ,the very best way of making the definition conform to this rule is to put to oneself these three questions3 #a4 ,does it include all of the species8 #b4 ,does it exclude all other species of the genus8 #c4 ,has it any unnecessary marks8 ,to exemplify3 ,let us ask the three questions relative to the following logical definitions3 7#a7 ,a parallelogram is a quadrilateral whose opposite sides are parallel4 7#b7 ,a bird is a biped with feathers4 ,questions3 7#a7 ,does the definition include all the parallelograms8 ,yes4 ,does it exclude all other quadrilaterals8 ,yes4 ,are there any unnecessary marks8 ,no4 7#b7 ,does it include all birds8 ,yes4 ,does it exclude all other bipeds8 ,yes4 ,any unnecessary marks8 ,no4 ,illogical ,according to the ,second ,rule4 7#a7 ,a man is a vertebrate animal4 7,too broad4 ,does not exclude other species of the genus1 such as horses1 dogs1 etc47 7#b7 ,a barn is a building where horses are kept4 7,too narrow4 ,does not include all of the species1 such as cow barn47 7#c7 ,an equilateral triangle is a triangle all of whose sides and angles are equal4 7,equal angles is an unnecessary mark47 ,the ,foregoing ,definitions ,made ,logical4 7#a7 ,a man is a rational biped4 7,proximate genus47 7#b7 ,a barn is a building where horses and cattle are kept and hay and grain are stored4 7#c7 ,an equilateral triangle is a triangle all of whose sides are equal4 ,,third ,,rule4 ,a definition must not repeat the name to be defined nor contain any synonym of it4 ,a violation of this rule is known as 8a circle in defining0 7circulus in definiendo74 ,there are some exceptions to this rule1 as in the case of compound words and a species which takes its name from its proximate genus4 ,to say that a hobby-horse is a horse1 or that an equilateral triangle is a triangle1 is not only allowable but necessary1 that the proximate genus may be used4 ,the following definitions are illogical according to the third rule3 7#a7 ,a teacher is one who teaches4 7#b7 ,life is the sum of the vital functions4 7#c7 ,a sensation is that which comes to the mind through the senses4 ,,fourth ,,rule4 ,a definition must not be expressed in obscure1 figurative or ambiguous language4 ,a violation of this rule is referred to in logic as 8defining the unknown by the still more unknown0 7ignotum per ignotius74 ,it is known that the purpose of definition is to make clear some obscure term1 consequently unless every word used is understood the chief aim of the definition has been defeated4 ,from this it must not be inferred that all definitions should be free from technical terms4 ,such a restriction would make the defining of many terms unsatisfactory and in a few cases practically impossible4 ,to the student of evolution the following definition by ,spencer is intelligible while to the uninitiated it would appear obscure3 8,evolution is a continuous change from an indefinite1 incoherent homogeneity to a definite coherent heterogeneity through successive differentiations and integrations40 ,this rule insists upon simple language when it is possible to use such in giving an accurate and comprehensive meaning to the term defined4 ,illogical ,definitions ,according to the ,fourth ,rule4 7#a7 8,a net is something which is reticulated and decussated1 with interstices between the intersections40 ,dr4 ,johnson4 7#b7 8,thought is only a cognition of the necessary relations of our concepts40 7#c7 8,the soul is the entelechy1 or first form of an organized body which has potential life40 ,aristotle4 ,,fifth ,,rule4 ,when possible the definition must be affirmative rather than negative4 ,the fact that there are a considerable number of terms which admit of a negative definition only1 takes from the force of this rule4 ,such terms as deafness1 inexpressible1 infidel and the like can best be defined negatively4 ,it likewise happens that when words are used in pairs it is expedient to define one affirmatively and the other negatively4 ,recall1 for example1 the definitions of relative and absolute terms3 8,a relative term is one which needs another term to make its meaning clear40 8,an absolute term is one which does not need another term to make its meaning clear40 ,illogical ,definitions ,according to the ,fifth ,rule4 7#a7 ,a gentleman is a man who is not rude4 7#b7 ,an element is a substance which is not a compound4 7#c7 ,an univocal term is a term which does not have more than one meaning4 #h4 ,,terms ,,which ,,cannot ,,be ,,defined ,,logically4 ,a logical definition insists upon a proximate genus and differentia4 ,but as there is no genus higher than the highest genus 7summum genus7 then surely such cannot be defined logically4 ,the words being and thing illustrate terms of this class4 ,moreover1 it is impossible to give a satisfactory definition of an individual 7infima species7 as no attributes can be mentioned which will distinguish definitely and permanently the individual from others of the class4 ,we may perceive the attributes but not those that are possessed solely by the individual4 ,to say that ,abraham ,lincoln was a man who was simple and honest is not a definition1 as other men have had the same characteristics4 ,again there are a few terms such as life1 death1 time and space which cannot be defined satisfactorily4 ,these terms seem to be in a class by themselves or of their own genus 7sui generis74 ,since a definition of a term is a brief explanation of it by means of its attributes1 it follows that collective terms and terms standing for a single attribute are incapable of definition4 ,such terms as group1 pain1 attribute1 belong to this class4 ,we may say1 then1 that there are some terms too high1 some too low and some too peculiar to come within the province of logical definition4 ,in short1 8summum genus10 8infima species0 and 8sui generis0 are incapable of definition4 #i4 ,,definitions ,,of ,,common ,,educational ,,terms4 7#a7 ,development is the process whereby the latent possibilities of an individual are unfolded or the invisible conditions of a situation are made apparent4 ,development means expansion according to principle1 while unfolding may or may not involve a principle4 7#b7 ,education is the process employed in developing systematically1 symmetrically and progressively all of the capabilities of a single life2 or 7#c7 ,education is the process of modifying experience in order to make the life as valuable as it ought to be4 7#d7 ,teaching is the art of occasioning those activities which result in knowledge1 power and skill4 ,it is the duty of the true teacher to inspire the child to activity along right lines4 ,through his own activity the child shapes his inner world which is sometimes termed character4 ,knowledge is anything known1 power is ability to act1 skill is a readiness of action4 7#e7 ,instruction is the art of occasioning those activities which result in knowledge4 ,instruction develops the understanding2 teaching develops character4 7#f7 ,training is the occasioning of those activities which1 by means of directed exercise1 result in power and skill4 ,training and education are not interchangeable4 ,training implies an outside authority1 while education1 which involves inner development1 may proceed without supervision4 7#g7 ,knowledge is anything acquired by the act of knowing4 7#h7 ,learning is the act of acquiring knowledge or skill4 7#i7 ,instruction1 training1 teaching1 learning and education all involve activity4 ,instruction arouses activity which results in knowledge2 training directs activity which produces power and skill2 teaching includes both instruction and training4 ,learning is an activity which results in knowledge and skill1 while education is a developing process which involves all the others4 7#aj7 ,a science is knowledge classified for the purpose of discovering general truths4 7#aa7 ,an art is a skillful application of knowledge and power to practice4 8,a science teaches us to know1 an art to do40 7#ab7 ,a fact is a single1 individual1 particular thing made or done4 ,a truth is general knowledge which exactly conforms to the facts4 ,a truth may be a definition1 rule1 law1 or principle4 7#ac7 ,a fact as opposed to hypothesis is an occurrence which is true beyond doubt4 ,an hypothesis is a supposition advanced to explain an occurrence or a group of occurrences4 ,a theory is a general hypothesis which has been partly verified4 7#ad7 ,theory as opposed to practice means general knowledge1 while practice involves the putting into operation one's theories4 7#ae7 ,a fact as opposed to phenomenon is something accomplished4 ,a phenomenon is something shown4 7#af7 ,a method-whole is any subdivision of the matter for instruction which leads to a generalization4 7#ag7 ,method is an orderly procedure according to a recognized system of rules and principles4 ,as the term is commonly used it includes not only the arrangement of the subject matter for instruction but the mode of presenting the same to the mind4 7#ah7 ,induction is the process of proceeding from the less general to the more general4 ,deduction is the process of proceeding from the more general to the less general4 7#ai7 ,the terms induction and deduction may have reference to forms of reasoning or to methods of teaching4 ,the inductive method is the method of deriving a general truth from individual instances4 ,the deductive method is the method of applying a general truth to individual instances4 ,the inductive method is objective1 while the deductive method is subjective4 ,induction is the method of discovery2 deduction is the method of instruction4 7#bj7 ,analysis is the process of separating a whole into its related parts4 ,synthesis is the process of uniting the related parts to form the whole4 7#ba7 ,the analytic method is the method of proceeding from the whole to the related parts4 ,the synthetic method is the method of proceeding from the related parts to the completed whole4 7#bb7 ,analysis and synthesis deal with single things1 while induction and deduction are concerned with classes of things4 7#bc7 ,the complete method consists of three elements3 7#a7 induction1 7#b7 deduction1 7#c7 verification or proof4 ,when the emphasis is placed on the inductive phase1 the complete method is sometimes termed the development method4 #aj4 ,,outline4 ,,definition4 7#a7 ,importance4 7#b7 ,the ,predicables4 ,genusspeciessummum genusinfima species4 ,proximate ,genus4 ,genus and ,species of ,natural ,history4 ,genus1 ,double meaning of ,differentia4 ,property4 ,accident4 ,separable1 ,inseparable4 7#c7 ,nature of ,definition4 7#d7 ,definition and ,division ,compared4 7#e7 ,the ,kinds of ,definitions4 7#a7 ,etymological4 7#b7 ,descriptive4 7#c7 ,logical4 ,,three ,,kinds ,,illustrated ,,and ,,compared4 7#f7 ,when the ,three ,kinds are ,serviceable4 7#g7 ,the ,rules of ,logical ,definition4 7#a7 ,essentials4 7#b7 ,same size4 7#c7 ,do not repeat4 7#d7 ,unambiguous4 7#e7 ,language affirmative4 7#h7 ,terms ,which ,cannot be ,defined ,logically4 ,summum genus4 ,infima species4 ,sui generis4 ,collective terms4 ,a single attribute4 #aa4 ,,summary4 7#a7 ,to be logical one must acquire the habit of accurate definition4 ,this topic ought to appeal strongly to the school teacher1 who should above all others make his work stand for clearness1 pointedness and continuity4 7#b7 ,a predicable is a term which can be affirmed or predicated of any subject4 ,the five predicables are ,genus1 ,species1 ,differentia1 ,property and ,accident4 7#a7 ,a ,genus is a term which stands for two or more subordinate classes4 7#b7 ,a ,species is a term which represents one of the subordinate classes4 ,the proximate genus of a species is the next class above the species1 while the summum genus is the highest possible class in any graded series of terms4 ,the lowest class is the infima species of that series4 ,the lowest class may be individual4 ,in natural history genus and species are not relative terms1 but absolute1 having a fixed place in the series of gradations4 ,the term genus possesses a double meaning3 it may be used to represent objects 7extensionally7 or qualities 7intensionally74 7#c7 ,the differentia is that attribute which distinguishes a given species from all the other species of the genus4 7#d7 ,a property of a term is any attribute which helps to make that term what it is4 ,differentia is a property according to definition4 ,some logicians would not include the differentia in the content of the term property4 7#e7 ,an accident of a term is any attribute which does not help to make it what it is4 ,some authorities divide accidents into separable and inseparable4 7#c7 ,a definition of a term is a statement of its meaning by enumerating its characteristic attributes4 7#d7 ,definitions explain a term intensionally1 while logical division explains a term extensionally4 7#e7 ,there are three kinds of definitions3 7#a7 etymological1 7#b7 descriptive1 7#c7 logical4 ,an etymological definition is based upon the derivation of the term2 a descriptive definition states the characteristic properties and accidents of a term1 while a logical definition is simply a statement of the differentia of a term4 7#f7 ,the etymological definition leads to precision of expression1 the descriptive definition is best adapted to the child-mind1 while the logical definition belongs to the realm of secondary education4 7#g7 ,five rules summarize the requirements to which a logical definition must conform4 ,in a word or two these five rules are3 ,every logical definition must 7#a7 state the genus and differentia1 7#b7 be equivalent to the species defined1 7#c7 not repeat the name to be defined1 7#d7 not be expressed in obscure language1 7#e7 commonly be affirmative4 7#h7 ,some terms are too high 7summum genus71 some too low 7infima species71 some too peculiar 7sui generis7 to come within the province of logical definition4 #ab4 ,,illustrative ,,exercises4 #a;a4 ,the italicized words in the following propositions are predicables because they are affirmed of the subject3 7#a7 8,this man weighs one hundred fifty pounds40 7#b7 8,a bird is a feathered biped40 7#c7 8,the earnest teacher is an indefatigable worker40 7#d7 8,walking is the most beneficial outdoor exercise40 #a;b4 ,underscore the predicables in the following3 7#a7 8,all men are rational40 7#b7 8,teachers must be just40 7#c7 8,every form of unhappiness springs from a wrong condition of the mind40 7#d7 8,calmness of mind is one of the beautiful jewels of wisdom40 #b;a4 ,to clarify our ideas it is an excellent plan to select a group of words belonging to the same genus with a view of defining them as simply and expeditiously as possible4 ,as an illustration building may be selected as a genus4 ,the word kind will suggest to us the species1 such as dwelling1 church1 theatre1 school1 barn1 bird-house1 granary and smoke-house4 ,next it is necessary to discover the basis of distinction4 ,this seems to be the use to which the building is put4 ,now we are ready for the definitions3 ,species ,genus ,differentia ,a dwelling is a building where people live4 ,a church is a building where people worship4 ,a theatre is a building where people act4 ,a school is a building where children are taught4 ,a barn is a building where domestic animals1 hay and grain are kept4 ,a bird-house is a building designed for birds4 ,a granary is a building where grain is stored4 ,a smoke-house is a building where meat is smoked4 #b;b4 ,by selecting man as the genus1 define the terms ,caucasian1 ,mongolian1 ,ethiopian1 ,malay and ,american ,indian4 ,treat the term chair in the same manner4 #c;a4 ,one may easily distinguish a property from an accident by asking himself the question1 8,would subtracting the attribute from the term alter its identity08 ,for example in the following1 ,i find that the words italicized are properties because subtracting each from the term changes its identity3 ,term ,attributes man age1 rationality1 possessions4 book binding1 leaves1 size1 color1 contents4 radium emits intense light and heat1 costs a million dollars a pound4 snail air-breathing mollusk1 moves slowly4 slush soft mud and snow1 six inches deep4 #c;b4 ,indicate the common attributes of the following terms1 underscoring the properties3 ,tree1 teacher1 garden1 house1 river4 #d4 ,the rules summarize well the essentials of the subject matter of the logical definition4 ,therefore1 it is highly important for the student to have these rules at the 8tip of the tongue40 ,with this in view a device of this nature may be helpful4 ,make each letter of the word rules stand for the initial letter of a suggestive word in each of the five rules4 ,for example3 r 7repeat71 u 7unambiguous71 l 7language affirmative71 e 7essential71 s 7same size74 ,with a little study 8r and repeat10 8u and unambiguous10 8l and language affirmative10 8e and essential10 8s and same size0 may be firmly linked together in the memory4 ,repeat suggests the third rule1 do not repeat the name1 etc42 unambiguous1 the fourth rule1 not ambiguous language1 etc42 language affirmative1 the fifth rule2 essentials1 the first rule2 same size1 the second rule1 subject and predicate must be of same size4 ,the fact that the rules are not recalled in order of treatment is inconsequential4 ,it is the writer's experience that fifteen minutes of concentrated study upon this device or one similar to it will indelibly stamp upon the mind these troublesome rules4 ,the student may be able to devise a more helpful keyword4 #ac4 ,,review ,,questions4 7#a7 ,why should the subject of definition appeal strongly to the school teacher8 7#b7 ,define a predicable4 7#c7 ,name in order the five predicables4 7#d7 ,define and illustrate the terms genus and species4 7#e7 ,explain the terms summum genus1 infima species1 sui generis4 7#f7 ,illustrate proximate genus4 7#g7 ,explain the terms genus and species as used in natural history4 7#h7 ,exemplify the double meaning of the genus man4 7#i7 ,define and illustrate differentia4 7#aj7 ,in what sense is the species a richer term than the genus8 7#aa7 ,distinguish between property and accident4 7#ab7 ,illustrate separable and inseparable accidents4 7#ac7 ,give descriptive definitions of the following1 indicating the five predicables3 logic1 general term1 non-connotative term1 obversion4 7#ad7 ,define definition2 illustrate4 7#ae7 ,distinguish between definition and division4 7#af7 ,name1 define and illustrate the three kinds of definitions4 7#ag7 ,distinguish between real and verbal definitions4 7#ah7 ,define in three ways the following3 king1 government1 city1 metal4 7#ai7 ,state the rules of logical definition4 7#bj7 ,what words may be used as cues to aid in recalling the rules for logical definition8 7#ba7 ,under what circumstances will the wise teacher make use of each of three kinds of definitions8 7#bb7 ,relative to the second rule for logical definition what are the three questions that one should ask himself8 7#bc7 ,explain the exceptions to the third rule4 7#bd7 ,in connection with the fourth rule what may be said as to the use of technical terms8 7#be7 ,what facts take from the force of the fifth rule8 7#bf7 ,what classes of words do not admit of logical definition8 ,illustrate4 7#bg7 ,define education1 teaching1 instruction1 training4 7#bh7 ,distinguish by illustration between induction and synthesis2 deduction and analysis4 #ad4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,why should the scholar be tempted to speak and write illogically8 7#b7 ,name the parts of speech that may be classed as predicables4 7#c7 ,explain the ten categories as given by ,aristotle4 7#d7 ,show that genus and species are relative terms4 7#e7 ,why should the definition be needed most in the abstract sciences1 such as theology1 ethics1 political economy1 juris-prudence and psychology8 7#f7 ,define sin1 life1 wrong1 personality1 habit1 character4 7#g7 ,from the viewpoint of natural history find the species in the series of terms of which polygon is a member4 7#h7 ,what is the plural of differentia8 7#i7 ,why should logic insist upon the proximate genus8 7#aj7 7a7 ,man is a rational animal4 7b7 ,man is a rational biped 7proximate genus74 ,in the case of the immature mind the first definition would be clearer4 ,why8 7#aa7 8,a property of a term is any mark or characteristic which belongs to that term40 ,is this definition logical8 ,give reasons4 7#ab7 ,what is the difference between the logical and the popular conception of property8 7#ac7 ,is there any difference between the logical and popular conception of accidents8 7#ad7 8,the term conferentia might be used to stand for the essence of the genus1 as the term differentia represents the essence of the species40#f ,explain this4 7#ae7 ,john ,stuart ,mill affirms that there is no such thing as a real definition4 ,discuss this4 7#af7 ,in your opinion1 of the five rules of logical definition what one is violated most by the average teacher8 ,give reasons4 7#ag7 ,distinguish between symbol and content4 7#ah7 ,why are descriptive definitions best for young children8 ,what educational principle is involved8 7#ai7 ,from the standpoint of the five rules for logical definition criticise the following3 7#a7 ,a man is a reasonable vertebrate4 7#b7 ,a gentleman is a man with no visible means of support4 7#c7 ,a man is an organized entity whose cognitive powers function rationally4 7#d7 ,a metal is an element with a metallic luster4 7#e7 ,a triangle is a figure of three sides4 7#f7 ,a teacher is one who imparts knowledge4 7#g7 ,education is the process of drawing out all that is beautiful in the body and noble in the soul4 7#h7 ,a democrat is a man who believes in free trade4 7#i7 ,a government is a commonwealth controlled by direct vote of the people4 7#bj7 ,write the foregoing definitions in logical form4 7#ba7 ,since man is the only animal given to laughter1 why is not the following a logical definition3 8,man is a laughing animal40 7#bb7 8,a logical definition should contain the species1 the genus and the appropriate differentia40 ,is there any reason for using the term appropriate8 7#bc7 ,in connection with genus and species explain subaltern4 7#bd7 ,is laughter a property of human being or an accident8 7#be7 ,show how a pedagogue may be an instructor but not a teacher4 7#bf7 ,illustrate the complete method4 7#bg7 ,show that induction may consist of a series of analyses2 also a series of syntheses4 ,,chapter #g4 ,,logical ,,division ,,and ,,classification4 #a4 ,,nature ,,of ,,logical ,,division4 ,the term genus is used for any class name which stands for two or more subordinate classes while the term species is made to stand for any one of the subordinate classes4 ,the proximate genus of any species is the next class above4 ,for example the proximate genus of man is biped1 not animal4 ,logical division is the process of separating a proximate genus into its co-ordinate species4 ,,illustrations3 ,genus ,species ,fixed stars ,planets 7#a7 ,heavenly bodies ,satellites ,comets ,meteors ,nebulae ,leptocardians ,fishes 7#b7 ,vertebrates ,amphibians ,reptiles ,birds ,mammals ,caucasian ,mongolian 7#c7 ,man ,malay ,ethiopian ,american ,indian ,monarchy 7#d7 ,government ,aristocracy ,democracy #b4 ,,logical ,,division ,,distinguished ,,from ,,enumeration4 ,when the genus is separated at once into individual objects the process is not logical division1 but simple enumeration4 ,logical division implies a separating into smaller class terms1 each term being a genus of still smaller subdivisions4 ,this process may be continued till the last division gives individuals as species4 ,enumeration takes place when the first subdivision results in a list of individuals4 ,to illustrate3 ,logical ,division4 ,science teacher ,teacher ,mathematics teacher ,english teacher ,modern language teacher ,enumeration4 ,john ,j4 ,brown ,teacher ,h4 ,g4 ,white ,mary ,jones ,alice ,smith #c4 ,,logical ,,division ,,as ,,partition4 ,partition is the process of separating an individual thing into its parts4 ,the partition is quantitative or mathematical when the separation is in terms of space or time1 but when otherwise the partition becomes qualitative or logical4 ,or to put it in another way1 the partition is mathematical when the separation gives parts and logical when the separation gives ingredients4 ,to illustrate3 branches quantitative leaves or roots 7mathematical7 trunk 7#a7 ,tree qualitative woody fibre or capillary attraction 7logical7 sap chlorophyll quantitative roof or frame-work 7mathematical7 foundation 7#b7 ,house qualitative wood or iron 7logical7 stone plaster ,an easy way to determine that the separation involves logical division proper and not partition is to affirm the connection between a class and a sub-class4 ,to wit3 ,a man is a biped2 a square is a rectangle2 a ,caucasian is a man1 etc4 ,if such an affirmation cannot be made then the separation involved is not properly logical division but probably partition4 ,for example it cannot be said that a roof is a house1 or that sap is a tree4 ,it is seen1 then1 that a logical division of any genus may be summarized in the form of a series of judgments of which a species is the subject and the genus is the predicate4 ,for example1 by a logical division quadrilaterals may be divided into trapeziums1 trapezoids and parallelograms2 this process may then be summarized in a series of three judgments3 7#a7 ,a trapezium is a quadrilateral2 7#b7 ,a trapezoid is a quadrilateral2 7#c7 ,a parallelogram is a quadrilateral4 #d4 ,,rules ,,of ,,logical ,,division4 ,when the logical division of a genus is under consideration there are four rules which should be observed4 ,,first ,,rule4 ,there must be but one principle of division 7fundamentum divisionis74 ,to divide mankind into white man1 ,australian1 yellow man1 ,african and red man is a violation of this rule as the two principles of color and geographical location are involved4 ,a division in which more than one principle is used is sometimes referred to as cross division because the various species cross each other4 ,for example in the foregoing there are many white men who are ,australians4 ,this rule applies only to one division4 ,where there is a series of divisions a new principle may be employed in each division4 ,for example1 in dividing triangles into scalene1 isosceles and equilateral1 the equality of sides is the principle involved1 but1 in subdividing isosceles triangles into right angled and oblique angled1 the principle employed concerns the nature of the angle4 ,,second ,,rule4 ,the co-ordinate species must be mutually exclusive4 ,there must be no overlapping4 ,the illustration given in the first rule is likewise a violation of this rule4 ,another example in which this second rule is not obeyed may be found in most geometries where triangles are divided into scalene1 isosceles and equilateral4 ,here the second and third classes are not mutually exclusive since all equilateral triangles are isosceles according to the usual definition1 8,an isosceles triangle is a triangle having two equal sides40 ,all equilateral triangles have two equal sides4 ,,third ,,rule4 ,the division must be exhaustive4 ,that is1 the species taken together must equal the whole genus4 ,the sum of the species must be co-extensive with the genus4 ,dividing man into ,caucasian1 ,ethiopian and ,mongolian would be a violation of this rule1 as there are at least two other species of man1 ,malay and ,american ,indian4 ,a distinction should be made between an exhaustive division and a complete division as the latter is not a logical requirement4 ,to divide government into monarchy1 aristocracy and democracy is exhaustive but incomplete4 ,exhaustive because there is no other kind of government1 all the species are included2 but incomplete in that monarchy may be divided into absolute and limited2 democracy into pure and representative4 ,,fourth ,,rule4 ,the division must proceed from the proximate genus to the immediate species4 ,there should be no sudden jumps from a high genus to a low species4 ,the division must be gradual and continuous2 step by step4 ,to divide government into limited monarchy1 absolute monarchy1 pure democracy and representative democracy would be a violation of this rule1 as government is the proximate genus of monarchy1 not of limited monarchy1 therefore one step has been omitted4 ,such an omission involves a step from grandfather to grandchild1 so to speak1 the generation of father having been left out4 ,a violation of this rule is most insidious when some of the species of a subdivision are immediate while others are not4 ,to wit3 dividing government into monarchy1 aristocracy1 pure democracy and republic1 or dividing quadrilaterals into trapeziums1 trapezoids1 rectangles1 squares1 rhomboids and rhombs4 #e4 ,,dichotomy4 ,dichotomy comes from the ,greek1 meaning to cut in two4 ,dichotomy is a continual division of a genus into two species which are contradictory in nature4 ,contradictory terms are such as admit of no middle ground4 ,they divide the whole universe of thought into two classes4 ,for example1 honest and not-honest1 pure and impure1 perfect and imperfect1 are contradictory terms4 ,dichotomy thus affords an easy opportunity for an exhaustive division as in the use of contradictories nothing in the universe need be omitted4 ,an historical illustration of dichotomy is the 8,tree of ,porphyry0 named after ,porphyrius1 a ,neo-,platonic philosopher of the third century4 ,tree of ,porphyry4 ,substance4 _/ _/ ,corporeal ,incorporeal ,body _/ _/ ,animate ,inanimate ,living ,being _/ _/ ,sensible ,insensible ,animal _/ _/ ,rational ,irrational ,man _/ _/ _/ ,socrates ,plato ,other ,men ,this kind of division is not altogether satisfactory as the negative side is too indefinite4 ,on the other hand1 if both subdivisions are made positive then there is danger of making the opposing terms contrary rather than contradictory4 ,this1 of course1 would be a serious logical fallacy1 as contrary terms admit of middle ground while contradictory terms give no choice1 it is either the one or the other4 ,the use of dichotomy becomes evident in situations where new and unexpected discoveries may be made4 ,without disturbing the classification the new species may be appended to the negative side of the division4 ,the following illustrates3 ,vertebrates ,leptocardians ,not-leptocardians ,fish ,not-fish ,amphibians ,not-amphibians ,reptiles ,not-reptiles ,birds ,not-birds ,mammals ,not-mammals ,the ,new ,species #f4 ,,classification,,compared ,,with ,,division4 ,classification is the process of grouping notions according to their resemblances or connections4 ,so far as results are concerned there is no difference between logical division and classification4 ,both processes may give us the same orderly scheme of heads and subheads4 ,the difference lies in the process itself4 ,division is deductive in nature as it proceeds from the more general genus to the less general species4 ,while classification is inductive as it groups the less general species under the more general genus4 ,division differentiates unity into multiplicity1 while classification reduces multiplicity to unity4 ,it follows that the one is the inverse of the other4 ,the difference in the mode of procedure may be illustrated by using the common classification or division of triangles4 ,for example3 ,without any knowledge of the kinds of triangles the student discovers by examining the various shapes of many triangles that there is a group in which none of the sides are equal4 ,for the lack of a better name he terms these non-equilateral 7scalene74 ,further observation discloses another group in which two of the sides are equal4 ,these he names bi-equilateral 7isosceles74 ,finally a third group is designated as tri-equilateral 7equilateral74 ,this process is classification4 ,division would consist in separating the genus triangle into the three kindsscalene1 isosceles1 equilateral4 #g4 ,,kinds ,,of ,,classification,,artificial ,,and ,,natural4 ,an artificial classification is one in which the grouping is made on the basis of some arbitrary connection4 ,cataloguing alphabetically the books in a library illustrates this kind of classification4 ,likewise the arrangement of the names in a directory or a telephone book4 ,the connecting mark being the initial letter of the title or name4 ,the reason why ,mills and ,meyers are put in the same group is that both names happen to commence with the letter ,m4 ,artificial classifications are resorted to for some special purpose1 designed by man1 not by nature4 ,consequently artificial classifications are sometimes called special or working classifications4 ,a natural classification is one in which the grouping is made on the basis of some inherent mark of resemblance4 ,classifications in animal and plant life are the best illustrations of this kind4 ,such classifications are suggested by nature and not by man1 and may1 therefore1 be called general or scientific4 ,the main aim of natural classification is to derive general truths and arrange knowledge so that it may be easily remembered4 #h4 ,,two ,,rules ,,of ,,classification4 ,the rules of logical division are applicable in the making of a logical classification4 ,in addition to these an artificial classification should be made to conform to the one rule3 ,the classification must be appropriate to the purpose in hand4 ,likewise a natural classification should be made to conform to the rule3 ,every classification should afford opportunity for the greatest possible number of general assertions4 #i4 ,,use ,,of ,,division ,,and ,,classification ,,in ,,the ,,school ,,room4 ,it has been stated that classification and division aim at the same result4 ,classification reduces multiplicity to unity while division differentiates unity into multiplicity4 ,in short1 division is deductive while classification is inductive in mode of procedure4 ,therefore1 classification should be used in those situations which call for induction and division in cases where deduction is the better method4 ,speaking generally1 classification should be used with small children when the essential thing is to present the concrete facts with a view of leading the children to discover for themselves the truths contained therein4 ,with older pupils division may be used1 if the purpose is to set in order facts which are already known4 #aj4 ,,topical ,,outline4 ,,logical ,,division ,,and ,,classification4 7#a7 ,nature of ,logical ,division4 ,genusspecies4 ,illustrations4 7#b7 ,logical ,division ,distinguished from ,enumeration4 ,illustrations4 7#c7 ,logical ,division and ,partition4 ,quantitativequalitative4 ,how summarized4 7#d7 ,four ,rules of ,logical ,division4 7#a7 ,one principlecross division4 7#b7 ,mutually exclusive4 7#c7 ,exhaustivecomplete4 7#d7 ,immediate species4 7#e7 ,dichotomy4 ,contradictory terms4 ,tree of ,porphyry4 ,use illustrated4 7#f7 ,classification ,compared with ,division4 7#g7 ,kinds4 ,artificial,natural4 7#h7 ,two ,rules of ,classification4 7#a7 ,appropriate4 7#b7 ,afford many ,assertions4 7#i7 ,use of ,division and ,classification4 #aa4 ,,summary4 7#a7 ,logical division is the process of separating a proximate genus into its co-ordinate species4 7#b7 ,the first subdivision in a logical division gives class terms1 while the first subdivision in an enumeration gives individual objects4 7#c7 ,partition is the process of separating an individual thing into its parts4 ,these parts may be either quantitative or qualitative4 ,a logical division of any genus may be summarized in a series of judgments of which a species is the subject and the genus is the predicate4 7#d7 ,the four rules of logical division are3 the division must 7#a7 be based on one principle1 7#b7 have species mutually exclusive1 7#c7 be exhaustive and 7#d7 proceed from proximate genus to immediate species4 ,a violation of the first rule gives a cross division4 ,exhaustive division is easily confused with a complete or finished division4 7#e7 ,dichotomy is a continual division of a genus into two species which are contradictory in nature4 ,an historical illustration of dichotomy is the ,tree of ,porphyry4 ,dichotomy is of service in the field of new and unexpected discoveries4 7#f7 ,classification is the process of grouping notions according to their resemblances or connections4 ,classification is inductive in nature1 division deductive4 ,classification unifies1 division differentiates4 7#g7 ,an artificial classification is made on the basis of some arbitrary connection2 a natural classification1 on some inherent mark of resemblance4 7#h7 ,the rules of logical division are applicable in any classification4 ,in addition to these a classification should 7#a7 be appropriate and 7#b7 afford opportunity for the greatest possible number of assertions4 7#i7 ,classification should be the mode of procedure in the lower grades1 division in the higher grades4 #ab4 ,,review ,,questions4 7#a7 ,define and illustrate logical division4 7#b7 ,what is the meaning of proximate genus8 7#c7 ,how does logical division differ from enumeration8 ,illustrate4 7#d7 ,distinguish between logical division1 and physical division or partition4 7#e7 ,illustrate a quantitative partition2 a qualitative partition4 7#f7 ,illustrate how a logical division may be summarized in the form of a series of judgments4 7#g7 ,state and explain the rules of logical division4 7#h7 ,state the rules violated in the following divisions1 explaining in full3 ,primary ,secondary 7#a7 ,education ,collegiate ,technical ,scientific ,professional ,infancy 7#b7 ,life ,childhood ,youth ,old age ,caucasian ,ethiopian 7#c7 ,man ,malay ,mongolian ,american ,cement ,frame 7#d7 ,buildings ,stone ,dwellings ,barns ,churches 7#i7 ,show the difference between contradictory and opposite terms4 7#aj7 ,define dichotomy4 7#aa7 ,illustrate the ,tree of ,porphyry and indicate its use to scientists4 7#ab7 ,illustrate the difference between classification and division4 7#ac7 ,why should classification be the mode of procedure when dealing with immature minds8 7#ad7 ,illustrate the difference between an artificial and a natural classification4 7#ae7 ,state and explain the two rules of classification4 7#af7 ,show which of the following divisions are logical and which are not3 7#a7 ,the manifestations of the mind into knowing1 thinking and feeling4 7#b7 ,books into mathematical and non-mathematical4 7#c7 ,students into those who are industrious1 athletic and shiftless4 7#d7 ,flowers into roses1 carnations and lilies4 7#e7 ,planets into those which are larger than the earth and those which are smaller4 #ac4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,analyze by mathematical partition the terms world1 plant1 book4 7#b7 ,analyze by logical partition the terms granite1 water1 air4 7#c7 ,what rule is violated if the logical division is applied to the genus rather than the proximate genus8 7#d7 ,divide logically the following terms3 school1 religion1 book1 vegetable1 life4 7#e7 8,each new subdivision may adopt a new principle of division40 ,illustrate this4 7#f7 ,explain and illustrate the meaning of the terms super-ordinate1 sub-ordinate and co-ordinate4 7#g7 ,define and illustrate metaphysical division and verbal division4 7#h7 ,give a definition of an isosceles triangle which will make logical the division of triangles into scalene1 isosceles and equilateral4 7#i7 8,the evolution of all truth develops progressively through three stages40 8,the first is the thesis2 the second is the antithesis2 the third is the synthesis40 ,explain this in terms of trichotomy4 7#aj7 ,illustrate the difference between a complete division and an exhaustive division4 7#aa7 ,show in what ways1 if any1 the following divisions violate the rules of logical division4 #a ,memory 7,history7 ,human ,learning #b ,imagination 7,poetry7 7by ,bacon7 #c ,reason 7,philosophy7 or 7the ,sciences7 #a ,mathematics #b ,astronomy ,sciences #c ,physics 7by ,comte7 #d ,chemistry #e ,biology #f ,sociology #g ,morals ,,chapter #h4 ,,logical ,,propositions #a4 ,,the ,,nature ,,of ,,logical ,,propositions4 ,judging has been defined as the process of conjoining or disjoining notions4 ,this may be put in another way3 8,judging is the process of asserting or denying the agreement between two notions40 ,the product of the act of judging is a judgment and when judgments are put in word-form such expressions are called logical propositions4 ,definition3 ,a logical proposition is a judgment expressed in words4 ,just as percept and concept notions are expressed by means of logical terms so judgment notions may be expressed by logical propositions4 ,to illustrate3 ,the terms the squirrel and cracking a nut express two notions1 and when an agreement between them is asserted and the product is expressed in word form1 then such an expression becomes the logical proposition1 8,the squirrel is cracking a nut40 ,the following being expressed judgments are logical propositions3 7#a7 ,all men are mortal4 7#b7 ,some men are wise4 7#c7 ,no men are immortal4 7#d7 ,some men are not wise4 7#e7 ,no sane person is a lover of vice4 7#f7 ,some good orators are not good statesmen4 7#g7 ,every man is fallible4 7#h7 ,if it rains1 ,i shall not go4 7#i7 ,he is either sane or insane4 #b4 ,,kinds ,,of ,,logical ,,propositions4 ,there are three kinds of logical propositions2 namely1 categorical1 hypothetical and disjunctive4 ,a categorical proposition is one in which the assertion is made unconditionally4 ,an hypothetical proposition is one in which the assertion depends upon a condition4 ,a disjunctive proposition is one which asserts an alternative4 ,,the ,,three ,,kinds ,,illustrated3 7#a7 8,every dog has his day40 ,categorical4 7#b7 8,if you do your best1 success will reward you40 ,hypothetical4 7#c7 8,he is either stupid or indolent40 ,disjunctive4 7#d7 8,all vices are reprehensible40 ,categorical4 7#e7 8,either you are very talented or very industrious40 ,disjunctive4 7#f7 8,if capital punishment does not aid society1 it should be abolished40 ,hypothetical4 7#g7 8,you may go provided your teacher is willing40 ,hypothetical4 7#h7 8,no intelligent man can ignore the practice of temperance40 ,categorical4 ,by studying the illustrations it will be observed that the categorical propositions are direct1 bold1 assertive statements1 whereas the hypothetical are limited by conditions which make them less forceful4 ,in the second proposition1 for example1 8success will reward you10 is limited by the condition1 8,if you do your best40 ,the disjunctive may be regarded as categorical in form1 but hypothetical in meaning1 because in such a proposition as1 8,he is either1 stupid or indolent10 a direct assertion is made which suggests the categorical1 and yet it may be implied that1 if he is stupid then he is not indolent2 this is indicative of the hypothetical4 ,some logicians classify propositions as categorical and conditional1 the conditional being subdivided into hypothetical and disjunctive4 ,the first classification seems preferable1 however1 as it conforms to the three modes of reasoning4 ,the common word-signs of the categorical proposition are all1 every1 each1 any1 no and some1 while those of the hypothetical are if1 even if1 unless1 although1 though1 provided that1 when1 or any word or group of words denoting a condition4 ,the disjunctive symbols are eitheror4 #c4 ,,the ,,four ,,elements ,,of ,a ,,categorical ,,proposition4 ,every categorical proposition should have four elements2 namely1 the quantity sign1 the logical subject1 the copula and the logical predicate4 ,in the foregoing categorical propositions the quantity signs are respectively1 every1 all and no4 ,in any case the quantity sign is always attached to the subject and indicates its breadth or extension4 ,for example1 in the two propositions1 8,all men are mortal0 and 8,some men are wise10 the quantity sign all makes the term man much broader than does the quantity sign some4 ,the logical subject of a categorical proposition is the term of which something is affirmed or denied1 whereas the logical predicate of a categorical proposition is the term which is affirmed or denied of the subject4 ,in the two propositions1 8,all men are mortal0 and 8,no men are immortal10 the term about which something is affirmed or denied is men1 while the terms which are affirmed and denied of the subject are respectively mortal and immortal4 8,men0 is1 therefore1 the logical subject of each proposition1 while 8mortal0 is the logical predicate of the first and 8immortal0 the logical predicate of the second4 ,the copula is the connecting word between the logical subject and predicate and denotes whether or not the latter is affirmed or denied of the former4 ,the copula is always some form of 8to be0 or its equivalent4 ,when the predicate is denied of the subject1 8not0 may be used with the copula and considered a part of it4 ,to illustrate3 in the logical proposition1 8,some men are not wise10 8are not0 may be regarded as the copula4 ,the four elements are indicated in the following categorical propositions3 ,quantity sign ,logical subject ,copula ,logical predicate ,all fixed stars are self-luminous ,no wise man is going to steal ,some quadrupeds are domestic animals ,some glittering things are not gold ,some boys are not discreet ,a few men are multi-millionaires ,every citizen is duty-bound to vote ,the student must ever keep in mind the fact that to be absolutely logical all categorical propositions must be expressed in terms of the four elements4 ,however1 life is too short and man is too busy to speak always in terms of the four elements4 ,moreover1 to be logical may often compel an awkwardness of expression and a lack of euphony which could hardly be tolerated4 ,for these reasons the utterances in ordinary conversation are frequently illogical so far as the four elements are concerned1 though not necessarily illogical in meaning4 ,when it is desired to test the validity of any series of statements leading up to some generalization1 it may become necessary to express the statement in terms of the four elements4 ,the student should gain some facility in this1 otherwise he may be readily led into fallacious reasoning4 ,the following statements taken at random from newspapers are given in the original and then expressed in terms of the four elements3 ,the ,original ,in ,terms of the ,four ,elements 7#a7 ,you came too late4 7#a7 ,the person is one who came too late4 7#b7 ,i saw the swell turnout 7#b7 ,the man was one who saw the swell coming along4 turnout coming along4 7#c7 ,all of the men walked4 7#c7 ,all of the men were those who walked4 7#d7 ,the robbers cut a hole 7#d7 ,all the robbers were the ones who in this floor4 cut a hole in this floor4 7#e7 ,some of these flew away4 7#e7 ,some birds were those which flew away4 7#f7 ,the rain interfered with 7#f7 ,the rain was that which interfered the attendance4 with the attendance4 7#g7 ,our habits make or 7#g7 ,all our habits are forces which unmake us4 make or unmake us4 7#h7 ,we all had a fine time4 7#h7 ,all the party were those who had a fine time4 ,in argumentative discourse it is often sufficient to 8think the proposition0 in terms of the four elements without taking the time to actually express it4 #d4 ,,logical ,,and ,,grammatical ,,subject ,,and ,,predicate ,,distinguished4 ,the grammatical subject is one word while the logical subject is the grammatical subject with all its modifiers except the quantity sign4 ,for example3 in the proposition1 8,all white men are ,caucasians10 men is the grammatical subject1 while white men is the logical subject4 ,all being the quantity sign simply indicates the extension of men and is not a part of the logical subject4 ,the grammatical predicate is the verb-form together with any predicate noun or adjective1 while the logical predicate is the predicate word or words and all its modifiers4 ,the grammatical predicate includes the copula1 but the logical predicate never includes the copula4 ,the grammatical predicate does not include the object1 while the logical predicate always includes what is equivalent to the object and all its modifiers4 ,to illustrate3 in the proposition1 8,some men are wise10 are wise is the grammatical predicate1 while wise is the logical predicate4 ,and in the proposition1 8,he burned the red house on the hill10 burned is the grammatical predicate1 while the one who burned the red house on the hill is the logical predicate4 #e4 ,,the ,,four ,,kinds ,,of ,,categorical ,,propositions4 ,categorical propositions are divided according to their quantity into ,universal and ,particular and according to their quality into ,affirmative and ,negative4 ,a universal proposition is one in which the predicate refers to the whole of the logical subject4 ,,illustrations3 7#a7 ,all men are mortal4 7#b7 ,all civilized men cook their food4 7#c7 ,no dogs are immortal4 7#d7 ,every man was once a boy4 ,considering the first proposition1 8mortal10 the logical predicate1 refers to the whole of the logical subject 8men40 ,similarly 8cook their food0 refers to the whole of the term 8civilized men02 8immortal0 to the whole of the term 8dogs10 and 8once a boy0 to the whole of the term 8man40 ,in considering the definition of a universal proposition it is necessary to keep in mind the distinction between a logical and a grammatical subject1 as in the second proposition the logical predicate1 8cook their food10 refers to only a part of the grammatical subject1 men1 and1 therefore1 the proposition might fallaciously be termed a particular proposition rather than a universal4 ,a particular proposition is one in which the predicate refers to only a part of the logical subject4 ,,illustrations3 7#a7 ,some men are wise4 7#b7 ,some animals are not quadrupeds4 7#c7 ,most elements are metals4 7#d7 ,many children are mischievous4 ,in the foregoing propositions some1 most and many are quantity signs and1 therefore1 must not be considered as a part of the logical subjects4 ,considering the logical subjects and predicates in order1 the term wise refers to only a part of the men in the world1 quadrupeds to only a part of the animals1 metals to only a part of the elements and mischievous to only a part of the children4 ,an affirmative proposition is one which expresses an agreement between subject and predicate4 ,a negative proposition is one which expresses a disagreement between subject and predicate4 ,affirmative propositions conjoin terms1 negative propositions disjoin terms4 ,in the first the agreement is affirmed2 in the second the agreement is denied4 ,,illustrations3 ,none of the captives escaped4 ,negative4 ,some teachers are just4 ,affirmative4 ,all trees grow towards heaven4 ,affirmative4 ,some people are not companionable4 ,negative4 ,no person is above criticism4 ,negative4 ,dividing both universal and particular propositions as to quality1 gives four kinds2 namely1 universal affirmative1 universal negative1 particular affirmative and particular negative4 ,no topic in logic demands greater familiarity than these four types1 as every proposition must be reduced to one of the four before it can be used as a basis of reasoning4 ,for the sake of brevity the symbols ,a1 ,e1 ,i and ,o are used to designate respectively the universal affirmative1 the universal negative1 the particular affirmative and the particular negative4 ,a and ,i1 symbolizing the affirmative propositions1 are the first and second vowels in ,affirmo1 while ,e and ,o1 symbolizing the negatives1 are the vowels in ,nego4 ,the common sign of the universal affirmative1 or the ,a proposition is all2 of the universal negative1 or ,e proposition no2 of the particular affirmative1 or ,i proposition some2 of the particular negative1 or ,o proposition some with not as a part of the copula4 ,the accompanying classification summarizes these facts1 ,s and ,p being used to symbolize the terms 8subject0 and 8predicate40 ,illustrations ,affirmative-,a ,all ,s is ,p ,categorical ,universal ,negative-,e ,no ,s is ,p ,propositions ,affirmative-,i ,some ,s is ,p ,particular ,negative-,o ,some ,s is not ,p ,henceforth the symbols ,a1 ,e1 ,i1 ,o will be used to designate the four kinds of categorical propositions4 ,the propositions have other quantity signs aside from the ones used above4 ,these may be summarized3 ,aall1 every1 each1 any1 whole4 ,eno1 none1 all-not4 ,quantity signs of ,isome1 certain1 most1 a few1 many1 the greatest part1 any number4 ,osome - - not1 few4 #f4 ,,propositions ,,which ,,do ,,not ,,conform ,,to ,,the ,,logical ,,type4 ,it has been observed that all expressed judgments must be reduced to one of the four logical types ,a1 ,e1 ,i or ,o1 before they can be used argumentatively4 ,logic insists upon definiteness and clearnessthere must be no ambiguity1 no opportunity for a wrong interpretation4 ,from this viewpoint the four types fulfill every requirement4 ,their meaning cannot be misunderstood4 ,to any one with normal intelligence their significance may be made perfectly clear4 ,any argument when once put in terms of the four types may be spelled out with mathematical precision4 ,in consequence it is of prime importance that the four types not only be well understood1 but that a certain facility be gained in reducing ordinary conversation to some one of these types4 7#a7 ,indefinite and ,elliptical ,propositions4 ,it is known that every logical proposition must be expressed in terms of the four elementsquantity sign1 logical subject1 copula and logical predicate1 consequently the four types ,a1 ,e1 ,i and ,o which epitomize every form of logical proposition1 are expressed in terms of these four elements4 ,but in common conversation often the quantity sign1 as well as the copula1 is omitted4 ,see section #c4 ,propositions without the quantity sign are called indefinite1 while those with the suppressed copula may be termed elliptical propositions4 ,both may be made logical as the attending illustrations will indicate3 ,illogical ,logical ,indefinite ,men are fighting animals4 ,all men are fighting animals4 7,a7 ,lilies are not roses4 ,no lilies are roses4 7,e7 ,good is the object of moral ,all good is the object of moral approbation4 approbation4 7,a7 ,perfect happiness is ,in all cases perfect happiness impossible4 is impossible4 7,a7 ,elliptical ,fashion rules the world4 ,all fashions are ruling the world4 7,a7 ,trees grow4 ,all trees are plants which grow4 7,a7 ,children play4 ,all children are playful4 7,a7 ,some men cheat4 ,some men are persons who cheat4 7,i7 ,here it is noted that the logical form of some propositions is not always the most forceful4 ,often the logical form gives an awkward construction and should be resorted to only for purposes of logical argument4 ,the reduction of either kind to the logical form must be determined by the meaning of the proposition4 ,as a usual thing the indefinite is universal 7either an ,a or an ,e7 in meaning1 while the problem of the elliptical is to give it in terms of the copula1 expressed with as little awkwardness as possible4 ,general truths1 because attended with no quantity sign1 might be classed as indefinite propositions1 though their universality is so apparent that they may be unhesitatingly classed as universals4 ,,illustrations3 8,things equal to the same thing are equal to each other40 8,trees grow in direct opposition to gravity40 8,honesty is the best policy40 8,a stitch in time saves nine40 ,because the indefinite proposition is so frequently of a general nature1 it is sometimes classed as general rather than indefinite4 ,sir ,william ,hamilton would class the indefinite as an indesignate proposition4 7#b7 ,grammatical ,sentences4 ,the grammarian divides sentences into five kinds2 namely1 declarative1 interrogative1 imperative1 optative1 exclamatory4 ,but logic recognizes only the declarative1 as it has already been seen that the four logical types are declarative in nature4 ,a logical proposition1 then1 is always a sentence1 but all sentences are not logical propositions4 ,the four kinds of sentences which are not logical propositions may be usually reduced to one of the four types as the attending illustrations will indicate3 ,illogical ,logical ,interrogative4 ,do men have ,the question is asked1 ,do men have the power of reason8 the power of reason8#g 7,a7 ,imperative4 8,thou shalt not ,all men are commanded not to steal40 steal1 or you are one who should not steal4 7,e7 ,optative4 8,i would ,i had a ,i am one who desires a million million40 dollars4 7,a7 ,exclamatory4 8,oh1 how you ,you are one who frightened me4 7,a7 frightened me60 7#c7 ,individual ,propositions4 ,an individual proposition is one which has a singular subject2 e4 g41 ,abraham ,lincoln was an honest man4 ,peter the ,great was ,russia's greatest ruler4 ,the maple tree in my yard is dying of old age4 ,these propositions1 having a singular term as subject1 are individual or singular in nature4 ,as the predicate refers to the whole of the logical subject1 individual propositions are classed as universal4 7#d7 ,plurative ,propositions4 ,plurative propositions are those introduced by 8most10 8few10 8a few10 or equivalent quantity signs4 ,for example1 8,most birds are useful to man02 8,few men know how to live02 8,a few of the prisoners escaped10 are plurative propositions4 8,most0 means more than half1 while 8few0 and 8a few0 mean less than half4 ,in either case the proposition is particular4 ,stated logically1 the illustrative propositions would take the form of 8,some birds are useful to man02 8,some men do not know how to live02 8,some of the prisoners escaped40 ,the reader will observe the difference in significance between few and a few4 ,the former is negative in character and when introducing a proposition makes it a particular negative 7,o74 ,the latter always introduces a particular affirmative 7,i74 7#e7 ,partitive ,propositions4 ,partitive propositions are particulars which imply a complementary opposite4 ,these arise through the ambiguous use of all-not1 some and few4 ,all-not may sometimes be interpreted as not all and sometimes as no4 ,to illustrate3 ,the proposition1 8,all men are not mortal10 is distinctly a universal negative or an ,e1 while the proposition1 8,all that glitters is not gold10 is a particular negative or an ,o4 ,the logical form of the first is1 8,no men are mortal10 and of the second1 8,some glittering things are not gold40 ,when used in the 8not-all0 sense1 the proposition is partitive because if the ,o-meaning is intended the ,i is implied4 ,for example1 8,all that glitters is not gold10 is partitive because the statement implies that some glittering things are gold 7,i7 as well as the complement1 8,some glittering things are not gold0 7,o74 ,a knowledge of both the affirmative and negative aspects is taken for granted in the statement of either the one or the other4 8,all-not10 then1 is negative in any case1 but universal when it means no and particular when it means not all4 ,any proposition is partitive in nature when the quantity sign is not all1 or all-not interpreted as the equivalent of not all4 ,it may be observed here that all has two distinct uses4 ,first1 it may be used in a collective sense2 second1 in a distributive sense4 ,for example3 ,all is used in the collective sense in such propositions as1 8,all the members of the football team weighed exactly one ton10 or 8,all the angles of the triangle are equal to two right angles40 ,using all in the distributive sense would make true these3 8,all the members of the football team weigh more than #adj pounds02 8,all the angles of a triangle are less than two right angles40 ,all is used collectively when reference is made to an aggregate1 but distributively when reference is made to each4 ,the quantity sign some is likewise ambiguous1 as it may mean 7#a7 some onlysome1 but not all1 or 7#b7 some at leastsome1 it may be all or not all4 ,when 8some0 is used as the quantity sign of any particular proposition which has been accepted as logical1 the second meaning1 8some at least10 is always implied4 ,this interpretation of 8some0 will be explained more in detail in a succeeding section4 ,when some is used in the sense of some only1 the partitive nature of the proposition is apparent1 as both ,i and ,o are implied4 ,for example1 with reference to the human family1 to say that 8some only are wise0 necessitates an investigation1 which leads to the discovery that some are wise1 while others are not wise4 ,if the proposition be an ,i1 then its complementary ,o is implied1 or if it be an ,o1 the ,i is implied4 ,few given as a sign of a plurative proposition also serves as a sign of the partitive4 ,the plurative aspect is prominent when it is said that 8,few men can be millionaires0 and emphasis is placed upon the meaning that 8,most men cannot be millionaires40 ,but when emphasis is given to 8few10 as meaning few only rather than the most are not1 then the ,i and the ,o are both implied2 e4 g41 ,some men become millionaires1 but the most do not4 ,to put it in a word1 8all-not10 8some0 and 8few0 introduce partitive propositions when the meaning implies both an ,i and an ,o4 ,when treating such in logic the meaning which seems to be given the greater prominence must be accepted4 ,surely in the statement1 8,all that glitters is not gold10 the ,o-interpretation is the one intended2 namely1 8,some things which glitter are not gold40 ,,illustrations3 7#a7 8,all men are not honest40 7#b7 8,few men live to be a hundred40 7#c7 8,some men are consistent40 ,the first proposition with the emphasis placed upon all suggesting that some men are not honest1 is the intended proposition while some men are honest is the implied4 ,in reducing it to the logical form the intended proposition is the one which should be used4 ,with the emphasis upon few and some1 the second and third propositions may be interpreted as follows3 7#b7 ,intended proposition1 ,some men do not live to be a hundred4 ,implied proposition1 ,some men do live to be a hundred4 7#c7 ,intended proposition1 ,some men are consistent4 ,implied proposition1 ,some men are not consistent4 7#f7 ,exceptive ,propositions4 ,these are introduced by such signs as all except1 all but1 all save4 ,to wit3 7#a7 8,all except ,james and ,john may be excused02 7#b7 8,all but a few of the culprits have been arrested02 7#c7 8,all birds save the ,english sparrow are serviceable to man0 are exceptive propositions4 ,exceptive propositions are universal when the exceptions are mentioned4 ,universal propositions necessitate a subject more or less definite1 as the predicate of such must refer to the whole of a definite subject4 ,it follows that in exceptive statements definiteness is secured when the exceptions are mentioned1 therefore it becomes clear how all such propositions must be universal4 ,of the illustrations1 the first and third propositions are universal4 ,any exceptive proposition is particular when the exceptions are referred to in general terms or when the subject is followed by et cetera4 ,the second illustrative proposition is particular4 7#g7 ,exclusive ,propositions4 ,of all propositions which vary from the logical form the exclusive is the most misleading4 ,exclusives are accompanied by such words as 8only10 8alone10 8none but10 and 8except40 ,their peculiarity rests in the fact that reference is made to the whole of the predicate1 but only to a part of the subject4 ,for example1 in the exclusive proposition1 8,only elements are metals10 metals is referred to as a whole while elements is considered only in part4 ,the true meaning is 8,some elements are all metals10 or to put it in logical form1 8,all metals are elements40 ,the easiest way to deal with an exclusive is to interchange subject and predicate 7convert simply7 and call the proposition an ,a4 ,,process ,,illustrated3 ,exclusive ,proposition ,reduced to ,logical ,form #a4 ,none but high school ,all who enter ,training ,school graduates may enter must be high school graduates4 ,training ,school4 #b4 ,only first-class ,all parlor cars are for passengers are allowed in first-class passengers4 parlor cars4 #c4 ,residents alone are ,all who are licensed to teach are licensed to teach4 residents4 #d4 ,no admittance except on ,all who have business may be business4 admitted4 #e4 ,only bad men are not-wise4 ,all who are not-wise are bad men4 #f4 ,only some men are wise4 ,all who are wise are men4 ,it is claimed by good authority that the real nature of the exclusive is best expressed by negating the subject and calling the proposition an ,e2 e4 g41 exclusive3 8,only elements are metals02 logical form3 8,no not-elements are metals0 7,e74 ,in a succeeding chapter it is explained how an ,e admits of first simple conversion and then obversion4 ,the following illustrate these two processes3 ,original ,e3 8,no not-elements are metals40 ,simple conversion3 8,no metals are not-elements40 ,obversion3 8,all metals are elements40 ,from this it may be seen that the statement1 8,the easiest way to deal with an exclusive is to interchange subject and predicate and call the proposition an ,a10 is substantially correct4 7#h7 ,inverted ,propositions4 ,the poet often employs the inverted proposition1 illustrated by the following3 8,blessed are the merciful20 8,great is this man of war40 ,an interchanging of subject and predicate makes these poetical constructions logical2 e4 g41 8,all the merciful are blessed20 8,this man of war is great40 ,,note4,the student should not be misled by the relative clause4 ,often it may be interpreted as a part of the predicate rather than the subject4 ,to wit3 8,no man is a friend who betrays a confidence02 clearly the logical subject is no man who betrays a confidence4 #g4 ,,propositions ,,which ,,are ,,not ,,necessarily ,,illogical4 7#a7 ,analytic and ,synthetic ,propositions4 ,an analytic proposition is one in which the predicate gives information already implied in the subject4 ,thus1 8,fire burns10 8,water is wet10 8,a triangle has three angles0 are analytic propositions because the predicates do not give added information to one who has any conception of the subjects4 ,because the attribute mentioned by the predicate is an essential one1 analytic propositions are sometimes termed essential propositions4 ,other names for the same kind of proposition are verbal and explicative4 ,a synthetic proposition is one in which the predicate gives information not necessarily implied in the subject4 8,fire protects men from the wild animal40 8,a cubic foot of water weighs #fb lbs40 8,the sum of the interior angles of a triangle is equal to two right angles40 ,these are synthetic because a common conception of the meaning of the subject would not need to include the information given by the predicate4 ,other names for synthetic propositions are accidental1 real and ampliative4 ,the distinction between analytic and synthetic propositions is not so clear as would on first thought appear4 8,fire burns0 might give added information to the child or savage who knows only of the light emitted by fire4 ,to them1 then1 the proposition would be synthetic4 ,the distinction must be based upon the assumption that the same words mean about the same thing to people in general4 ,this analytic-synthetic division of propositions finds a significance in the domain of philosophy4 ,to the logician the distinction is of slight importance save in the so-called verbal disputes1 viz43 disputes which turn on the meaning of words4 7#b7 ,modal and ,pure ,propositions4 ,a modal proposition states the mode or manner in which the predicate belongs to the subject4 ,the signs of modal propositions are the adverbs of time1 place1 degree1 manner4 ,illustrations3 8,james is walking rapidly40 8,honesty is always the best policy40 8,aristotle was probably the greatest thinker of ancient times40 ,a pure proposition simply states that the predicate belongs1 or does not belong1 to the subject4 ,illustrations3 8,james is walking40 8,honesty is the best policy40 8,aristotle was the greatest thinker of ancient times40 ,some logicians refer to modal propositions as being such as indicate degrees of belief4 ,such words as 8probably10 8certainly10 etc41 would indicate their modality4 ,as logic has to do with the pure proposition and not the modal1 the difference of opinion is of little import4 7#c7 ,truistic ,propositions4 ,a truistic proposition is one in which the predicate repeats the words and the meaning of the subject4 ,illustrations3 8,a man is a man10 8,a beast is a beast10 8,a traitor is a traitor10 8,what ,i have done ,i have done40 ,the truistic proposition is of little importance except in cases where the subject is used extensionally while the predicate is used intensionally4 ,in the illustration1 8,a man is a man10 the subject merely stands for a member of the man family1 while the predicate may indicate certain manly qualities4 ,against such ambiguities the logician must be on guard4 #h4 ,,the ,,relation ,,between ,,subject ,,and ,,predicate4 ,in ,chapter #e the extension and intension of terms was explained4 ,the student recalls1 for instance1 that the term 8man0 may be used to denote objects1 as 8white man10 8black man10 8red man10 etc4 ,in this sense the term 8man0 is used extensionally4 ,but when made to stand for the attributes 8rationality10 8power of speech10 etc41 the term 8man0 is used intensionally4 ,in considering the relation between subject and predicate it is customary to employ the terms in an extensional sense only1 since such a restriction serves the purpose of syllogistic reasoning and conversion4 ,let us1 then1 give attention to the extension of the subject and predicate of the categorical propositions ,a1 ,e1 ,i1 ,o4 7#a7 ,the ,universal ,affirmative or ,a ,proposition4 ,all ,s is ,p symbolizes the ,a proposition4 ,this may be interpreted as meaning that all of the subject belongs to a part of the predicate1 or that all of the subject belongs to all of the predicate4 ,the first interpretation is the usual one and may be illustrated by the following propositions3 #a4 8,all men are mortal40 #b4 8,all trees grow40 #c4 8,all metals are elements40 ,it is obvious that the subjects of these propositions include every specimen of the particular class mentioned4 ,for example3 ,the subject all men includes every specimen of the human family2 all trees includes every object of that class2 all metals covers everything which the scientist classes as such4 ,in the three propositions1 then1 reference is made to the whole subject but to only a part of the predicate1 as other beings beside men1 such as the horse1 are mortal2 and other plants aside from trees1 such as the sun flower1 grow2 other substances1 namely oxygen1 are elements4 ,for the sake of making the logical meaning of the four propositions clearer1 recourse may be made to ,euler's diagrams1 so named because the ,swiss mathematician and logician1 ,leonhard ,euler1 first used them4 ,the first illustration of the ,a proposition1 8,all men are mortal10 may be represented by two circles1 a larger circle standing for the predicate1 mortal1 and a smaller circle entirely inside the larger representing the subject1 men4 ,thus3 ,illustration3 ,,fig4 #a4 ,it is evident that all of the smaller circle belongs to the larger4 ,this diagram will then fit any proposition where it may be said that all of the subject belongs to a part of the predicate1 or which may be symbolized as 8,all ,s is some ,p40 7,all the subject is some of the predicate47 ,the student knows that circles are plane surfaces and when such a statement as 8,all men are mortal0 is given1 reference is made to only that part of the 8mortal0 circle which is directly underneath the 8men0 circle4 ,nothing has been said relative to the remaining part of the 8mortal0 circle4 8,a0 propositions which may be interpreted as meaning 8,all ,s is all ,p0 are called co-extensive ,a's because the subject and predicate are exactly equal in extension4 ,such propositions are best illustrated by definitions2 e4 g43 #a4 8,a man is a rational biped40 #b4 8,a trigon is a polygon of three sides40 #c4 8,teaching is the art of occasioning those activities which result in knowledge1 power and skill40 ,to represent the meaning of the co-extensive ,a by the ,euler diagram1 two circles of the same size may be drawn1 one coinciding at every point with the other4 ,if the first circle is drawn heavily in black and the second dotted in red1 it will make clear to the eye that there are two circles4 7#b7 ,the ,universal ,negative or ,e ,proposition4 8,no ,s is ,p0 best symbolizes the ,e proposition1 though sometimes the universal negative is written 8,all ,s is not ,p40 ,this latter form1 as has been explained1 is ambiguous and therefore illogical4 8,no ,s is ,p0 surely means that no part of the subject belongs to any part of the predicate and no part of the predicate belongs to any part of the subject4 ,the subject and predicate are mutually exclusive4 ,the following illustrate the ,e proposition3 #a4 8,no man is immortal40 #b4 8,no true teacher works for money40 #c4 8,no thorough student can remain unwise40 ,the ,e proposition may be represented by two circles1 the one entirely without the other as in ,fig4 #b3 ,illustration3 ,,fig4 #b4 7#c7 ,the ,particular ,affirmative or ,i ,proposition4 ,this may be symbolized as 8,some ,s is ,p10 and considered as meaning that a part of the subject belongs to a part of the predicate4 ,it has already been noted that 8some0 is ambiguous and that its logical signification is 8some at least40 7,it may be all or it may not be all47 ,for example1 the only logical interpretation which can be placed on 8,some men are wise0 is1 that the investigation has resulted in finding only a part of the man family wise4 ,whether or not all are wise is unknown as the entire field has not received attention4 ,in no case can it be assumed that all the others are not wise4 ,the ,i proposition illustrated3 #a4 8,some men are wise40 #b4 8,some animals are vertebrates40 #c4 8,some teachers are inspiring40 ,the meaning of the ,i proposition may be represented by two circles intersecting each other3 ,illustration3 ,,fig4 #c4 ,the significant feature of the diagram is the shaded part which represents a part of the 8men0 circle as belonging to a part of the 8wise0 circle4 ,the unshaded part of each circle is the unknown field4 7#d7 ,the ,particular ,negative or ,o ,proposition4 ,the common symbolization of the ,o is 8,some ,s is not ,p40 ,put in statement form3 ,some of the subject is excluded from the whole of the predicate4 ,here1 as in the ,i1 the same logical import must be given to some2 e4 g41 in the proposition1 8,some men are not wise10 our knowledge is confined to the group who are not wise4 ,whether or not the others are wise or not-wise is unknown4 ,illustrations of the ,o proposition3 #a4 8,some men are not wise40 #b4 8,some laws are not just40 #c4 8,some novels are not helpful40 ,the significance of the ,o proposition may be shown by two intersecting circles as in ,fig4 #d3 ,illustration3 ,,fig4 #d4 ,a similar diagram represents the ,i proposition1 the only difference being in the part shaded4 ,in the ,o proposition the investigated field is all of the 8men0 circle outside of the 8wise0 circle1 while in the ,i proposition the known field is that part of the 8men0 circle inside the 8wise0 circle4 ,in comparing the four diagrams the student will note that the affirmative propositions are inclusive1 while the negative propositions are exclusive4 7#e7 ,the ,distribution of ,subject and ,predicate4 ,a term is said to be distributed when it is referred to as a definite whole4 ,in the proposition1 8,all men are mortal10 the subject all men is considered as a whole4 8,all men0 stands for every specimen of the human race2 not a single one has been left out4 ,again1 the whole is definite2 any one1 if he were given the time and opportunity1 could ascertain by actual count just how many 8all men0 represented4 ,it should be observed that if the word definite is not incorporated in the definition of a distributed term1 there is afforded an opportunity for error4 ,the attending illustrations will make this clear3 #a4 8,all the students except ,john and ,james are dismissed40 #b4 8,all the students except ,john1 ,james1 etc41 are dismissed40 ,the subject of the first proposition is distributed1 while the subject of the second is undistributed4 ,reasons3 ,the first subject1 8,all the students except ,john and ,james10 is referred to as a whole and that whole is definite1 therefore1 it is distributed2 the second subject1 8,all the students except ,john1 ,james1 etc410 is referred to as a whole1 but as the whole is not definite1 the term is not distributed4 ,because all is the quantity sign of the second subject the casual observer might easily be misled in designating it as a distributed term4 ,here it may be well to explain that when reference is made to subject or predicate the logical subject or predicate is meant4 ,unless this is constantly kept in mind error results2 e4 g41 in the proposition1 8,all white men are ,caucasians10 the logical subject is 8white men10 not 8men40 ,if the subject were 8men10 it would be undistributed1 as the whole of the man family is not considered1 but the actual subject1 being 8white men10 is distributed because the predicate refers to all white men4 ,recurring to the illustration1 8,all men are mortal10 we have concluded that the subject 8all men0 is distributed4 ,the predicate1 8mortal10 however1 is undistributed1 as reference is made to it only in part2 i4 e41 there are other beings aside from men that are mortal1 such as 8trees10 8horses10 8dogs10 etc4 ,in all ,a propositions of the type of 8all men are mortal10 the subject is distributed while the predicate is undistributed4 ,this relation is clearly shown by the diagrammatical illustration1 ,fig4 #a4 ,here all of the 8men0 circle is identical with only a part of the 8mortal0 circle4 ,in other words1 the whole of the 8men0 circle is considered1 while reference is made to only a part of the 8mortal0 circle4 ,in the case of the co-extensive ,a both subject and predicate are distributed4 ,relative to the co-extensive 8,all men are rational animals10 it could likewise be said that 8all rational animals are men10 or that 8all men are all of the rational animals40 ,reference is thus made to all of the definite predicate as well as to all of the definite subject4 ,in the ,e propositions1 such as 8,no men are immortal10 the whole of the subject is excluded from the whole of the predicate4 ,this makes evident the fact that both terms are distributed4 ,see ,fig4 #b4 ,the ,i proposition1 such as 8,some men are wise10 concerns itself with only a part of the subject and only a part of the predicate1 consequently neither subject nor predicate is distributed4 ,this relation is verified by the representation1 ,fig4 #c4 ,in the ,o proposition the subject is undistributed1 while the predicate is distributed4 ,for example1 in the proposition1 8,some men are not wise10 8some men0 would indicate that only a part of the logical subject is under consideration4 ,but the predicate is distributed because 8some men0 is denied of the whole of the predicate1 8wise40 ,this may become clear by studying ,fig4 #d4 ,here all of the shaded part which stands for the subject1 8some men10 is excluded from the whole of the 8wise0 circle4 ,but all of the shaded part is only a part of the entire 8men0 circle1 consequently the subject which the shaded part represents 7some men7 is undistributed4 ,the predicate1 8wise10 however1 is distributed1 as the subject is excluded from every part of it4 ,it is well to remember that not1 when used with the copula1 distributes the predicate which follows it4 ,if the student is to succeed in testing the value of arguments1 he must ever have 8at the tip of his tongue0 his knowledge of the distribution of the terms of the four logical propositions4 ,with this in view the following schemes are offered3 ,i4 ,subject ,predicate ,a distributed undistributed ,e distributed distributed ,i undistributed undistributed ,o undistributed distributed ,,ii4 ,a distributed undistributed ,o undistributed distributed ,e distributed distributed ,i undistributed undistributed ,,iii4 ,a ,all ,s is ,p ,e ,no ,s is ,p ,i ,some ,s is ,p ,o ,some ,s is not ,p ,referring to scheme ,,ii it may be observed that ,a and ,o contradict each other2 i4 e41 where ,a is distributed ,o is undistributed and vice versa4 ,a similar relation exists between ,e and ,i4 ,in scheme ,,iii the bracket under the symbol indicates the term which is distributed4 ,,iv4 ,as a fourth scheme a 8key word0 might be adopted4 ,any of these three might be used3 7#a7 saepeo1 or 7#b7 asebinop1 or 7#c7 uaesneop4 ,the significance of 8saepeo0 is this3 8s0 stands for subject distributed1 8p0 for predicate distributed1 8a0 8e0 8o0 for the logical propositions where any distribution occurs4 ,putting the letters together gives this3 subject distributed of propositions ,a and ,e1 predicate distributed of propositions ,e and ,o4 ,similarly1 8asebinop0 stands for this3 8as10 a distributes its subject2 8eb0 e distributes both2 8in10 i distributes neither2 8op10 o distributes the predicate4 ,in the coined word 8uaesneop0 appear six letters which compose 8saepeo10 and the letters have the same significance4 ,the two additional letters1 u and n1 stand for universal and negative4 ,the interpretation of the entire word1 therefore1 is this3 8uaes10 the universals a and e distribute their subjects2 neop1 the negatives e and o distribute their p redicates4 ,it seems to me that the last word is the most helpful as it emphasizes the two facts which are the most used2 namely1 7#a7 ,only the universals distribute their subjects2 7#b7 ,only the negatives distribute their predicates4 ,if the student will visualize 8uaesneop0 so thoroughly as never to forget it1 he will not experience difficulty in determining the distribution of the terms of the four logical propositions4 #i4 ,,outline4 ,,logical ,,propositions4 7#a7 ,the nature of logical propositions4 7#b7 ,kinds of logical propositions4 ,categorical ,hypothetical ,disjunctive 7#c7 ,the four elements of a categorical proposition4 7#d7 ,logical and grammatical subject and predicate distinguished4 7#e7 ,the four kinds of categorical propositions4 ,universal affirmative ,a ,universal negative ,e ,particular affirmative ,i ,particular negative ,o 7#f7 ,propositions which do not conform to the logical type4 ,indefinite and elliptical ,grammatical sentences ,individual ,plurative ,partitive ,exceptive ,exclusive ,inverted 7#g7 ,propositions not necessarily illogical4 ,analytic and synthetic ,modal and pure ,truistic 7#h7 ,the relation between subject and predicate of the four logical propositions4 ,euler's diagrams ,distribution of subject and predicate ,uaesneop ,asebinop ,saepeo #aj4 ,,summary4 7#a7 ,a logical proposition is a judgment expressed in words4 7#b7 ,the three kinds of logical propositions are categorical1 hypothetical1 disjunctive4 ,a categorical proposition is one in which the assertion is made unconditionally4 ,a hypothetical proposition is one in which the assertion depends upon a condition4 ,a disjunctive proposition is one which asserts an alternative4 ,the most common word-signs of the categorical proposition are 8all10 8no10 8some0 and 8some-not10 of the hypothetical1 8if0 and of the disjunctive1 8either-or40 7#c7 ,every logical categorical proposition has the four elements3 quantity sign1 subject1 copula and predicate4 ,the quantity sign indicates the extension of the proposition2 the logical subject is that of which something is affirmed or denied2 the logical predicate is the term which is affirmed or denied of the subject2 the copula is always some form of 8to be0 and is used to connect subject and predicate4 8,not0 is sometimes used with the copula4 ,the statements of ordinary conversation are usually not expressed in terms of the four elements1 but must be1 before they can be used in testing arguments4 7#d7 ,one word usually constitutes the grammatical subject while a word with all its modifiers goes to make up the logical subject4 ,the verb with any predicate word is the grammatical predicate4 ,the logical predicate is all which follows the copulait may include the predicate-word and all its modifiers as well as the modified object4 7#e7 ,categorical propositions are divided into four kinds2 universal affirmative 7,a71 universal negative 7,e71 particular affirmative 7,i71 particular negative 7,o74 ,for the sake of brevity these four are respectively denoted by the vowels ,a1 ,e1 ,i1 ,o4 ,an ,a proposition is one in which the predicate affirms something of all of the logical subject4 ,an ,e proposition is one in which the predicate denies something of all of the logical subject4 ,an ,i proposition is one in which the predicate affirms something of a part of the logical subject4 ,an ,o proposition is one in which the predicate denies something of a part of the logical subject4 ,every proposition must be reduced to one of the four types before it can be used as a basis of argumentation4 ,it is incumbent on the student to recognize these four types with precision and accuracy4 7#f7 ,there are a few proposition types which are recognized as being illogical in form4 ,these may be defined as follows3 7#a7 ,an indefinite proposition is one without the quantity sign4 ,it usually may be classed as universal4 7#b7 ,an elliptical proposition is one in which the copula is suppressed4 7#c7 ,an individual proposition is one which has a singular subject4 ,it is universal in content4 7#d7 ,plurative propositions are those introduced by 8most10 8a few0 or some equivalent quantity sign4 ,these are particular in meaning4 7#e7 ,partitive propositions are particulars which imply a complementary opposite4 ,these arise through the ambiguous use of 8all-not10 8some0 and 8few40 8,all-not0 sometimes means 8no10 while at other times it may mean 8not-all40 ,if the quantity sign means the latter1 then it introduces a partitive proposition4 8,some0 may mean 8some only10 or 8some at least40 ,the latter is the logical meaning4 ,the former interpretation makes the proposition partitive4 ,when 8few0 means 8few only10 it is partitive in nature4 7#f7 ,exceptive propositions are those introduced by such signs as 8all except10 8all but10 8all save10 etc4 ,they are universal only when the exceptions are mentioned4 7#g7 ,exclusive propositions are those introduced by such words as 8only10 8alone10 8none but0 and 8except40 ,in an exclusive the predicate and not the subject is distributed4 ,consequently the easiest way to make an exclusive logical is to interchange subject and predicate and call it an ,a4 7#h7 ,an inverted proposition is one where the predicate precedes the subject4 ,interchanging them gives the logical form4 ,of the grammatical sentences only the declarative is logical4 ,the relative clause1 though out of place1 must be used with the word it modifies4 7#g7 ,there are other propositions1 though not illogical1 to which the logician usually gives some attention4 ,these may be defined as follows3 7#a7 ,an analytical proposition is one in which the predicate gives information already implied in the subject4 7#b7 ,a synthetic proposition is one in which the predicate gives information not implied in the subject4 7#c7 ,a modal proposition is one which states the manner in which the predicate belongs to the subject4 ,the adverbs of time1 place1 degree and manner are the signs of the modal proposition4 7#d7 ,a pure proposition simply states that the predicate belongs or does not belong to the subject4 7#e7 ,a truistic or tautologous proposition is one in which the predicate repeats the words and meaning of the subject4 7#h7 ,in considering the relation which may exist between subject and predicate1 the two terms are employed in extension only1 as this use best serves the interests of inference4 ,the extensional relation between subject and predicate of the four logical propositions may be stated as follows3 ,ordinary ,a,all of the subject belongs to a part of the predicate4 ,co-extensive ,a,all of the subject belongs to all of the predicate4 ,e,none of the subject belongs to any part of the predicate4 ,i,some of the subject belongs to some of the predicate4 ,o,some of the subject is excluded from the whole of the predicate4 ,in general it may be said that the affirmative propositions are inclusive while the negatives are exclusive4 ,a term is said to be distributed when it is referred to as a definite whole4 8,a0 distributes the logical subject only1 8,e0 both logical subject and logical predicate1 8,i0 neither logical subject nor logical predicate1 8,o0 the logical predicate only4 ,the co-extensive 8,a0 distributes both subject and predicate4 ,it is essential that the student know by heart the distribution of the terms of the logical propositions4 ,some keyword like uaesneop may be used as an aid to the memory4 ,this means the universals ,a and ,e distribute their subjects1 while the negatives ,e and ,o distribute their predicates4 #aa4 ,,illustrative ,,exercises4 7#a;a7 ,examine the following list of propositions with a view to classifying them as 8,a's10 8,e's10 8,i's0 or 8,o's40 ,e #a4 8,none of the inmates voted40 ,a #b4 8,benj4 ,franklin was the best educated ,american40 ,i #c4 8,some doctors deem it right to lie to their patients40 ,a #d4 8,all earnest teachers need to observe the teaching of others40 ,i #e4 8,some politicians are honest40 ,a #f4 8,fools rush in where angels fear to tread40 ,o #g4 8,some proverbs are not true to life40 ,e #h4 8,no man should infringe upon the rights of others40 ,i recall that an affirmative proposition in which the predicate refers to the whole of the subject is an ,a1 while one where the predicate refers to only a part of the subject is an ,i4 ,further1 a negative proposition where the predicate refers to the whole of the subject is an ,e1 while one in which the predicate refers to only a part of the subject is an ,o4 ,with these facts in mind1 ,i classify the propositions as indicated4 7#a;b7 ,in a similar manner classify as to quantity and quality the following3 7#a7 8,all worthy workers grow to look like their work40 7#b7 8,every dog has his day40 7#c7 8,some of the presidents were not popular40 7#d7 8,no unskilled laborer can afford to own an automobile40 7#e7 8,some of the #8election prophets' were sadly mistaken40 7#b;a7 ,classify the following propositions and make the illogical1 logical3 7#a7 8,only first-class passengers may ride in parlor cars40 7#b7 8,haste makes waste40 7#c7 8,few men know how to act under stress40 7#d7 8,all which seems to ring true is not true40 7#e7 8,members alone are admitted40 7#f7 8,none but men of integrity need apply40 7#g7 8,horses trot40 7#h7 8,blessed are they which are persecuted for righteousness sake40 ,the first proposition is an exclusive and may be made logical by converting and calling it an ,a1 viz43 8,all who ride in parlor cars are first-class passengers40 7,a7 ,the second is indefinite and elliptical and is made logical by prefixing the universal quantity sign and expressing in terms of the four elements4 ,the logical form is1 8,all who make haste are those who are wasteful40 7,a7 ,the third is plurative in nature and means1 8,most men do not know how to act under stress40 ,it would be classed as an ,o4 ,the fourth is partitive in nature because of the ambiguous use of 8allnot40 ,it means1 8,some who seem to ring true are not true40 7,o7 ,the fifth is an exclusive4 ,by converting and changing to an ,a the proposition takes the logical form1 8,all who are admitted are members40 ,the sixth is likewise an exclusive1 the logical form being1 8,all who apply must be men of integrity40 ,the seventh is an elliptical proposition4 ,logical form3 8,all horses are trotting animals40 ,the eighth is an inverted or poetical proposition4 ,it is made logical by interchanging subject and predicate4 ,logical form3 8,those who are persecuted for righteousness sake are blessed40 7#b;b7 ,classify the attending propositions and change to the logical form1 if necessary3 7#a7 8,only truthful men are honest40 7#b7 8,the stokers alone were saved40 7#c7 8,all who run do not think40 7#d7 8,honesty is the best policy40 7#e7 8,they laugh that win40 7#f7 8,the good alone are happy40 7#g7 8,knowledge is power40 7#h7 8,only the actions of the just smell sweet and blossom in the dust40 #ab4 ,,review ,,questions4 7#a7 ,define and illustrate logical propositions4 7#b7 ,define and exemplify the three kinds of logical propositions4 7#c7 ,what are the usual quantity signs of the four kinds of propositions8 7#d7 ,name and define the four elements of a logical proposition4 7#e7 ,select from the printed page five propositions which are not expressed in terms of the four elements1 and so express them4 7#f7 ,distinguish between logical and grammatical subject2 likewise between logical and grammatical predicate4 7#g7 ,define and illustrate the four kinds of categorical propositions4 7#h7 ,what makes an understanding of the four logical propositions so important8 7#i7 ,give the unusual quantity signs of the logical propositions4 7#aj7 ,what should guide one in making an indefinite proposition logical8 7#aa7 ,how are general truths usually classified8 7#ab7 ,change birds fly to the logical form4 7#ac7 ,how many and what kinds of grammatical sentences are logical8 7#ad7 ,how would the logician deal with interrogative sentences8 7#ae7 ,give illustrations of individual propositions4 ,how are they usually classified8 7#af7 ,explain the logical mode of dealing with the plurative proposition4 7#ag7 ,exemplify the ambiguity of 8all-not10 8some0 and 8few40 7#ah7 ,why are propositions introduced by 8all-not10 8some0 and 8few0 called partitive8 7#ai7 ,use 8all0 in both a partitive and collective sense4 ,which signification has logic adopted8 7#bj7 ,when are exceptive propositions universal and when particular8 7#ba7 ,what is an exclusive proposition8 7#bb7 ,explain by circles the exclusive4 7#bc7 ,tell in full how to change an exclusive to logical form4 7#bd7 ,tell how the logician would deal with such poetical expressions as 8,blessed are the pure in heart10 8,tell me not in mournful numbers10 8,strenuous is the man of state40 7#be7 ,what distinction does the logician make between analytic and synthetic propositions8 7#bf7 ,illustrate the difference between the so-called modal and pure propositions4 7#bg7 ,explain and illustrate the truistic proposition4 7#bh7 ,show by circles the relation existing between the subject and predicate of all the logical propositions4 7#bi7 ,state in good ,english the relation between the subject and predicate of all the logical propositions4 7#cj7 ,relative to the distribution of terms apply the words 8uaesneop0 and 8asebinop40 ,which one is the more serviceable8 7#ca7 ,distinguish between the grammatical and logical subject4 7#cb7 ,explain by circles the distribution of the terms of the four logical propositions4 7#cc7 ,the statement1 8,a part of the subject is excluded from the whole of the predicate10 describes which proposition8 ,explain how it indicates that the predicate is distributed4 #ac4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,show that a judgment may be an individual notion as well as a general notion4 7#b7 ,many logicians classify logical propositions in this wise3 ,categorical ,proposition ,conditional ,hypothetical ,disjunctive ,give arguments for and against such a classification4 7#c7 8,all men are bipeds0 is a judgment of extension1 while 8,man is wise0 is a judgment of intension4 ,explain4 7#d7 8,to be logical is to be pedantic40 ,discuss this4 7#e7 ,why is the proposition1 8,he runs10 illogical8 ,make it logical4 7#f7 ,point out the reasons for calling1 8,white men are ,caucasians10 a particular proposition4 7#g7 ,what makes it necessary to change the propositions of ordinary conversation to those of the four logical types8 7#h7 ,some would call the individual proposition particular4 ,argue the question4 7#i7 ,make a list of five propositions in common speech and show how their partitive implication may mislead4 7#aj7 ,explain by circles some only and some at least4 7#aa7 ,explain how 8et cetera0 may change a universal to a particular proposition4 7#ab7 8,the real nature of an exclusive is best shown by negating the subject and calling the proposition an ,e40 ,give arguments for and against this statement4 7#ac7 ,show that with the immature mind all propositions must be synthetical4 7#ad7 ,explain how a proposition may be truistic in form but not in meaning4 7#ae7 ,show by the ,euler diagram how easy it is for the careless student to think that an 8,o0 does not distribute its predicate4 7#af7 ,explain by the use of two pads 7a small yellow one and a large white one7 the distribution of terms4 7#ag7 ,when the logician makes reference to the subject of a proposition1 show that he should exercise care in designating it as the logical subject4 ,,chapter #i4 ,,immediate ,,inference,,opposition4 #a4 ,,the ,,nature ,,of ,,inference4 ,inference is the thought process of deriving a judgment from one or two antecedent judgments4 ,the process is simply a matter of expressing explicitly in a final judgment1 a truth that was implied in one or two previous judgments4 ,to exemplify3 ,from the antecedent truth1 that 8,all teachers should be fair minded10 one may derive a consequent truth that 8,this teacher1 ,albert ,white1 should be fair minded40 ,or from the statement1 8,all men are mortal10 one may derive the judgment1 8,no men are immortal40 ,because the ground is wet we conclude that it has rained4 ,if all dogs are quadrupeds then surely some dogs are quadrupeds4 ,finally from the two propositions1 8,all training school students are high school graduates10 and 8,mary ,jones is a training school student10 we are led to conclude that 8,mary ,jones is a high school graduate40 #b4 ,,immediate ,,and ,,mediate ,,inference4 ,it has been noted that a truth may be derived from a consideration of one or two antecedent judgments4 ,to illustrate further3 ,from the judgment1 8,all men are fallible10 we may derive the conclusion that 8,no men are infallible02 or1 from the two judgments1 8,all men are fallible10 and 8,socrates was a man10 we may readily infer that 8,socrates was fallible40 ,these two modes of inference take the names of immediate inference and mediate inference4 ,let us express these two kinds in equation form3 ,i4 ,equation ,form1 ,ordinary ,form4 ,using ,initial ,letters4 ,antecedent judgment3 ,all men are fallible4 ,all m are f ,conclusion3 ,no men are infallible4 ,no m are i ,,ii4 ,first antecedent judgment3 ,all men are fallible4 ,all m are f ,second antecedent judgment3 ,socrates was a man4 ,s was m ,conclusion3 ,socrates was fallible4 ,s was f ,giving attention to the antecedent judgments of the second argument it is noted that the terms 8f0 and 8,s0 are referred to the common term 8m40 ,in logic this common term is known as the middle term4 ,as there is but one antecedent judgment in the first argument there can be no common or middle term4 ,the first argument is an illustration of immediate inference2 the second of mediate inference4 ,this suggests the definitions3 ,immediate inference is inference without the use of a middle term4 ,mediate inference is inference by means of a middle term4 #c4 ,,the ,,forms ,,of ,,immediate ,,inference4 ,many logicians recognize four forms of immediate inference4 ,these four forms are 7#a7 opposition1 7#b7 obversion1 7#c7 conversion1 7#d7 contraversion4#h 7#a7 ,,immediate ,,inference ,,by ,,opposition4 ,we have learned that to be logical all categorical assertions must be reduced to some one of the four propositions1 ,a1 ,e1 ,i1 ,o4 ,if these four logical propositions be given the same subject and predicate1 certain definite relations will become evident2 therefore1 ,opposition is said to exist between propositions which are given the same subject and predicate1 but differ in quality1 or in quantity1 or in both4 ,the following illustrative outline will make this clear3 #a4 ,original ,proposition4 ,i4 ,all men are mortal4 7,a7 ,,ii4 ,no men are immortal4 7,e7 ,,iii4 ,some men are wise4 7,i7 ,,iv4 ,some men are mortal4 7,i7 ,v4 ,some men are not wise4 7,o7 ,,vi4 ,some men are not immortal4 7,o7 #b4 ,opposite in ,quantity4 ,i4 ,some men are mortal4 7,i7 ,,ii4 ,some men are not immortal4 7,o7 ,,iii4 ,all men are wise4 7,a7 ,,iv4 ,all men are mortal4 7,a7 ,v4 ,no men are wise4 7,e7 ,,vi4 ,no men are immortal4 7,e7 #c4 ,opposite in ,quality4 ,i4 ,no men are mortal4 7,e7 ,,ii4 ,all men are immortal4 7,a7 ,,iii4 ,some men are not wise4 7,o7 ,,iv4 ,some men are not mortal4 7,o7 ,v4 ,some men are wise4 7,i7 ,,vi4 ,some men are immortal4 7,i7 #d4 ,opposite in ,both4 ,i4 ,some men are not mortal4 7,o7 ,,ii4 ,some men are immortal4 7,i7 ,,iii4 ,no men are wise4 7,e7 ,,iv4 ,no men are mortal4 7,e7 ,v4 ,all men are wise4 7,a7 ,,vi4 ,all men are immortal4 7,a7 ,granting the truth of the propositions in the first column1 it follows that those in the second column differ in quantity4 ,that is1 in 8,some men are mortal0 a smaller number of men is referred to than in 8,all men are mortal40 ,a similar variation in quantity obtains with the other propositions in the second column4 ,moreover1 the propositions in the third column are the negative of the corresponding ones in the first2 while the fourth column propositions differ from the first in both quantity and quality4 ,thus opposition exists to a greater or less degree between all4 ,we may now ask ourselves the question1 8,when the propositions are related to each other in opposition which ones are true and which ones are false80 ,giving attention to the propositions in row 8,i10 we note that if the universal affirmative1 8,all men are mortal10 is true1 then the particular affirmative1 8,some men are mortal10 is likewise true2 because of the principle1 8,what is true of the whole of the class is true of a part of that class40 ,but the universal negative1 8,no men are mortal10 and the particular negative1 8,some men are not mortal10 are both false4 ,briefly stated3 ,if ,a is true1 then ,i is true1 but1 both ,e and ,o are false4 ,regarding row 8,,ii0 we may conclude that if ,e is true1 then ,o is likewise true1 but both ,a and ,i are false4 ,as to rows 8,,iii0 and 8,,iv10 granting the truth of the ,i propositions1 8,some men are wise0 and 8,some men are mortal10 we are able to assert that of the two ,a propositions1 8,all men are wise10 and 8,all men are mortal10 the first is false while the second is true4 ,a is1 therefore1 indeterminate1 or doubtful4 ,of the ,o propositions1 8,some men are not wise10 is true while1 8,some men are not mortal10 is false4 ,therefore1 ,o is doubtful4 ,both of the ,e propositions are false4 ,hence1 the conclusion relative to rows 8,,iii0 and 8,,iv0 is3 ,if ,i is true1 ,a and ,o are doubtful1 while ,e is false4 ,concerning rows 8,v0 and 8,,vi0 it will be seen without further explanation that if ,o is true1 then ,e and ,i are doubtful and ,a is false4 ,,the ,,scheme ,,of ,,opposition4 ,the conditions of opposition are easily comprehended and remembered when recourse is made to the following scheme3 ,a ,e ,i ,o ,if ,a be true true false true false ,if ,e be true false true false true ,if ,i be true doubt false true doubt ,if ,o be true false doubt doubt true ,to use the above scheme1 read horizontally from left to right4 ,for example3 ,if ,a be true1 then all in the row opposite obtains2 that is1 ,a is true1 ,e is false1 ,i is true1 and ,o is false4 7,we take it for granted that the student will see that the first column belongs to ,a1 the second to ,e1 the third to ,i1 and the fourth to ,o47 ,if ,e be true1 then ,a is false1 ,e is true1 ,i is false1 ,o is true1 etc4 ,the whole of opposition is comprehended in two facts which are based upon one principle4 ,this is the principle3 ,whatever may be said of the entire class may be said of a part of that class4 ,to put it in another way3 ,whatever is affirmed of all may be affirmed of some1 or1 ,whatever is denied of all may be denied of some4 ,to illustrate3 ,accepted truth3 ,all planets rotate4 7,a7 ,accepted inference3 ,some planets rotate4 7,i7 or ,accepted truth3 ,no planet is a sun4 7,e7 ,accepted inference3 ,some planets are not suns4 7,o7 ,these are the two facts3 ,first1 a particular affirmative may be derived from a universal affirmative4 ,second1 a particular negative may be derived from a universal negative4 ,or1 more briefly3 ,an ,i may be derived from an ,a1 and an ,o from an ,e4 ,,square ,,of ,,opposition4 ,illustration3 7 ,square of ,opposition7 ,aristotle represented the relations of the four logical propositions by what is termed the square of opposition4 ,viewed from the standpoint of the square1 the relations may be summed up as follows3 #a4 ,contrary ,propositions4 ,why so named4 ,as related to each other1 ,a and ,e are said to be contrary because they seem to express contrariety to the greatest degree4 ,relation stated4 ,if one is true1 the other must be false1 but both may be false4 ,illustrations4 7#a7 ,if one is true1 the other must be false2 e4 g41 if ,a is true1 as 8,all metals are elements10 then ,e is false1 as 8,no metals are elements40 ,or1 if ,e is true1 as 8,no birds are quadrupeds10 then ,a is false1 as 8,all birds are quadrupeds40 7#b7 ,both may be false4 ,if ,a is false1 as 8,all men are wise10 then ,e may be false1 as 8,no men are wise40 #b4 ,subcontrary ,propositions4 ,why so named4 ,propositions ,i and ,o are said to be related to each other in a subcontrary manner because they are contrary as to each other and 8under0 their universals ,a and ,e4 ,relation stated4 ,if one is false1 the other must be true1 or1 both may be true4 ,illustrations4 7#a7 ,if one is false1 the other must be true4 ,if ,i is false1 as 8,some metals are compounds10 then1 ,o is true1 as 8,some metals 7at least7 are not compounds40 ,or1 if ,o is false1 as 8,some metals are not elements10 then ,i is true1 as 8,some metals are elements40 7#b7 ,both may be true4 ,if ,i is true1 as 8,some men are wise10 then ,o also may be true1 as 8,some men are not wise40 #c4 ,subalterns4 ,why so named4 ,etymologically considered subaltern means under the one1 thus proposition ,i is under ,a1 and ,o is under ,e4 ,relation stated4 ,first ,relation4 ,subalterns are related to each other as are the universals and particulars2 hence1 7#a7 ,if the universal is true1 the particular under it is also true2 while if the particular is true1 the corresponding universal may1 or1 may not1 be true4 ,illustrations4 7a7 ,if the universal is true1 the particular under it is true4 ,if ,a is true1 as 8,all metals are elements10 then ,i is true1 as 8,some metals are elements40 ,or1 if ,e is true1 as 8,no metals are compounds10 then1 ,o is also true1 as 8,some metals 7at least7 are not compounds40 7b7 ,if the particular is true1 the corresponding universal may1 or1 may not1 be true4 ,if ,i is true1 as 8,some men are wise10 or1 8,some men are mortal10 then ,a may be false1 as 8,all men are wise10 or1 ,a may be true1 as 8,all men are mortal40 ,or1 if ,o is true1 as 8,some men are not wise10 or1 8,some men are not immortal10 then ,e may be false1 as 8,no men are wise02 or1 true1 as 8,no men are immortal40 ,second ,relation4 7#b7 ,if the universal is false1 the particular under it may or may not be true1 but1 if the particular is false1 the universal above it must be false4 ,illustrations4 7a7 ,if the universal is false1 the particular under it may or may not be true4 ,if ,a is false1 as 8,all metals are compounds10 or 8,all men are wise10 then ,i may be false1 as 8,some metals are compounds10 or1 ,i may be true1 as 8,some men are wise40 ,or1 if ,e is false1 as 8,no men are mortal10 or1 8,no men are wise10 then ,o may be false1 as 8,some men are not mortal10 or1 ,o may be true1 as 8,some men are not wise40 7b7 ,if the particular is false1 the universal above it must be false4 ,if ,i is false1 as 8,some men are trees10 then ,a is false1 as 8,all men are trees40 ,or1 if ,o is false1 as 8,some men are not bipeds10 then ,e is also false1 as 8,no men are bipeds40 #d4 ,contradictory ,propositions4 ,why so named4 ,the propositions ,a and ,o1 likewise ,e and ,i1 are called contradictory propositions because they oppose each other in both quantity and quality4 ,they are mutually opposed to each other or absolutely contradictory4 ,relation stated4 ,if one is true the other must be false4 ,illustrations4 7#a7 ,a and ,o compared4 ,if ,a is true1 as 8,all metals are elements10 then1 ,o is false1 as 8,some metals are not elements40 ,or1 if ,o is true1 as 8,some metals are not compounds10 then ,a is false1 as 8,all metals are compounds40 7#b7 ,e and ,i compared4 ,if ,e is true1 as 8,no birds are quadrupeds10 then ,i is false1 as 8,some birds are quadrupeds40 ,or1 if ,i is true1 as 8,some birds are bipeds10 then ,e is false1 as 8,no birds are bipeds40 ,the chief value of the square of opposition springs from the contradictory propositions4 ,the square shows conclusively that any universal affirmative assertion 7an ,a7 may best be contradicted by proving a particular negative 7an ,o74 ,for example3 ,to satisfactorily refute the statement that1 in this section1 all birds migrate to the south in winter1 it would be sufficient to prove that the ,english sparrow and starling do not migrate to the south4 ,the square likewise makes evident that any universal negative 7an ,e7 may be conclusively denied by establishing the truth of a particular affirmative 7an ,i74 ,to illustrate3 ,the easiest way to prove the falsity of 8,no trusts are honest0 is to present facts showing that at least trusts ,a and ,b are honest4 ,the ,individual ,proposition4 ,an individual proposition is one with an individual subject such as 8,aristotle was wise40 ,in logic1 the individual proposition is classed as a universal4 ,this seems to be a bit irregular1 as with the individual proposition there is no particular1 while1 the strictly logical universal always implies a particular4 ,because of this variation from the true logical form the relations1 as indicated by the square of opposition1 do not apply to the individual proposition4 ,for example3 ,according to the square ,a and ,e are contrary1 but1 when individual1 ,a and ,e contradict each other1 as 8,aristotle was wise0 7,a78,aristotle was not wise0 7,e74 ,,chapter #aj4 ,,immediate ,,inference 7,,continued7,,obversion1 ,,conversion1 ,,contraversion ,,and ,,inversion4 7#b7 ,,immediate ,,inference ,,by ,,obversion4 ,obversion is the process of changing a proposition from the affirmative form to its equivalent negative or from the negative form to its equivalent affirmative4 ,some authorities refer to this process as 8,inference by ,privitive ,conception10 but ,obversion seems to be a better term4 ,obversion is based upon the principle that two negatives are equivalent to one affirmative4 ,with this double negative principle in mind let us experiment with the four logical propositions1 ,a1 ,e1 ,i1 ,o4 ,the ,a ,proposition4 ,example3 8,all thoughtful men are wise40 ,insert the double negative and the proposition reads3 8,all thoughtful men are not not-wise40 ,changed to the logical form this becomes3 8,no thoughtful men are not-wise40 ,simplified and we have1 finally3 8,no thoughtful men are unwise40 ,thus by the process of obversion we have passed from the original proposition1 8,all thoughtful men are wise10 to 8,no thoughtful men are unwise40 ,in the first proposition the subject 8thoughtful men0 is denied of the predicate 8unwise40 ,assuming that 8unwise0 is the contradictory of 8wise10 then3 8,what is affirmed of a predicate may be denied of its contradictory40 ,recourse to circles will make this clearer4 ,in the previous chapter it has been suggested that not bisects the world4 ,for example3 ,what can not be included in the wise class may be placed under the not-wise or unwise class4 ,likewise a circle bisects spacethere is the space inside the circle and the space outside the circle4 ,let the space inside the circle represent all wise beings1 then the space outside the circle would represent all not-wise or unwise beings2 e4 g41 ,illustration3 ,,fig4 #e4 ,now representing thoughtful men by a smaller circle and placing it inside the larger we have1 ,illustration3 ,,fig4 #f4 ,referring to ,fig4 #f we note that all of the smaller circle belongs to the larger or that none of the smaller circle belongs to the space outside of the larger4 ,hence the two propositions3 8,all thoughtful men are wise0 7,a71 and 8,no thoughtful men are unwise0 7,e7 have virtually the same meaning though the same subject is related to different predicates4 ,the use of the positive or negative form depends upon circumstances4 ,often the negative puts the thought in a more forceful way4 ,in passing from1 8,all thoughtful men are wise10 to 8,no thoughtful men are unwise10 it was necessary to prefix not to the predicate wise and substitute for not its equivalent un4 ,if the original predicate were unwise or not-wise1 then the reverse order of dropping the un or not could be followed4 ,this process of prefixing the not to an affirmative predicate or of dropping the not from a negative predicate is referred to as negating the predicate4 ,before substituting in1 im1 un1 etc41 for not1 one must make sure that the substitution really gives the contradictory2 there are some logicians who claim that unwise1 for instance1 is not the contradictory of wise4 ,in comparing the first proposition with the second it is observed that the first is an ,a1 while the second is an ,e1 also that the predicate of the first was negated to form the predicate of the second4 ,thus the rule3 ,negate the predicate and change ,a to ,e4 ,to sum up3 ,the obversion of an ,a proposition4 #a4 ,principle3 ,two negatives are equivalent to one affirmative4 #b4 ,rule3 ,negate the predicate and change the ,a to an ,e by using the sign no instead of all4 #c4 ,process illustrated4 ,the ,original ,proposition 7,a7 ,the ,obverse 7,e7 ,all men are mortal4 ,no men are immortal4 ,all maples are trees4 ,no maples are not-trees4 ,all teachers should be ,no teacher should be sympathetic4 un-sympathetic4 ,all pain is unpleasant4 ,no pain is pleasant4 ,all men are imperfect4 ,no men are perfect4 ,all birds are feathered ,no birds are non-feathered animals4 animals4 ,all men are not-trees4 ,no men are trees4 ,all scalene triangles are ,no scalene triangles are non-equilateral4 equilateral4 ,the ,e ,proposition4 ,it is obvious that the process of obverting an ,e is simply the reverse of obverting an ,a4 ,consequently1 the same principle obtains2 whereas the process may be illustrated by reading the foregoing illustrations reversely4 ,the rule for obverting ,e is3 ,negate the predicate and change the ,e to an ,a by changing the sign no to all4 ,the ,i ,proposition4 ,let us note the result when the double negative principle is applied to the ,i proposition4 ,original3 8,some men are wise40 ,adding two negatives3 8,some men are not not-wise40 ,the foregoing simplified3 8,some men are not unwise40 ,in comparing the first proposition with the last it is observed that the first is an ,i while the last is an ,o2 it is also observed that the predicate of the first was negated in order to form the predicate of the last4 ,thus the rule3 8,negate the predicate and change the ,i to an ,o40 ,the use of circles may make this clearer3 ,illustration3 ,,fig4 #g4 ,the significant part of ,fig4 #g is that which is inked4 ,here we have represented the part of the 8men0 circle which is common to the 8wise0 circle4 ,thus the inked part represents 8,some men are wise40 ,if the inked part is entirely inside of the 8wise0 circle1 no part of it can belong to the 8unwise0 space without4 ,thus the obverse1 8,some men are not unwise40 ,summary4 ,the obversion of an ,i proposition4 #a4 ,principle3 ,same as with ,a4 #b4 ,rule3 ,negate the predicate and change the ,i to an ,o4 #c4 ,process illustrated4 ,the ,original ,proposition 7,i7 ,the ,obverse 7,o7 ,some water is pure4 ,some water is not impure4 ,some curves are perfect4 ,some curves are not imperfect4 ,some friends are loyal4 ,some friends are not disloyal4 ,some men are true4 ,some men are not not-true4 ,some precious stones are ,some precious stones are not imperfect4 perfect4 ,some plants are not-trees4 ,some plants are not trees4 ,some boys are not-honest4 ,some boys are not honest4 ,it must be borne in mind that when 8not0 is used without the hyphen it makes the proposition negative1 because when 8unhyphened10 8not0 must be thought of in connection with the copula and not in connection with the predicate2 while 8not0 attached to the predicate with a hyphen simply makes the predicate negative without affecting the quality of the proposition2 e4 g41 8,some plants are not trees0 is a negative proposition1 while 8,some plants are not-trees0 is an affirmative proposition with a negative predicate4 ,it may not be clearly seen how it is possible1 by following the rule given1 to pass from such a proposition as 8,some plants are not-trees10 to 8,some plants are not trees40 ,let us illustrate the steps3 #a4 ,the original3 8,some plants are not-trees40 #b4 ,negating predicate3 8,some plants are trees40 #c4 ,changing to an ,o3 8,some plants are not trees40 ,dropping the not from 8#a0 and then adding it again to 8#b0 is simply putting into operation the double negative idea1 so that there is no violation of the principle4 ,the ,o ,proposition4 ,o bears the same relation to ,i that ,e bears to ,a4 ,the principle involved is the same4 ,the process is illustrated by reading reversely the scheme of illustrations under ,i4 ,the rule is as follows3 ,to obvert an ,o negate the predicate and change the ,o to an ,i by eliminating the not4 ,summary of ,obverting the ,four ,logical ,propositions4 #a4 ,principle3 ,two negatives are equivalent to one affirmative4 #b4 ,rules3 7#a7 ,a to ,e ,negate the predicate 7#b7 ,e to ,a and change 7#c7 ,i to ,o 7#d7 ,o to ,i 7#c7 ,,immediate ,,inference ,,by ,,conversion4 ,conversion is the process of inferring from a given proposition another which has1 as its subject1 the predicate of the given proposition1 and1 as its predicate1 the subject of the given proposition4 ,it is simply a matter of transposing subject and predicate4 ,the original proposition is called the convertend while the derived proposition is named the converse4 ,the process of conversion is limited by two rules4 ,first rule4 ,no term must be distributed in the converse which is not distributed in the convertend4 ,second rule4 ,the quality of the converse must be the same as that of the convertend4 ,more briefly3 7#a7 ,do not distribute an undistributed term4 7#b7 ,do not change the quality4 ,we recall that a term is distributed when it is referred to as a definite whole4 ,an undistributed term is referred to only in part4 ,the principle underlying rule 8#a10 therefore1 is the one which forms the basis of inference by opposition2 namely1 8,whatever may be said of the entire class may be said of a part of that class40 ,the converse of this is not true1 that is1 8,what is said of part of a class cannot be said of the whole of that class40 ,when we distribute an undistributed term we are saying of the whole class what was said only of a part of that class4 ,this is fallacious4 ,on the other hand1 we may say of a part what was said of the whole1 or 8undistribute0 a distributed term4 ,we recall that the conclusion of the whole matter of inference by opposition was1 that only an ,i could be inferred from an ,a and only an ,o from an ,e1 or to put it in another way3 ,only an affirmative from an affirmative and only a negative from a negative4 ,this establishes the truth of the second rule in conversion3 8,do not change the quality40 ,let us apply the two rules to the four logical propositions4 ,converting an ,a proposition4 ,take as a type1 8,all horses are quadrupeds40 ,here the subject 8horses0 is distributed1 but the predicate 8quadrupeds0 is undistributed4 ,in transposing subject and predicate we cannot distribute the term 8quadrupeds10 according to the rule which says1 8,do not distribute an undistributed term40 ,hence in interchanging subject and predicate we cannot say1 8,all quadrupeds are horses10 but must limit the assertion to1 8,some quadrupeds are horses40 ,logicians call this process ,conversion by ,limitation4 ,conversion by ,limitation ,exemplified ,further4 ,convertend4 ,converse4 ,all metals are elements4 ,some elements are metals4 ,all bees buzz4 ,some buzzing insects are bees4 ,all men are fallible4 ,some fallible beings are men4 ,all good teachers are ,some sympathetic persons are good sympathetic4 teachers4 ,the conclusions from the foregoing are these3 ,first1 the usual mode of converting an ,a is to interchange subject and predicate1 limiting the latter by the word 8some0 or a word of similar significance4 ,second1 this mode is called conversion by limitation4 ,third1 the converse of an ,a is an ,i4 ,the ,co-extensive ,a4 ,in the conversion of ,a propositions there is the one exception of 8co-extensive ,a's10 such as truisms and definitions4 ,it will be remembered that with these both subject and predicate are distributed2 hence1 they may be interchanged without limiting the predicate by 8some40 ,to illustrate3 ,the converse of the truism1 8,a man is a man40 is 8,a man is a man10 while the converse of the definition1 8,a man is a rational animal10 is 8,a rational animal is a man40 ,this mode of interchanging subject and predicate without limiting the latter is called ,simple ,conversion4 ,the ordinary ,a proposition is thus converted by limitation1 while the co-extensive ,a is converted simply4 ,converting an ,e proposition4 ,as both terms of the ,e proposition are distributed it is not possible to violate the rule of distribution4 ,it is to be remembered that no fallacy is committed by 8undistributing0 a term which is already distributed4 ,illustrations4 ,convertend4 ,converse4 ,no men are immortal4 ,no immortals are men4 ,simply4 ,no birds are quadrupeds4 ,no quadrupeds are birds4 ,simply4 ,no metals are compounds4 ,no compounds are metals4 ,simply4 ,no men are immortal4 ,some immortals 7at least7 are not men4 ,limitation4 ,no birds are quadrupeds4 ,some quadrupeds are not birds4 ,limitation4 ,no metals are compounds4 ,some compounds are not metals4 ,limitation4 ,three facts are evident relative to the converting of an ,e4 ,first3 ,an ,e proposition may be converted either simply or by limitation4 ,second3 ,e may be converted into either ,e or ,o4 ,third3 ,if the converse is an ,o then is the inference a weakened one1 being particular when it could just as well be universal4 ,converting an ,i proposition4 ,with an ,i proposition neither term is distributed4 ,thus care must be used lest an undistributed term in the convertend be distributed in the converse4 ,illustrations3 ,convertend4 ,converse4 ,some men are wise4 ,some wise beings are men4 ,some teachers scold4 ,some who scold are teachers4 ,some high school graduates ,some who enter college are high enter college4 school graduates4 ,some ,americans live simply4 ,some who live simply are ,americans4 ,from the foregoing we conclude first1 that ,i is converted simply2 second1 that ,i is converted into ,i4 ,the ,o ,proposition4 ,with an ,o proposition the subject is undistributed while the predicate is distributed4 ,this condition presents a peculiar difficulty4 ,consider1 for example1 the ,o proposition1 8,some men are not wise40 ,convert this into1 8,some wise beings are not men10 and the undistributed subject of the convertend1 which is 8men10 becomes the distributed predicate of the converse4 ,thus the ,o proposition cannot be converted without violating the rule for distribution4 ,a ,summary of ,how the ,four ,logical ,propositions ,may be ,converted4 #a4 ,a4 ,the ordinary ,a proposition may be converted by limitation only4 ,the co-extensive ,a may be converted simply4 #b4 ,e4 ,the ,e proposition is converted simply4 ,the ,e may also be converted by limitation1 but the inference thus obtained is weakened4 #c4 ,i4 ,the ,i proposition may be converted simply only4 #d4 ,o4 ,the ,o proposition cannot be converted4 7#d7 ,,inference ,,by ,,contraversion4 7,contraposition74 ,this mode of inference is usually referred to as inference by contraposition1 but contraversion1 indicating more definitely the nature of the process1 is a better term4 ,contraversion involves two steps3 ,first1 obversion2 second1 conversion4 ,the same principles and rules evident in these two processes obtain in inference by contraversion4 ,the following scheme1 therefore1 ought to be sufficient to make the matter clear3 ,inference by ,contraversion4 #a4 ,the ,given ,proposition4 #b4 ,obverted4 ,a4 ,all men are mortal4 ,no men are immortal4 ,all trees are plants4 ,no trees are not-plants4 ,e4 ,no men are infallible4 ,all men are fallible4 ,no men are trees4 ,all men are not-trees4 ,i4 ,some men are wise4 ,some men are not not-wise4 ,o4 ,some water is not pure4 ,some water is impure4 ,some houses are not white4 ,some houses are not-white4 #c4 ,converted2 giving the contraverse of the original proposition4 ,no immortals are men4 ,no not-plants are trees4 ,some fallible beings are men4 ,some not-trees are men4 ,an ,o cannot be converted1 consequently the contraversion of an ,i is impossible4 ,some impure liquids are water4 ,some not-white buildings are houses4 ,it is indicated in the foregoing scheme that 8,i0 cannot be contraverted4 ,this is due to the fact that the obverse of an ,i is an ,o1 and it will be remembered that 8,o0 cannot be converted4 ,all the other propositions admit of contraversion4 #d4 ,,epitome ,,of ,,the ,,four ,,processes ,,of ,,immediate ,,inference ,,in ,,connection ,,with ,,the ,,four ,,logical ,,propositions4 99,proposition,name of ,inference ,principle symbolized ,process symbolized involved ,a ,all ,s is ,opposition ,some ,s is ,what is said of all may ,p ,p 7,i7 be said of some4 ,obversion ,no ,s is ,two negatives are not-,p 7,e7 equivalent to one affirmative4 ,conversion by,some ,p is ,an undistributed term ,limitation ,s 7,i7 cannot be distributed4 ,contraversion,no not-,p ,same principles which is ,s 7,e7 obtain in obverting ,a and converting ,e4 ,e ,no ,s is ,p ,opposition ,some ,s is ,what is said of all may not ,p 7,o7 be said of some4 ,obversion ,all ,s is ,two negatives are not-,p 7,a7 equivalent to one affirmative4 ,simple ,no ,p is ,s ,distribution not ,conversion 7,e7 affected4 ,contraversion,some not-,p ,an undistributed term is ,s 7,i7 cannot be distributed4 ,i ,some ,s is ,p,opposition ,doubtful ,none4 ,obversion ,some ,s ,two negatives are is not equivalent to one not-,p 7,o7 affirmative4 ,conversion ,some ,p is ,distribution not ,s 7,i7 affected4 ,contraversion,impossible ,none4 ,o ,some ,s is ,opposition ,doubtful ,none4 not ,p ,obversion ,some ,s is ,two negatives are not-,p 7,i7 equivalent to one affirmative4 ,conversion ,impossible ,none4 ,contraversion,some not-,p ,same as in obversion of is ,s 7,i7 ,o and conversion of ,i4 99 - ,name of proposition - 8,s0 represents any subject and 8,p0 any predicate4 ,,inference ,,by ,,inversion4 ,some logicians treat of a form of immediate inference known as inversion though it is of small importance and of little practical value4 ,the process can be applied only to propositions ,a and ,e4 ,in the one case the contradictory subject is limited by 8some0 and then denied of the predicate1 whereas1 in the other case1 the contradictory subject is merely affirmed of the predicate4 ,illustrations4 ,the ,given ,proposition4 ,the ,inverse4 ,i4 ,all ,s is ,p4 7,a7 ,some not-,s is not ,p4 7,o7 ,all planets rotate4 ,some not-planets do not rotate4 ,,ii4 ,no ,s is ,p4 7,e7 ,some not-,s is ,p4 7,i7 ,no men are immortal4 ,some not-men are immortal4 ,from the foregoing we are able to conclude that the inverse of 8,a0 is found by negating the subject and changing to an 8,o02 while the inverse of 8,e0 is found by negating the subject and changing to an 8,i40 #e4 ,,outline4 ,,immediate ,,inference,,opposition,,obversion1 ,,conversion1 ,,contraversion ,,and ,,inversion4 #a4 ,the ,nature of ,inference4 #b4 ,immediate and ,mediate ,inference4 #c4 ,the ,forms of ,immediate ,inference4 7#a7 ,opposition4 7a7 ,scheme of ,opposition4 7b7 ,square of ,opposition4 7#b7 ,obversion4 7#c7 ,conversion4 7a7 ,simply4 7b7 ,by ,limitation4 7#d7 ,contraversion4 ,inversion4 #f4 ,,summary4 #a4 ,inference is the thought process of deriving a judgment from one or two antecedent judgments4 #b4 ,immediate inference is inference without the use of a middle term4 ,mediate inference is inference by means of a middle term4 #c4 ,the four common forms of immediate inference are 7#a7 opposition1 7#b7 obversion1 7#c7 conversion1 7#d7 contraversion4 7#a7 ,the name opposition stands for certain definite relations which exist between the logical propositions when they are given the same subject and predicate4 ,the one principle underlying opposition is3 ,whatever is said of the entire class may be said of a part of that class4 ,the two statements which sum up opposition are first1 an ,i may be derived from an ,a2 and second1 an ,o may be derived from an ,e4 ,the crucial fact made obvious by the square of opposition is that ,a and ,o are mutually contradictory2 likewise ,e and ,i4 7#b7 ,obversion is the process of passing from an affirmative to its equivalent negative or from a negative to its equivalent affirmative4 8,two negatives are equivalent to one affirmative10 is the basic principle of obversion4 ,the proposition ,a may be obverted by negating the predicate and changing to an ,e4 8,e0 is obverted by negating the predicate and changing to an ,a4 8,i0 is obverted by negating the predicate and changing to an ,o4 8,o0 is obverted by negating the predicate and changing to an ,i4 7#c7 ,conversion is the process of inferring from a given proposition another which has as its subject the predicate of the given proposition and as its predicate the subject of the given proposition4 ,conversion is limited by the two rules1 7#a7 do not distribute an undistributed term2 7#b7 do not change the quality4 ,to convert an ,a interchange subject and predicate1 limiting the latter by some1 or a word of like significance4 ,this is called conversion by limitation4 ,the co-extensive ,a may be converted without limiting the predicate4 ,this is called simple conversion4 ,an ,e proposition may be converted either simply or by limitation4 ,when converted by limitation the inference is a weakened one4 ,an ,i proposition is converted simply only4 ,the ,o proposition does not admit of conversion4 7#d7 ,immediate inference by contraversion is a process involving first obversion and then conversion4 8,a10 8,e0 and 8,o0 may be contraverted2 8,i0 cannot be contraverted4 #g4 ,,illustrative ,,exercises4 7#a;a7 ,from the antecedent judgment1 8,all weeds are plants10 ,i am able to derive by immediate inference these judgments3 7#a7 8,all weeds are not not-plants10 or 8,no weeds are not plants40 7#b7 8,no not-plants are weeds40 7#c7 8,some plants are weeds40 7#d7 8,some weeds are plants40 7#a;b7 8,all vertebrates have a backbone40 ,from the foregoing judgment derive immediately five different conclusions4 7#b;a7 8,all good citizens try to vote10 8,albert ,white is a good citizen10 ,hence1 8,albert ,white will try to vote40 ,i know that the above is an example of mediate inference because the two antecedent judgments make use of the middle term1 8good citizen40 7#b;b7 ,why is the following illustrative of mediate inference8 8,all wise men are close observers10 8,all wise men are thoughtful10 ,hence1 8,some thoughtful men are close observers40 7#c;a7 ,derive immediate inferences by opposition from the following3 7#a7 8,good men are wise40 7#b7 8,no teacher can afford to be unjust40 7#c7 8,all birds fly40 7#d7 8,none of the inner planets are as large as the earth40 ,i first determine that 8#a0 and 8#c0 are ,a propositions1 while 8#b0 and 8#d0 are ,e's4 ,then ,i recall that by opposition an ,i may be derived from an ,a and an ,o from an ,e4 ,hence1 the inferences are3 7#a7 8,some good men are wise40 7#b7 8,some teachers cannot afford to be unjust40 7#c7 8,some birds fly40 7#d7 8,some of the inner planets are not so large as the earth40 7#c;b7 ,derive by opposition inferences from the following3 7#a7 8,no true woman will neglect her home for society40 7#b7 8,all patriotic men love the flag40 7#c7 8,fools rush in where angels fear to tread40 7#d;a7 ,obvert the following3 7#a7 8,all earnest teachers are diligent students40 7#b7 8,no self-respecting man can afford to be careless in his personal appearance40 7#c7 8,some of the great teachers of the past did not practice what they preached40 7#d7 8,some weeds are beautiful40 ,i determine first the logical character of each proposition1 finding the first to be an ,a1 the second an ,e1 the third an ,o and the fourth an ,i4 ,then ,i recall that in obversion the predicate must always be negated and an ,a must be changed to an ,e or an ,e to an ,a2 also an ,i must be changed to an ,o or an ,o to an ,i4 ,hence1 the obverse of each proposition is3 7#a7 8,no earnest teacher is a not-diligent student40 7#b7 8,all self-respecting men can afford to be not-careless 7careful7 in their personal appearance40 7#c7 8,some of the great teachers of the past did not-practice 7failed to practice7 what they preached40 7#d7 8,some weeds are not not-beautiful40 7#d;b7 ,infer by obversion from the following3 7#a7 8,all roses are beautiful40 7#b7 8,none of the members of the stock exchange are dishonest40 7#c7 8,some pupils are not industrious40 7#d7 8,some teachers are tactful40 7#e;a7 ,convert the following3 7#a7 8,all that glitters is not gold40 7#b7 8,all good men are wise40 7#c7 8,some books are to be chewed and digested40 7#d7 8,no man is perfectly happy40 ,it is first necessary to determine the logical character of each proposition4 ,carelessness might lead one to call the first proposition an ,a because it is introduced by the quantity sign 8all40 ,but on second thought we note that the meaning is to the effect that some glittering things are not gold2 this is an ,o4 ,it is clear that the second is an ,a1 the third an ,i and the fourth an ,e4 ,it is now expedient to recall the rules regarding conversion4 ,these are1 7#a7 do not distribute an undistributed term2 7#b7 do not change the quality4 ,we may now attempt to interchange the subject and predicate of each proposition1 with the following results3 7#a7 ,conversion impossible4 7#b7 8,some wise men are good men40 7#c7 8,some things to be chewed and digested are books40 7#d7 8,no perfectly happy being is a man40 ,when attempting to convert proposition 7#a71 ,i find that the subject which is undistributed becomes distributed1 hence the rule pertaining to distribution is violated4 ,this conclusion is verified by recalling the fact that an ,o proposition cannot be converted4 ,the second proposition1 being an ,a1 is converted by limitation2 while the third and fourth are converted simply1 as is the natural procedure with all ,i's and ,e's4 7#e;b7 ,convert these propositions3 7#a7 8,blessed are the meek40 7,all the meek are blessed47 7#b7 8,none but material bodies gravitate40 7,all gravitating bodies are material47 7#c7 8,gold is not a compound substance40 7#d7 8,usually cruel men are cowards40 ,,note4,the first proposition is poetical while the second is an exclusive4 7#f;a7 ,contravert the following propositions3 7#a7 8,all virtue is praiseworthy40 7#b7 8,some teachers are not tactful40 7#c7 8,a man who lies is not to be trusted40 ,contraversion consists in obverting first1 and then converting2 consequently1 the contraverse of the three propositions is as follows3 7#a7 8,no unpraiseworthy deed is virtue40 7#b7 8,some not-tactful persons are teachers40 7#c7 8,some untrustworthy men are those who lie40 7#f;b7 ,write the contraverse of the following3 7#a7 8,all honest men pay their debts40 7#b7 8,all men are rational40 7#c7 8,nearly all the troops have left the town40 7#d7 8,some teachers are not patient40 7#g;a7 ,the attending scheme indicates the logical process and rule involved in passing from one proposition to another3 ,a4 8,all men are imperfect40 ,process3 ,obversion4 ,rule3 ,negate predicate and change to ,e4 ,e4 8,no men are perfect40 ,process3 ,simple ,conversion4 ,rule3 ,interchange subject and predicate4 ,e4 8,no perfect beings are men40 ,process3 ,contraversion4 ,rule3 ,obvert and then convert4 ,i4 8,some not-men are perfect beings40 7#g;b7 ,treat in a manner similar to the above the proposition1 8,all horses are quadrupeds40 #h4 ,,review ,,questions4 7#a7 ,what is inference8 7#b7 ,what is the meaning of antecedent8 7#c7 ,define 7#a7 judging1 7#b7 a judgment4 7#d7 ,all roses are beautiful1 ,this flower is a rose1 ,this flower is beautiful4 ,write this example of mediate inference in equation form4 ,name the middle term4 7#e7 ,define immediate inference4 ,illustrate4 7#f7 ,define mediate inference4 ,illustrate4 7#g7 ,name the five forms of immediate inference4 7#h7 ,what principle is involved in inference by opposition8 7#i7 ,draw the scheme of opposition4 7#aj7 ,make use of this scheme in deriving inferences from the following propositions3 7a7 8,good men are wise40 7b7 8,no king is infallible40 7c7 8,cattle are ruminants40 7d7 8,all who cheat the railroads are not honest40 7#aa7 ,what are contradictory propositions8 ,illustrate4 7#ab7 ,what would be the simplest way of disproving the statement that 8,no great religious teacher has been consistent80 7#ac7 ,why are ,a and ,e said to be contrary propositions8 7#ad7 ,define obversion4 7#ae7 ,by what other name is obversion known8 7#af7 ,state the basic principle of obversion4 7#ag7 ,illustrate the process known as negating the predicate4 7#ah7 ,state the rule for obverting an ,a proposition4 7#ai7 ,obvert the following3 7#a7 8,all the boys in my room are industrious40 7#b7 8,honesty is the best policy40 7#c7 8,only the industrious are truly successful40 7#bj7 ,first state the rule and then obvert the following3 7#a7 8,some plants are biennial40 7#b7 8,planets are not suns40 7#c7 8,blessed are the merciful40 7#d7 8,these samples are not perfect40 7#ba7 ,define conversion4 7#bb7 ,state and illustrate the rules which condition the process of conversion4 7#bc7 ,convert1 if possible1 the following3 7#a7 8,some men practice sophistry40 7#b7 8,few men know how to live40 7#c7 8,some of the inhabitants are not civilized40 7#d7 8,all the world is a stage40 7#e7 8,none of my pupils failed40 7#f7 8,experience is a hard taskmaster40 7#bd7 ,why may co-extensive propositions be converted simply8 7#be7 ,describe the process of inference by contraversion4 #i4 ,,problems ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,what ground is there for the belief that immediate inference1 so called1 is merely a matter of the interpretation of propositions8 7#b7 ,is there any difference between reasoning and inference8 7#c7 ,when the conclusion is reached that two rooms are of the same width1 because each is five yards wide1 what is the middle term8 7#d7 ,put in equation form3 ,all teachers instruct1 ,john ,jones is a teacher1 ,john ,jones instructs4 ,show that the equations are not absolutely true4 7#e7 ,indicate the true relation between the subjects and predicates of the foregoing by using the algebraic signs and 4 7#f7 ,why cannot an ,a be derived from an ,i8 7#g7 ,why cannot an ,o be derived from an ,a8 7#h7 ,the basic principle of obversion is 8,two negatives are equivalent to one affirmative40 ,show by means of circles that this is not absolutely true2 take as an illustrative proposition1 8,no men are not mortal40 7#i7 ,show that agreeable and disagreeable are not contradictory terms4 7#aj7 ,why should the logician class individual propositions as universal8 7#aa7 ,show by circles that there is a difference in signification between1 8,some men are not wise0 and 8,some men are not-wise40 7#ab7 ,show by circles that the ,o proposition cannot be converted4 7#ac7 8,the ,i proposition cannot be contraverted40 ,make this clear4 7#ad7 ,is there any difference in meaning between1 8,all illogical work is unscholarly0 and 8,no illogical work is scholarly80 ,explain by circles4 7#ae7 ,state the logical process involved in passing from each proposition to its succeeding one3 7#a7 8,all men are imperfect40 7#b7 8,no men are perfect40 7#c7 8,no perfect beings are men40 7#d7 8,some not-men are perfect beings40 7#e7 8,some perfect beings are not-men40 7#f7 8,some perfect beings are not men40 7#af7 ,it is sometimes said that in sub-contraries there is really no opposition4 ,do you agree8 ,give arguments4 ,,chapter #aa4 ,,mediate ,,inference4 ,,the ,,syllogism4 #a4 ,,inference ,,and ,,reasoning4 ,inference has been defined as both a product and a process4 ,when used to indicate a process the term inference becomes synonomous with reasoning4 ,if logicians could agree to confine inference to the product and reasoning to the process1 it would remove an ambiguity which is more or less misleading4 ,but since this has not become the custom1 we shall use inference as indicating the process as well as the product4 ,definitions,middle ,term ,explained4 ,inference is the thought process of deriving a judgment from one or two antecedent judgments4 ,mediate inference is inference by means of a middle term4 ,reasoning of this nature involves three terms1 two of which are compared with a third or middle term1 and then related to each other to form a new judgment4 ,the middle term is the common unit1 or the standard by which the other terms are measured4 ,to illustrate3 ,if ,john and ,james are each six feet tall1 then plainly1 they are of the same height4 ,the standard1 or middle term1 is 8six feet tall40 #b4 ,,the ,,syllogism4 ,just as the judgment is expressed by means of the proposition1 so mediate inference is best expressed by means of the syllogism4#i ,the following are syllogisms3 7#a7 ,james is six feet tall1 ,john is six feet tall1 ,hence ,james is as tall as ,john4 7#b7 ,all true teachers are just1 ,you are a true teacher1 ,hence you are just4 7#c7 ,all men are mortal1 ,you are a man1 ,hence you are mortal4 #c4 ,,the ,,rules ,,of ,,the ,,syllogism4 ,all syllogistic reasoning is conditioned by the following eight rules3 7#a7 ,a syllogism must have three1 and only three1 different terms4 7#b7 ,a syllogism must have three1 and only three1 propositions4 7#c7 ,the middle term must be distributed at least once4 7#d7 ,no term must be distributed in the conclusion which is not also distributed in a premise4 7#e7 ,no conclusion can be drawn from two negative premises4 7#f7 ,if one premise be negative1 the conclusion must be negative2 and conversely1 to prove a negative conclusion1 one of the premises must be negative4 7#g7 ,no conclusion can be drawn from two particular premises4 7#h7 ,if one premise be particular1 the conclusion must be particular4 ,these rules are exceedingly important1 as their observance is necessary in all mediate reasoning4 ,the student needs1 not only to understand the meaning of these rules1 but he needs to commit them to memory so thoroughly that they may be recalled without hesitation or mistake4 ,to aid the memory1 the eight rules may be divided into these four groups3 ,i4 ,rules one and two relate to the composition of the syllogism4 ,,ii4 ,rules three and four pertain to the distribution of terms4 ,,iii4 ,rules five and six have reference to negative premises4 ,,iv4 ,rules seven and eight concern particular premises4 #d4 ,,rules ,,of ,,the ,,syllogism ,,explained4 7#a7 ,a syllogism must have three and only three terms4 ,it is common to represent the various syllogistic forms by symbols1 the same symbols always standing for the same terms4 ,in this treatment we shall let capital ,g stand for the major term1 as 8major0 means greater2 capital ,s for the minor term1 as 8minor0 means smaller1 and capital ,m for the middle term4 ,g1 ,s and ,m1 the initial letters of greater 7major71 smaller 7minor7 and middle1 will be the constant symbols for these terms2 just as ,a1 ,e1 ,i and ,o are used as the constant symbols for the four logical propositions4 ,illustration4 ,syllogism written in full3 ,all men are mortal1 ,socrates is a man1 7,therefore7 ,socrates is mortal4 ,syllogism symbolized3 ,all ,m is ,g ,s is ,m ,s is ,g ,the major term is always the predicate and the minor term the subject of the conclusion4 ,the conclusion of the foregoing syllogism is1 8,socrates is mortal40 ,since ,g stands for the predicate of every conclusion1 then it stands for 8mortal10 the predicate of the above conclusion4 ,for a similar reason1 ,s stands for the subject1 namely1 8,socrates02 while ,m represents the middle term1 8man40 ,since every syllogism must have three propositions1 and since it takes two terms to form a proposition1 then it follows that every syllogism must contain six terms4 ,but1 as no syllogism can have more than three different terms1 we conclude that each term of the syllogism must be used twice4 ,in the foregoing example1 ,g thus appears1 not only in the last proposition1 or conclusion1 but in the first proposition also4 ,similarly1 both ,s and ,m occur twice4 ,every logical syllogism1 then1 contains first1 a major term1 which is always the predicate of the conclusion and appears once in the premises2 second1 a minor term1 which is always the subject of the conclusion and appears once in the premises2 and third1 a middle term to which the other two terms are referred4 ,there are two ways of locating the middle term2 first1 it is the term which is used in both the premises2 second1 it is the term which never appears in the conclusion4 ,likewise1 there are two ways of locating the major and minor terms2 first1 the major term is always the predicate and the minor term the subject of the conclusion2 second1 the major term is usually the broader and the minor term the narrower of the two4 ,if the major and minor terms seem to be of about the same extension or breadth1 then the term in the first proposition1 which is not the middle term1 is the major4 ,in the attending syllogisms the three terms are designated3 7middle7 7major7 7#a7 ,all true teachers are sympathetic1 7minor7 7middle7 ,you are a true teacher1 7minor7 7major7 ,you are sympathetic4 7major7 7middle7 7#b7 ,no shell fish are vertebrates1 7minor7 7middle7 ,all trout are vertebrates1 7minor7 7major7 ,no trout are shell fish4 ,the necessity of having but three different terms in any syllogism may be understood by supposing that there are four different terms2 then it would follow that there could be no standard or common link4 ,in the axiom1 8,things equal to the same thing are equal to each other10 the same thing is the common standard or link4 ,two things which equal two different things are not equal to each other4 ,the impossibility of reasoning from four terms may be shown by circles4 ,all men are mortal4 ,all trees grow4 ,illustration3 ,,fig4 #h4 ,these circles show that no connection can be established between either group4 ,using four terms in any syllogism is known as the fallacy of four terms4 7#b7 ,a syllogism must have three and only three propositions4 ,the proposition containing the major term is called the major premise1 while the one containing the minor term is called the minor premise4 ,in a strictly logical syllogism the major premise is written first1 the minor premise second and the conclusion third4 ,in common parlance1 however1 the minor premise or even the conclusion may appear first4 ,the conclusion of a syllogism is always preceded by therefore1 or its equivalent1 which may be written or understood4 ,the premises always answer the question1 ,why is the conclusion true8 ,the premises are often preceded by such words as for and because4 ,the attending irregular syllogisms are arranged logically and the premises and conclusions indicated3 7#a;a7 ,illogical4 8,you must take an examination because all who enter the school are examined and you1 as ,i understand it1 are planning to enter40 7#b;a7 8,some of these books are not well bound1 for they are going to pieces as no well bound book would do40 7#a;b7 ,logical4 ,all who enter this school are examined1 ,major premise4 ,you are planning to enter this school1 ,minor premise4 ,you must be examined4 ,conclusion4 7#b;b7 ,no well bound book goes to pieces1 ,major premise4 ,some of these books are going to pieces1 ,minor premise4 ,some of these books are not well bound4 ,conclusion4 ,the fact that all syllogisms must have three and only three premises follows from rule 8#a40 ,one premise must compare the middle term with the 8major02 another premise must compare the middle term with the 8minor02 while the conclusion links together the 8major0 and the 8minor40 7#c7 ,the middle term must be distributed at least once4 ,the rule is usually given in this way1 8,the middle term must be distributed once at least1 and must not be ambiguous40 ,in this treatment the last part of the rule has been omitted because it must be apparent to the student that a middle term used in two senses is virtually equivalent to two different terms2 such an 8ambiguous middle0 would1 in consequence1 give a syllogism of four terms4 ,rules #c and #d are of greater importance than the others because they are more frequently violated4 ,if the middle term is not distributed at least once1 the fallacy is referred to as 8undistributed middle40 ,if the distributed major term of the conclusion is not distributed in the major premise1 then the fallacy is called1 8illicit process of the major term02 and finally1 if the distributed minor term of the conclusion is not distributed in the minor premise the fallacy is denominated an 8illicit process of the minor term40 ,these two illicit processes may be abbreviated to illicit major and illicit minor4 ,recall that any term is distributed when it is referred to as a definite whole4 ,unless the whole of the middle term is considered it fails to become a common standard of comparison4 ,this becomes clear when recourse is made to the circles4 ,illustration4 ,syllogism in which the middle term is not distributed3 ,all men are mortal1 ,all trees are mortal1 ,all trees are men4 ,all the propositions are ,a's and consequently the predicates of each are undistributed1 as ,a distributes the subject only4 ,therefore the middle term1 8mortal10 is not distributed in either of the premises and thus the fallacy4 ,fallacy shown by circles3 ,illustration3 ,,fig4 #i4 ,these circles indicate the correct meaning of the two premises4 ,by them it is seen that all of the 8men0 circle belongs to the 8mortal0 circle and all of the 8tree0 circle belongs to the 8mortal0 circle1 but in this case there is no connection between the 8men0 and 8tree0 circles4 ,thus1 to say that 8,all trees are men10 is fallacious4 ,we have no right to either affirm or deny the connection between men and trees4 ,if 8mortal0 were distributed we would have this right as the following will make clear3 ,all men are mortal1 ,no stones are mortal1 ,no stones are men4 ,illustration3 ,,fig4 #aj4 ,here the middle term mortal is distributed in the second premise as in it the subject 8stones0 is excluded from the entire mortal territory4 ,this conclusion is verified by the formal statement that 8,e0 distributes both subject and predicate4 ,since all of the 8men0 circle belongs to the 8mortal0 circle and none of the 8stones0 circle belongs to the 8mortal0 circle then none of the 8stones0 circle can belong to the 8men0 circle4 7#d7 ,no term must be distributed in the conclusion which is not also distributed in its premise4 ,it has been affirmed that a term is distributed when it is referred to as a definite whole4 ,to put it in another way1 a term is distributed when it is employed in its fullest sense4 ,it is obvious that we should not employ a term in its fullest sense in the conclusion when it has been used only in a partial sense in its premise4 ,what is said of the part cannot necessarily be said of the whole4 ,for example3 ,because some men are honest it does not follow that all men are honest4 ,of course the converse of this is true1 namely1 if it could be proved that all men are honest then surely it would follow that some of the men are honest4 ,to put it briefly3 ,what is true of all is true of some but what is true of some is not necessarily true of all4 ,to distribute a term in the conclusion when it is not distributed in the premise where it occurs is equivalent to saying1 8what is true of some is true of all40 ,this error which violates rule 8#d0 leads to the two fallacies of illicit process of the major and minor terms4 ,the following illustrate the two fallacies4 ,syllogism illustrating illicit major3 ,all trees grow1 ,no men are trees1 ,no men grow4 ,the first premise is an ,a and consequently its subject is distributed4 ,the second premise and conclusion being ,e's have both subject and predicate distributed4 ,thus grow1 as used in the conclusion1 is distributed1 but1 as used in the major premise1 it is not distributed4 ,fallacy shown by circles3 ,illustration3 ,,fig4 #aa4 ,here all of the 8tree0 circle belongs to the 8grow0 circle and none of the 8men0 circle belongs to the 8tree0 circle1 hence the diagram correctly represents the meaning of the two premises and shows the fallacy of concluding that no men grow4 ,the 8men0 circle1 being entirely within the 8grow0 circle1 indicates that all men grow4 ,syllogism illustrating illicit minor3 ,all true teachers are just1 ,all true teachers are sympathetic1 ,all the sympathetic are just4 ,each proposition being an ,a distributes its subject4 ,but the subject of the conclusion which is 8the sympathetic0 is not distributed in the minor premise1 as an ,a proposition distributes its subject only4 ,hence the fallacy of illicit minor4 ,fallacy shown by circles3 ,illustration3 ,,fig4 #ab4 ,the diagram correctly represents the two premises since all of the 8true teacher0 circle belongs to both the 8just0 and 8sympathetic0 circles4 ,but all of the 8sympathetic0 circle does not belong to the 8just0 circle4 ,hence the fallacy4 7#e7 ,no conclusion can be drawn from two negative premises4 ,when two terms are both denied of a third term1 it is quite impossible to draw any conclusion relative to the two terms1 as the absolute exclusion of the third term eliminates any possibility of a common link or standard4 ,the circles will make this apparent3 ,no men are immortal1 ,no trees are immortal1 ,illustration3 ,,fig4 #ac4 8,no trees are men0 is the conclusion represented by ,fig4 #ac4 ,other possible conclusions are1 8,all trees are men10 8,all men are trees0 and 8,some men are trees40 ,it is thus seen that no definite conclusion can be drawn4 ,it may now be said that when the major and minor terms are used in two negative premises the connection between them is indeterminate4 ,this violation of rule 8#e0 may be termed the fallacy of two negatives4 7#f7 ,if one premise be negative the conclusion must be negative2 and conversely1 to prove a negative conclusion one of the premises must be negative4 ,referring to the first part of this rule1 it may be said of two terms that if one is affirmed and the other denied of a third term1 then the two terms must be denied of each other4 ,the attending syllogism and its 8circled0 representation will throw light upon this3 ,no men are immortal1 ,all ,americans are men1 ,no ,americans are immortal4 ,illustration3 ,,fig4 #ad4 ,since none of the 8men0 circle belongs to the 8immortal0 circle and all of the 8,american0 circle is inside the 8men0 circle1 it is evident that none of the 8,american0 circle can belong to any part of the 8immortal0 circle4 ,thus it is manifest that an affirmative conclusion like1 8,all ,americans are immortal10 is invalid4 ,the converse of rule #f1 8,to prove a negative conclusion1 one of the premises must be negative10 may be explained by the general principle in logic that when two terms are known to disagree1 one must agree with a third term while the other must disagree4 ,if both agreed with a third1 then the conclusion would of necessity be affirmative4 ,if both disagreed no conclusion could be drawn4 ,a violation of rule #f may be called the fallacy of negative conclusion4 7#g7 ,no conclusion can be drawn from two particular premises4 ,proof3 7#a7 ,all the possible combinations of the two particular premises ,i and ,o are1 7#a7 ,,io1 7#b7 ,,oi1 7#c7 ,,ii1 7#d7 ,,oo4 8,,io0 considered4 7#b7 ,since ,o is a negative premise the conclusion would have to be negative according to rule #f4 7,if one premise is negative1 the conclusion must be negative47 7#c7 ,if the conclusion is negative1 then its predicate1 which is the major term1 must be distributed4 7,all negative propositions distribute their predicates47 7#d7 ,if the major term is distributed in the conclusion1 it must be distributed in the major premise1 rule #d4 7,no term must be distributed in the conclusion1 which is not also distributed in one of the premises47 7#e7 ,hence two terms must be distributed in the premises1 the major term according to 7#d7 and the middle term according to rule #c4 7#f7 ,but ,i distributes neither term and ,o distributes its predicate only2 ,i and ,o together1 then1 distribute but one term4 7#g7 ,to draw a negative conclusion the premises must distribute two terms1 the middle and the major1 according to the foregoing4 7#h7 ,hence a conclusion from ,i and ,o is untenable4 ,the same may be said of 8,,oi40 8,,ii0 considered4 7#a7 ,the ,i proposition distributes neither subject nor predicate1 hence the premises 8,,ii0 would distribute no term4 7#b7 ,but the middle term must be distributed at least once according to rule #c4 7#c7 ,therefore no conclusion can be drawn from 8,,ii40 ,a valid conclusion from 8,,oo0 is impossible according to rule #e4 7#h7 ,if one premise be particular the conclusion must be particular4 ,proof3 ,the possible combinations conditioned by rule #h are ,,ai1 ,,ao1 ,,ei1 ,,eo1 ,,io1 ,,ii1 ,,oo4 8,,ai0 considered4 7#a7 ,proposition ,a distributes its subject1 proposition ,i neither2 hence 8,,ai0 together distribute but one term4 7#b7 ,according to rule #c this one term must be the middle term4 7#c7 ,the minor term must1 therefore1 be undistributed in the minor premise1 and in consequence undistributed in the conclusion4 7#d7 ,but this undistributed minor term is the subject of the conclusion2 hence said conclusion must be particular1 as only particulars have an undistributed subject4 8,,ao0 and 8,,ei0 considered4 ,proof3 7#a7 8,,ao0 distribute two terms2 so do 8,,ei40 7#b7 ,both 8,,ao0 and 8,,ei0 must have negative conclusions according to rule #f4 7#c7 ,a negative conclusion distributes its predicate which is the major term4 7#d7 ,the major term and the middle term must be distributed in the premises4 ,rules #d and #c4 7#e7 ,thus the third term1 which is the minor1 cannot be distributed in the minor premise and1 consequently1 the minor cannot be distributed in the conclusion4 7#f7 ,this necessitates a particular conclusion4 ,premises ,,eo and ,,oo1 being negative1 cannot yield a conclusion according to rule #e2 similarly1 neither can the particulars ,,io and ,,ii because of rule #g4 #e4 ,,the ,,dictum ,,of ,,aristotle4 ,aristotle gives an axiom on which all syllogistic inference is based4 ,indeed from this fundamental principle the significant rules of the syllogism could be derived4 ,the dictum is stated in this wise3 8,whatever is predicated1 whether affirmatively or negatively1 of a term distributed may be predicated in the manner of everything contained under it40 ,the following statements represent various ways of explaining this dictum3 7#a7 ,whatever is said of a term used in its fullest sense may likewise be said of that term when used only in a partial sense4 7#b7 ,what is true of the whole is true of the part4 7#c7 8,what pertains to the higher class pertains also to the lower40 ,since this dictum is the basic principle underlying the important rules of the syllogism1 it is unnecessary to dwell longer upon it2 because an explanation of the rules is1 virtually1 an explanation of the dictum4 #f4 ,,canons ,,of ,,the ,,syllogism4 ,the dictum of ,aristotle is ostensibly a self-evident truth1 and some logicians have put this truth in the form of three axiomatic statements which are known as the canons of the syllogism4 ,these are as follows3 7#a7 8,two terms agreeing with one and the same third term agree with each other40 7#b7 8,two terms of which one agrees and the other does not agree with one and the same third term1 do not agree with each other40 7#c7 8,two terms both disagreeing with one and the same third term may or may not agree with each other40 ,making use of the symbols as explained on a previous page of this chapter1 it will be seen that the first canon conforms to this syllogistic type3 ,all ,m is ,g ,all ,s is ,m ,all ,s is ,g ,the two terms are ,s and ,g1 while ,m is the third term4 ,the attending symbolizations illustrate1 respectively1 the second and third canons3 ,no ,m is ,g ,all ,s is ,m ,no ,s is ,g ,no ,m is ,g ,no ,s is ,m ,conclusion indeterminate4 #g4 ,,three ,,mathematical ,,axioms4 ,analogous to the three canons treated in 8#f10 there are certain mathematical axioms which are here stated3 7#a7 8,things equal to the same thing are equal to each other40 7#b7 8,one thing equal to and the other thing not equal to the same third thing are not equal to each other40 7#c7 8,things not equal to the same thing may or may not equal each other40 ,illustrations of the three axioms3 7#a7 ,if x equals #e1 and y equals #e1 then x equals y4 7#b7 ,if x equals #e1 and y does not equal #e1 then x does not equal y4 7#c7 ,if x does not equal #e1 and y does not equal #e1 then x may or may not equal y4 #h4 ,,outline4 ,,mediate ,,inference4 7#a7 ,inference and reasoning4 ,definitions4 ,middle term explained4 7#b7 ,the analogy between the judgment and the syllogism4 7#c7 ,rules of the syllogism given4 ,eight in number4 7#d7 ,rules of the syllogism explained3 ,rule #a4 ,syllogistic symbols4 ,major1 minor1 and middle terms2 how found4 ,fallacy of four terms4 ,rule #b4 ,major and minor premises and conclusion1 how determined4 ,logical arrangement4 ,reason for three propositions4 ,rule #c4 ,reason for omitting 8ambiguous middle0 from rule4 ,undistributed and distributed middle explained4 ,rule #d4 ,illicit major and minor explained and illustrated4 ,rule #e4 ,fallacy of two negatives4 ,rule #f4 ,fallacy of negative conclusion4 ,rule #g4 ,fallacy of two particulars4 ,rule #h4 ,fallacy of particular conclusion4 7#e7 ,aristotle's dictum4 7#f7 ,canons of the syllogism4 7#g7 ,mathematical axioms4 #i4 ,,summary4 7#a7 ,inference is a term used to denote a process as well as a product4 ,as a process reasoning and inference are in reality synonomous terms4 ,inference is a thought process of deriving a judgment from one or two antecedent judgments4 ,mediate inference is inference by means of a middle term4 ,mediate inference makes use of three terms1 two of which are compared with a third term as a standard4 ,this third term is called the middle term4 7#b7 ,the syllogism is the common mode of expression for mediate inference4 7#c7 ,valid syllogistic reasoning is conditioned by eight rules4 ,the first and second relate to the composition of the syllogism2 the third and fourth to the distribution of terms2 the fifth and sixth to negative premises2 the seventh and eighth to particular premises4 7#d7 ,all syllogisms must have three terms3 the major1 the minor1 and the middle4 ,the middle term occurs twice in the premises but never appears in the conclusion4 ,the minor term is always the subject1 and the major term the predicate of the conclusion4 ,the major term is usually broader than the minor4 ,no conclusion can be drawn from four terms4 ,to attempt this gives rise to the fallacy of four terms4 ,all syllogisms must have three propositions1 the major and the minor premises1 and the conclusion4 ,the major premise first and the minor second is the more logical arrangement1 although the common conversational form is to use the minor premise first4 ,ambiguous middle amounts to the fallacy of four terms4 ,unless the middle term is distributed at least once in the syllogism1 it fails to become a common standard4 ,distributing a term in the conclusion1 without its being distributed in its premise1 is equivalent to asserting that1 8,what is true of a part is true of the whole40 ,this error results in the fallacies of illicit major and minor4 ,a conclusion from two negatives is impossible1 because of the total exclusion of the middle term4 ,of two terms1 if one is affirmed and the other denied of a third term1 then they must be denied of each other2 and1 conversely1 if two terms are to be denied of each other1 one must be affirmed and the other denied of a given third term4 ,this fundamental principle necessitates deriving a negative conclusion from two premises when one is negative4 ,it1 likewise1 compels the converse of this4 ,a valid conclusion from two particulars is untenable because of the two negative fallacies1 or some fallacy relative to the distribution of terms4 ,one particular premise forces a particular conclusion because of the fallacies of two negatives1 two particulars1 and illicit minor4 7#e7 ,aristotle's dictum simplified means1 8,what is true of the whole is true of the part40 7#f7 ,the canons of the syllogism1 three in number1 are3 7#a7 8,two terms agreeing with one and the same third term agree with each other40 7#b7 8,two terms of which one agrees and the other does not agree with one and the same third term do not agree with each other40 7#c7 8,two terms both disagreeing with one and the same third term may or may not agree with each other40 7#g7 ,the foregoing canons may be stated as mathematical axioms4 #aj4 ,,illustrative ,,exercises4 7#a;a7 ,make use of the proper symbols and indicate the three terms of each of the attending syllogisms3 7#a7 ,all fixed stars twinkle1 ,vega is a fixed star1 ,vega twinkles4 7#b7 ,all men are rational beings1 ,no tree is a rational being1 ,no trees are men4 7#c7 ,all good citizens are law abiding1 ,all good citizens vote1 ,some who vote are law abiding4 ,i recall that the three terms are the middle1 the major and the minor1 and that the 8middle0 does not occur in the conclusion1 whereas the 8major0 is always the predicate and the 8minor0 the subject of the conclusion4 ,the symbols ,m1 ,g and ,s being the initial letters of middle1 greater and smaller1 ,i make use of these in designating the three terms1 as the following will illustrate3 ,m ,g 7#a7 ,all fixed stars twinkle1 ,s ,m ,vega is a fixed star1 ,s ,g ,vega twinkles4 8,twinkles0 being the predicate of the conclusion is designated as being the major term by putting the letter ,g above it4 ,then 8,g0 is placed above the term 8twinkle0 in the first premise4 8,s0 is placed above the subject of the conclusion to indicate that it is the minor term4 8,s0 is also placed above 8,vega10 the minor term1 as found in the second premise4 ,the remaining term1 8fixed stars10 must be the middle term1 therefore ,i place 8,m0 above it4 ,the fact that 8fixed star0 does not occur in the conclusion verifies this4 ,using only the symbols1 the syllogism takes this form3 ,all ,m is ,g ,s is ,m ,s is ,g ,using the symbols to represent the other syllogisms1 we have 7#b7 ,all ,g is ,m ,no ,s is ,m ,no ,s is ,g 7#c7 ,all ,m is ,g ,all ,m is ,s ,some ,s is ,g 7#a;b7 ,indicate by symbols the three terms of the following syllogisms3 7#a7 ,no trees are men1 ,all rational beings are men1 ,no rational being is a tree4 7#b7 ,all men have the power of speech1 ,you are a man1 ,you have the power of speech4 7#c7 ,some men are wise1 ,all men are rational1 ,some rational beings are wise4 7#b;a7 ,illustrate by syllogism the fallacy of undistributed middle4 ,an easy way is to use the middle term as the predicate of two ,a premises4 ,this yields the fallacy because an ,a proposition does not distribute the predicate4 ,the illustration3 distributed terms underscored4 ,all true teachers are students1 ,all scholars are students1 ,all scholars are true teachers4 7#b;b7 ,give two illustrations of undistributed middle4 7#c;a7 ,give syllogistic illustrations of the fallacies of illicit major and minor4 ,illicit ,major4 ,use the middle term as the subject of an ,a proposition1 and then as the predicate of an ,e proposition4 ,this would necessitate a negative conclusion in which the major term is distributed4 ,but the major term is not distributed in the major premise1 hence the fallacy4 ,illustration in which the distributed terms are underscored3 ,all men are mortal1 ,no trees are men1 ,no trees are mortal4 ,illicit ,minor4 ,to illustrate this fallacy one may use the middle term as the subject of two ,a premises4 ,this would give an ,a conclusion in which the subject is distributed4 ,but this same term is not distributed in its premise because here it is used as the predicate of an ,a4 ,illustration3 ,all earnest students study1 ,all earnest students desire to succeed1 ,all who desire to succeed study4 #aa4 ,,review ,,questions4 7#a7 ,distinguish between inference and reasoning4 7#b7 ,define inference4 ,mediate inference4 7#c7 ,illustrate the difference between mediate and immediate inference4 7#d7 ,explain by illustration the use of the middle term4 7#e7 ,exemplify the syllogism4 7#f7 ,state the rules of the syllogism4 7#g7 ,from the attending syllogisms select the three terms3 7#a7 ,all patriotic citizens vote1 ,you are a patriotic citizen1 ,you should vote4 7#b7 ,no honest man would misrepresent1 7but7 ,john ,smith did misrepresent1 ,john ,smith is not honest4 7#h7 ,symbolize the foregoing syllogisms4 7#i7 ,illustrate by syllogisms the fallacy of four terms4 7#aj7 ,indicate by circles that a valid conclusion cannot be drawn from four terms4 7#aa7 ,why must a syllogism have three and only three propositions8 7#ab7 ,indicate how the three propositions of an argument may be designated4 ,what is the logical arrangement8 7#ac7 ,show that an ambiguous middle amounts to a fallacy of four terms4 7#ad7 ,explain and illustrate undistributed middle1 illicit major1 illicit minor4 7#ae7 ,exemplify the fallacies of question 8#ad0 by using circles4 7#af7 ,explain by circles why a conclusion cannot be drawn from two negatives4 7#ag7 ,make clear that a negative conclusion must follow1 if one premise be negative4 7#ah7 ,state and explain the principle which underlies the rule1 8,if the conclusion is negative one premise must be negative40 7#ai7 ,prove by the process of elimination that no conclusion can be drawn from two particulars4 7#bj7 ,in a way similar to that of question 8#ai0 show that if one premise be particular the conclusion must be particular4 7#ba7 ,state and explain ,aristotle's dictum4 7#bb7 ,state the canons of the syllogism4 7#bc7 ,symbolize and explain by circles the three canons4 7#bd7 ,illustrate the three mathematical axioms which the canons suggest4 #ab4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,give an illustration of a valid conclusion being drawn from four terms4 7#b7 ,explain by circles the foregoing4 7#c7 ,from three different business transactions1 select the middle term of comparison4 7#d7 ,why should not those who are given to much which is argumentative1 speak in syllogistic terms8 7#e7 8,he is a man of high ideals1 and you know him to be strictly honest1 therefore you have no excuse for not voting for him40 ,recast this quotation with a view of making a logical syllogism4 7#f7 ,show by circles that there may be a vital difference between a syllogism of three terms and an equation of three terms4 7#g7 ,indicate by illustration that in conversational argumentation the minor premise naturally comes first4 7#h7 ,show by circles the meaning of 8indeterminate conclusion40 7#i7 ,rule five states that no conclusion can be drawn from two negatives4 ,defend this rule in connection with the following syllogism1 which seems to contain a valid conclusion3 ,any statement which is not true cannot be accepted1 ,this statement is not true1 ,it cannot be accepted4 7#aj7 ,if the conclusion is particular1 must one premise be particular8 ,explain4 ,,chapter #ab4 ,,figures ,,and ,,moods ,,of ,,the ,,syllogism4 #a4 ,,the ,,four ,,figures ,,of ,,the ,,syllogism4 ,by a figure of a syllogism is meant some particular arrangement of the three terms in the two premises4 ,the conclusion is eliminated from this discussion1 because in it the arrangement of the terms is constant1 the major term always being used as the predicate of the conclusion and the minor as the subject4 ,using the symbols ,m1 ,g and ,s1 we find that there are four possible arrangements and1 therefore1 but four figures4 ,these may be represented as follows3 ,first ,second ,third ,fourth figure figure figure figure ,m ,g ,g ,m ,m ,g ,g ,m ,s ,m ,s ,m ,m ,s ,m ,s ,s ,g ,s ,g ,s ,g ,s ,g ,no matter what the syllogism1 if it is to be proved 8logical10 it should be made to fit one of the four figure-types4 ,to be sure1 it may fit the figure without being logical1 but it cannot be strictly logical without fitting the figure4 ,the following valid syllogisms conform to the four figures as will be seen by the symbolized terms3 ,m ,g ,first figure3 ,all men are mortal1 ,s ,m ,socrates is a man1 ,s ,g ,socrates is mortal4 ,m ,g ,s ,m ,s ,g ,g ,m ,second figure3 ,all good citizens love their country1 ,s ,m ,no criminal loves his country1 ,s ,g ,no criminal is a good citizen4 ,g ,m ,s ,m ,s ,g ,m ,g ,third figure3 ,all good citizens are law abiding1 ,m ,s ,all good citizens vote1 ,s ,g ,some who vote are law abiding4 ,m ,g ,m ,s ,s ,g ,g ,m ,fourth figure3 ,some teachers are fair minded1 ,m ,s ,all who are fair minded are just1 ,s ,g ,some just persons are teachers4 ,g ,m ,m ,s ,s ,g ,here1 then1 are the types that represent all the syllogisms which mediate inference may use4 ,logic recognizes no other4 ,since every successful student of logic must be familiar with the four figures1 the following may be used as a suggestive aid to reproducing the figures at will3 ,first4 ,it is easy for any one to remember this syllogism3 ,all men are mortal1 ,socrates is a man1 ,socrates is mortal4 ,in fact1 it comes down to us from the time of ,aristotle1 and is therefore a patriot of many generations to whom the faithful should touch their hats4 ,let us1 then1 be ready to reproduce this syllogism with automatic precision1 since it will enable us to know at once the position of the terms in the first figure4 ,second4 ,converting the terms of the major premise of the first figure gives the second figure1 as1 e4 g43 ,first figure4 ,second figure4 ,m ,g 7,convert7 ,g ,m ,s ,m ,s ,m ,s ,g ,s ,g ,third4 ,converting the terms of the minor premise of the first figure gives the third figure1 as1 e4 g43 ,first figure4 ,third figure4 ,m ,g ,m ,g ,s ,m 7,convert7 ,m ,s ,s ,g ,s ,m ,fourth4 ,converting the terms of both the major and minor premises of the first figure gives the fourth1 as1 e4 g43 ,first figure4 ,fourth figure4 ,m ,g 7,convert7 ,g ,m ,s ,m 7,convert7 ,m ,s ,s ,g ,s ,g ,to summarize3 ,the second1 third and fourth figures may be derived from the first4 ,converting the major premise of the first figure gives the second figure2 converting the minor premise gives the third figure2 and converting both premises gives the fourth figure4 #b4 ,,the ,,moods ,,of ,,the ,,syllogism4 ,by the mood of a syllogism is meant some particular arrangement of the propositions which compose the syllogisms4 8,mood0 stands for an arrangement of the propositions1 while 8figure0 represents an arrangement of the terms in any syllogism4 ,combining any three of the four logical propositions gives a mood1 as1 e4 g41 7#a7 ,e 7#b7 ,a 7#c7 ,e ,a ,i ,i ,e ,i ,o are moods4 ,the first one has an ,e proposition for the major premise1 an ,a for the minor and an ,e for the conclusion4 ,this syllogism represents the first mood given above3 ,e ,no men are trees1 ,a ,all ,americans are men1 ,e ,no ,americans are trees4 ,it would not be difficult to determine by actual experiment1 just how many moods could be formed1 and of these1 how many would admit of valid conclusions4 ,it may be seen that there are sixty-four permutations of the four logical propositions1 taken three at a time4 ,these are in part3 7#a7 7#b7 7#c7 7#d7 7#e7 7#f7 7#g7 7#h7 ,a ,a ,a ,a ,a ,a ,a ,a ,a ,a ,a ,a ,e ,e ,e ,e ,a ,e ,i ,o ,a ,e ,i ,o 7#i7 7#aj7 7#aa7 7#ab7 7#ac7 7#ad7 7#ae7 7#af7 ,a ,a ,a ,a ,a ,a ,a ,a ,i ,i ,i ,i ,o ,o ,o ,o ,a ,e ,i ,o ,a ,e ,i ,o ,and so the permutations could be continued4 ,substituting ,e for the major premise of the above group would give another group of sixteen1 while a like substitution of ,i and ,o would result in two more groups1 sixteen in each4 ,this gives sixty-four in all4#aj #c4 ,,testing ,,the ,,validity ,,of ,,the ,,moods4 ,in order to put the moods to good use1 it is necessary to ascertain which ones yield a valid conclusion in any figure4 ,if each were valid in all of the four figures1 there would be #bef4 ,but it is obvious that such is not the case4 ,referring to the sixteen permutations given above1 we find that the 8negative-conclusion0 rule makes invalid #b1 #d1 #e1 #g1 #aj1 #ab1 #ac and #ae2 whereas the rule for particulars throws out #i and #ad4 ,this leaves the following as the probable valid moods in one or more of the figures3 #a1 #c1 #f1 #h1 #aa1 #af4 ,but to be certain of this the investigation must be ,a continued4 ,the mood ,a has stood the test of the rules for negative and ,a particular conclusions2 now let us test this mood from the standpoint of the distribution of terms1 using it in all four figures3 ,first ,second ,third ,fourth ,a ,m ,g ,g ,m ,m ,g ,g ,m ,a ,s ,m ,s ,m ,m ,s ,m ,s ,a ,s ,g ,s ,g ,s ,g ,s ,g ,as an ,a proposition distributes its subject only1 we underscore the subject of each proposition in all the figures4 7,this underscoring is a simple way to indicate distribution47 ,we now find that the mood is valid in the first figure1 because the middle term is distributed at least once2 namely1 in the major premise1 and there is no term distributed in the conclusion which is not already distributed in the premise where it occurs4 ,on the other hand1 the mood ,a ,a is invalid in the second1 because of 8undistributed middle10 and ,a invalid in the third and fourth1 because ,s is distributed in the conclusion but not distributed in the premise where it occurs 7illicit minor74 ,let us try ,,aii in the four figures3 ,a ,m ,g ,g ,m ,m ,g ,g ,m ,i ,s ,m ,s ,m ,m ,s ,m ,s ,i ,s ,g ,s ,g ,s ,g ,s ,g ,we underscore the subject of the ,a proposition in each of the four figures4 ,as ,i distributes neither subject nor predicate1 no other term ,a should be underscored4 ,it is now evident that ,i is not valid in figures ,i two and four1 because in both figures the middle term is undistributed 7undistributed middle74 ,in a like manner all the other moods might be tested4 ,logicians1 who have done this1 have found #bd to be valid4 ,five of these have weakened conclusions2 i4 e41 a particular conclusion when it could just as well ,a be universal4 ,e illustrates this as the conclusion could be ,e4 ,this ,o syllogism exemplifies the weakened conclusion3 ,a ,all trees grow1 ,e ,no sticks are trees1 ,o ,some sticks do not grow4 ,this conclusion is true1 since 8some0 means 8some at least40 ,yet the conclusion is weak1 because there is nothing to interfere with the broader and stronger conclusion that1 8,no sticks grow40 ,there are1 therefore1 only #ai valid and serviceable moods4 ,these are as follows3 7#a7 7#b7 7#c7 7#d7 7#e7 7#f7 ,a ,e ,a ,e ,first figure ,a ,a ,i ,i #d ,a ,e ,i ,o ,e ,a ,a ,e ,second figure ,a ,e ,o ,i #h ,e ,e ,o ,o ,a ,i ,a ,e ,o ,e ,third figure ,a ,a ,i ,a ,a ,i #ad ,i ,i ,i ,o ,o ,o ,a ,a ,i ,e ,e ,fourth figure ,a ,e ,a ,a ,i #ai ,i ,e ,i ,o ,o ,a ,of these nineteen moods it is not much of a tax to remember that ,a is ,a ,e valid only in the first figure2 whereas ,a is valid in the first and ,e ,a ,e second figures2 ,i in the first and third2 while ,i is valid in all4 ,this ,i ,o knowledge1 however1 should be used only as one would employ the answers in arithmetic4 ,testing the validity of a mood in the four figures is an exceedingly valuable thought-exercise1 which a knowledge of the final result might easily vitiate4 ,it is1 no doubt1 best to test the value of any mood without such knowledge1 and then compare the result by referring to the foregoing list of valid moods4 ,it is not always wise to work with the answer in mind1 yet it is most satisfying to know of a certainty that one's reasoning has led to a truth which others have verified4 #d4 ,,special ,,canons ,,of ,,the ,,four ,,figures4 ,as a deductive exercise in clear1 logical thought1 the indirect proof involved in establishing certain principles underlying the four figures1 is of immense value4 ,on no account should this section be omitted4 ,the mere fact that it appears to be a difficult section is proof positive that the student is in need of just such exercises4 ,canons of the first figure4 7#a7 ,the minor premise must be affirmative4 7#b7 ,the major premise must be universal4 ,problem3 ,the minor premise must be affirmative4 ,data3 ,given the form of the first figure1 which is1 ,m ,g ,s ,m ,s ,g ,proof3 7#a7 ,if the minor premise is not affirmative then it must be negative2 because affirmative and negative propositions1 being contradictory in nature1 admit of no middle ground4 7#b7 ,if the minor premise is negative1 the conclusion must be negative2 for the reason that a negative premise necessitates a negative conclusion4 7#c7 ,if the conclusion is negative then its predicate1 ,g1 must be distributed2 since all negatives distribute their predicates4 7#d7 ,if the predicate of the conclusion1 which is the major term1 is distributed1 then it must be distributed in the premise where it occurs1 which is the major premise2 for any term which is distributed in the conclusion must be distributed in the premise where it occurs4 7#e7 ,if the major term1 which is the predicate of the major premise1 is distributed1 then the major premise must be negative2 because only negatives distribute their predicates4 7#f7 ,the result of this argument1 then1 gives two negative premises1 and we know from rule #c that a conclusion from two negatives is untenable4 7#g7 ,since the minor premise cannot be negative1 it must be affirmative4 ,problem3 ,to prove that the major premise must be universal4 ,data3 ,given the form of the first figure3 ,m ,g ,s ,m ,s ,g ,proof3 7#a7 ,the predicate of the minor premise1 ,m1 which is the middle term1 is undistributed2 because no affirmative proposition distributes its predicate4 7#b7 ,the middle term must be distributed in the major premise2 since in any syllogism the middle term must be distributed at least once4 7#c7 ,as the middle term1 ,m1 used as the subject of the major premise1 must be distributed1 then the major premise must be universal2 because only universals distribute their subjects4 ,epitome4 ,in the first figure1 the minor premise must be affirmative1 since making it negative necessitates making the major premise negative also2 the major premise must be universal in order to distribute the middle term at least once4 ,special canons of the second figure4 7#a7 ,one premise must be negative4 7#b7 ,the major premise must be universal4 ,problem3 ,to prove that one premise must be negative4 ,data3 ,given the form of the second figure3 ,g ,m ,s ,m ,s ,g ,proof3 7#a7 ,the middle term1 ,m1 is the predicate of both premises4 7#b7 ,the middle term must be distributed at least once1 according to rule #c4 7#c7 ,hence one premise must be negative2 since only negatives distribute their predicates4 ,problem3 ,to prove that the major premise must be universal4 ,data3 ,given the form of the second figure3 ,g ,m ,s ,m ,s ,g ,proof3 7#a7 ,as one premise must be negative1 it follows that the conclusion must be negative according to rule #f4 7#b7 ,if the conclusion is negative1 then its predicate1 ,g1 the major term1 must be distributed2 since all negatives distribute their predicates4 7#c7 ,when distributed in the conclusion1 the major term1 ,g1 must also be distributed in the major premise1 where it is used as the subject4 ,see rule #d4 7#d7 ,hence the major premise must be universal2 for only universals distribute their subjects4 ,epitome4 ,in the second figure one premise must be negative in order to distribute the middle term at least once2 and the major premise must be universal that the major term1 which is distributed in the conclusion1 may be distributed in the premise where it occurs4 ,canons of the third figure4 7#a7 ,the minor premise must be affirmative4 7#b7 ,the conclusion must be particular4 ,problem3 ,to prove that the minor premise must be affirmative4 ,data3 ,given the form of the third figure1 which is1 ,m ,g ,m ,s ,s ,g ,proof3 7#a7 ,suppose the minor premise were negative1 then the conclusion would have to be negative1 and this would distribute the predicate ,g4 7#b7 ,a distributed predicate would necessitate its being distributed in the major premise4 7#c7 ,but ,g1 being the conclusion of the major premise1 could be distributed only by a negative proposition4 7#d7 ,this would result in two negatives2 therefore no conclusion could be drawn1 if the minor premise were negative4 ,problem3 ,to prove that the conclusion must be particular4 ,data3 ,given the form of the third figure3 ,m ,g ,m ,s ,s ,g ,proof3 7#a7 ,the minor term1 which is the predicate of the affirmative minor premise1 is undistributed2 because no affirmative distributes its predicate4 7#b7 ,if undistributed in the premise1 then the minor term must remain undistributed in the conclusion1 where it is used as the subject4 7#c7 ,the conclusion must1 then1 be particular2 since all universals distribute their subjects4 ,epitome4 ,in the third figure1 unless the minor premise be affirmative1 there can be no conclusion2 since a negative minor would necessitate a negative major4 ,an affirmative minor compels a particular conclusion1 in order that the minor term1 in the conclusion1 may remain undistributed4 ,canons of the fourth figure4 7#a7 ,if the major premise is affirmative1 the minor premise must be universal4 7#b7 ,if the minor premise is affirmative1 the conclusion must be particular4 7#c7 ,if either premise is negative1 the major must be universal4 ,problem3 ,to prove that if the major is affirmative1 the minor must be universal4 ,data3 ,given the form of the fourth figure3 ,g ,m ,m ,s ,s ,g ,proof3 7#a7 ,if the major premise is affirmative1 then its predicate which is the middle term1 ,m1 is undistributed2 for no affirmative distributes its predicate4 7#b7 ,the middle term must then be distributed in the 8minor0 according to rule #c4 7#c7 ,then the 8minor0 must be universal2 since only universals distribute their subjects4 ,problem3 ,to prove that if the minor is affirmative1 the conclusion must be particular4 ,data3 ,given the form of the fourth figure3 ,g ,m ,m ,s ,s ,g ,proof3 7#a7 ,if the minor premise be affirmative1 then ,s1 its predicate1 must be undistributed2 because no affirmative distributes its predicate4 7#b7 ,since ,s is undistributed in the minor premise1 it must remain undistributed in the conclusion where it is used as the subject4 ,problem3 ,to prove that if either premise is negative1 the major must be universal4 ,data3 ,given the form of the fourth figure3 ,g ,m ,m ,s ,s ,g ,proof3 7#a7 ,if one of the premises is negative1 then the conclusion must be negative according to rule #f4 7#b7 ,if the conclusion is negative1 then the predicate1 ,g1 must be distributed4 7#c7 ,if ,g is distributed in the conclusion1 it must be distributed in the major premise4 7#d7 ,the major premise must be universal2 as ,g is used as its subject1 and only universals distribute their subjects4 ,epitome4 ,in the fourth figure1 if the 8major0 is affirmative1 the 8minor0 must be universal in order to distribute the middle term4 ,if the minor is affirmative1 the conclusion must be particular2 otherwise the fallacy of illicit minor would result4 ,if either premise is negative1 the major must be universal to avoid the fallacy of illicit major4 #e4 ,,special ,,canons ,,related4 ,after a particular mood has been tested in the regular way1 it has been intimated that the student may refer to the tabulated list of valid moods to ascertain1 with a certainty1 the validity of his reasoning4 ,this is equivalent to referring to the answers in arithmetic2 for if the student is unable to find the mood in the figure in which he has proved it valid1 then he knows that he has made some mistake in his reasoning4 ,a second check1 though not absolute1 is to recall the special canons of section four4 ,if1 for example1 our reasoning has led ,a us to believe that ,e is valid in the first figure1 we may recall that ,e the minor premise of the first figure must be affirmative and therefore ,,aee cannot be valid4 ,a few suggestions relative to memorizing the special canons may not be out of place4 ,the two canons of the first figure must be committed1 and then it may be remembered that the second figure is the negative figure of logic4 ,other figures may yield a negative conclusion1 but the second must yield a negative conclusion4 ,since a negative conclusion necessitates a negative premise1 it follows that the second figure must always appear with one premise negative4 ,the other canon which pertains to the major premise is the same as the 8major premise0 canon of the first figure4 ,the third figure is the particular figure of logic4 ,other figures may yield particular conclusions1 but the third must do so4 ,this helps us to remember the canon that the conclusion of the third figure must be particular4 ,the other canon which relates to the minor premise is the same as the 8minor premise0 canon of the first figure4 ,the canons of the fourth figure are in reality a summary of the canons of the other three figures4 #f4 ,,mnemonic ,,lines4 ,as a device for remembering the #ai valid moods1 the logicians of an earlier day originated a combination of coined words which1 though rather unscientific1 may be easily committed to memory4 ,since1 however1 it is of much more value to test the moods by means of the general rules of the syllogism than it is to try to remember these moods1 the mnemonic lines are of slight value4 ,they are treated here merely as an item of historical interest4 7#a7 ,barbara1 ,celarent1 ,darii1 ,ferioque prioris2 7#b7 ,cesare1 ,camestres1 ,festino1 ,baroko1 secund2 7#c7 ,tertia1 ,darapti1 ,disamis1 ,datisi1 ,felapton1 ,bokardo1 ,ferison1 habet2 ,quarta insuper addit 7#d7 ,bramantip1 ,camenes1 ,dimaris1 ,fesapo1 ,fresison4 ,the only letters in these lines which mean nothing are l1 n1 r1 t and small b and d2 all the others have a signification4 ,for example1 the vowels of the italicized words signify the various valid moods1 as e4 g41 the first line indicates the moods ,,aaa1 ,,eae1 ,,aii1 ,,eio4 ,the ,latin words1 printed in ordinary type1 are intended to make evident that the moods indicated by the artificial italicized words of the first line1 belong to the first figure2 that the moods of the next four words1 belong to the second figure2 while the third figure includes the next six1 and the fourth figure the last five4 ,it is now seen that ,festino1 for example1 stands for that mood of the second figure which has an ,e for its major premise1 an ,i for its minor premise1 and an ,o for its conclusion4 ,the first figure was called by ,aristotle the perfect figure1 whereas the second and third were the imperfect figures4 ,the fourth figure was given no place in the works of ,aristotle2 its discovery is credited to ,galen1 a celebrated teacher of medicine of the second century4 ,according to ,aristotle1 the first figure is the most serviceable and the most convincing and1 therefore1 as a final test of their validity1 the moods of the other figures should be changed to the first4 ,this process in logic is termed ,reduction4 ,in this reduction of the imperfect figures to the perfect1 the capital letters of the artificial words1 together with s1 p1 m1 and k1 have a definite meaning4 ,the capital letters indicate that certain moods of the imperfect figures can be reduced to the corresponding moods of the first figure2 e4 g41 ,festino 7eio7 of the second figure1 ,felapton 7eao7 of the third figure1 and ,fesapo 7eao7 of the fourth figure may all be reduced to ,ferio 7eio7 of the first figure4 ,this is known because ,f is the initial letter of each word4 s signifies that the proposition denoted by the preceding vowel is to be converted simply4 ,to illustrate3 s ,e in ,fesapo means that the major premise ,e of the mood ,a of the fourth ,o figure must be converted simply in order to change the mood to ,ferio of the first figure4 p indicates that the proposition represented by the vowel which precedes p must be converted by limitation 7per accidens74 m 7mutare7 makes evident that the premises are to be interchanged1 the major of the old becoming the minor of the new1 and the minor of the old becoming the major of the new4 k denotes that the mood1 such as ,baroko1 must be reduced by a special process known as indirect reduction4 ,these directions may now be followed as illustrative of the process of reduction4 ,a 7#a7 ,given3 ,a syllogism in ,darapti ,a ,i ,m ,g ,a ,all true teachers are just1 ,m ,s ,a ,all true teachers are sympathetic1 ,s ,g ,i ,some sympathetic persons are just4 ,a ,the symbols indicate that the mood is ,a or is in ,darapti and that this ,i mood is used in the third figure4 ,a ,problem3 ,to reduce ,a of the third figure to some mood of the first ,i figure4 ,process3 ,d1 being the initial letter of ,darapti1 suggests that its mood must be reduced to one indicated by a word of the first figure ,a whose initial letter is ,d4 ,this mood is in ,darii1 or is ,i4 ,i ,the p in ,darapti indicates that the proposition represented by the preceding vowel must be converted by limitation4 ,this proposition is the minor premise2 converting it by limitation gives3 8,some sympathetic persons are true teachers40 ,as there are no other significant letters the reduction is complete and we have this3 ,m ,g ,a ,all true teachers are just1 ,s ,m ,i ,some sympathetic persons are true teachers1 ,s ,g ,i ,some sympathetic persons are just4 ,a ,the symbolization indicates that the mood is ,i of the first figure1 or ,i is in ,darii4 ,a 7#b7 ,given3 ,a syllogism in ,camestres ,e ,e ,g ,m ,a ,all true teachers are just1 ,s ,m ,e ,no one who shows partiality is just1 ,s ,g ,e ,no one who shows partiality is a true teacher4 ,the symbols show that the mood is ,,aee of the second figure or in ,camestres4 ,judging from the initial letter ,c1 the mood in ,camestres ,e must be reduced to the mood in ,celarent ,a4 ,e ,the letter m between a and e indicates that the major and minor premises of the given syllogism must be interchanged4 ,the letters following both e's suggest that the minor premise and the conclusion of the syllogism must be converted simply4 ,this is the resulting syllogism3 ,m ,g ,e ,no just person shows partiality1 ,s ,m ,a ,all true teachers are just persons1 ,s ,g ,e ,no true teacher shows partiality4 ,e ,here1 then1 is the ,a of the first figure or the mood in ,celarent4 ,e ,according to the ancient theory1 reduction is necessary as a matter of final and absolute proof that the conclusion follows from the given premises4 ,but1 as this claim has been satisfactorily refuted by modern logicians1 we need not give more space to the process4 ,the meaning of k1 as related to 8indirect reduction10 is explained in most of the earlier works on logic4 ,see ,hyslop1 page #aic4 #g4 ,,relative ,,value ,,of ,,the ,,four ,,figures4 ,the first figure4 ,the first figure is known as the perfect figure2 because it is the only one which proves all of the four logical propositions4 ,recalling the moods of the first figure makes this evident3 ,a ,e ,a ,e ,a ,a ,i ,i ,a ,e ,i ,o ,it is likewise the more natural figure2 because it is the only one which uses both the subject and predicate of the conclusion in the same relative places as they appear in the premises4 ,symbolizing the figure makes this apparent3 ,m ,g ,s ,m ,s ,g ,the first figure1 being the only figure which proves a 8universal affirmation0 7,a71 is used most by the scientist2 as the object of science is to establish universal affirmative truths4 ,the second figure4 ,as the second figure conditions negative conclusions only1 it is called the figure of disproof1 or the exclusive figure4 ,it is easy to see how negative conclusions may be used to narrow the inquiry down to one definite theory4 ,for example1 suppose it is desired to ascertain which boy of the five broke the window2 by a series of deductions the teacher may be able to prove that the culprit is not ,a1 not ,b1 not ,c and not ,d2 hence the guilty one must be ,e4 ,this figure is virtually the one used in diagnosing most diseases4 ,the third figure4 ,the third figure admits of particular conclusions only1 and in consequence is of little value to the scientist4 ,since1 however1 the easiest way to contradict a universal affirmative 7,a7 or a universal negative 7,e71 is to prove the truth1 respectively1 of a particular negative 7,o7 and a particular affirmative 7,i71 it follows that the third figure serves a purpose4 ,the fourth figure4 ,this figure is so nearly like the first that it is of little value2 in fact1 it may be changed to the first by simply interchanging the major and minor premises4 ,some authorities refuse to recognize the fourth figure4 #h4 ,,outline4 ,,figures ,,and ,,moods ,,of ,,the ,,syllogism4 7#a7 ,the four figures of the syllogism4 ,definitionsymbolization4 ,illustrationsdevice for remembering4 7#b7 ,the moods of the syllogism4 ,twenty-four valid4 7#c7 ,testing the validity of the moods4 ,application of the general rules of the syllogism4 ,weakened conclusionfive4 ,nineteen useful moods4 ,a thought exercise4 7#d7 ,special canons of the four figures4 ,proof of the two canons of the first figure4 ,proof of the two canons of the second figure4 ,proof of the two canons of the third figure4 ,proof of the three canons of the fourth figure4 7#e7 ,special canons related4 ,used as checks4 7#f7 ,mnemonic lines4 ,their use explained4 ,reduction4 7#g7 ,relative value of the four figures4 #i4 ,,summary4 7#a7 ,by a syllogistic figure is meant some particular arrangement of the three terms in the two premises4 ,this arrangement yields four figures which are designated by the position of the middle term4 ,to be logical1 any syllogism must conform to one of the four figures4 ,the first figure is suggested by the position of the terms of the 8,socrates is mortal0 syllogism4 ,the second is derived by converting the major premise of the first2 while the third figure results from converting the minor premise of the first1 and the fourth by converting both major and minor of the first4 7#b7 ,by a mood of a syllogism is meant some particular arrangement of the propositions which compose it4 ,there are #fd moods but only #bd are valid4 7#c7 ,the validity of the various moods may be tested by applying to them the rules of the syllogism4 ,no mood is valid if it violates any one of the eight rules4 ,a 8weakened conclusion0 is a particular conclusion which could just as well be universal4 ,of the #bd valid moods five have weakened conclusions4 ,this leaves but #ai useful moods4 ,testing the validity of the various moods in the four figures is a most valuable thought exercise4 7#d7 ,the deductive exercise involved in establishing certain special canons of the four figures is of immense value and should not be omitted4 ,in the first figure it may be proved 7#a7 that the minor premise must be affirmative2 since making it negative necessitates making the major premise negative1 and no conclusion can be drawn from two negatives2 7#b7 that the major premise must be universal in order to distribute the middle term at least once4 ,in the second figure it may be proved 7#a7 that one premise must be negative in order to distribute the middle term2 7#b7 that the major premise must be universal in order to distribute its subject1 which is distributed in the negative conclusion where it appears as the predicate4 ,in the third figure it may be proved 7#a7 that the minor premise must be affirmative in order to prevent the 8two negative0 fallacy2 7#b7 that an affirmative minor necessitates a particular conclusion1 because the minor term in the conclusion must remain undistributed4 ,in the fourth figure it may be proved 7#a7 that if the major is affirmative1 the minor must be universal in order to distribute the middle term2 7#b7 that if the minor is affirmative1 the conclusion must be particular in order to avoid committing the fallacy of illicit minor2 7#c7 that if either premise is negative1 the major must be universal to avoid the fallacy of illicit major4 7#e7 ,a knowledge of the special canons is helpful in that it may be used to check fallacious reasoning4 7#f7 ,certain mnemonic lines were used by the ,schoolmen as an aid in recalling the nineteen valid moods1 and also as a suggestive device to aid in the process known as ,reduction4 ,the process of reduction is merely a matter of changing to the first figure the moods of the other figures4 ,this process is no longer thought to be necessary4 7#g7 ,the first figure1 called the perfect figure1 is the one used most by scientists1 as it is the only figure which proves a universal affirmative truth4 ,the second figure is the negative1 or figure of disproof1 and is used mainly for the purpose of eliminating all the conditions of the inquiry save one4 ,the third figure serves a purpose in affording an easy way to contradict a universal assertion2 this is the figure of particulars4 ,the fourth figure1 because it so closely resembles the first1 is of little value4 #aj4 ,,illustrative ,,exercises4 ,question #a;a4 ,by making use of the rules for negatives and particulars1 ,o ,a ,a test the validity of the following moods3 ,i ,i ,a ,a ,a ,i ,answer3 ,the first mood has the negative ,o as its major premise1 and the affirmative ,a as its conclusion2 the mood is thus invalid2 because a negative premise necessitates a negative conclusion according to rule #f4 ,the second mood contains the particular proposition ,i as its minor premise1 and thus should have a particular conclusion according to rule #h4 ,but the conclusion ,a is universal and1 therefore1 the mood is invalid4 ,the premises of the third mood are universal and the conclusion particular4 ,the mood1 however1 is valid1 because rule #h does not work both ways1 as does rule #f4 ,when a universal can just as well be drawn1 then the particular becomes a weakened conclusion4 7#a;b7 ,using the rules for negatives and particulars1 test the validity ,a ,e ,e of the following3 ,a ,o ,a ,e ,o ,o 7#b;a7 ,paying no regard to 8figure10 derive as many conclusions as possible from the following sets of premises3 ,e ,a ,i ,e ,answer3 ,e4 ,the major premise of this mood1 being negative1 ,i necessitates a negative conclusion1 according to rule #f1 and the minor premise1 being particular1 compels a particular conclusion1 according to rule #h4 ,since the conclusion must be negative and particular1 then ,e ,o is the only one which can be drawn4 ,the completed mood is ,i4 ,o ,a4 ,this mood must have a negative conclusion1 because the minor ,e premise is negative2 this would necessitate either ,e or ,o2 but ,o as a conclusion would be1 in this case1 a weakened one2 since ,e distributing both terms would necessarily distribute the minor2 which fact would permit the minor to be distributed in the conclusion4 ,thus the conclusion could just as well be universal as particular4 ,the ,a completed mood is ,e4 ,e 7#b;b7 ,from the following sets of premises derive as many conclusions as possible paying no attention to figure3 ,e ,a ,o ,a ,a ,a 7#c;a7 ,making use of all the general rules of the syllogism1 test the ,a validity of the following mood in all the figures3 ,a4 ,i ,answer3 #a #b #c #d ,a ,m ,g ,g ,m ,m ,g ,g ,m ,a ,s ,m ,s ,m ,m ,s ,m ,s ,i ,s ,g ,s ,g ,s ,g ,s ,g ,an underscored symbol indicates a distributed term4 ,since ,a distributes its subject1 the subjects of both premises are underscored in all the figures4 ,no term is underscored in the conclusions2 since ,i distributes neither term4 ,in the first figure the middle term is distributed in the major premise1 and no term is distributed in the conclusion4 ,since both premises are affirmative1 the rules for negatives are not applicable2 and as a particular may be drawn from two universals1 if there is no violation of the rules for distribution1 this mood seems to be valid in the first figure4 ,it is1 however1 a weakened conclusion2 since an ,a could just as well be drawn4 ,the mood is invalid in the second figure because of undistributed middle1 but valid in both the third and fourth2 since in both cases the middle term is distributed at least once4 7#c;b7 ,determine the validity of the attending moods in all the figures ,i ,a ,e giving reasons3 ,a ,o ,a4 ,i ,o ,o #aa4 ,,review ,,questions4 7#a7 ,define a logical figure and illustrate by means of some ordinary syllogistic argument4 7#b7 ,symbolize the four figures and give suggestions for remembering them4 7#c7 ,write syllogisms which illustrate each of the four figures4 7#d7 ,define mood as it is used in logic4 ,illustrate4 7#e7 ,how many moods are valid8 7#f7 ,explain by illustration a 8weakened conclusion40 ,a ,e 7#g7 ,test the validity of ,e in the third figure2 of ,i in the third4 ,e ,o 7#h7 ,independent of all helps1 prove the truth of the canons of the first figure4 7#i7 ,in a similar way prove the canons of the second1 third and fourth figures4 7#aj7 ,so far as testing arguments is concerned1 what use may be made of the special canons of the syllogism8 7#aa7 ,offer a few suggestions for remembering the special canons4 7#ab7 ,why did ,aristotle attach so much importance to reduction in logic8 7#ac7 ,justify calling the first figure the 8perfect figure10 and the others the 8imperfect figures40 7#ad7 ,treat of the relative value of the four figures4 7#ae7 ,show by illustration that the second figure is the exclusive figure4 ,e ,o ,i 7#af7 ,test the following moods in all the figures3 ,i ,a ,a ,a ,o ,i ,a ,e ,e ,a ,a ,e ,a ,a ,a ,e ,i ,a ,e ,i ,e ,o ,a ,i4 ,o ,o ,o ,o ,e ,i ,i ,i ,i #ab4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,give an illustration of a syllogism in the fourth figure which might just as well be written in the first figure4 7#b7 ,may a syllogism1 which is invalid in the fourth figure1 be made valid by writing it in the form of the first figure8 ,prove it4 7#c7 ,show why it is impossible to apply all the rules of the 999999 7#d7 ,show the difference between a direct and an indirect proof4 ,a 7#e7 ,show that ,a is valid in the first figure when the major premise ,o 7,a7 is co-extensive4 7#f7 ,the third figure is known as the figure of particular conclusions4 ,why should not the second canon of that figure be1 8,one premise must be particular0 rather than 8,the conclusion must be particular80 7#g7 ,show that there is some ground for thinking that1 as a final test1 moods in the other figures should be reduced to the first4 7#h7 ,illustrate the fact that the second figure is the figure of disproof2 whereas the third is the figure of contradictions4 7#i7 8,to be logical a syllogism must conform to one of the four figures1 but this does not mean1 necessarily1 that all arguments must conform to some figure40 ,explain this4 ,,chapter #ac4 ,,incomplete ,,syllogisms ,,and ,,irregular ,,arguments4 #a4 ,,enthymeme4 ,an enthymeme is a syllogism in which one of the three propositions is omitted4 ,suppressing the major premise gives an enthymeme of the first order2 whereas if the minor premise be suppressed1 the enthymeme becomes one of the second order2 while omitting the conclusions gives an enthymeme of the third order4 ,illustrations3 ,complete syllogism4 ,all true teachers are just1 ,you are a true teacher1 7,hence7 ,you are just4 ,enthymeme of first order2 major premise omitted4 44444444444444444444444444 ,you are a true teacher1 7,hence7 ,you are just4 ,enthymeme of second order2 minor premise omitted4 ,all true teachers are just1 44444444444444444444444444 7,hence7 ,you are just4 ,enthymeme of the third order2 conclusion omitted4 ,all true teachers are just1 7,and7 ,you are a true teacher1 44444444444444444444444444 ,to argue in terms of the complete syllogism is the unusual1 not the usual method4 ,we have a way of abbreviating our remarks2 expressing only the necessary and leaving the obvious to be taken for granted4 ,thus the enthymeme becomes the natural form of expression4 ,but the mere fact that a part of the argument is omitted1 makes it more essential for the student to think clearly and with careful continuity1 that no error may intrude itself4 ,probably the most common enthymemes are those of the first order4 ,this may be explained by the fact that the major premise is usually the most universal of the three propositions1 and1 in consequence1 the one which would be the most generally understood4 ,the following represent enthymemes of this order1 gleaned from the ordinary conversation of ordinary people3 7#a7 8,your beets won't grow1 because you are planting them in the wrong time of the moon40 7#b7 8,you1 being a member of the ,sunday ,school1 should be ashamed of such language40 7#c7 8,being the son of your father1 you ought to have some pride in this matter40 7#d7 8,we are going to have an open winter1 because ,i have observed that the hornets' nests are near the ground40 7#e7 8,you had better put in lots of coal1 for ,i have noticed that the squirrels have gathered in more nuts than usual40 ,judging from these enthymemes1 it would seem to be more natural to assert the conclusion and follow this by a reason in the form of a minor premise1 leaving the major to the intelligence of the auditor4 ,the enthymeme of the second order occurs only infrequently1 since it seems to be an unnatural mode of expression1 though sometimes it appears to lend emphasis to the conclusion2 e4 g41 8,all untrustworthy boys come to a bad end1 and ,i predict that you will come to a bad end40 ,enthymemes of the third order are commonly used for the sake of emphasis1 as the following make evident3 7#a7 8,no business man wants an indolent boy1 and you are indolent40 7#b7 8,all successful teachers are interested in their work1 and you plan to be a successful teacher40 7#c7 8,humility is a sign of greatness1 and ,lincoln possessed this quality40 #b4 ,,epicheirema4 ,an epicheirema is a syllogism in which one or both of the premises is an enthymeme4 ,to put it in another way3 ,an epicheirema is a syllogism in which one or both of the premises is supported by a reason4 ,when one premise is an enthymeme the syllogism is termed a single epicheirema2 whereas when both premises are enthymemes it becomes a double epicheirema4 ,single epicheirema4 ,all men are mortal1 because all men die1 ,socrates was a man1 ,socrates was mortal4 ,double epicheirema4 ,all men are mortal1 because all men die1 ,socrates was a man1 because he was a rational animal1 ,socrates was mortal4 ,it is obvious that supporting each premise with a reason lends strength to the argument4 ,this justifies the use of the epicheirema4 #c4 ,,polysyllogism4 ,a polysyllogism is a series of syllogisms in which the conclusion of a preceding syllogism becomes a premise of a succeeding one4 ,the syllogism in the series whose conclusion becomes a premise of the succeeding syllogism is termed a prosyllogism2 while the syllogism which uses as one of its premises the conclusion of the preceding syllogism is called an episyllogism4 ,illustrations4 ,a quadruped is an animal1 ,a dog is a quadruped1 ,prosyllogism ,polysyllogism ,a dog is an animal4 ,fido is a dog1 ,episyllogism ,fido is an animal4 ,all who libel an associate are unprofessional1 ,this teacher has libelled ,prosyllogism her associate1 ,polysyllogism ,this teacher is unprofessional4 ,all who are unprofessional ,episyllogism should be disciplined1 ,this teacher should be disciplined4 #d4 ,,sorites4 ,a sorites is a series of syllogisms in which all of the conclusions are omitted except the last one4 ,just as the epicheirema is a combination of enthymemes of the first and second orders1 so the sorites is a combination of enthymemes of the third order4 ,if each conclusion were written1 the sorites would take the form of prosyllogisms and episyllogisms4 ,two forms of the sorites are recognized by logicians4 ,these are the progressive or ,aristotelian1 and the regressive or ,goclenian4 ,illustrations4 ,progressive ,symbolized4 ,put in ,word ,form4 ,all ,a is ,b ,thomas ,arnold was a teacher1 ,all ,b is ,c ,a teacher is a man1 ,all ,c is ,d ,a man is a biped1 ,all ,d is ,e ,a biped is an animal1 ,hence all ,a is ,e ,hence ,thomas ,arnold was an animal4 ,regressive ,all ,a is ,b ,a biped is an animal1 ,all ,c is ,a ,a man is a biped1 ,all ,d is ,c ,a teacher is a man1 ,all ,e is ,d ,thomas ,arnold was a teacher1 ,hence all ,e is ,b ,hence ,thomas ,arnold was an animal4 ,when regarded from the viewpoint of extension1 the progressive sorites proceeds from the smaller to the larger while the regressive is the converse of this4 ,the point may be illustrated by circles3 ,illustration3 ,,fig4 #ae4 ,circle #a stands for ,thomas ,arnold4 ,circle #b stands for teacher4 ,circle #c stands for man4 ,circle #d stands for biped4 ,circle #e stands for animal4 ,the progressive sorites proceeds from the smaller circle to the larger1 thus3 ,all of circle #a belongs to #b ,all of circle #b belongs to #c ,all of circle #c belongs to #d ,all of circle #d belongs to #e ,hence1 ,all of circle #a belongs to #e ,the regressive sorites proceeds from the larger to the smaller2 i4 e43 ,all of circle #d belongs to #e ,all of circle #c belongs to #d ,all of circle #b belongs to #c ,all of circle #a belongs to #b ,hence1 ,all of circle #a belongs to #e ,other differences become apparent when the omitted conclusions are expressed4 ,progressive ,symbolized ,word ,form ,all ,a is ,b ,t4 ,arnold was a teacher1 7,a7 ,all ,b is ,c ,a teacher is a man1 7,a7 ,all ,a is ,c ,t4 ,arnold was a man4 7,a7 ,all ,c is ,d ,a man is a biped1 7,a7 ,all ,a is ,d ,t4 ,arnold was a biped4 7,a7 ,all ,d is ,e ,a biped is an animal1 7,a7 ,all ,a is ,e ,t4 ,arnold was an animal4 7,a7 ,in the three completed syllogisms it becomes evident that the progressive sorites uses the minor as its first premise and in consequence takes the form of the fourth figure1 though the reasoning is according to the first figure4 ,the progressive sorites must conform to the following rules3 7#a7 ,the first premise may be universal or particular1 all the others must be universal4 7#b7 ,the last premise may be affirmative or negative2 all the others must be affirmative4 ,a violation of the first rule would result in undistributed middle2 whereas a violation of the second rule would give illicit major4 ,these rules may be illustrated by giving attention to the symbols of the foregoing completed syllogisms4 ,the first completed syllogism of the sorites is3 ,all ,a is ,b ,all ,b is ,c ,all ,a is ,c ,securing a logical arrangement by interchanging the major and minor premises gives3 7,m7 7,g7 7,a7 ,all ,b is ,c 7,first premise universal7 7,s7 7,m7 7,a7 ,all ,a is ,b 7,s7 7,g7 7,a7 ,all ,a is ,c ,applying the rules we find this syllogism valid1 or we may recall that ,a ,a is valid in the first figure4 ,a ,let us now make the first premise of the sorites particular and test4 ,some ,a is ,b ,all ,b is ,c ,some ,a is ,c ,arranged logically3 7,m7 7,g7 7,a7 ,all ,b is ,c 7,s7 7,m7 7,i7 ,some ,a is ,b 7,s7 7,g7 7,i7 ,some ,a is ,c ,proof3 ,since one premise is particular the conclusion must be particular4 7,rule #g7 ,as there are no negatives in the argument1 only one conclusion is possible2 namely1 a particular affirmative 7,i74 ,thus1 instead of the conclusion1 8,all ,a is ,c10 which is an 7,a71 it must be1 8,some ,a is ,c10 or an 7,i74 ,underscoring the distributed term1 it is seen that the middle term is distributed in the major premise and that no term is distributed in the conclusion4 ,thus the mood is valid4 ,this is 8checked0 when we recall that ,,aii is always valid in the first figure4 ,we have now shown that the first premise of a progressive sorites may be universal or particular4 ,let us further proceed to prove that all the other premises must be universal4 ,data3 ,given the first completed syllogism of the sorites3 ,all ,a is ,b ,all ,b is ,c ,all ,a is ,c ,proof3 ,let any other premise1 such as the second1 be particular2 this gives the following3 ,all ,a is ,b ,some ,b is ,c ,some ,a is ,c ,arranged logically3 ,mood1 figure1 and distribution indicated4 7,m7 7,g7 7,i7 ,some ,b is ,c 7,s7 7,m7 7,a7 ,all ,a is ,b 7,s7 7,g7 7,i7 ,some ,a is ,c ,we note at once that the middle term is undistributed1 hence the ,i mood ,a is invalid in the first figure2 reference to the valid moods in ,i figure one 8checks0 this conclusion4 ,since no premise1 other than the first1 can be particular1 then all save the first must be universal4 ,the truth of the first rule has been demonstrated1 and now we may follow a similar plan to prove the truth of the second rule4 ,problem3 ,to prove that the last premise may be negative4#aa ,data3 ,given the last completed syllogism3 ,all ,a is ,d ,all ,d is ,e ,all ,a is ,e ,let us make the last premise negative 7,e7 and test the result4 7,as all but the first must be universal we cannot use an ,o47 ,all ,a is ,d ,no ,d is ,e ,no ,a is ,e ,arranged logically and symbolized3 7,m7 7,g7 7,e7 ,no ,d is ,e 7,s7 7,m7 7,a7 ,all ,a is ,d 7,s7 7,g7 7,e7 ,no ,a is ,e ,proof3 ,negative premise2 negative conclusion4 ,no particulars4 ,middle term distributed in major premise4 ,no term distributed in conclusion which is not distributed in premise where it occurs4 ,syllogism valid4 ,we must now prove that all the other premises must be affirmative4 ,problem3 ,to prove that no other premise can be negative1 or that all others must be affirmative4 ,data3 ,given last syllogism of sorites with the first premise negative4 7,any other may be taken47 ,no ,a is ,d ,all ,d is ,e ,no ,a is ,e ,arranged logically and symbolized3 7,m7 7,g7 7,a7 ,all ,d is ,e 7,s7 7,m7 7,e7 ,no ,a is ,d 7,s7 7,g7 7,e7 ,no ,a is ,e ,proof3 8,g0 is distributed in the conclusion but not in the major premise4 ,fallacy of illicit major4 ,hence no other premise can be negative4 ,we may now consider the completed syllogisms of the regressive sorites4 ,all ,a is ,b ,all ,c is ,a ,all ,c is ,b ,all ,d is ,c ,all ,d is ,b ,all ,e is ,d ,all ,e is ,b ,by examining the foregoing it becomes apparent that the regressive sorites1 both in form and in the reasoning1 adapts itself to the first figure4 ,the rules of the regressive sorites are just the reverse of the progressive4 ,these are3 7#a7 ,the first premise may be negative2 all the others must be affirmative4 7#b7 ,the last premise may be particular2 all the others must be universal4 ,it would be a valuable exercise for the student to test these rules according to the plan pursued in treating the progressive sorites4 #e4 ,,irregular ,,arguments4 ,it has been intimated that a syllogistic argument1 in order to be logical1 should be made to conform to the rules of the syllogism4 ,it must not be inferred from this1 however1 that all deductive reasoning is included by the logical forms here treated4 ,there seem to be arguments which yield valid conclusions1 and yet which are not logical in the strict sense of the word4 ,the following illustrate some of these forms3 7#a7 ,quantitative ,arguments4 ,john is taller than ,james1 ,albert is taller than ,john1 ,albert is taller than ,james4 ,here1 apparently1 is a fallacy of four terms3 these four terms are 7#a7 ,john1 7#b7 taller than ,james1 7#c7 ,albert1 7#d7 taller than ,john4 ,yet we know that the argument is valid4 ,there is not a particle of doubt in the mind relative to the truth of the conclusion that 8,albert is taller than ,james40 ,we are consequently forced to the inference that such quantitative arguments lie outside the field of syllogistic reasoning4 ,the argument involves this new principle1 8,whatever is greater than a second thing which is greater than a third thing is itself greater than a third thing40 ,there are many other arguments similar to this which are not syllogistic in nature4 ,to wit3 ,a equals ,b1 ,b equals ,c1 ,c equals ,d2 ,a equals ,d4 ,a is a brother of ,b1 ,b is a brother of ,c1 ,c is a brother of ,d2 ,a is a brother of ,d4 ,a is west of ,b1 ,b is west of ,c1 ,c is west of ,d2 ,a is west of ,d4 7#b7 ,plurative ,arguments4 ,these are arguments in which the propositions are introduced by more or most2 e4 g43 ,most 7more than half7 of the team are seniors1 ,most 7at least half7 of the team are under twenty1 ,some students under twenty are seniors4 ,i ,here we have an ,i which is evidently valid4 ,no term distributed and yet ,i the conclusion is unquestionably true4 ,this is due to the fact that the propositions are so worded as to force an overlapping of the major and minor terms4 ,the student may illustrate this relation by circles4 #f4 ,,outline4 ,,incomplete ,,syllogisms ,,and ,,irregular ,,arguments4 7#a7 ,enthymeme4 ,first1 second and third orders4 ,natural form4 7#b7 ,epicheirema4 ,single1 double4 7#c7 ,polysyllogism4 ,prosyllogism1 episyllogism4 7#d7 ,sorites4 ,progressive1 regressive4 ,two rules of each4 7#e7 ,irregular ,arguments4 ,quantitative1 plurative4 #g4 ,,summary4 7#a7 ,an enthymeme is a syllogism in which one of the three propositions is omitted4 ,suppressing the major premise gives an enthymeme of the first order2 omitting the minor gives one of the second order2 while omitting the conclusion gives one of the third order4 ,the enthymeme is really the natural form of expression4 ,enthymemes of the first order are the most common while those of the third order are the most emphatic4 7#b7 ,an epicheirema is a syllogism in which one or more of the premises is an enthymeme4 ,an epicheirema is said to be single when but one premise is an enthymeme1 and double when both premises are enthymemes4 7#c7 ,a polysyllogism is a series of syllogisms in which the conclusion of the preceding syllogism becomes a premise of the succeeding one4 ,the one of the series whose conclusion becomes a premise is termed a prosyllogism2 while the one which uses the conclusion as a premise is called an episyllogism4 7#d7 ,a sorites is a series of syllogisms in which all the conclusions are omitted except the last one4 ,the two kinds of sorites are the progressive and regressive4 ,the progressive uses the 8minor0 as its first premise and adopts the form of the fourth figure1 whereas the regressive uses the 8major0 as its first premise and adopts the form of the first figure4 ,the two rules of the progressive sorites are1 7#a7 8,the first premise may be particular1 all the others must be universal02 7#b7 8,the last premise may be negative1 all the others must be affirmative40 ,the two rules of the regressive are1 7#a7 8,the first premise may be negative1 all the others must be affirmative02 7#b7 8,the last premise may be particular1 all the others must be universal04 7#e7 ,irregular arguments are such as yield valid conclusions and yet do not conform to the syllogistic rules4 ,the quantitative argument expresses quantity and contains four terms4 ,this argument is based on the principle1 8,what ever is greater than a second thing which is greater than a third thing is itself greater than a third thing40 ,plurative arguments are introduced by 8more0 or 8most0 and give in consequence a valid conclusion from two particulars4 ,this is due to the overlapping of the major and minor terms4 #h4 ,,review ,,questions4 7#a7 ,define and illustrate an enthymeme4 7#b7 ,illustrate the enthymemes of the three orders and point out their distinct uses4 7#c7 ,why should the enthymeme demand closer thought than the ordinary syllogism8 7#d7 ,define and illustrate the epicheirema4 7#e7 ,of what use is the epicheirema8 ,illustrate4 7#f7 ,define and illustrate a prosyllogism and an episyllogism4 7#g7 ,why are polysyllogisms so called8 7#h7 ,define and illustrate the sorites4 7#i7 ,relate the sorites and the epicheirema to the enthymeme4 7#aj7 ,illustrate the two forms of sorites4 7#aa7 ,explain the two forms of sorites by means of a diagram4 7#ab7 ,prove the truth of the two rules of the progressive sorites4 7#ac7 ,illustrate two kinds of irregular arguments and show that they are valid4 7#ad7 ,complete the five enthymemes of page #bdh and indicate their mood and figure4 #i4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,why should enthymemes of the second order be less common than those of the first8 7#b7 ,you desire to make it evident to a child that a small beginning often leads to a momentous ending2 do so in terms of the enthymeme of the first order4 7#c7 ,show that prosyllogism and episyllogism are relative terms4 7#d7 ,when the common premise of the 8pro0 and 8epi0 syllogism is omitted what abbreviated form results8 7#e7 ,from the viewpoint of your definition criticise this3 8,a sorites is a series of prosyllogisms and episyllogisms in which all of the conclusions are suppressed except the last40 7#f7 ,prove the truth of the two rules of the regressive sorites4 7#g7 ,show that the prosyllogism and the episyllogism may be progressive or regressive4 7#h7 8,reasoning from cause to effect0is such progressive or regressive8 ,explain4 7#i7 ,which is inductive in nature1 the progressive form of reasoning or the regressive8 ,explain4 7#aj7 ,test the validity of the enthymemes on pages #bdh and #bdi4 7#aa7 8,a sorites is at least as immediately convincing as the chain of syllogisms into which it can be decomposed40 ,discuss this4 ,,chapter #ad4 ,,categorical ,,arguments ,,tested ,,according ,,to ,,form4 #a4 ,,arguments ,,of ,,form ,,and ,,matter4 ,the matter relative to the syllogism treated in chapters #aa1 #ab and #ac is given primarily to enable the reader to test the validity of categorical arguments4 ,such arguments must be viewed from the two standpoints of form and matter1 since it is one of the chief purposes of logic to enable the student to detect fallacious reasoning1 no matter how subtly it may be concealed4 ,therefore1 that one may gain marked facility in this kind of work1 it becomes necessary to proceed with thoroughness and confidence4 ,the meaning of arguments and the various material fallacies may be treated later2 but we are now equipped with sufficient knowledge and experience to test the validity of arguments from the viewpoint of form4 #b4 ,,order ,,of ,,procedure ,,in ,,the ,,formal ,,testing ,,of ,,arguments4 ,in testing categorical arguments three things are essential2 first1 to follow a definite plan2 second1 to give reasons2 third1 to give the author the benefit of the doubt4 ,in view of these essentials1 we suggest this outline which may be helpful to the inexperienced3 7#a7 ,arrange logically and complete the syllogism4 7#b7 ,determine the figure and mood by using symbols4 7#c7 ,apply the rules for negatives and particulars4 7#d7 ,indicate the distribution by underscoring the terms distributed4 7#e7 ,apply the rules for distribution4 7#f7 ,name fallacies1 if any1 giving reasons4 ,we recall that to be strictly logical any categorical argument must take this form3 first1 major premise2 second1 minor premise2 third1 conclusion4 ,often in common conversation either the minor premise or conclusion is given first4 ,illustrations of this3 7#a7 8,he cannot be a gentleman 7conclusion72 for no gentleman would do such a thing 7major premise71 and there is no doubt but that he did it0 7minor premise74 7#b7 8,he has the making of a good teacher 7conclusion72 because he not only knows1 but he knows how to impart what he knows 7minor premise71 and this is a sure sign of a good teacher0 7major premise74 ,when the argument appears in this illogical form1 the first duty of the student is to arrange it logically4 ,to do this he must be able to recognize readily the premises and the conclusion4 ,to this end these facts may be of assistance3 7#a7 ,a premise always answers the question 8,why01 and is often introduced by such words as 8for10 8because10 8since10 and the like4 7#b7 ,the conclusion is usually introduced by 8therefore10 8hence10 8it follows10 etc4 7#c7 ,when there are no word-signs those mentioned in the foregoing may be inserted with a view of determining which is the conclusion1 and which are the premises4 ,suggestions relative to completing abbreviated arguments3 7#a7 ,if the conclusion is to be supplied1 select the term used twice in the premises2 this1 the middle term1 must not appear in the conclusion4 ,the other two terms may now be connected 7copulated7 to form the conclusion1 the narrower term 7minor7 being used as the subject1 unless it occurs in what clearly seems to be the major premise4 7#b7 ,if either premise is to be supplied1 unite the middle term with the subject of the conclusion for the minor premise1 and with the predicate of the conclusion for the major premise4 7#c7 ,in supplying any missing proposition1 care should be taken to make the argument valid1 if this can be done in conformity with good ,english1 good sense1 and the rules of logic4 ,as regards the determination of the figure it is well to locate the middle term first1 placing above it the symbol ,m4 ,then 8,g0 7greater7 may be placed above the major term and 8,s0 7smaller7 above the minor4 #c4 ,,illustrative ,,exercises ,,in ,,testing ,,arguments ,,which ,,are ,,already ,,complete1 ,,regular1 ,,and ,,logically ,,arranged4 ,m ,g 7#a7 ,a ,all dogs are quadrupeds1 ,s ,m ,a ,all greyhounds are dogs1 ,s ,g ,a ,all greyhounds are quadrupeds4 ,a ,this argument is in the first figure1 the mood being ,a4 ,all ,a the propositions are affirmative and universal1 consequently the rules pertaining to negatives and particulars are inapplicable4 8,a0 distributes the subject only1 hence all the subjects are underscored4 ,the middle term 8dog0 is distributed in the major premise1 and the minor term 8greyhound10 which is distributed in the conclusion1 is likewise distributed in the minor premise4 ,the argument is1 therefore1 valid in form4 ,this may be verified by referring to a list of valid moods in the first figure4 ,g ,m 7#b7 ,e ,no prejudiced person is open to conviction1 ,s ,m ,a ,all fair minded persons are open to conviction1 ,s ,g ,e ,no fair minded person is prejudiced4 ,e ,the argument is in the second figure2 mood ,a4 ,there is one ,e negative premise and the conclusion is negative2 no particulars4 8,e0 distributes both terms1 8,a0 the subject only4 ,the middle term is distributed in the major premise4 ,both major and minor terms are distributed in the conclusion1 but they are likewise distributed in the premises where they are used4 ,the argument is1 therefore1 valid4 ,reference to the valid moods of the second figure confirms this conclusion4 ,m ,g 7#c7 ,a ,all good citizens vote1 ,m ,s ,a ,all good citizens obey the law1 ,s ,g ,a ,all who obey the law vote4 ,a ,the mood is ,a used in the third figure4 ,all the propositions are ,a ,a's1 hence the negative and particular rules are inapplicable4 8,a0 distributes its subject4 ,the middle term is distributed in both premises4 8,all who obey the law0 is distributed in the conclusion but not in the premise where it is used4 ,therefore the argument is invalid4 ,a ,the fallacy being illicit minor4 ,a is not found in the third ,a figure's list of valid moods4 ,m ,g 7#d7 ,a ,all good citizens vote1 ,s ,m ,e ,no criminal is a good citizen1 ,s ,g ,e ,no criminal votes4 ,a ,the mood of this argument is ,e used in the first figure4 ,one premise ,e negative2 conclusion negative2 no particulars4 8,a0 distributes the subject only2 8,e0 both subject and predicate4 ,the middle term1 8good citizens10 is distributed in both premises4 ,the major term1 8votes10 is distributed in the conclusion but not in the premise where it is used4 ,a ,the argument is invalid1 the fallacy being illicit major4 ,e is not ,e found in the first figure's list of valid moods4 ,g ,m 7#e7 ,a ,all true teachers are sympathetic1 ,s ,m ,a ,all lovers of children are sympathetic1 ,s ,g ,a ,all lovers of children are true teachers4 ,a ,the mood of this argument is ,a used in the second figure4 ,there are ,a no negatives and no particulars4 8,a0 distributes its subject only4 ,the middle term1 8sympathetic10 is distributed in neither premise1 hence the argument is invalid4 ,fallacy of undistributed middle4 ,referring ,a to the list of valid moods1 we do not find ,a in the second figure4 ,a ,m ,g 7#f7 ,a ,all thoughtful men are humane1 ,s ,m ,a ,all good citizens are thoughtful men1 ,s ,g ,i ,some good citizens are humane4 ,a ,the mood is ,a in the first figure4 ,no negatives2 no particulars4 8,a0 ,i distributes its subject only2 8,i0 distributes neither term4 ,middle term1 distributed in the major premise2 no term distributed in the conclusion4 ,the argument is1 therefore1 valid4 ,the conclusion is weakened as it ,a could just as well be an ,a4 ,the mood ,a in the first figure is valid1 ,i but of little value because of the weakened conclusion4 #d4 ,,illustrative ,,exercise ,,in ,,testing ,,completed ,,arguments1 ,,one ,,or ,,both ,,premises ,,being ,,illogical4 ,arguments containing exclusive propositions4 7#a7 ,only first class passengers may ride in the parlor car1 ,all these are first class passengers1 ,they may ride in the parlor car4 ,propositions introduced by such words as only1 none but1 alone and their equivalents are exclusive propositions4 ,since these distribute their predicates1 but do not distribute their subjects1 the most convenient way of dealing with them is to interchange subject and predicate and then regard them as 8,a0 propositions4 ,as the first proposition of the argument is an exclusive1 we must deal with it accordingly4 ,interchanging subject and predicate and introducing it with all places the argument in this form3 ,g ,m ,a 7,all7 ,the parlor car is reserved for first class passengers1 ,s ,m ,a ,all these are first class passengers1 ,s ,g ,a ,all these may ride in the parlor car4 ,a ,the mood of this argument is ,a in the second figure4 ,no negatives2 ,a no particulars4 8,a0 distributes its subject only2 the middle term is thus undistributed4 ,the argument is invalid1 the fallacy being that of undistributed middle4 7#b7 8,no one but a thief would take these books without asking for them1 and it has been proved that you took the books2 that is the reason ,i have called you a thief40 ,it is clear that 8no one but0 is equivalent to 8only40 ,thus the first proposition of the argument is an exclusive1 and may be made logical by interchanging subject and predicate and calling it an 8,a40 ,as a result of this the argument takes the following form3 ,m ,g ,a 7,all7 ,these books were taken by a thief1 ,s ,m ,a ,you took these books1 ,s ,g ,a ,you are a thief4 ,we have now had sufficient experience to recognize the validity of mood ,,aaa in the first figure4 7#c7 8,none but the brave deserve the fair1 ,and you are not fair40 ,making the exclusive logical and completing gives3 ,m ,g ,a 7,all7 ,the fair deserve the brave1 ,s ,m ,e ,you are not fair1 ,s ,g ,e ,you do not deserve the brave4 ,a ,the mood of this argument is ,e used in the first figure4 ,there ,e is a negative premise1 also a negative conclusion2 no particulars4 ,the middle term is distributed twice4 ,the major term 8brave0 is distributed in the conclusion but not in the major premise2 hence the argument is invalid1 the fallacy being illicit major4 ,,note4,there may be some doubt in the student's mind as to the proposition 8,none but the brave deserve the fair10 really meaning 8,all the fair deserve the brave40 ,this doubt may be better satisfied by treating the exclusive in the second way as indicated on page #acg1 to wit3 ,negate the subject of the exclusive1 then give it the form of the regular 8,e40 ,this results in 8,no not-brave persons deserve the fair10 which1 after first converting and then obverting becomes1 8,all the fair deserve the brave40 ,arguments ,containing ,individual ,propositions4 7#d7 8,george ,washington never told a lie1 but you1 when tempted1 yielded with no qualms of conscience40 ,completing1 and arranging logically gives3 ,e ,george ,washington never told a lie1 ,a ,you did tell a lie1 ,e ,you 7in this respect7 are not like ,george ,washington4 ,treated properly this argument proves to be valid2 the student1 however1 is apt to deal with such in this wise3 ,o ,george ,washington never told a lie1 ,i ,you did tell a lie1 ,o ,you 7in this respect7 are not like ,george ,washington4 ,when placed in this mood the argument is invalid2 since the major term1 which is distributed in the conclusion1 is not distributed in the premise where it occurs 7illicit major74 ,it is the tendency on the part of students to classify as particular1 a proposition which has as its subject a singular term4 ,such propositions we have learned to call individual4 ,the cause of this tendency is easily explained3 ,consider the propositions1 7#a7 8,this man is mortal02 7#b7 8,some men are mortal02 7#c7 8,all men are mortal40 ,in the first instance 8mortal0 refers to the subject 8man0 which is narrower in significance than 8some men0 to which 8mortal0 of the second proposition refers4 ,in consequence1 it is very natural to infer that if1 8,some men are mortal10 is particular1 then1 8,this man is mortal10 is likewise particular4 ,the error springs from a wrong conception of particular as used in logic2 the content of the term has little to do with extension1 but is chiefly concerned with indefiniteness4 ,a particular proposition is one in which the predicate refers to only a part of an indefinite subject4 ,if the subject is referred to as a whole1 and this whole is more or less definite1 then the proposition is universal4 ,since 8mortal0 refers to the whole of the definite term 8this man10 as positively as it refers to the whole of 8all men10 there is as much justification in calling the first proposition universal as there is in calling the third universal4 ,it may be remembered1 then1 that logicians class as universal all individual propositions4 ,arguments ,containing ,partitive ,propositions4 7#e7 ,all that glitters is not gold1 ,tinsel glitters1 ,tinsel is not gold4 ,the quantity sign 8all0 when used with 8not0 is ambiguous2 it may mean 8no0 or 8some-not40 ,the only way to determine which meaning is intended is to try both these quantity signs1 selecting the one which seems to fit best the author's meaning4 ,when 8all-not0 means 8some-not0 the proposition which it introduces is called a partitive proposition2 since such always suggests a complementary proposition4 7,see page #acc47 ,for example1 8,some glittering things are not gold10 suggests its complement1 8,some glittering things are gold40 ,in testing the foregoing argument it is clear that 8,all that glitters is not gold0 does not mean 8,no glittering thing is gold10 so much as it implies 8,some glittering things are not gold40 ,thus the argument takes this form3 ,m ,g ,o ,some glittering things are not gold1 ,s ,m ,a ,tinsel glitters1 ,s ,g ,e ,tinsel is not gold4 ,o ,the mood is ,a in the first figure4 ,there is one negative premise ,e 7,o71 and the conclusion is negative4 ,there is one particular premise 7,o71 but the conclusion is not particular4 ,this makes the argument invalid according to rule #h2 viz43 8,a particular premise necessitates a particular conclusion40 ,carrying the test still further it will be seen that there is likewise the fallacy of undistributed middle4 ,other arguments where one of the premises is partitive4 8,all scholars are not wise and1 therefore1 ,aristotle was not wise40 8,all democrats are not free-traders1 but most of the men of this particular club are democrats1 and hence they are of a different faith 7not free-traders740 8,all the members of the club are not good players1 and ,james belongs to the club40 8,all educated men do not write good ,english2 therefore1 you ought not to express surprise when informed that ,x1 though an educated man1 uses poor ,english40 ,the major premise in each of the foregoing is partitive in nature and should be changed to the following form before the argument is tested2 taking these in order we have3 8,some scholars are not wise02 8,some democrats are not free-traders02 8,some of the members of the club are not good players02 8,some educated men do not write good ,english40 ,let us test the validity of the last one3 7#f7 ,o ,some educated men do not write good ,english1 ------------------------------------ ,a ,x is an educated man1 -- ,e ,x does not write good ,english 7uses poor ,english74 -- ------------------------------------ ,like the first one of the list1 this is invalid inasmuch as a particular premise should yield a particular conclusion1 not one which is universal4 ,the argument also contains the fallacy of undistributed middle4 ,arguments ,containing ,inverted ,propositions4 7#g7 8,blessed are the merciful3 for they shall obtain mercy40 ,the first proposition1 being poetical in construction1 is typical of the inverted form4 ,these are usually made logical by simple conversion4 ,since premises usually follow 8for10 or equivalent word-signs1 it is easy to see that 8for they shall obtain mercy0 is one of the premises2 while the other1 the broader of the two1 is understood4 ,arranged logically the argument assumes this form3 ,m ,g ,a ,those who obtain mercy are blessed1 ------------------------ ,s ,m ,a ,the merciful shall obtain mercy1 ---------------- ,s ,g ,a ,the merciful are blessed4 ---------------- ,a ,here we have the mood ,a in the first figure1 which we know to be ,a valid4 ,other arguments where one of the propositions is inverted4 8,blessed are the pure in heart3 for they shall see ,god40 8,to thine own self be true1 and it must follow1 as the night the day1 thou canst not then be false to any man40 8,a king thou art and1 therefore1 thy commands shall be1 yea1 must be obeyed40 ,taking the inverted propositions in order and making each logical1 the following is the result3 8,the pure in heart are blessed02 8,you be true to yourself1 and444402 8,you are a king1 therefore44440 #e4 ,,arguments ,,which ,,are ,,incomplete ,,and ,,more ,,or ,,less ,,irregular4 7#a7 8,he must be a star player2 for he played fullback on the team which won the championship40 7#b7 8,the man is not to be trusted2 because he served a term of #ij days in jail40 7#c7 8,only material bodies gravitate1 and ether does not gravitate40 7#d7 8,if only fools despise knowledge1 this man cannot be a fool40 7#e7 8,a charitable man has no merit in relieving distress2 because he merely does what is pleasing to himself40 7#f7 8,it is evident that all who get justice buy it2 since only the rich get it40 ,the above arguments thrown into logical form and validity or invalidity stated3 7,the student should test these in detail47 ,m 7#a7 ,a ,all belonging to the team which won the championship were ,g star players1 ,s ,m ,a ,he played with the team which won the championship1 ,s ,g ,a ,he is a star player4 ,valid in form4 ,m ,g 7#b7 ,e ,one who serves a term of #ij days in jail is not to be trusted1 ,s ,m ,a ,this man served a term of #ij days in jail1 ,s ,g ,e ,this man is not to be trusted4 ,valid in form4 ,m ,g 7#c7 ,a ,all gravitating bodies are material1 ,s ,m ,e ,ether does not gravitate1 ,s ,g ,e ,ether is not material4 ,illicit major4 ,m ,g 7#d7 ,a ,all who despise knowledge are fools1 ,s ,m ,e ,this man does not despise knowledge1 ,s ,g ,e ,this man is not a fool4 ,illicit major4 ,m 7#e7 ,e ,no one who merely does what is pleasing to himself has ,g merit in relieving distress1 ,s ,m ,a ,a charitable man merely does what is pleasing to himself1 ,s ,g ,e ,no charitable man has merit in relieving distress4 ,valid in form4 ,m ,g 7#f7 ,a ,all the rich buy justice1 ,s ,m ,a ,all who get justice are rich1 ,s ,g ,a ,all who get justice buy it4 ,valid in form4 ,in supplying suppressed premises the critic is duty bound to give the author the benefit of the doubt1 if by so doing no principle in logic is violated and the proposition conforms to good ,english and good sense4 ,often it is not easy to perceive in the abbreviated argument the meaning intended2 in such instances all legitimate effort should be directed to making the argument valid4 ,to illustrate3 ,in supplying the major premise of argument 8#f0 it would be easy to make it1 8,all justice is bought by the rich02 in consequence the critic could pronounce the argument invalid as the middle term would be undistributed4 ,before asserting that an argument is fallacious because it has four terms rather than three1 the student must make sure that there are no synonyms or equivalents used4 ,in argument 8#d10 for instance1 there are apparently the four terms3 7#a7 8foolish10 7#b7 8despise knowledge10 7#c7 8man10 7#d7 8fool02 but to regard 8foolish0 and 8fool0 as synonyms does not seem like undue liberty4 ,the following arguments further illustrate this need of recognizing synonyms3 8,human beings are accountable for their conduct2 brutes1 not being human1 are therefore free from responsibility40 7,not accountable for their conduct47 8,not all educated men spell correctly2 because one often finds mistakes in the writings of college graduates40 7,educated men47 8,modern education is not popular in this state2 for it increases the tax rate1 and the popularity of everything1 which touches the pocket of these frugal ,yankees1 7increases the tax rate7 is very short lived40 7,not popular47 ,in common parlance the use of synonyms is so prevalent that ready ability to substitute equivalents in word1 phrase1 and clause form is needed by him who would be skillful in testing all kinds of arguments4 ,it has already become apparent to the student that the number of the noun or the tense of the verb is of small logical consequence4 ,a very large proportion of the formal fallacies in argumentation concern the rules of distribution which are summarized in the dictum 8,what may be said of the whole may be said of part of that whole40 #f4 ,,common ,,mistakes ,,of ,,students ,,in ,,testing ,,arguments4 ,the most common mistakes made by the student when testing arguments are as follows3 7#a7 ,using the exclusive as an 8,a0 without interchanging subject and predicate2 e4 g41 interpreting the proposition1 8,only high school graduates may enter the training school10 as meaning 8,all high school graduates may enter the training school40 7#b7 ,calling individual propositions particular2 e4 g41 interpreting 8,socrates is mortal0 as an 8,i0 rather than an 8,a40 7#c7 ,signifying that partitive propositions are 8,a's0 rather than 8,o's02 e4 g41 8,all that glitters is not gold0 interpreted as meaning that 8,all glittering things are gold10 rather than 8,some glittering things are not gold40 7,a74 7#d7 ,concluding that a fallacy of four terms has been committed when two terms are synonomous4 7#e7 ,failing to interchange the subject and predicate of inverted propositions4 #g4 ,,outline4 ,,categorical ,,arguments ,,tested ,,according ,,to ,,form4 7#a7 ,arguments of form and matter4 7#b7 ,order of procedure in the formal testing of arguments4 ,the outline4 ,determining premises and conclusion4 ,completing abbreviated arguments4 7#c7 ,illustrative exercises in testing arguments which are complete and whose premises are logical4 7#d7 ,illustrative exercises in testing completed arguments1 one or both of whose premises are illogical4 ,exclusive premises1 individual premises1 partitive premises1 inverted premises4 7#e7 ,incomplete and irregular arguments4 7#f7 ,common mistakes of the student4 #h4 ,,summary4 7#a7 ,in determining their validity1 arguments must be tested from the two viewpoints of form and matter4 7#b7 ,in testing categorical arguments it is quite necessary to be definite1 to give reasons1 and to give the author the benefit of the doubt4 ,with this in view the attending outline is suggestive3 #a4 ,arrange logically and complete4 #b4 ,determine the figure and mood4 #c4 ,apply rules for negatives and particulars4 #d4 ,indicate distribution4 #e4 ,apply rules for distribution4 #f4 ,name fallacies1 if any1 giving reasons4 ,the logical arrangement of syllogistic arguments is #a4 ,major premise4 #b4 ,minor premise4 #c4 ,conclusion4 ,any proposition in a syllogism which answers the question 8,why80 is a premise1 whereas the conclusion follows 8therefore01 or its equivalent either written or understood4 ,if a conclusion is to be supplied1 unite the two terms which are used but once in the premises1 using the 8minor premise term0 as the subject4 ,if a premise is to be supplied1 unite the middle term with the 8minor0 to form the minor premise and with the 8major0 to form the major premise4 7#c7 ,arguments which are regular1 complete1 and logically arranged1 may be tested by symbolizing the mood and figure1 underscoring the distributed terms1 and then applying the general rules of the syllogism4 7#d7 ,arguments with illogical premises may not be tested with impunity till the faulty premises are made logical4 ,the exclusive1 an illogical proposition introduced by only1 alone1 none but1 and the like1 may be made logical by interchanging subject and predicate and calling the proposition an ,a4 ,the individual proposition is one with a singular subject4 ,in testing1 individual propositions are classed as universal4 ,propositions introduced by 8all-not0 are usually given the significance of 8some-not04 ,these are called partitive propositions1 which in the testing1 should be denominated 8,o's04 ,inverted propositions when subjected to the test for validity must be converted simply and then classified4 7,usually as ,a's47 7#e7 ,in supplying propositions which are taken for granted1 the aim should be to make the argument valid1 provided this can be done without violating the rules of logic1 ,english1 and common sense4 ,ability to substitute equivalent words1 phrases1 or clauses is demanded of the student of logic1 inasmuch as such substitution is frequently needed in the testing of arguments4 ,number and tense have little significance in dealing with arguments4 7#f7 ,the common mistakes of students made in testing arguments concern exclusive1 partitive and inverted propositions1 and an inability to recognize expressions equivalent in meaning4 #i4 ,,review ,,questions4 7#a7 ,name and explain the two standpoints from which all arguments must be viewed4 7#b7 ,give an outline of procedure which may be serviceable in the testing of categorical arguments4 7#c7 ,give illustrations showing that the logical order of categorical arguments is not the usual mode of procedure in common parlance4 7#d7 ,offer suggestions which may aid in designating a premise2 a conclusion4 7#e7 ,how would you proceed in forming any one of the three propositions of a syllogism when the other two are given8 7#f7 ,designate the premises and the conclusion in the following1 supplying any proposition which may be omitted1 also arrange logically and test the validity4 7#a7 8,the people of this country are suffering from an overdose of prosperity2 consequently a period of hard times will be a valuable lesson40 7,the conclusion should be recast so as to read1 8,a period of hard times will cure the people of this country40 ,the minor premise is1 8,those who suffer from an overdose of prosperity may be cured by a period of hard times407 7#b7 8,i am a teacher2 you are not what ,i am2 hence you are not a teacher40 7#c7 8,to kill a man is murder1 therefore war is murder40 7#d7 8,you have not adopted the best policy since honesty has always been and will always be the best policy40 7#e7 8,since the road is criminally mismanaged1 why should not the authorities be indicted as criminals80 7#f7 8,early to bed and early to rise makes a man healthy1 wealthy and wise4 ,i am none of these2 hence my sleeping hours have been wrong40 7#g7 ,illustrate a weakened conclusion4 7#h7 ,explain the exclusive proposition and indicate how the logician should treat it4 7#i7 ,arrange logically and test the following3 7#a7 ,only weak men become intemperate1 and ,edgar ,allen ,poe was surely intemperate4 7#b7 ,no admittance except on business2 hence you cannot be admitted4 7#c7 ,virtuous acts are praiseworthy1 and indiscriminate giving is not a virtuous act4 7#aj7 ,explain why individual propositions are classed as universal4 7#aa7 ,write an argument whose major premise is a partitive proposition2 arrange logically and test validity4 7#ab7 ,arrange and test this argument3 8,blessed are the poor in spirit3 for theirs is the kingdom of heaven40 7#ac7 ,complete1 arrange and test4 7#a7 8,the object of war is to settle disputes2 hence soldiers are the best peacemakers40 7#b7 8,the various species of brutes being created to prey upon one another proves that man is intended to prey upon them40 7#c7 8,the end of everything is its perfection2 death being the end of life is its perfection40 7#d7 8,all the trees of the yard make a thick shade and this is one of them40 7#e7 8,minds of moderate caliber ordinarily condemn everything which is beyond their range1 and his is such a mind40 7#f7 8,the best of all medicines are fresh air and sleep1 and you are sorely in need of both40 7#g7 8,every hen comes from an egg2 every egg comes from a hen2 therefore every egg comes from an egg40 7#h7 8,he cannot have been thereotherwise ,i should have seen him40 7#ad7 8,it is fair to give the author the benefit of the doubt when we set ourselves up as censors worthy of the name40 ,explain this4 7#ae7 ,illustrate by citing arguments the need of detecting terms which are equivalents in signification4 7#af7 ,how does the logician look upon number and tense as treated in grammar8 7#ag7 ,illustrate and test an argument in which one of the premises is elliptical4 7#ah7 ,summarize the most common mistakes made by students in the testing of categorical arguments2 illustrate these mistakes and then write in logical form4 #aj4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,give illustrations of arguments which are valid in form but invalid in meaning4 ,explain4 7#b7 ,may an argument be valid in meaning but invalid in form8 ,exemplify4 7#c7 ,put a simple problem in arithmetic in syllogistic form and show that the minor premise naturally comes first4 7#d7 ,in the practice of law is there any custom analogous to giving the author the benefit of the doubt in logical argumentation8 7#e7 ,test in detail the following arguments3 7#a7 8,all wise presidents strive to give heed to the demands of the people1 but this president has not done so40 7#b7 8,the existence of ,god is not universally believed1 hence it cannot be true40 7#c7 8,the institution has prospered under the present rgime therefore why change it80 7#d7 8,the man is guilty because seven out of the nine witnesses so testified40 7#e7 8,i know three men who cleared not less than ten thousand dollars in this business2 and why cannot ,i do as much80 7#f7 8,only members may vote and1 since you are not a member1 you will not be allowed to vote40 ,change the exclusive in this argument in the two ways suggested in ,chapter #h1 page #abf4 ,test the argument in both cases4 7#g7 ,show by illustration that the quantity sign 8all0 when used with 8not0 may in some cases mean 8no0 and in others 8some-not04 7#h7 ,make two selections from some poet of authority representing arguments with an inverted premise4 7#i7 ,select from news papers three arguments which seem to illustrate the fallacy of four terms but which in reality do not4 ,explain4 7#aj7 ,wherein could the elliptical proposition lead to error8 7#aa7 ,put the following in syllogistic form and test3 7#a7 8,that persons may reason without language is proven by the circumstances that infants reason and yet have no language40 7#b7 8,the scriptures cannot come from ,god because they contain some things which cannot be comprehended by man40 7#c7 8,when ,columbus was sailing the ocean in search of a new world1 he fell in with a flock of land birds and concluded that he could not be far from land40 7#d7 8,bolingbroke in arguing against the truth of the ,christian religion shows that the ,christian religion has bred contentions40 8,burke answered him by showing that civil government had bred contentions40 ,,chapter #ae4 ,,hypothetical ,,arguments1 ,,and ,,disjunctive ,,arguments ,,including ,,the ,,dilemma4 #a4 ,,three ,,kinds ,,of ,,arguments4 ,the proposition1 constituting the basic unit of the argument1 would of necessity be indicative of the nature of said argument2 therefore the three general kinds of propositions1 categorical1 hypothetical and disjunctive1 suggest the three kinds of arguments which are in turn categorical1 hypothetical and disjunctive4 ,categorical arguments are those in which all of the propositions are categorical4 ,since this kind has been treated1 it remains for us to consider the other two4 #b4 ,,hypothetical ,,arguments4 ,we have observed that a hypothetical proposition is one in which the assertion depends on a condition2 for example1 in the proposition1 8,if it is pleasant1 ,i will call on you to-morrow10 the calling depends on the state of the weather4 8,i will call on you to-morrow10 is the assertion which is limited by the condition1 8,if the weather is pleasant40 ,definition3 ,the hypothetical argument or syllogism is one in which the major premise is hypothetical and the minor premise categorical4 ,,illustration3 ,if the people are right more than half of the time1 the world will progress2 ,and the people are right more than half of the time1 ,hence the world will progress4 ,in contradistinction to disjunctives1 hypothetical propositions and hypothetical syllogisms are frequently referred to as 8conjunctive40 #c4 ,,the ,,antecedent ,,and ,,consequent4 ,facility in detecting the antecedent and consequent of hypotheticals is required in order to deal intelligently with the argument4 ,the hypothetical proposition has been defined as one in which the assertion is limited by a condition4 ,the consequent is the assertion and usually follows 7though not always7 the antecedent which is the limiting condition4 ,first the antecedent and then the consequent is the logical order as the derivative meaning of the words antecedent and consequent would indicate4 ,the antecedent is introduced by such words as 8if10 8though10 8unless10 8suppose10 8granted that10 8when10 etc4 ,,illustrations3 ,antecedent4 ,consequent4 #a4 ,if you study1 you will pass4 #b4 ,if it rains1 it is cloudy4 #c4 ,if two is added to three1 the result is five4 #d4 ,if you are temperate1 you will live to a ripe old age4 ,consequent4 ,antecedent4 #e4 ,i will go1 unless you wire me to the contrary4 #f4 ,i will pay you1 when you present your bill4 #g4 ,i shall make the trip in granted that ,i have no accidents4 ten hours1 #h4 ,my overcoat would not have if the door had been locked4 been stolen1 #d4 ,,two ,,kinds ,,of ,,hypothetical ,,arguments4 ,the two kinds of hypothetical syllogisms are the constructive and destructive4 ,a constructive hypothetical syllogism is one in which the minor premise affirms the antecedent4 ,a destructive hypothetical syllogism is one in which the minor premise denies the consequent4 ,the constructive hypothetical is sometimes referred to as the 8modus ponens02 whereas the destructive hypothetical is called the 8modus tollens40 ,,illustrations3 ,constructive ,hypothetical ,syllogisms4 ,symbols4 ,words4 ,if ,a is ,b1 ,c is ,d ,if you are diligent1 you will succeed2 ,a is ,b ,and you are diligent1 ,c is ,d ,therefore you will succeed4 ,destructive ,hypothetical ,syllogisms4 ,if ,a is ,b1 ,c is ,d ,if you had been diligent1 you would have succeeded2 ,c is not ,d ,but you did not succeed1 ,a is not ,b ,therefore you were not diligent4 #e4 ,,the ,,rule ,,and ,,two ,,fallacies ,,of ,,the ,,hypothetical ,,argument4 ,from a given hypothetical proposition it is possible to construct four different hypothetical syllogisms1 as the attending illustrations make evident3 ,consider the hypothetical proposition 8,if it has rained1 the ground is damp40 7#a7 ,minor premise affirms antecedent4 ,if it has rained1 the ground is damp2 ,it has rained1 ,therefore the ground is damp4 7#b7 ,minor premise denies antecedent4 ,if it has rained1 the ground is damp2 ,it has not rained1 ,therefore the ground is not damp4 7#c7 ,minor premise affirms consequent4 ,if it has rained1 the ground is damp2 ,the ground is damp1 ,therefore it has rained4 7#d7 ,minor premise denies the consequent4 ,if it has rained1 the ground is damp2 ,the ground is not damp1 ,therefore it has not rained4 ,without any knowledge of the rules of the hypothetical syllogism let us strive to determine how many of the foregoing are valid4 ,relative to the first1 it would be impossible for any rain to fall without making the ground somewhat damp2 a few drops would be sufficient4 ,in short1 if the antecedent happens1 the consequent must follow4 ,it seems1 therefore1 that the first argument is valid4 ,considering the second3 rain is not the only cause for the dampness of the ground1 as it might result from the falling of dew1 or from a dense fog2 no rain does not necessarily mean no dampness4 ,it is clear that if the antecedent does not happen1 the consequent may or may not follow4 ,thus it appears that the second argument is invalid4 ,attention to the third makes evident a condition similar to the second3 the ground may be made damp by agencies other than rain1 such as fog and dew4 ,thus the third argument is likewise invalid4 ,but in the fourth argument it is obvious that if the ground is not damp1 then there could have been neither rain1 nor fog1 nor dew4 ,no dampness shuts out all of the conditions1 including the rain4 ,therefore the fourth argument is valid4 ,this investigation suggests a rule for hypothetical arguments4 ,since only the first and fourth arguments are valid1 this is the rule which must obtain3 ,the minor premise should either affirm the antecedent or deny the consequent4 ,any violation of this rule would result in the fallacies of denying the antecedent or affirming the consequent4 ,there is one exception to this rule which must not be overlooked2 viz43 ,if the antecedent and consequent of the hypothetical proposition are co-extensive then both may be either affirmed or denied4 ,,illustrations3 7#a7 ,if the rectangle is equilateral1 then it is a square2 ,the rectangle is equilateral1 ,it is a square4 7#b7 ,if the rectangle is equilateral1 then it is a square2 ,the rectangle is not equilateral1 ,the rectangle is not a square4 7#c7 ,if the rectangle is equilateral1 then it is a square2 ,it is a square1 ,the rectangle is equilateral4 7#d7 ,if the rectangle is equilateral1 then it is a square2 ,it is not a square1 ,the rectangle is not equilateral4 #f4 ,,hypothetical ,,arguments ,,reduced ,,to ,,the ,,categorical ,,form4 ,the hypothetical syllogism so closely resembles the categorical that it may be changed to it by a slight alteration in the wording4 ,after testing the hypothetical by its own rule1 it may be expedient to reduce the argument to the categorical form1 and subject it to a second test in which the categorical rules are applied4 ,this reduction usually necessitates two steps2 first1 change the propositions which represent the antecedent and consequent to a subject term and a predicate term respectively and then unite them to form the major premise2 second1 supply a new minor term1 if necessary4 ,illustrations of ,reduction2 and ,comparison of ,hypothetical and ,categorical ,fallacies3 ,hypothetical ,form3 7#a7 ,if it has rained1 the ground is damp2 ,it has rained1 ,the ground is damp4 ,categorical ,form3 ,m ,g ,a ,the falling rain makes the ground damp1 ,s ,m ,a ,in this case rain has fallen1 ,s ,g ,a ,in this case the ground is damp ground4 ,it is seen that the argument in the hypothetical form is valid as the minor premise affirms the antecedent4 ,reducing to the categorical gives ,a to the argument the mode ,a in the first figure which we know to be ,a valid4 ,hypothetical3 7#b7 ,if one were wise1 he would study2 ,but you will not study1 ,you are not wise4 ,categorical3 ,g ,m ,a ,a wise person would study1 ,s ,m ,e ,you will not study1 ,s ,g ,e ,you are not wise4 ,in the hypothetical form the argument is valid since the minor premise ,a denies the consequent4 ,reducing to the categorical gives mood ,e in ,e the second figure4 ,this is valid4 ,hypothetical3 7#c7 ,if the wind blows from the south1 it will rain2 ,but the wind is not blowing from the south1 ,hence it is not going to rain4 ,categorical3 ,m ,g ,a ,south wind brings rain1 ,s ,m ,e ,this wind is not a south wind1 ,s ,g ,e ,this wind will not bring rain4 ,hypothetically considered1 the minor premise denies the antecedent and consequently the argument is invalid4 ,reducing to the categorical form1 it is found that the major term is distributed in the conclusion1 but is not distributed in the major premise2 hence the fallacy of illicit major is committed4 ,hypothetical3 7#d7 ,if a man is just1 he will obey the golden rule2 ,this judge has obeyed the golden rule1 ,hence he is just4 ,categorical3 ,g ,m ,a ,a just man will obey the golden rule1 ,s ,m ,a ,this judge has obeyed the golden rule1 ,s ,g ,a ,this judge is a just man4 ,hypothetically considered1 the minor premise affirms the consequent and thus the argument is fallacious2 when changed to the categorical we find the fallacy of undistributed middle4 ,if other examples were taken1 it could be proved that the hypothetical fallacy of denying the antecedent is usually equivalent to the categorical fallacy of illicit major2 whereas the hypothetical fallacy of affirming the consequent amounts to undistributed middle4 ,in reducing some hypotheticals it is necessary to make use of such expressions as1 8the case of0 or 8the circumstances that40 ,the attending argument will illustrate this3 ,if ,jefferson was right1 man was created free and equal2 7but7 ,man was not created free and equal1 ,jefferson was not right4 ,reduced to the categorical3 ,g ,the case of ,jefferson being right is the case of man being created ,m free and equal2 ,s ,m ,man was not created free and equal1 ,s ,g ,jefferson 7this man7 was not right4 ,the argument is valid in both cases4 #g4 ,,illustrative ,,exercise ,,testing ,,hypothetical ,,arguments ,,of ,,all ,,kinds4 ,the following brief outline may be followed in testing hypothetical arguments3 #a4 ,arrange logically4 #b4 ,determine antecedent and consequent4 #c4 ,apply the hypothetical rule2 name fallacies giving reasons4 #d4 ,reduce to categorical form4 #e4 ,apply the categorical rules1 giving fallacies with reasons4 7#a7 ,if a man is properly educated1 he will not despise manual labor2 therefore ,i conclude that you have not been properly educated1 since you dislike to work with your hands4 ,arranged logically and antecedent and consequent indicated3 ,if a man is properly educated 7antecedent71 he will not despise manual labor 7consequent72 ,you despise manual labor 7dislike to work with your hands71 ,you have not been properly educated4 ,the minor premise denies the consequent1 hence the argument is valid according to the rule1 8,the minor premise must affirm the antecedent or deny the consequent40 ,the student should note that the consequent is negative and therefore its denial must be an affirmative proposition4 ,reduced to the categorical3 ,g ,m ,e ,a properly educated man will not despise manual labor2 ,s ,m ,a ,you despise manual labor1 ,s ,g ,e ,you have not been properly educated4 ,regarded categorically this is valid4 ,why8 7#b7 8,if one believes in the tenets of the democratic party1 then he should vote for its candidates2 and since ,a does believe in them ,i have asked him to vote for me40 ,arranged1 and antecedent and consequent indicated4 ,if one believes in the tenets of the democratic party 7antecedent71 then he should vote for its candidates 7consequent72 ,and ,a does believe in these tenets1 ,he should vote for its candidates 7,i have asked him to vote for me74 ,the minor premise affirms the antecedent and thus the argument is valid according to rule4 ,reduced to the categorical3 ,m ,a ,one who believes in the tenets of the democratic party should ,g vote for its candidates1 ,s ,m ,a ,a believes in these tenets1 ,s ,g ,a ,a should vote for its candidates4 ,a ,reduced to the categorical gives mood ,a in the first figure and this ,a we know to be valid4 7#c7 8,if the weather had not been pleasant1 ,i could not have come2 but as the weather is pleasant1 here ,i am40 ,arranged and antecedent and consequent indicated3 ,if the weather had not been pleasant 7antecedent71 ,i could not have come 7consequent72 ,the weather is pleasant1 ,i have come 7here ,i am74 ,the minor premise denies the antecedent and consequently the argument is invalid according to the rule4 7,an affirmative minor premise denies a negative antecedent47 ,reduced to the categorical3 ,e ,unpleasant weather would not permit me to come1 ,e ,this weather is not unpleasant1 ,a ,this weather enabled me to come4 ,fallacy of two negative premises4 7#d7 8,if one pays his debts1 he will not be #8black-listed'2 but since you are #8black-listed1' ,i conclude that you have not paid your debts40 ,arranged logically and antecedent and consequent indicated3 ,if one pays his debts 7antecedent71 he will not be 8black-listed0 7consequent72 ,you are 8black-listed10 ,you have not paid your debts4 ,the minor premise denies the consequent hence the argument is valid4 ,reduced to categorical form3 ,g ,m ,e ,no one who pays his debts is black listed1 ,s ,m ,a ,you are black listed1 ,s ,g ,e ,you have not paid your debts4 ,e ,the mood ,a in the second figure is valid4 ,e 7#e7 8,men would do right for the sake of themselves1 if they appreciated the law of retribution2 but they never think of that40 ,arranged1 completed1 and tested3 ,if they appreciated the law of retribution 7antecedent71 men would do right for the sake of themselves 7consequent72 ,but they do not appreciate the law of retribution 7never think of that71 ,hence they do not do right for the sake of themselves4 ,fallacy of denying the antecedent4 ,reduced to the categorical3 ,m ,a ,the case of men appreciating the law of retribution1 is the case ,g of men doing right for the sake of themselves2 ,s ,m ,e ,but men do not appreciate the law of retribution1 ,s ,g ,e ,men do not do right for the sake of themselves4 ,fallacy of illicit major4 7#f7 8,if an animal is a vertebrate1 then it must have a backbone2 but the books say that this animal is not a vertebrate1 hence it cannot have a backbone40 ,since the minor premise denies the antecedent it would appear that the argument is invalid2 yet common knowledge and common sense dictate that the conclusion is true4 ,surely no invertebrate can have a backbone4 ,as a matter of fact the antecedent and consequent are co-extensive and therefore the hypothetical rule is not applicable4 ,reduced to the categorical3 ,m ,g ,a ,vertebrates must have a backbone 7,co-extensive71 ,s ,m ,e ,this animal is not a vertebrate1 ,e ,this animal cannot have a backbone4 ,as co-extensive ,a's distribute their predicates the possibility of there being a fallacy of illicit major is forestalled4 ,categorically considered the argument is likewise valid4 #h4 ,,disjunctive ,,arguments4 ,it has been observed that a disjunctive proposition is one which expresses an alternative4 ,a disjunctive syllogism is one in which the major premise is a disjunctive proposition4 ,,illustration3 ,the boy is either honest or dishonest1 ,he is honest1 ,he is not dishonest4 #i4 ,,the ,,two ,,kinds ,,of ,,disjunctive ,,arguments4 ,the two forms of disjunctive arguments are the one which by affirming denies and the one which by denying affirms4 ,the former is known by the ,latin words 8modus ponendo tollens02 while the latter is termed the 8modus tollendo ponens40 ,,illustrations3 7#a7 ,by affirming denies4 ,the defendant is either guilty or innocent1 ,he is guilty1 ,he is not innocent4 or ,the defendant is either guilty or innocent1 ,he is innocent1 ,he is not guilty4 7#b7 ,by denying affirms4 ,the defendant is either guilty or innocent1 ,he is not guilty1 ,he is innocent4 or ,the defendant is either guilty or innocent1 ,he is not innocent1 ,he is guilty4 #aj4 ,,the ,,first ,,rule ,,of ,,disjunctive ,,arguments4 ,it may be said that disjunctive arguments depend on two rules4 ,this is the first3 ,the major premise must assert a logical disjunction4 ,a logical disjunction involves two requisites2 first1 the alternatives must be mutually exclusive2 second1 the enumeration must be complete4 ,illustrations of illogical major premise4 ,terms not mutually exclusive3 ,this boy is either inattentive or indolent1 ,he is not inattentive1 ,he is indolent4 ,it is obvious that the boy might be both inattentive and indolent4 ,experience teaches that the qualities are usually concurrent1 and to assume that the boy must be either one or the other is a clear case of 8begging the question40 ,some logicians maintain that 8eitheror0 signify that both alternatives cannot be false1 but that both may be true4 ,if this viewpoint were adopted1 the major premise of the illustration would not be a case of begging the question4 ,it is unnecessary to argue the point1 if it is made perfectly clear which view is to obtain in this discussion4 ,briefly stated the two points are these4 ,first opinion3 8,eitheror0 when used logically1 mean that if the first alternative is false the second must be true1 or if the first alternative is true the second must be false4 ,second opinion3 8,eitheror0 when used logically mean that if the first alternative is false1 the second must be true2 but if the first alternative is true1 the other may or may not be true4 ,this treatise adopts the first opinion4 ,with us all alternative arguments to be logical must be mutually contradictory2 i4 e41 when one is false1 the other must be true and when one is true the other must be false2 both cannot be false1 neither can both be true4 ,when it is intended that this implication should not obtain1 then the expressed alternative will take this form1 8,the boy is either inattentive or indolent or both40 ,other examples where the terms of the disjunctive may not be mutually exclusive3 7#a7 8,lord ,bacon was either exceedingly studious or phenomenally bright40 7,undoubtedly he was both47 7#b7 8,this teacher is a graduate either of ,harvard or of ,yale40 7,perhaps both47 7#c7 8,the defendant is either a liar or a thief40 7,the one often leads to the other47 7#d7 8,to succeed one must either seize the opportunity as it passes or make his own40 7,the best success results from doing both47 ,incomplete enumeration3 ,the cause of the disease was either the water or the milk1 ,it was not the milk1 ,it was the water4 ,when such an argument as this is advanced1 it must be with the knowledge that every other alternative has received satisfactory investigation4 ,without this assurance one could justly claim that the disease might have been caused by the meat or fish supply4 ,complete enumeration means that the investigation has narrowed the facts to the boundary of the field covered by the alternatives4 ,the fallacy of incomplete enumeration is also one of 8begging the question40 ,other examples of a possible incomplete enumeration3 7#a7 8,jones lives either in ,boston or ,new ,york40 7#b7 8,mary is studying either algebra or geometry40 7#c7 8,he either committed suicide or was lynched40 7#d7 8,either the ,giants or the ,boston ,americans will win the pennant40 #aa4 ,,second ,,rule ,,of ,,disjunctive ,,arguments4 ,the second rule is made so self evident by the first that there is little need of a detailed discussion concerning it4 ,the rule is this3 ,when the minor premise affirms or denies one of the alternatives of a logical disjunction1 the conclusion must1 in order1 deny or affirm all of the others4 ,to put it differently3 ,when the 8minor0 affirms1 the conclusion must deny every other alternative1 and vice versa4 ,when there are but two alternatives reference to any of the foregoing disjunctive arguments will make the rule clear4 ,there may be1 however1 more than two alternatives4 ,in such a case1 if the first rule is observed then the second becomes applicable4 ,,illustrations3 7#a7 ,john ,doe lives either in ,boston1 ,albany1 or ,new ,york2 ,he lives in ,new ,york1 ,he does not live in either ,boston or ,albany4 or ,he does not live in ,new ,york1 ,he lives in either ,boston or ,albany4 7#b7 ,the season must have been either summer1 or autumn1 or winter1 or spring2 ,it was neither autumn1 nor winter1 nor spring1 ,it must have been summer4 or ,it was either autumn1 or winter1 or spring1 ,it could not have been summer4 #ab4 ,,reduction ,,of ,,the ,,disjunctive ,,argument ,,to ,,the ,,hypothetical ,,and ,,then ,,to ,,the ,,categorical4 ,it would seem that the laws of the disjunctive contradict those of the categorical syllogism2 for we apparently derive from two affirmatives a negative conclusion1 and we also derive an affirmative conclusion when one premise is negative4 ,this objection is seen to be nugatory when the disjunctive is reduced to the categorical form4 ,the reduction involves the two steps of first changing the disjunctive to the hypothetical form and then to the categorical form4 ,the following illustrations will suffice to make the matter clear3 7#a7 ,disjunctive4 ,a is either ,b or ,c ,a is ,b ,a is not ,c ,hypothetical4 ,if ,a is ,b1 then ,a is not ,c ,a is ,b ,a is not ,c ,categorical4 ,the case of ,a being ,b is the case of ,a not being ,c ,in this case ,a is ,b ,a is not ,c 7#b7 ,disjunctive4 ,the defendant is either guilty or innocent2 ,he is not innocent1 ,he is guilty4 ,hypothetical4 ,if the defendant is guilty1 then he is not innocent2 ,but he is guilty1 ,he is not innocent4 ,categorical4 ,the case of the defendant being guilty is the case of the defendant not being innocent1 ,in this case the defendant is guilty1 ,in this case the defendant is not innocent4 #ac4 ,,the ,,dilemma4 ,the majority of us are acquainted with the dilemma as related to the activities of life4 ,one is in a dilemma when there are two courses open to him but neither is particularly enticing4 ,one is placed in a dilemma when he is forced to choose the lesser of two evils4 ,for example1 one may1 without the proper equipment1 be overtaken by a heavy rain storm2 he seeks the shelter of a wayside shed2 the rain continues so that he is forced either to miss his train1 or to endure the discomfort of a drenching4 ,thus the logical dilemma limits one to a choice between alternatives1 either one of which might well be avoided4 ,definition4 ,the dilemma is a syllogism in which the major premise consists of two or more hypothetical propositions1 while the minor premise is a disjunctive proposition4 ,it being a combination of hypothetical and disjunctive propositions the dilemma is sometimes appropriately referred to as the 8hypothetico-disjunctive0 argument4 ,the order of the premises is indifferent1 yet it seems to be more natural to use the hypothetical first2 thus the definition4 #ad4 ,,four ,,forms4 ,the four forms of the dilemma are the simple constructive1 the simple destructive1 the complex constructive1 and the complex destructive4 ,the following symbolizations illustrate these four kinds3 ,simple ,constructive ,dilemma4 ,if ,a is ,b1 ,w is ,x2 and if ,c is ,d1 ,w is ,x1 ,but either ,a is ,b or ,c is ,d1 ,hence ,w is ,x4 ,this is termed a simple dilemma because there is but one consequent2 namely1 ,w is ,x4 ,the conclusion being affirmative makes it constructive4 ,simple ,destructive ,dilemma4 ,if ,a is ,b1 ,w is ,x2 and if ,a is ,b1 ,y is ,z1 ,but either ,w is not ,x or ,y is not ,z1 ,hence ,a is not ,b4 ,this is simple because there is but one antecedent1 ,a is ,b1 and destructive because the conclusion is negative4 ,complex ,constructive ,dilemma4 ,if ,a is ,b1 ,w is ,x2 and if ,c is ,d1 ,y is ,z1 ,but either ,a is ,b or ,c is ,d1 ,hence either ,w is ,x or ,y is ,z4 ,this is complex because there are two antecedents and two consequents2 constructive1 inasmuch as the conclusion is affirmative4 ,complex ,destructive ,dilemma4 ,if ,a is ,b1 ,w is ,x2 and if ,c is ,d1 ,y is ,z1 ,but either ,w is not ,x or ,y is not ,z1 ,hence either ,a is not ,b or ,c is not ,d4 ,this is complex because there are two antecedents as well as two consequents1 and destructive because the conclusion is negative4 ,briefly3 7#a7 ,a simple dilemma is one where either the antecedent or consequent is repeated2 whereas if neither is repeated the dilemma is complex4 7#b7 ,a constructive dilemma contains an affirmative conclusion2 while a destructive dilemma uses a negative conclusion4 7#c7 ,a simple dilemma has as its conclusion a categorical proposition2 whereas the conclusion of a complex dilemma is always disjunctive4 ,if the number of antecedents and consequents be increased1 a trilemma1 tetralemma1 etc41 may result4 ,,illustration,trilemma4 ,if ,a is ,b1 ,w is ,x2 and if ,c is ,d1 ,y is ,z2 and if ,e is ,f1 ,u is ,v1 ,but either ,a is ,b1 or ,c is ,d1 or ,e is ,f1 ,hence either ,w is ,x1 or ,y is ,z1 or ,u is ,v4 ,some authorities define a dilemma as a syllogism in which the 8major-hypothetical0 has more than one antecedent while the 8minor0 must be disjunctive4 ,this viewpoint necessarily excludes the second form or the simple destructive dilemma4 ,the weight of authority1 however1 appears to favor the classification here recommended4 #ae4 ,,the ,,one ,,rule ,,involved ,,in ,,dilemmatic ,,arguments4 ,since the major premise of the dilemma is hypothetical1 the rule for testing such would of necessity be the hypothetical rule2 namely1 8,the minor premise must either affirm the antecedent or deny the consequent40 ,as this rule and the fallacies incident to it have been treated in detail1 further discussion is unnecessary4 #af4 ,,illustrative ,,exercise ,,testing ,,disjunctive ,,and ,,dilemmatic ,,arguments4 7#a7 ,if the arithmetic contains useful facts1 it will help to good citizenship2 and if it trains the powers of reason1 it will help to good citizenship1 ,but the arithmetic either contains useful facts or trains the powers of reason1 ,hence it will help to good citizenship4 ,this is a simple constructive dilemma in which the minor premise affirms the antecedents4 ,the argument is1 therefore1 valid since it conforms to the rules of the hypothetical syllogism4 ,the fact that the minor premise may not be a perfect disjunctive does not invalidate the conclusion1 inasmuch as it is perfectly obvious that if the arithmetic fulfilled both the requirements of the antecedents1 the conclusion would still obtain4 ,it may1 therefore1 be inferred that if the dilemma conforms to the rules of the hypothetical argument1 it is valid1 though the disjunctive proposition which it contains may not be strictly logical4 7#b7 ,a man is either temperate or intemperate2 and1 as ,i have seen you drunk several times1 ,i conclude that you are intemperate4 ,arranged logically4 ,a man is either temperate or intemperate1 ,you are not temperate1 ,you are intemperate4 ,it would seem that the major premise is a logical disjunctive1 since temperate and intemperate indicate that the alternatives are mutually exclusive and the enumeration complete4 ,and since the minor premise denies one alternative while the conclusion affirms the other1 we may infer that the argument is valid4 7#c7 ,if a man is honest1 he will either pay his debts or explain2 but this fellow paid no heed to the repeated notifications4 ,arranged logically4 ,if a man is honest1 he will pay his debts2 and if he is honest1 he will explain in case he cannot pay1 ,this man neither paid his debt1 nor explained1 ,this man is not honest4 ,this is a simple destructive dilemma1 and since the minor premise denies the consequents it is valid4 7#d7 ,a voter must either favor protection or free trade2 and since you do not favor protection1 you must be a free trader4 ,the disjunctive is not logical as one might believe in universal reciprocity4 ,the argument is1 therefore1 invalid4 ,why8 7#e7 ,if a man were loyal1 he would not be unduly critical2 and if he were wise1 he would not be too loquacious2 but ,i find this clerk has been both unduly critical and too loquacious2 hence ,i consider that he has been not only unwise but strikingly disloyal4 ,this complex dilemma is valid since the minor premise denies the two consequents4 #ag4 ,,ordinary ,,experiences ,,related ,,to ,,the ,,disjunctive ,,proposition ,,and ,,hypothetical ,,argument4 7#a7 ,one desires to take a certain trip which involves various routes2 information from time tables reveals the fact that there are three routes ,a1 ,b1 and ,c4 ,concerning the conditions of the journey the most important factor is the matter of comfort4 ,further investigation makes evident that route ,b will be the most comfortable one1 and consequently is the route selected4 ,putting this ordinary experience in argumentative form gives the following3 ,the route is to be either ,a1 or ,b1 or ,c2 ,i will take route ,a2 if it is the most comfortable2 7co-extensive7 ,a is not the most comfortable route1 ,hence ,i will not take route ,a4 ,if ,b is the most comfortable route1 ,i will take it2 ,b is the most comfortable route1 ,hence ,i will take route ,b4 7#b7 ,the symptoms suggest either malarial or typhoid fever2 the physician is undecided till a blood test makes evident that it is not typhoid4 ,considered argumentatively4 ,this disease is either malarial or typhoid fever2 ,if it is typhoid1 the blood will reveal certain evidences2 ,but the blood does not reveal these evidences1 ,hence the disease is not typhoid4 7#c7 ,the natural bent of the youth suggests the profession of either the ministry or teaching4 ,he finally decides to follow the one in which he can best serve his fellows4 ,this1 after mature deliberation1 appears to him to be the work of the teacher4 ,thrown into the form of an argument the following results3 ,i am best fitted for either the pulpit or the schoolroom2 ,if the schoolroom furnishes the richest field for helping my fellows1 ,i will choose that work2 ,the schoolroom does appear to furnish such a field1 ,hence ,i will choose the work of the teacher4 ,it would appear from these ordinary experiences that frequently we are brought face to face with a choice of alternatives which are not unattractive1 as in the case of the dilemma4 ,moreover1 some condition suggests itself which1 if proved or disproved1 will lead to a choice of one of these alternatives4 ,such circumstances when thrown into the form of an argument present a disjunctive proposition followed by a hypothetical argument4 ,to put it differently3 ,often in our daily affairs a most prominent limiting condition induces us to select one out of several alternatives4 ,these alternatives are not dilemmatic in nature4 #ah4 ,,outline4 ,,hypothetical ,,arguments1 ,,and ,,disjunctive ,,arguments ,,including ,,the ,,dilemma4 7#a7 ,three kinds of arguments ,categorical1 hypothetical1 disjunctive4 7#b7 ,hypothetical arguments ,defined1 illustrated4 7#c7 ,antecedent and consequent4 ,how determined1 illustrations4 7#d7 ,two kinds of hypothetical arguments ,constructive1 destructive1 illustrations4 7#e7 ,rule and two fallacies of the hypothetical argument4 ,illustrations and application of rules4 ,fallacy of denying antecedent4 ,fallacy of affirming consequent4 ,co-extensive hypotheticals4 7#f7 ,hypothetical arguments reduced to the categorical form4 ,rule1 illustrations4 ,hypothetical and categorical arguments compared4 7#g7 ,illustrative exercises testing hypothetical arguments of all kinds4 7#h7 ,disjunctive arguments4 ,defined1 illustrated4 7#i7 ,two kinds of disjunctive arguments4 ,by 8affirming denies10 by 8denying affirms40 ,illustration4 7#aj7 ,first rule4 ,stated1 illustrated4 7#aa7 ,second rule ,stated1 illustrated4 7#ab7 ,reduction of disjunctive argument ,two steps4 7#ac7 ,the dilemma ,definition4 7#ad7 ,four forms of dilemmatic arguments ,simple constructive1 simple destructive1 ,complex constructive1 complex destructive4 ,illustrations4 7#ae7 ,the rule4 7#af7 ,illustrative exercises testing disjunctive and dilemmatic arguments4 7#ag7 ,ordinary experiences related to the disjunctive proposition and hypothetical argument4 #ai4 ,,summary4 7#a7 ,just as there are three kinds of propositions so there are three kinds of arguments2 namely1 categorical1 hypothetical1 disjunctive4 7#b7 ,categorical syllogistic arguments are those in which all of the propositions are categorical4 ,hypothetical syllogistic arguments are those in which the major premise is hypothetical4 ,in contradistinction to disjunctives1 hypothetical arguments may be referred to as 8conjunctive04 7#c7 ,the hypothetical proposition is composed of antecedent and consequent2 the former being the limiting condition2 while the latter is the direct assertion4 ,as the words indicate the antecedent usually precedes the consequent4 ,the signs of the antecedent are 8if10 8though10 8unless10 8suppose10 8granted that10 8when10 etc4 7#d7 ,the two kinds of hypothetical syllogisms are the constructive and destructive2 the former is involved when the minor premise affirms the antecedent2 the latter when the minor premise denies the consequent4 ,these two kinds are sometimes referred to as 8modus ponens0 and 8modus tollens0 respectively4 7#e7 ,out of the four possible hypothetical syllogisms only two are valid as investigation proves this rule3 ,the minor premise must affirm the antecedent or deny the consequent4 ,in the case of the hypothetical proposition being co-extensive1 the rule does not apply4 7#f7 ,hypothetical arguments may be reduced to the categorical by contracting the antecedent of the hypothetical proposition to form the subject-term1 and by contracting the consequent of the hypothetical proposition to form the predicate-term of the major premise of the categorical syllogism4 ,if it is necessary1 supply a new minor term4 ,denying the antecedent is a matter of illicit major2 whereas affirming the consequent is equivalent to undistributed middle4 7#g7 ,hypothetical arguments may be tested by following this outline3 7#a7 ,arrange logically4 7#b7 ,determine antecedent and consequent4 7#c7 ,apply hypothetical rule4 7#d7 ,reduce to categorical form4 7#e7 ,apply categorical rules4 7#h7 ,a disjunctive syllogism is one in which the major premise is a disjunctive proposition4 7#i7 ,the two kinds of disjunctives are those which 8by affirming deny0 and those which 8by denying affirm40 7#aj7 ,in testing disjunctive arguments there are two rules involved3 ,first1 8,the major premise must assert a logical disjunction40 ,this necessitates the two requisites 8the alternatives must be mutually exclusive0 and the 8enumeration must be complete40 ,the two opinions relative to the nature of an alternative assertion are1 first1 if one is false1 the other must be true and vice versa2 and second1 if one is false1 the other must be true1 but both may be true4 ,the first is adopted in this discussion4 ,second4 ,the second rule involved is 8,when the minor premise affirms or denies one of the alternatives of a logical disjunctive the conclusion must deny or affirm all of the others40 7#aa7 ,subjecting the disjunctive arguments to the categorical test gives evidence to the close relation existing between the two forms4 ,a logical disjunctive proves to be logical when reduced to the categorical4 ,the reduction entails the two steps1 first1 reduce to the hypothetical2 second1 reduce to the categorical4 7#ab7 ,the logical meaning of the dilemma is suggested by the popular conception4 ,one is said to be in a dilemma when two courses are open to him1 neither of which is specially attractive4 ,a logical dilemma presents two alternatives either one of which might well be avoided4 ,the major premise of the dilemma is hypothetical2 while the minor is disjunctive4 7#ac7 ,the four forms of the dilemma are the simple constructive1 the simple destructive1 the complex constructive and the complex destructive4 7#ad7 ,the dilemma is subject to the hypothetical rule which is1 8,the minor premise must either affirm the antecedent or deny the consequent40 7#ae7 ,the minor premise need not be a logical disjunctive provided the major conforms to the hypothetical rule4 7#af7 ,frequently when ordinary experiences are reduced to augmentative form they present a disjunctive proposition followed by a hypothetical argument4 #bj4 ,,review ,,questions4 7#a7 ,relate the three kinds of arguments to the three general kinds of propositions4 7#b7 ,define and illustrate the hypothetical argument4 7#c7 ,explain the term conjunctive with reference to hypothetical arguments4 7#d7 ,explain and illustrate antecedent and consequent in hypothetical arguments4 7#e7 ,select from the following the antecedent and consequent3 7#a7 8,i usually succeed when ,i try40 7#b7 8,i will not undertake it unless you guarantee half of the sum needed40 7#c7 8,though ,i speak with the tongues of men and of angels1 and have not charity1 ,i am become as sounding brass or a tinkling cymbal40 7#f7 ,illustrate the two kinds of hypothetical syllogisms which are valid4 7#g7 ,state and explain the rule to which hypothetical arguments must conform4 7#h7 ,state and exemplify the one exception to the hypothetical rule4 7#i7 ,explain how hypothetical arguments may be reduced to the categorical form4 ,illustrate4 7#aj7 ,show by illustration that denying the antecedent is equivalent to illicit major1 while affirming the consequent is equivalent to undistributed middle4 7#aa7 ,reduce to the categorical form and test3 8,if ,napoleon had possessed more of the spirit of ,washington1 he would have been less famous but a better man than he was2 but he did not possess the spirit of the #8,father of ,his ,country4'0 7#ab7 ,test according to outline the following hypothetical arguments3 7#a7 8,if it be a good thing to have faith1 then certainly he who believes in the bible of a pagan has faith and must have a good thing40 7#b7 8,if a #aj-;inch charge burst inside of a tank1 there would be nothing left of the tank4 ,it would be blown into small pieces40 7#c7 8,if the plate found had been originally on the outside of the ship1 ,i should have judged that there must be green paint on it1 but ,i could not find green paint on that part of the ship40 7#d7 8,if ,i mistake not1 you are the man who did not pay me for that pair of shoes4 ,i am sure that you are the man as ,i never forget a face40 7#e7 8,if the maxim #8,early to bed and early to rise makes one healthy1 wealthy and wise' were true1 ,i would have been a millionaire long ago40 7#ac7 ,define and illustrate a disjunctive argument4 7#ad7 ,exemplify the two kinds of disjunctive arguments4 7#ae7 ,what is meant by a logical disjunction8 7#af7 8,the alternatives must be mutually exclusive40 ,explain this1 illustrating fully4 7#ag7 ,cite cases where the enumeration is not complete4 7#ah7 ,state in complete form both of the rules to which all disjunctive arguments must conform4 7#ai7 ,show by illustration how the disjunctive syllogism may be reduced to the categorical4 7#bj7 ,define and illustrate the dilemma4 7#ba7 ,give examples1 using symbols1 of the four dilemmatic forms4 ,explain why these forms are so named4 7#bb7 ,why does the hypothetical rule apply to the dilemmatic syllogism8 7#bc7 ,test the validity of the following3 ,give reasons4 7#a7 8,if a substance is solid it possesses elasticity and so also it does if it be a liquid or gaseous2 but all substances are either solid1 liquid or gaseous2 therefore1 all substances possess elasticity40 7#b7 8,if men were prudent1 they would act morally for their own good2 if benevolent1 for the good of others4 ,but many men will not act morally1 either for their own good or that of others2 such men1 therefore1 are not prudent or benevolent40 7#c7 8,if the majority of those who use public houses are prepared to close them1 legislation is unnecessary2 but if they are not prepared for such a measure1 then to force it upon them by outside pressure is both dangerous and unjust40 7#d7 8,the man is either a liar or a fool and in either case he is beneath my attention40 7#e7 8,either he is sincere or else he is the most astute impostor the world has ever produced2 for me ,i prefer to think him sincere40 7#bd7 ,explain the relation that many experiences appear to bear toward an argument introduced by a disjunctive proposition and followed by a hypothetical syllogism4 ,illustrate4 #ba4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,may both premises of a hypothetical argument be hypothetical propositions8 ,explain4 ,see ,fowler p4 #aae4 7#b7 ,which of the two is valid8 ,explain4 7#a7 ,if ,a is ,b1 ,c is ,d ,if ,a is ,b1 ,e is ,f ,if ,c is ,d1 ,e is ,f 7#b7 ,if ,a is ,b1 ,c is ,d ,if ,c is ,d1 ,e is ,f ,if ,a is ,b1 ,e is ,f 7#c7 ,show by circles that two of the possible four hypothetical arguments are invalid4 7#d7 ,what categorical rules does the hypothetical argument seem to violate8 ,explain4 7#e7 ,originate a hypothetical syllogism whose antecedent and consequent are both negative4 ,test its validity4 7#f7 ,originate a co-extensive hypothetical argument and show that four valid syllogisms may be derived from it4 7#g7 ,explain by word and illustration the two meanings which may be attached to 8either-or40 7#h7 ,if we accepted the opinion that both alternates of a disjunctive may be true1 which kind of disjunctive argument would it invalidate8 7#i7 ,in a logical disjunction what law of thought is involved8 ,explain4 7#aj7 ,why do the laws of the disjunctive seem to contradict the categorical rules8 ,explain fully4 7#aa7 ,show by drawing on common experience that a logical dilemma is closely related to the popular conception of dilemma4 7#ab7 ,illustrate by symbols and then place in good ,english a pentalemma4 7#ac7 ,state a definition of a dilemma which excludes the simple destructive form4 7#ad7 ,give a common experience which1 when thrown into argumentative form1 results in a disjunctive proposition followed by a hypothetical syllogism4 ,coin a name for such a combination4 ,,chapter #af4 ,,the ,,logical ,,fallacies ,,of ,,deductive ,,reasoning4 #a4 ,a ,,negative ,,aspect4 ,it has been remarked that 8,logic as a science makes known the laws and forms of thought and as an art suggests conditions which must be fulfilled to think rightly40 ,in recent chapters we have discussed the second aspect of the definition2 in these we have attempted to answer the question1 8,what rules must be followed in order to reason correctly80 ,we are now ready to treat the same aspect from a negative point of view namely1 what errors must be avoided in order to reason correctly8 ,what are the fallacies which we must strive to avoid in our own thinking1 and attempt to correct in the thinking of others8 #b4 ,,paralogism ,,and ,,sophism4 8,fallacy0 comes from the ,latin fallacia1 meaning deceptive or erroneous1 and therefore a fallacy in logic is any error in reasoning which has an appearance of correctness4 ,if the writer or speaker is himself deceived by the fallacy1 then such is called a ,paralogism2 but if the fallacy is committed by him for the expressed purpose of deceiving others1 then such becomes a ,sophism4 ,during the time of the ,schoolmen the ,sophism was in such high repute that it required even a ,socrates to puncture this ignominious bubble of vain trickery4 ,in fact1 ,socrates1 the greatest of all pagan educators1 led the crusade which has relegated to the 8logical dust bin0 the notion that skill in the art of framing sophisms is a scholarly accomplishment4 ,many believe modern sophistry to be the chief social and commercial evil of the day1 and to ,socrates must be given the credit for teaching us to look upon those who would practice sophism with righteous indignation and pronounced disgust4 ,however1 paralogism and not sophism is the more legitimate field for the student of logic2 his problem being1 8,what are the common errors which ,i1 as a writer and speaker1 must strive to avoid80 #c4 ,a ,,division ,,of ,,the ,,deductive ,,fallacies4 ,the mistakes of induction will occupy our attention in a later chapter4 ,we are now concerned with the fallacies of deduction4 ,any classification or division of the deductive fallacies must of necessity be faulty4 ,even the labors of ,aristotle in this regard are now pronounced crude and unsatisfactory4 ,this is due to the divergence of opinion as to the signification of some of the fallacies1 as well as to the fact that no division is free from the fault of an overlapping of the species4 ,as a result of this lack of unanimity in definition and lack of ability in making the species mutually exclusive1 any division of the deductive fallacies must be more or less illogical4 ,aristotle divides the fallacies of deduction into two groups3 7#a7 ,fallacies in dictione1 or formal fallacies4 7#b7 ,fallacies extra dictionem1 or material fallacies4 ,this division has received universal approval and though many distinctions made by him have been abandoned1 yet most logicians retain his phraseology4 ,since many of the technical terms which ,aristotle used have lived through the generations under the conventional meaning which he assigned to them1 it becomes less confusing to adhere as closely as possible to these terms4 ,therefore1 in the attending division only those changes have been made which progress and experience have forced upon us4 ,what remains of this chapter will be devoted to explaining these fallacies as they appear in this division4 ,for the sake of clearness and definiteness it is strongly recommended that the student study the outline extensively enough to be able to reproduce it4 ,fallacies4 ,formal 7,in dictione7 #a4 ,opposition #a4 ,immediate #b4 ,obversion inference #c4 ,conversion #d4 ,contraversion #e4 ,four terms #f4 ,undistributed middle #b4 ,categorical #g4 ,illicit major arguments #h4 ,illicit minor #i4 ,negative premises #aj4 ,particular premises #c4 ,hypothetical #aa4 ,denying the antecedent arguments #ab4 ,affirming the consequent #d4 ,disjunctive #ac4 ,illogical disjunction arguments ,material 7,in dictionem7 #a4 ,ambiguous middle #b4 ,amphibology #a4 ,in ,language #c4 ,accent ,equivocation #d4 ,composition #e4 ,division #f4 ,figure of speech #a4 ,accident #b4 ,converse accident #b4 ,in ,thought #c4 ,irrelevant conclusion ,assumption #d4 ,non sequitur #e4 ,false cause #f4 ,complex question #g4 ,begging the question #d4 ,,general ,,divisions ,,explained4 ,the formal fallacies are those which concern the form of the argument rather than the meaning4 ,these fallacies arise from an improper use of words as arbitrary signs of thought1 not from any inconsistency in the thought itself4 ,to commit a formal fallacy we must violate one of the specific rules of logic4 ,for this reason the formal fallacies are easier of comprehension4 ,moreover1 because of this definiteness logicians are better able to come to some agreement as to their content and import4 ,classing the fallacies of immediate inference as formal is somewhat of an innovation2 but since they occur because of the breaking of certain definite rules1 and since immediate inference is a matter of changing the form without altering the meaning1 we believe there is some justification for this position4 ,some would class 8immediate inference0 fallacies with the material fallacies of language4 ,the material fallacies are fallacies of meaning and not of form4 ,they are those arising from inconsistency in thought1 and from imperfect ways of interpreting this thought as it appears in language4 ,no very specific rules of logic are violated by them and for this reason there are those who would entirely eliminate the material fallacies from the field of logic4 ,but since thought is even more subtle than form in its deceitful machinations1 we believe that the material fallacy calls for special attention on the part of the logician4 ,material fallacies are divided into two kinds4 ,first1 those which have reference to wrong thinking1 or fallacies in thought2 and1 second1 those which are due mainly to an incorrect interpretation of words1 or fallacies in language4 ,the former result from inconsistency and unreasonableness in thought1 whereas the latter come from lack of precision in expression4 #e4 ,,fallacies ,,of ,,immediate ,,inference4 ,fallacies of immediate inference arise from some violation of the rules which this topic enunciates4 7#a7 ,opposition4 ,among other statements opposition posits these two3 7#a7 ,when the particular is true its opposing universal is indeterminate2 7#b7 ,a universal negative does not necessarily contradict a universal affirmative4 ,these signify that neither an ,a nor an ,e must be assumed to be true when the corresponding ,i or ,o is true1 and that ,e may not always contradict ,a1 nor ,o contradict ,i4 ,,illustrations ,,of ,,fallacies ,,of ,,opposition4 7#a7 ,since some men are wise1 then ,i may conclude that all men are wise4 7#b7 ,i have contradicted his statement 8all men are honest0 by proving that no men are honest4 ,there is little difference between fallacies like 7#a7 and fallacies of converse accident4 ,concerning illustration 7#b71 both statements are false2 but to contradict we know that if one is false1 the other must be true4 7#b7 ,obversion4 8,two negatives are equivalent to one affirmative10 is the principle underlying obversion4 ,the most common fallacy in obversion springs from using one negative instead of two4 ,,illustrations ,,of ,,fallacious ,,obversion4 7a7 ,original3 ,some men are not wise4 ,obverse3 7incorrect7 ,some men are wise4 7b7 ,original3 ,all true teachers are just4 ,obverse3 7incorrect7 ,all true teachers are not just4 7#c7 ,conversion4 ,conversion involves the interchanging of the subject and predicate of a proposition without affecting the distribution2 in consequence the usual fallacy incident to this interchange is distributing an undistributed term4 ,,illustrations ,,of ,,fallacy ,,of ,,conversion4 7a7 ,original3 ,all fixed stars are heavenly bodies4 ,converted3 7incorrectly7 ,all heavenly bodies are fixed stars4 7b7 ,original3 ,some men are not wise4 ,converted3 7incorrectly7 ,some wise beings are not men4 7#d7 ,contraversion4 ,as this process involves the two steps of obversion and conversion1 fallacies appertaining to contraversion would relate to these two steps4 ,,illustrations ,,of ,,fallacies ,,of ,,contraversion4 7a7 ,original3 ,no honest man fails to pay his debts4 ,contraverted3 7incorrectly7 ,some who do not pay their debts are honest men4 7b7 ,original3 ,some animals are quadrupeds4 ,contraverted3 7incorrectly7 ,some not-quadrupeds are not animals4 ,the formal fallacies of categorical1 hypothetical1 and disjunctive arguments have received detailed treatment in chapters #aa1 #ad and #ae2 we may1 therefore1 devote our attention to the material fallacies without further delay4 #f4 ,,fallacies ,,of ,,language4 7,equivocation47 ,these are the fallacies of double meaning4 ,it is known that an equivocal term is one which permits two or more interpretations2 similarly a proposition which admits of two or more interpretations may be denominated equivocal4 ,thus the term equivocation has come to stand for all errors in language resulting from a possibility of more than one interpretation4 ,this justifies the position of referring to all of the six fallacies in language as fallacies also of equivocation4 7#a7 ,ambiguous middle4 ,ambiguous middle explains itself4 ,it is the fallacy of giving to the middle term a double meaning4 ,in form the argument may contain but three terms1 yet in meaning there are in reality four terms4 ,for this reason ambiguous middle and the fallacy of four terms appear to be about one and the same thing2 but in this treatment we shall regard them as mutually exclusive1 and this is the distinction3 ,invalid arguments of 8ambiguous middle0 have only three terms in form but four terms in meaning4 ,this signifies that the middle term though identical in form is given a double meaning4 ,invalid arguments of 8four terms0 always have four terms in both form and meaning2 they are 8logical quadrupeds0 in every sense of the word4 ,,illustrations4 ,ambiguous middle4 7a7 8,necessity is the mother of invention10 ,bread is a necessity1 ,bread is the mother of invention4 7b7 8,nothing is better than wisdom10 ,dry bread is better than nothing1 ,dry bread is better than wisdom4 7c7 ,a church is a force for good in any community1 ,a slate roof is good for a church1 ,a slate roof is a force for good in any community4 ,fallacies of four terms4 7a7 ,all true teachers are just1 ,john ,doe is an educator1 ,john ,doe is just4 7b7 ,milk is nourishing1 ,this substance is a white fluid1 ,this substance is nourishing4 7c7 ,thieves should be imprisoned1 ,this man has taken what does not belong to him1 ,this man should be imprisoned4 ,in the 8four-term0 fallacies1 observe that the four terms occur in the premises4 ,when a fourth term is introduced in the conclusion1 the material fallacy of non sequitur has been committed4 7#b7 ,amphibology 7or amphiboly74 ,amphibology is a fallacy resulting from an ambiguous proposition rather than from the ambiguity of any particular term4 ,the fallacy of amphibology is committed when the spoken or written proposition conveys more than one meaning4 ,the ancient oracles indulged in this sort of fallacy1 the reason for such indulgence being obvious2 the oracles were not too positive as to the outcome of their prognostications1 and therefore were especially careful to cover every emergency4 ,a careless use of relative clauses and prepositional phrases often results in the fallacy of amphibology4 ,,illustrations ,,of ,,the ,,fallacy ,,of ,,amphibology4 7a7 8,you the enemy will slay40 7b7 8,the ,duke yet lives that ,henry shall depose40 7c7 8,wanted a piano by a young lady made of mahogany40 7d7 8,you your father will punish40 7#c7 ,accent4 ,this fallacy springs from placing undue emphasis on some word or group of words4 ,naturally such accentuation may convey a meaning entirely foreign to the author's intent4 ,newspapers are guilty of this fallacy when they select a few words from a speech and use them as headlines without further explanation4 ,a politician may quote a sentence uttered by an opponent and fail to relate it to what preceded or followed4 ,a cartoonist may arouse the prejudice of public opinion by giving ridiculous emphasis to some idiosyncracy possessed by the subject of his attack4 ,,illustrations ,,of ,,fallacies ,,of ,,accent4 7a7 8,thou shalt not bear false witness against thy neighbor40 ,by giving undue emphasis to neighbor1 the notion is clearly conveyed that one may bear false witness against all who are not neighbors4 7b7 8,you must not crib when taking my examinations40 7c7 ,what the 8,spellbinder0 said4 8,i may say1 as a side remark1 that the labor unions are guilty of developing a nation of shirks1 when they prohibit a phenomenally efficient workman from doing his best40 8,i do not wish to be misunderstood in this40 8,i believe in labor unions but in this particular they are dead wrong40 ,what the newspaper reported4 7,headline7 8,the ,labor ,union ,scored as a ,training ,school for ,shirks40 8 said in his speech in ,hall that the ,union was responsible for the development of a nation of shirks40 8,a good man10 said he1 8is not permitted to do his best work40 7#d7 ,composition4 ,the fallacy of composition is committed when it is assumed that what is true distributively is likewise true collectively4 ,a term is used in a distributive sense when it is applied to each individual of the class2 whereas a term is used in a collective sense when it is applied to the class considered as one whole4 8,all0 meaning each one considered separately and 8all0 meaning the whole furnishes a frequent pitfall for this fallacy4 ,,illustrations ,,of ,,the ,,fallacy ,,of ,,composition4 7a7 8,every member of the team is a star player2 hence ,i expect that the entire aggregation will be a winner40 7b7 8,all the men of the jury are fair minded2 therefore we have good reason for supposing that the jury's verdict will be in accord with the rules of justice40 7c7 8,thirteen and twenty-three are odd numbers2 thirty-six is equal to thirteen and twenty-three2 hence thirty-six is an odd number40 7d7 8,all the angles of a triangle are less than two right angles2 hence the angles ,x1 ,y and ,z are less than two right angles40 7e7 ,in governmental affairs the assumption1 that a law which benefits one section will benefit all1 is a fallacy of composition4 7#e7 ,division4 ,the fallacy of division is committed when it is assumed that what is true collectively is true distributively4 ,division is the converse of composition4 ,composition is a fallacious procedure from a distributive to a collective use2 while division is a fallacious procedure from a collective to a distributive use4 ,the fallacy of division may be illustrated by giving the converse of the illustrations under composition3 7a7 8,the team is a star playing team2 and since ,smith is the #8first baseman' of the team1 he must be a star player40 7b7 8,the jury rendered a just decision2 hence the foreman is a fair minded man40 7c7 ,thirty-seven is an odd number1 ,nine and twenty-eight are thirty-seven1 ,nine and twenty-eight are odd numbers4 7d7 ,all the angles of a triangle are equal to two right angles1 ,a is an angle of a triangle1 ,a is equal to two right angles4 7#f7 ,figure of ,speech4 ,this fallacy results from assuming that words of the same root have the same meaning4 ,since the same root-word may be used as a noun1 verb1 adjective1 etc41 it does not follow that in these various forms it retains a common meaning4 8,address0 as a noun and 8address0 as a verb convey two distinct meanings4 ,the following are examples of this fallacy3 7a7 ,no designing person should be trusted1 ,this architect is a designer1 ,this architect should not be trusted4 7b7 ,justifiable investigation is wise1 ,this man is a just investigator1 ,this man is wise4 ,these fallacies are not classed as those of 8four terms0 because two terms so closely resemble each other in form1 and yet they are not fallacies of ambiguous middle2 since the middle terms are not identical in form4 #g4 ,,fallacies ,,in ,,thought4 ,the fallacies in thought arise through a tendency to assume as true that which demands further proof4 ,any one who is more anxious to be right than to win will make sure that nothing has been taken for granted which should receive further investigation1 or that no truth has been given a presumptuous twist in order to make it fit the particular case under discussion4 ,because these errors in thought may be attributed chiefly to undue assumptions1 we may denominate them as the fallacies of assumption4 7#a7 ,accident4 ,the fallacy of accident occurs when one reasons from a general truth to an accidental case4 ,doctrinaires and theoretic enthusiasts are partial to this fallacy4 ,it is so easy to lay down a general formula or remedy and then attempt to apply it to every accidental circumstance4 ,grandmother with her catnip tea and mustard plaster1 however we may cherish the memory of the dear old soul1 was nevertheless guilty of the fallacy of accident4 ,applying maxims and proverbs to particular instances is still another way of committing the fallacy4 ,,examples ,,of ,,fallacies ,,of ,,accident4 7a7 8,honesty is the best policy10 thinks the physician as he reveals the cold1 hard truth to his patient and thus shortens the patient's life4 7b7 ,spirituous liquor in excess acts as a poison1 and therefore should not be used to resuscitate an extreme case4 7c7 8,what is bought in the market is eaten2 raw meat is bought in the market2 therefore it is eaten40 7d7 8,early to bed and early to rise makes one healthy1 wealthy and wise40 ,i shall practice this for ten years and by that time hope to be healthy1 wealthy and wise4 7e7 ,john has earned the enviable 787 reputation of being the 8worst boy in school10 hence he is going to be the worst boy in 8my grade40 7f7 ,mary is an inveterate whisperer2 and since ,i know that some one is whispering1 ,i am sure that that some one is ,mary4 7g7 ,being a convict1 he is not to be trusted4 7#b7 ,converse ,accident4 ,as the title implies this is the fallacy of reasoning from an accidental case to a general truth4 ,illustrations3 7a7 8,john has been a bad boy to-day2 and hence he is going to make trouble during the entire term40 7b7 8,this food is good for hens2 and hence it is good for all domestic fowls40 7c7 8,i know of several men who have been phenomenally serviceable to mankind1 and none of these men were college trained2 hence ,i conclude that college education is not essential to the attainment of the highest state of efficiency40 ,relative to both accident and converse accident1 it may be said that they obtain because all general truths1 such as rules1 principles1 definitions1 maxims1 etc41 have their exceptions2 and it is through these exceptions that the two fallacies are made possible4 ,accident and ,converse ,accident ,distinguished from ,division and ,composition4 ,the fallacy of accident1 we have learned1 occurs when one reasons from a general truth to an accidental case2 whereas the fallacy of division obtains when one reasons from a collective use of a term to a distributive use2 in both cases the procedure is from a larger unit to a smaller unit4 ,moreover1 with converse accident and composition1 the movement is from the smaller unit to the larger4 ,because of this similarity there is danger of confusing the two kinds of fallacies4 ,as a matter of distinction between the fallacies of accident1 and composition and division the attending comparative rsum may be of value3 7#a7 ,division is similar in movement to accident1 while composition resembles converse accident4 7#b7 ,a valuable cue for remembering which way division and accident move1 is to recall that division in arithmetic is a procedure from the larger unit to the smaller1 and therefore that division in logic would have the same signification4 7#c7 ,division and composition pertain to mathematical wholes2 while accident and converse accident relate to logical wholes4 7#d7 ,the aggregates of division and composition may be counted or enumerated easily2 while the accident and converse accident aggregates 7or generals7 are not easily enumerated4 7#e7 ,division and composition relate to logical terms1 whereas accident and converse accident relate to general truths4 7#f7 ,division and composition use a term in a collective sense and then in a separate or distributive sense1 or vice versa2 accident and converse accident use a thought in a general and then in an accidental sense1 or vice versa4 ,irrelevant ,conclusion 7,ignoratio ,elenchi74 ,the fallacy of irrelevant conclusion results when the argument does not squarely meet the point at issue4 ,it is the fallacy of arguing to the wrong point either purposely or through ignorance4 ,one in defense1 who has a weak case1 may be tempted to divert attention from the point in hand1 realizing that a close analysis of the matter in dispute will tend to his undoing4 ,in such instances 7#a7 the lawyer will abuse the plaintiff1 7#b7 the demagogue will tell humorous stories1 7#c7 the teacher will take advantage of the ignorance of the pupil1 7#d7 the scholar will refer to authority and 7#e7 the magnate will fall back upon the power of position and wealth4 ,these forms of 8rhetorical thinking0 are as harmful as they are popular1 and furnish one of the chief reasons for giving to the common people a better understanding of 8how to think0 as well as 8how not to think40 ,definite names have been given to the various forms of irrelevant conclusion which may be summarized as follows3 ,argumentum ad populum4 ,this is the fallacy of appealing to the feelings1 passions and prejudices of an audience rather than to their good sense and powers of reason4 ,it is probably the most common of the group4 ,to excite sympathy1 the lawyer for the defense may speak feelingly of the suffering that an unfavorable verdict will bring to the wife and children of the accused4 ,argumentum ad hominem4 ,here the character of the opponent is defamed with a view of discrediting him with the court or audience4 8,mud throwing0 in times of political agitation is a good example of this fallacy4 ,argumentum ad ignorantiam4 ,this fallacy comes from taking advantage of the ignorance of the opponent2 the fallacy assumes that the original supposition has been proved if one is unable to prove the contradictory of the original4 ,illustration3 ,mars is inhabited because no one is able to prove that ,mars is not inhabited4 ,argumentum ad baculum4 ,in this all argumentation is made to give way to the forces of personal opposition and to the power of money4 ,illustration3 ,a political committee seating those delegates only1 who will vote their way2 and1 doing this1 not from the merits of the case1 but because said committee happen to have a sufficient number of votes to 8put the thing through40 ,argumentum ad verecundiam4 ,this fallacy comes from supposing that the whole thing may be settled by citing some noted authority who apparently substantiates the argument advanced4 ,epitome of five forms of ,irrelevant ,conclusion3 7#a7 ,appealing to the audience4 7#b7 ,defaming the character of the opponent4 7#c7 ,inability to prove the contradictory4 7#d7 ,gaining the point by force4 7#e7 ,citing authority4 ,non ,sequitur 7,false ,consequent74 ,this is the fallacy of deriving a conclusion which does not follow from the premises4 ,the fallacy obtains whenever material appears in the conclusion1 which has no bearing on the case under discussion4 8,irrelevant conclusion0 pertains to the establishment of the premises while 8non sequitur0 is concerned with the conclusion only4 ,we know that a logical thinker constructs the conclusion from material already presented by the premises2 8,non sequitur0 uses material in the conclusion which is found in neither premise4 8,non sequitur0 differs from the fallacy of four terms in that the latter uses the fourth term in the premises while the former introduces the fourth term in the conclusion1 and in a form so well obscured that it sometimes escapes notice4 ,illustration3 ,all men are thinking animals1 ,socrates was a man1 ,socrates was a scholar4 ,it does not follow that because a man is a thinking animal that he will become scholarly4 ,false ,cause4 ,this is the fallacy of assuming that because two happenings have occurred together several times1 the one is the cause of the other4 ,this very common fallacy is due to lack of discrimination1 and to the exaggerations incident to fear and superstition4 ,illustrations3 7a7 ,planting vegetables which grow down1 such as the beet1 during the last two days of the waxing moon in order to have a larger yield4 ,so far as we know the moon has no influence over growing vegetables4 7b7 ,thirteen seated at a table is an indication that one of the number will die during the year4 ,this is one of the most absurd fallacies that has ever been visited upon an intelligent people4 ,it is seen that 8,false ,cause0 is closely related to 8,non ,sequitur40 ,complex ,question 7,double ,question74 ,this fallacy obtains when an assumption is put in the form of a question4 ,,illustrations3 7a7 ,a wise father who did not want to tempt beyond the yielding point his three-year-old son1 asked1 pointing to the scratches on the new mahogany piano1 8,freddie1 did you do that last night or this morning80 7b7 ,what caused you to desist from slandering your neighbors2 ,new ,year's resolutions or the preaching of ,dominie ,x8 7c7 ,a daily paper anecdote3 8,charles ,bradlaugh1 the noted ,english free-thinker1 once engaged in a discussion with a dissenting minister4 ,he insisted that the minister should answer questions by a simple yes or no1 asserting that every question should be replied to in that manner40 ,the reverend gentleman arose and said1 8,mr4 ,bradlaugh1 will you allow me to ask you a question on these terms80 8,certainly10 said ,mr4 ,bradlaugh4 8,then1 may ,i ask1 have you given up beating your wife80 ,begging the ,question 7,petitio ,principii74 ,this is a fallacy of deriving a conclusion from notions which in themselves demand proof4 ,the fallacy is not committed when the assertion is self-evident4 ,it is easy to claim that our opponent is begging the question as soon as we see that he is getting the better of us4 ,one may himself beg the question by being too ready to charge others with begging the question4 ,when the opponent adopts premises which are commonly accepted1 he does not beg the question4 ,one commits the fallacy when he seems to prove the conclusion more satisfactorily than he really does4 ,this he may accomplish by covertly taking for granted the truth of notions which have not the stamp of universal approval4 ,the fallacy of begging the question assumes three forms3 7#a7 ,the assumption of an unproved premise 7assumptio non probata74 ,in this either the major or the minor premise1 or both may demand more substantial proof4 ,it must be borne in mind1 however1 that the disputant must not ask for further proof after he has once accepted the premises1 or after the opponent has met his demands to the satisfaction of commonly accepted authority4 ,examples of begging the question by assuming unproved premises3 7a7 ,all patriotic citizens are honest at heart1 ,this man charged with graft is a patriotic citizen1 ,this man charged with graft is honest at heart4 8,all patriotic citizens are honest at heart10 is not an accepted truth and thus demands proof4 7b7 ,a famous sophism of the ,greek philosopher by which he proved that motion was impossible1 is an excellent illustration of an assumed premise3 8,if motion is possible1 a body must move either in the place where it is1 or in the place where it is not2 ,but a body cannot move in the place where it is2 and of course it cannot move where it is not1 ,therefore1 motion is impossible40 ,referring to this1 ,de ,morgan claims 8,movement is change1 and so a body requires two places in order to move40 ,a body cannot move in the place where it is1 but must be moved from place to place4 ,the major premise being assumed1 this sophism illustrates the fallacy of begging the question4 7c7 ,the most subtle form of begging the question is an enthymeme where the suppressed premise is the one assumed2 e4 g41 8,you1 being a teacher1 should not do as other people do40 ,completed and arranged the argument becomes3 ,no teacher should do as other people do1 ,you are a teacher1 ,you should not do as other people do4 ,surely the major premise demands proof4 7#b7 ,reasoning in a ,circle 7,circulus in probando74 ,this form of begging the question occurs1 8,when a conclusion is based upon a premise which in an earlier stage of the argument was itself based upon this very conclusion40 ,to put it in another way3 ,reasoning in a circle involves proving the truth of a conclusion by using a particular premise1 and then proving the truth of the particular premise by using the conclusion4 ,from premise to conclusion and from conclusion to premise completes the circle4 ,examples of begging the question by reasoning in a circle3 7a7 ,it is wrong because my conscience pricks me1 and my conscience pricks me because it is wrong4 7b7 8,the effeminate walk shows a lack of force2 because no forceful man walks that way40 7c7 ,says ,hamilton1 8,plato1 in his ,phoedo1 demonstrates the immortality of the soul from its simplicity2 and in the ,republic1 he demonstrates its simplicity from its immortality40 7#c7 ,question ,begging ,epithets and ,appellations4 ,this is the fallacy of assuming the point at issue by means of a carefully selected epithet4 ,scientists sometimes assume to clarify an inexplicable phenomenon by giving it a technical name4 ,politicians are exceedingly free with their epithets and appellations1 and the records of religious disputes prove that the theologian often resorted to this device4 ,examples of begging the question by using epithets and appellations3 7a7 ,we must attribute the disease to heredity4 7b7 ,the candidate for governor is an animated feather duster4 7c7 ,they call him ,blue ,charlie4 7d7 ,it is the policy of the big stick4 7e7 ,the muck-raker seldom makes an efficient servant of the people4 ,it is seen that the use of these epithets and appellations is simply a rhetorical device for the purpose of creating either a favorable or unfavorable impression4 #h4 ,,outline4 ,,the ,,logical ,,fallacies ,,of ,,deductive ,,reasoning4 7#a7 ,a negative aspect of definition of logic4 7#b7 ,paralogism and sophism4 ,distinguished4 ,mission of ,socrates4 7#c7 ,a division of the deductive fallacies4 ,more or less faulty4 ,aristotle's phraseology retained4 ,division given4 7#d7 ,general divisions explained4 ,formal and material4 ,material fallacies in language and in thought4 7#e7 ,fallacies of immediate inference4 ,opposition1 obversion1 conversion1 contraversion4 7#f7 ,fallacies in language 7also fallacies of equivocation74 ,ambiguous middledistinguished from four terms4 ,amphibology4 ,accent4 ,composition8all0 a pitfall4 ,division4 ,figure of speech4 7#g7 ,fallacies in thought7also fallacies of assumption74 ,accident4 ,converse accident4 ,made possible by exceptions4 ,accident and converse accident distinguished from composition and division4 ,comparative rsum4 ,irrelevant conclusion 7ignoratio elenchi74 ,argumentum ad populum4 ,argumentum ad hominem4 ,argumentum ad ignorantiam4 ,argumentum ad baculum4 ,argumentum ad verecundiam4 ,non sequitur 7false consequent74 ,false cause4 ,complex question4 ,begging the question 7petitio principii74 ,assumption of premise4 ,reasoning in a circle4 ,question begging epithets and appellations4 #i4 ,,summary4 7#a7 ,logic as a science makes known the laws and forms of thought and as an art suggests conditions which must be fulfilled in order to think rightly4 ,a discussion of the second phase of the definition would be incomplete without a consideration of the negative aspect as well as the positive4 ,such a viewpoint makes evident the question 8,what errors must be avoided in order to reason correctly80 ,an answer to this question is given under the caption of ,logical ,fallacies4 7#b7 ,a logical fallacy is any error in reasoning which has the appearance of correctness4 ,a fallacy which deceives the writer or speaker himself is termed a paralogism1 whereas a fallacy formed for the express purpose of deceiving another is denominated a sophism4 ,it was the pagan teacher ,socrates who taught modern thought to frown upon all forms of sophism2 these exist to-day much as they did in the olden time4 7#c7 ,because of disagreement as to definition1 and because of inability to prevent an overlapping of species1 any logical division of the deductive fallacies must be faulty4 ,in the division of the deductive fallacies1 this treatise retains the phraseology and form worked out by ,aristotle1 so far as such retention is consistent with the changes incident to the advances of time4 7#d7 ,formal fallacies occur because of careless and improper use of words as arbitrary signs4 ,formal fallacies are definite and easy of comprehension4 ,the material fallacies are due to certain inconsistencies in thought and to imperfect ways of interpreting language4 ,they are more subtle and thus more difficult of comprehension than the formal fallacies4 ,there are material fallacies in thought and material fallacies in language2 the former are due to looseness in thinking and the latter to lack of precision in expression4 7#e7 ,fallacies of opposition result most frequently from deriving universals from their corresponding particulars1 and from assuming to contradict affirmative universals by negative universals and affirmative particulars by negative particulars4 ,the common fallacy in the process of obversion consists in using one negative instead of two1 whereas the ordinary error of conversion is a matter of distributing an undistributed term4 ,fallacies of contraversion must involve either those of obversion or conversion since the process is a combination of the two4 7#f7 ,fallacies in language1 because they result from permitting more than one interpretation1 may be also denominated fallacies of equivocation4 7#a7 ,ambiguous middle is the fallacy of giving to the middle term a double meaning4 ,the fallacy of four terms1 as the name signifies1 exists when the argument has four terms in both form and meaning4 ,ambiguous middle is a matter of four terms in meaning but only three in form4 7#b7 ,the fallacy of amphibology is committed when the given proposition conveys more than one meaning4 ,in order to maintain their prestige the ancient oracles made use of this fallacy4 7#c7 ,the fallacy of accent springs from placing undue emphasis on some word or group of words4 ,newspaper and demagogues are prone to this error1 that they may thus create an unfavorable impression towards those whom they oppose4 7#d7 ,the fallacy of composition is committed when it is assumed that what is true distributively is likewise true collectively4 8,all0 meaning each one and 8all0 meaning the whole class often leads to the fallacy of composition4 7#e7 ,the fallacy of division is committed when it is assumed that what is true collectively is true distributively4 ,division is the converse of composition4 7#f7 ,the fallacy of figure of speech is occasioned by assuming that words of the same root have the same meaning4 7#g7 ,fallacies in thought are likewise called fallacies of assumption1 because of the tendency to assume as true something which demands further proof4 7#a7 ,the fallacy of accident occurs when one reasons from a general truth to an accident case4 ,it is the favored fallacy of the doctrinaire1 the reformer and the vender of 8cure-alls40 7#b7 ,the fallacy of converse accident occurs when one reasons from an accidental case to a general truth4 ,both accident and converse accident are made possible because rules1 definitions1 maxims1 etc41 have exceptions4 ,it is easy to confuse division and composition with the fallacies of accident4 ,division and composition are concerned with the collective and distributive use of terms1 whereas the fallacies of accident involve the use of notions in a general and accidental sense4 ,the former represent notions which may be counted or enumerated while the latter concern notions which are logical rather than numerical4 ,composition and division involve 8number of10 accident1 8meaning of40 7#c7 ,the fallacy of irrelevant conclusion results when the argument does not squarely meet the point at issue4 ,it is the fallacy of arguing to the wrong point either purposely or ignorantly4 ,this may be accomplished by 7#a7 appealing to sympathy of audience1 7#b7 defaming character of opponent1 7#c7 assuming that the fact is true because of inability to prove the contradictory1 7#d7 gaining point by force1 7#e7 citing authority4 7#d7 8,non sequitur0 is the fallacy of deriving a conclusion which does not follow from the premises4 ,it involves introducing new material in the conclusion4 7#e7 8,false cause0 is the fallacy of assuming that because two happenings have occurred together several times the one is the cause of the other4 ,the fallacy is due largely to the exaggerations of fear and superstition4 7#f7 ,the fallacy of complex question consists in putting an assumption in the form of a question4 7#g7 ,begging the question is the fallacy of deriving a conclusion from notions which in themselves demand proof4 ,this fallacy takes the three forms of 7#a7 the assumption of an unproved premise1 7#b7 reasoning in a circle1 7#c7 question begging epithets and appellations4 #aj4 ,,illustrative ,,exercises ,,in ,,the ,,testing ,,of ,,arguments ,,in ,,both ,,form ,,and ,,meaning4 7#a;a7 ,he who wilfully takes the life of another should be electrocuted1 ,this sharp shooter has wilfully taken the life of another1 ,hence he should be electrocuted4 ,a ,in form we know this argument to be valid since it is in mood ,a of ,a the first figure4 ,but as the conclusion does not meet with our approval1 we are forced to the belief that there must be a material fallacy4 ,such proves to be the case4 ,in the first instance1 8,wilfully takes the life of another0 is used in a personal1 individual1 selfish sense1 whereas in the second instance the expression is used in a general1 8servant-of-the-government0 signification4 ,the argument is1 therefore1 invalid1 the fallacy being ambiguous middle4 7#a;b7 ,from the viewpoint of both form and meaning test the following3 8,events which are not probable happen almost every day2 but what happens every day are very probable events2 therefore events which are not probable are very probable40 7#b;a7 ,the planets have those attributes needed in the support of life1 ,mars is a planet1 ,hence ,mars has those attributes needed in the support of life4 ,a ,this is valid in form ,a in the first figure4 ,the major premise posits ,a a fact which has not been proved2 the argument is therefore invalid in meaning1 the fallacy being that of begging the question4 7#b;b7 8,the end of a thing is its perfection2 death is the end of life1 therefore death is the perfection of life40 ,indicate the fallacy in the foregoing1 giving reasons4 7#c;a7 ,the countries of ,europe abound in beggars1 ,france is a country in ,europe1 ,france abounds in beggars4 8,the countries of ,europe0 in the major premise is used in a collective sense1 while the same expression in the minor premise is used in a distributive sense4 ,the argument is1 therefore1 invalid in meaning2 fallacy of division4 7#c;b7 ,state and explain the material fallacy in the following3 ,the states believe in the income tax principle2 hence ,vermont's vote will be favorable to this4 7#d;a7 8,on general principles ,i believe that one is better off when he abstains from both tea and coffee2 and this is the reason why ,i offer you a cup of hot water40 ,the individual to whom the hot water was offered might have been in great need of a mild stimulant4 ,here1 then1 is an exception to the general principle and the fallacy committed is clearly that of accident4 7#d;b7 8,books are a source both of instruction and amusement2 a table of logarithms is a book2 therefore it is a source both of instruction and amusement40 ,jevons4 ,designate with explanations the fallacy in the above argument4 7#e7 8,twice have ,i started out on ,friday and both times ,i had tire trouble40 ,fallacy of false cause4 7#f7 8,where do you spend your vacation1 in ,palestine or ,rome80 ,fallacy of complex question4 7#g7 8,of all the men of that department he seemed to be the most trustworthy1 and ,i pride myself on my ability to judge men in this regard2 but now even the police cannot find him40 ,the fact that the police cannot find him has nothing to do with the argument4 ,the fallacy is that of non sequitur4 7#h7 8,you must not whisper in my classes40 ,fallacy of accent4 7#i7 8,i am a ,progressive because ,i believe in progress40 ,fallacy of figure of speech4 7#aj7 8,i know it is true because ,i found it in our text book40 ,fallacy of irrelevant conclusion4 #aa4 ,,review ,,questions4 7#a7 ,give the negative aspect of the second part of the definition of logic4 7#b7 ,define and illustrate the term fallacy as it is used in logic4 7#c7 ,distinguish between a paralogism and a sophism4 7#d7 ,tell of the mission of ,socrates4 7#e7 ,what reasons may be given for such a divergence of opinion on a proper classification of the fallacies of deduction8 7#f7 ,give a complete outline1 without explanation1 of the deductive fallacies4 7#g7 ,distinguish between formal and material fallacies4 7#h7 ,explain the two kinds of material fallacies4 7#i7 ,illustrate the fallacies of immediate inference4 7#aj7 ,why should the fallacies in language be likewise termed fallacies of equivocation8 7#aa7 ,explain and illustrate ambiguous middle4 7#ab7 ,illustrate the fallacy of amphibology4 7#ac7 ,explain by illustration the fallacy of accent4 7#ad7 ,explain and exemplify the fallacies of composition and division4 7#ae7 ,illustrate the fallacy of figure of speech4 7#af7 ,give reasons for denominating the fallacies in thought as fallacies also of assumption4 7#ag7 ,define and illustrate the fallacies of accident and converse accident4 7#ah7 ,distinguish between the fallacies of composition and division and the two fallacies of accident4 7#ai7 8,every rule has its exception10 what has this to do with the fallacies of accident8 7#bj7 ,explain and illustrate the fallacy of irrelevant conclusion4 7#ba7 ,name the various ways in which irrelevant conclusion may be committed4 7#bb7 ,illustrate the fallacy of non sequitur4 7#bc7 ,explain the fallacy of false cause4 7#bd7 ,give examples of the complex question4 7#be7 ,how may the teacher use the complex question to advantage8 7#bf7 ,explain the fallacy of begging the question4 7#bg7 ,illustrate the three forms of begging the question4 7#bh7 ,from the viewpoint of form and meaning1 test the validity of the following3 7#a7 8,no soldiers should be brought into the field who are not well qualified to perform their part2 none but veterans are well qualified to perform their part1 therefore1 none but veterans should be brought into the field40 ,whately4 7#b7 8,for the proverb is true1 #8,that light gains make heavy purses2' for light gains come thick1 whereas great gains come but now and then40 ,bacon4 7#c7 8,whatever is given on the evidence of sense may be taken as a fact2 the existence of ,god1 therefore1 is not a fact1 for it is not evident to sense40 ,st4 ,andrew4 #ahif4 7#d7 8,all the trees in the park make a thick shade2 this is one of them1 therefore this tree makes a thick shade40 ,jevons4 7#e7 8,what we eat grew in the field2 loaves of bread are what we eat2 therefore loaves of bread grew in the fields40 ,jevons4 7#f7 8,who is most hungry eats most2 who eats least is most hungry2 therefore who eats least eats most40 ,jevons4 7#g7 8,great talkers should be cropped1 for they have no need of ears40 ,franklin4 7#h7 8,love your enemies1 for they tell you your faults40 ,franklin4 7#i7 8,all the works of ,shakespeare cannot be read in a day2 therefore the play of ,hamlet1 being one of the works of ,shakespeare1 cannot be read in a day40 ,jevons4 7#aj7 8,logic as it was cultivated by the schoolmen proved a fruitless study2 therefore logic as it is cultivated at the present day must be a fruitless study likewise40 ,jevons4 #ab4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,is there any difference in content between error and fallacy8 ,illustrate4 7#b7 ,in what ways do trusts indulge in sophisms8 7#c7 ,may the sophism be used conscientiously by the country doctor8 ,explain4 7#d7 ,give in substance ,aristotle's classification of fallacies4 7#e7 ,select the fallacies which could with justice be called fallacies of interpretation4 ,see ,creighton4 7#f7 ,explain in full the popular conception of equivocation4 7#g7 ,indicate the marks which distinguish the following3 ,ambiguous middle1 fallacy of four terms1 non sequitur1 figure of speech4 7#h7 8,why should ,jeremy ,bentham employ a person to read to him who habitually read in a monotonous tone of voice80 ,jevons,hill4 7#i7 ,originate a sentence of about ten words and through the fallacy of accent secure as many different meanings as possible4 7#aj7 ,show that the fallacy of figure of speech might be classed as a fallacy of four terms4 7#aa7 ,to what fallacies1 in your opinion1 are teachers especially given8 7#ab7 ,show that the fallacy of accident could be classed as one of ambiguous middle4 7#ac7 8,when the ,puritan settlers in ,new ,england passed their three famous resolutions,resolved1 first1 that the earth is the ,lord's and the fullness thereof2 secondly1 that he hath given it to his ,saints2 thirdly1 that we are his ,saints4 ,what fallacy did the ,puritan ,fathers commit80 ,ryland4 7#ad7 ,a ,dutchman afflicted with pneumonia arises at midnight and eats a large quantity of sauerkraut4 ,the ,dutchman gets well1 whereat his physician writes in his little book on remedies1 8,sauerkraut sure cure for pneumonia40 ,the physician was guilty of what fallacy8 ,why8 7#ae7 ,de ,morgan quotes from ,boccaccio this3 8,a servant who was roasting a stork for his master was prevailed upon by his sweetheart to cut off a leg for her to eat4 ,when the bird came upon the table the master desired to know what had become of the other leg4 ,the man answered that storks never had more than one leg4 ,the master1 very angry1 but determined to strike his servant dumb before he punished him1 took him next day into the fields where they saw storks1 standing each on one leg1 as storks do4 ,the servant turned triumphantly to his master2 on which the latter shouted1 and the birds put down their other legs and flew away4 ,ah1 sir1 said the servant1 you did not shout to the stork at dinner yesterday2 if you had done so he would have shown his other leg40 ,what fallacy does this quotation from ,boccaccio illustrate8 7#af7 ,why should begging the question and irrelevant conclusion be classed as fallacies of the 8forgotten issue80 7#ag7 ,from the standpoint of both form and meaning test the validity of the following3 7#a7 8,virtue is the child of knowledge and vice of ignorance2 therefore education1 periodical literature1 traveling1 ventilation1 drainage and the arts of life1 when fully carried out1 serve to make a population moral and happy40 ,hibben4 7#b7 8,the civil power has the right of ecclesiastical jurisdiction and administration1 therefore parliament may impose articles of faith on the church or suppress dioceses40 ,hibben4 7#c7 8,seeing that abundance of work is a sure sign of industrial prosperity1 it follows that fire and hurricane benefit industry1 because they undoubtedly create work40 ,st4 ,andrews#ahie4 7#d7 8,riches are for spending1 and spending for honor and good action2 therefore1 extraordinary expense must be limited by the worth of the occasion40 ,bacon4 7#e7 8,and let a man beware how he keepeth company with choleric and quarrelsome persons2 for they will engage him into their own quarrels40 ,bacon4 7#f7 8,he that resteth upon gains certain1 shall hardly grow to great riches2 and he that puts all upon adventures1 doth oftentimes break and come to poverty4 ,it is good1 therefore1 to guard adventures with certainties that they may uphold losses40 ,bacon4 ,,chapter #ag4 ,,inductive ,,reasoning4 #a4 ,,inductive ,,and ,,deductive ,,reasoning ,,distinguished4 ,it has been remarked that inference is the process of deriving a judgment from one or two antecedent judgments1 and that mediate inference is inference by means of a middle term4 ,but to reason by means of a middle term necessitates two judgments2 hence mediate inference might be defined as the process of deriving a judgment from two antecedent judgments4 ,in this treatment mediate inference and reasoning have been used interchangeably4 ,this1 then1 becomes our definition for reasoning3 ,reasoning is the process of deriving a judgment from two antecedent judgments4 ,the syllogism results when the process of reasoning is formally clothed in words4 ,moreover1 the conclusion of the syllogism may be more general than the premises or less general4 ,this suggests the two important kinds of reasoning2 namely1 inductive and deductive4 ,inductive reasoning is reasoning from less general premises to a more general conclusion4 ,deductive reasoning is reasoning from more general premises to a less general conclusion4 ,,illustration3 ,inductive ,syllogism4 ,deductive ,syllogism4 ,the robin1 crow1 sparrow1 ,all birds have wings1 etc4 have wings1 ,the robin1 crow1 sparrow1 ,the robin1 crow1 sparrow1 etc4 are birds1 etc4 are birds1 ,the robin1 crow1 sparrow1 ,all birds have wings4 etc4 have wings4 ,iron1 silver1 gold1 etc4 are ,all metals are elements1 elements1 ,iron1 silver1 gold1 etc4 are ,iron1 silver1 gold1 etc4 are metals1 metals1 ,iron1 silver1 gold1 etc4 are ,all metals are elements4 elements4 ,boston1 ,new ,york1 ,chicago1 ,all large cities have fine etc4 have fine harbors1 harbors4 ,boston1 ,new ,york1 ,chicago1 ,boston1 ,new ,york1 ,chicago1 etc4 etc4 are large cities1 are large cities1 ,all large cities have fine ,boston1 ,new ,york1 ,chicago1 etc4 harbors1 have fine harbors4 ,the student who is sufficiently familiar with the canons of the deductive syllogism will at once detect the fallacy of illicit minor in the foregoing inductive syllogisms2 i4 e41 8birds0 when used as the predicate of the minor premise of the first syllogism is undistributed1 but as the subject of the conclusion 8birds0 is distributed4 ,the same might be said concerning the terms 8metals0 and 8large cities40 ,a portion of this chapter will be devoted to answering this criticism4 ,at this point it may be stated that the inductive syllogism is not supposed to conform perfectly to the canons of the deductive syllogism4 #b4 ,,the ,,inductive ,,hazard4 ,referring to the first inductive syllogism of section one1 it is assumed that the robin1 crow and sparrow are representative birds1 and that we are thus justified in concluding that if these type birds have wings1 then all birds must have wings4 ,of course this is more or less of a conjecture or 8a hazard02 since birds without wings may exist in some undiscovered corner of the globe4 ,however1 inasmuch as the generalization concerns a representative quality1 we deem the assumption fairly well founded4 ,the logical right to take this 8leap into the unknown0 will be discussed later4 ,it will profit us at this time to realize more fully how essential the 8inductive hazard0 is to the progress of the world4 ,when the ,schoolmen of medival time refused to venture1 they failed to progress1 and thus came the dark days4 ,whenever man has ignored this ,god given instinct which leads to discovery1 the world has stood still4 ,this willingness to 8take a leap into the dark0 with the hope of finding1 in the shadow1 truth which would enhance man's power and increase his serviceableness1 has given to the world about all that is worth while4 ,it was the spirit of the hazard which pushed ,columbus to the discovery of a new world2 which gave ,newton the secrets of the motions of the universe2 which enabled ,edison to harness a multitude of lurking forces2 and ,morse and ,bell to reduce distance to its lowest terms4 ,in ordinary affairs with ordinary men those succeed best who manifest most a safe1 steady1 persistent spirit of discovery4 ,here1 then1 in the 8inductive hazard0 have we a most important phase of school life which1 in this day of making the work easy1 is being sadly neglected4 ,on the other hand1 an unregulated and insane spirit of venture may result in a great waste of energy1 and in the development of low ideals of recklessness and inaccuracy4 ,the 8inductive hazard0 must be cultivated2 yet it must be regulated as well1 and1 as the reader already realizes1 logic needs to concern itself mainly with this regulative aspect4 #c4 ,,the ,,complexity ,,of ,,the ,,problem ,,of ,,induction4 ,the problem of induction is much more complex than that of deduction because of these reasons3 ,first4 ,deduction as a process of reasoning was the only kind discussed by the logicians for two thousand years4 ,aristotle is called the father of deductive logic and this ,intellectual ,giant1 the greatest of ancient time and possibly of all time1 so perfected the form of deductive reasoning that1 up to the time of ,francis ,bacon1 no scholar possessed the temerity to gainsay its supremacy in the field of logical reasoning4 ,for twenty centuries ,aristotle's ,deductive ,logic was the ,logicians' ,bible4 ,on the other hand1 inductive reasoning1 though it was briefly discussed by ,aristotle1 received little attention till the versatile ,francis ,bacon placed it upon the stage of the thinking world4 ,this makes deduction nearly two thousand years older than induction4 ,time1 by eliminating the personal equation and exposing in various ways fallacious thinking1 tends to unify and universalize truth4 ,hence1 logicians are agreed so far as the fundamentals of deductive logic are concerned1 but are still at odds over the true conception and use of inductive logic4 ,a second reason for this confused status in the field of inductive logic is the fact of its being more closely related to the events of every day living4 ,induction is the natural method of childhood2 the popular method of the school room2 and the most used method of common life4 ,in consequence its ramifications are so varied and multitudinous1 that it will take centuries of thinking to reduce the doctrine of induction to that uniformity and definiteness which so distinguishes deduction4 #d4 ,,the ,,various ,,conceptions ,,of ,,induction4 ,the attending quotations will give the student a fair idea of the leading conceptions concerning induction3 7#a7 8,induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class1 or that what is true at certain times will be true under similar circumstances at all times40 8,induction1 as above defined1 is a process of inference2 it proceeds from the known to the unknown40 8,any process in which what seems the conclusion is no wider than the premises from which it is drawn1 does not fall within the meaning of the term40,j4 ,s4 ,mill1 ,a ,system of ,logic1 #ahib1 p4 #age4 7#b7 8,an induction is a generalization or an inference based upon propositions that state observed facts40 8,the truth inferred may be general or particular1 but it must be one which we cannot perceive in a single act of observation40,ballentine's ,inductive ,logic1 #ahif1 p4 #ad4 7#c7 8,induction is the process of inference by which we get at general truths from particular facts or cases40,ryland's ,logic1 #aijj1 p4 #adh4 7#d7 8,induction may be defined as the legitimate inference of the general from the particular1 or1 of the more general from the less general40,fowler1 #aije1 p4 #aj1 ,vol4 #b4 7#e7 8,the term induction has been used by logicians to denote this leap of the mind from the limitations of its positive knowledge to belief in universal laws40 8,in pedagogy1 however1 the term is applied to the whole process of arriving at general truths or principles40,salisbury's ,theory of ,teaching1 p4 #aef4 #e4 ,,induction ,,and ,,deduction ,,contiguous ,,processes4 ,if there is one thing above another which modern logic is emphasizing it is the unity of the mind and the contiguity of thinking4 ,induction and deduction are dove-tailed processes which characterize all thinking worthy of the name4 ,where induction ceases1 deduction commences1 and vice versa4 ,it becomes the function of inductive thinking to establish a connection between what has been experienced and what has not been experienced4 ,therefore1 the conclusion of an induction must always contain more than is implied in the premises4 ,the premises denote facts which have been observed2 whereas the conclusion denotes the observed facts of the premises plus analogous facts which have not been observed4 ,inductive thought ventures into the unknown1 and attempts to establish a bond of connection between it and something already known4 ,induction seeks new knowledge1 and does so by taking that 8leap into the dark0 already referred to as the 8inductive hazard40 ,as soon as the mind reaches a universal truth1 it sets to work to clarify this truth4 ,such is accomplished by reference to other facts which the universal is supposed to include2 and this application of the general to the particular is deduction4 ,induction discovers the new knowledge while deduction clarifies it4 #f4 ,,induction ,,an ,,assumption4 ,in this treatment induction as a general process has been subdivided into induction as a mode of inference and induction as a method4 ,induction as a mode of inference is the process of reasoning from less general premises to a more general conclusion2 whereas induction as a method is a procedure from the observation of individual facts to a realization of a universal truth4 ,in either case the conclusion of an inductive process always implies more than is contained in the premises4 ,this gives to the conclusion an uncertainty4 ,no induction is absolutely free from doubt except the so-called perfect induction1 which form will receive attention in a later section4 #g4 ,,universal ,,causation4 ,all inductive assumptions are made possible because of two lawsuniversal causation and uniformity of nature4 ,the law of universal causation may be stated in this wise3 ,nothing can occur without a cause and every cause has its effect4 8,it is a universal truth1 that every fact which has a beginning has a cause40,mill4 ,,simple ,,illustrations ,,of ,,universal ,,causation4 ,the sun rises in the east4 ,the boy throws a stone through the window4 ,a democratic wave sweeps the country4 ,prices of food stuff are high4 ,the bullet1 shot out into space1 finally falls to the earth4 ,each one of these occurrences has a cause4#ab ,that universal causation is a fundamental condition of all induction may be further illustrated4 ,the astronomer notes that the stars in the vicinity of ,vega seem to be moving outward from a common center2 whereas in the opposite part of the sky the stars seem to be moving inward toward a common center4 ,having observed this phenomenon1 the astronomer at once looks for a cause4 ,finally he decides that the phenomenon is due to the fact that the sun1 with his attending family1 is moving towards ,vega4 ,arranged1 the argument may take this form3 ,the stars in the vicinity of ,vega seem to be moving outward from a common center1 whereas in the opposite part of the sky the stars seem to be moving inward1 ,when descending a mountain the trees at the foot seem to move outward from1 and those at the top inward toward1 a common center1 ,when riding on the train the ties in front seem to move outward while those in the rear seem to move inward4 ,from this we conclude that the sun with the ,earth and other planets is moving toward a spot in the sky near ,vega4 ,were it not for the assumption that the phenomenon relative to the stars had a cause there could have been no induction4 ,moreover1 any investigation concerning 8democratic waves10 8prices of food stuffs10 etc41 must assume as a starting point that these phenomena have causes4 ,it would appear that the mind is not satisfied with a mere passive observation of the occurrences of the world but is inclined to reach out for the 8whys and wherefores40 ,due partly to this reason1 8universal causation0 is often referred to as an a priori law2 meaning that it is a law which cannot be proved1 but must be assumed in all thinking4 #h4 ,,the ,,law ,,of ,,the ,,uniformity ,,of ,,nature4 ,law stated3 ,the same antecedents are invariably followed by the same consequents4 8,that the course of nature is uniform is the fundamental principle of induction40,mill4 8,it is not enough to feel assured that nothing can happen without a cause 7causation72 ,i must also feel assured that the same cause will invariably be followed by the same effect40,fowler4 ,referring to the observed phenomenon of the outward movement of the stars about ,vega1 the astronomer might advance as an hypothesis the fact of the solar system's movement toward ,vega4 ,having done this he could then experiment with a view of verifying this hypothesis4 ,in this experiment he would attempt to introduce the same cause surrounded by similar circumstances1 and then watch for the same effect4 ,to make it concrete3 suppose the astronomer paints the side of a barn dark blue and bedecks this with stars of white4 ,then taking a position as far removed from the blue surface as his eyesight will permit1 he runs toward the barn watching the apparent movement of the artificial stars4 ,a similar experiment could be performed by substituting for the starred barn1 the stumps on a side hill4 ,in both experiments he assumes that like conditions will be followed by constant results4 ,that is1 in these particular cases1 advancing toward a group of objects is always followed by an apparent separation of said objects4 ,this law of uniformity of nature not only underlies inductive thinking but it really conditions all thinking4 ,it implies that the universe is a rational system functioning in a uniform manner4 ,moreover1 it suggests that the interpretations of the mind are likewise uniform and whenever the mind proves a fact to be a universal truth1 this truth will always remain a truth unless the conditions change4 ,in fact were it not for the uniformity of nature1 all activity whatsoever would be rendered nugatory4 ,because of this law we have a right to assume that grinding a knife under right conditions will always tend to sharpen it2 that surrounding a live seed with a proper environment will result in growth2 that water at the same altitude will boil at a constant temperature1 etc41 etc4 ,the student will discern the close connection between these two laws and the laws of thought4 ,there is really no distinctive mark between the law of causation and the law of sufficient reason1 while 8uniformity of nature0 includes identity as one of its distinctive features4 ,the laws differ1 however1 in their application1 8causation0 and 8uniformity of nature0 conditioning inductive thinking1 while the others are concerned with deductive thinking4 ,because 8uniformity of nature0 expresses facts of experience1 it is regarded as an empirical law1 as contrasted with the law of causation1 which is supposed to be based upon an innate mental conception or is an a priori law4 #i4 ,,inductive ,,assumption ,,justified4 ,the function of induction seems to be to universalize particulars4 ,the mind of man has ever been engaged in establishing connections among the concrete experiences of daily life4 ,this ability of his to generalize his individual experiences has been one of the chief agencies in elevating him to the position of 8,king of the animal world40 ,in this disposition to generalize man has taken it for granted that nature is honest2 that what she tells him under given conditions1 she will tell him again under identical conditions4 ,to put it in logical terms man can depend upon the invariability of nature's activities1 or upon the uniformity of nature4 ,here1 then1 is one of the most fundamental laws not only of induction but of all activity4 ,but this law implies a second quite as fundamental4 ,if every cause is invariably followed by the same effect under like conditions1 then it is thereby implied that every cause has an affect and every event is due to some cause4 ,this1 too1 is invariable4 ,in consequence of these facts man is justified in thinking that nature is not only honest and therefore 8she gives me confidence1 but her every activity means something and therefore she arouses my curiosity40 8,uniformity of nature0 engenders confidence1 8universal causation0 inspires the spirit of discovery and with these two weapons man is willing to venture into the jungle of the unknown4 ,why is man eager to undertake the 8inductive hazard80 ,because1 through the laws of universal causation and uniformity of nature1 his curiosity is aroused1 and he is given confidence in nature's activities4 #aj4 ,,three ,,forms ,,of ,,inductive ,,research4 ,induction is a matter of universalizing less universal experiences4 ,in this the process may assume any one of three forms1 namely3 7#a7 ,induction by simple enumeration2 7inductio per enumerationem72 7#b7 ,induction by analogy2 7#c7 ,induction by analysis4 ,,three ,,forms ,,illustrated3 7#a7 ,simple enumeration4 ,having observed a few instances the generalization is1 8,all birds have wings40 ,the certitude of this may now be strengthened by observing more birds and finding without exception that each has wings4 7#b7 ,analogy4 ,by noting on ,mars geometric markings which resemble canals1 the generalization is vouchsafed that ,mars is inhabited by human beings4 ,other similarities in atmospheric conditions1 existence of land and water1 etc41 tend to make this generalization more plausible4 7#c7 ,analysis4 ,by analyzing water taken from a certain spring1 it is found to contain hydrogen and oxygen in the proportion of #a to #h2 in consequence a generalization to this effect is posited4 ,analyses of specimens from other sources yield similar results and thus the generalization is given greater certitude4 ,as a usual thing the particular form which the induction assumes depends on the nature of the topic under investigation and also on the mental make-up of the investigator4 ,the general statement that all birds have wings could hardly be derived by means of analogy or analysis1 but is a matter of a casual observation of many instances4 ,moreover1 that mind given to accurate observation1 but not inclined to note resemblances or to carry on experiments1 would naturally follow the first inductive type4 ,on the other hand1 simple enumeration would be impossible in questions like the habitability of ,mars1 and would yield no results in cases requiring definite scientific experimentation like electrolysis4 ,it is worthy of note that some topics lend themselves to all three modes of procedure4 ,to wit3 7#a7 ,enumeration4 ,without being taught the rule the child is given a list of examples involving the dividing of a decimal by a decimal and is asked to solve them4 ,by comparing his answers with those in the book1 he somewhat accidentally discovers what seems to be the correct rule for pointing off in the quotient4 ,by following this rule and each time comparing answers he establishes the truth4 7#b7 ,analogy4 ,if 4#bd 4#f is the first example1 the child may resort to the well known process of dividing a common fraction by a 7 #bd #fj #bd #d 7 common fraction1 7 1 7 then1 because of their close 7 #ajj #ajj #fj #aj 7 resemblance1 he may reason that decimal fractions should yield the same result4 7#c7 ,analysis4 ,here the child reasons that since division of decimals is the inverse of multiplication of decimals1 the rule for pointing off might be the inverse of the multiplication rule4 ,by trying this out and proving his answer in each example1 he becomes convinced of the correctness of his reasoning4 #aa4 ,,induction ,,by ,,simple ,,enumeration4 ,as its name implies this type of inductive research consists in observing many instances which may exemplify the particular uniformity under consideration4 ,the process is quantitative rather than qualitative1 the certitude of the generalization depending on the mass of facts collected rather than on any striking resemblance or any detailed analysis4 ,the aim is to observe1 accurately if not scientifically1 instance after instance until all doubt is removed4 ,the outcome of such observation may be three fold4 7#a7 ,the enumeration may be complete4 ,this gives the so-called 8perfect induction0 which will receive attention later4 7#b7 ,the enumeration may be incomplete and without exceptions2 generalizing in this way from uncontradicted experience gives what are termed 8empirical0 truths4 7#c7 ,the enumeration may be incomplete with exceptions4 ,it is obvious that this type of induction could give no valid generalization2 but the result may be put in the form of a ratio between the uniformities and the exceptions4 ,such a procedure is a mere 8calculation of chances0 and the result simply an expressed probability4 ,,the ,,three ,,kinds ,,of ,,simple ,,enumeration ,,illustrated4 ,the subject to receive investigation is a school examination4 7#a7 ,complete enumeration4 ,every paper is read and marked2 this leads to the generalization1 8,all the class have passed40 7#b7 ,incomplete enumeration with no exceptions4 ,representative papers are read and marked in which no failures are found4 ,generalization1 8,probably all of the class have passed40 7#c7 ,incomplete enumeration with exceptions4 ,representative papers are read and marked in which there are #bj failures out of the hundred papers examined4 ,generalization1 8,probably about #hj of the class have passed40 ,briefly1 simple enumeration may take the form of 7#a7 a perfect induction1 7#b7 a probable induction1 7#c7 a mere calculation of chances4 ,the first necessitates completed experience1 the second uncontradicted experience and the third contradicted experience4 #ab4 ,,induction ,,by ,,analogy4 ,induction by analogy assumes that if two 7or more7 things resemble each other in certain respects1 they belong to the same type1 and1 therefore1 any fact known of the one may be affirmed of the other4 ,,the ,,type4 ,as the definition implies1 analogy involves an extensive use of types2 let us1 therefore1 become better acquainted with them as instruments in analogical inductions4 ,a type is one of a group which embodies the essential characteristics of that group4 ,how easy and natural it is to dismiss a complex topic with the citing of an example which may be regarded as a type2 how common is the use of examples in the school room6 ,on second thought it becomes apparent that analogical induction by example or type is the most common of all forms of induction either as a method or a mode of inference4 ,analogy by example 7or type7 assumes that if two or more things are of the same type1 they resemble each other in every essential property4 ,illustrations of analogical inductions by example or type4 7#a7 ,mathematics4 ,example3 a b a b a ab ab b a #b;ab b ,inductive ,inference3 ,the square of the sum of two quantities is equal to the square of the first1 plus twice the first by the second1 plus the square of the second4 7#b7 ,nature4 ,this corn sent me as a sample produced heavy1 full ears1 and many of them2 hence 7inductive inference71 if ,i plant corn like this sample under like conditions1 ,i will receive in return heavy1 full ears1 and many of them4 7#c7 ,geography4 ,cities like ,new ,york1 located on the coast1 possess a larger foreign element than the inland cities like ,philadelphia4 7#d7 ,grammar4 ,a noun is the name of anything1 as the examples1 8,george ,washington0 and 8house0 would indicate4 ,in deriving a generalization from one or two examples the prime essential is to select types which are truly representative4 ,often the example used is a special type and in consequence does not exemplify all of the essential characteristics of the group4 ,to teach the nature of a parallelogram by using a rectangle only1 is an easy way to commit this error2 or one may affirm that the class can easily cover the work1 when the judgment is based entirely on knowledge concerning the brightest one of the grade4 ,type work when judicially used is a positive time saver and a very present help in times of perplexity4 ,let the skillful teacher use types and examples extensively yet cautiously4 ,,the ,,mark ,,of ,,similarity4 ,as opposed to analogy by type there is a second form2 namely1 analogy by one or more similar marks or qualities4 ,this form is best described by the definition3 ,when two things resemble each other in a few marks or qualities they resemble each other in other marks or qualities4 ,illustrations of analogy by marks4 7#a7 ,noting that two students have the same surname1 ,i infer that they are brothers4 7#b7 ,a man with a book under his arm rings the door bell and asks to see 8the lady of the house40 ,at once the conclusion is drawn that the caller is a book agent4 7#c7 ,two automobiles1 resembling each other in shape of body1 force one to the conclusion that the machines are of the same make4 ,,the ,,errors ,,of ,,analogy ,,by ,,marks ,,of ,,similarity4 ,it follows that analogy by example gives generalizations of much greater certitude than analogy by one or two marks of resemblance4 ,here is a field bespattered from boundary to boundary with erroneous thinking4 ,the principle of resemblance being an innate tendency1 this form of error is most common with the immature4 ,the child reasons by analogy when he invests the poodle with the despised cognomen of 8kitty02 or honors every man who wears glasses with 8papa40 ,in the childhood of the race natural events were interpreted by means of analogy4 ,the wind blowing through the trees made sounds much like the human voice2 hence these noises were attributed to spirits4 ,primeval man was led to believe by analogy that everything which moved was alive4 ,we may1 therefore1 think of our revered forbear as engaged in the undignified task of running after his shadow1 or chasing a leaf around a stump4 ,,the ,,value ,,of ,,analogy4 ,analogy being rich in its suggestions is the favored process of the scientist and inventor4 ,newton reasoned by analogy when he tentatively affirmed of the moon what he positively knew of the apple4 ,franklin's reasoning was analogical when he discovered the identity of the electric spark and lightning4 ,because this form of induction so often leads to error and at best involves a degree of probability far below induction by analysis1 some logicians are inclined to ignore its generalizations altogether4 ,others deem this a mistake because of these reasons3 ,first4 ,analogy is serviceable to a high degree in suggesting hypotheses which may be advanced either for the purpose of explanation or verification4 ,it has already been indicated that analogy is the common instrument used by the inventor and discoverer4 ,second4 ,the principle of analogy1 in reality1 lies at the basis of classification2 because in this1 things are grouped according to their resemblances4 ,third4 ,analogical induction affords valuable training in originality and initiative4 ,a mind which easily and naturally discerns analogies is 8fertile in new ideas40 ,,requirements ,,of ,a ,,true ,,analogy4 ,it has been remarked that the certitude of an induction by simple enumeration depends upon the number of uncontradicted instances4 ,in analogy the case is different as the process emphasizes the weight of the points of resemblance rather than the number4 ,in substance the requirements of a logical analogy are three4 ,first4 ,the points of resemblance must be representative and not exceptional4 ,for example3 ,the argument that ,mars is inhabited because it has two moons is of little worth1 since we have no proof that moonshine is essential to life2 this point of resemblance is not representative4 ,on the other hand1 if the basis of argument is the fact that ,mars has an atmosphere1 the conclusion carries some weight2 as air seems to be essential to life4 ,second4 ,the points of resemblance must outweigh the points of difference4 ,that is1 the ratio of probability must always be in favor of the resembling instances4 ,since it is not a matter of numbers but of weight1 a numerical proportion like this would be misleading3 ,resemblances3 ,differences #aj3f4 ,it is obvious that the six differences might more than outweigh the ten resemblances4 ,the safer way1 if it were possible1 would be to attach a value to each point of resemblance or difference1 and then express the proportion in terms of the sums of these values4 ,third4 ,there must be no difference which is absolutely incompatible with the affirmation which we wish to prove4 ,for example1 the fact that the moon has no atmosphere renders nugatory any attempt to prove the habitability of the moon4 #ac4 ,,induction ,,by ,,analysis4 ,this1 the third form of inductive research1 is by far the most important4 ,simple enumeration1 because it depends upon the number of observed instances1 consumes much time2 while we have already noted how easy it is for analogy to lead to error4 ,at the best1 the conclusion of these methods must be subjected to analytic investigation1 if we are seeking universal validity4 ,induction by analysis is superior to the other forms because it secures a higher degree of probability and is a positive time saver4 ,defined4 ,we have learned that analysis is the process of separating a whole into its related parts4 ,we thus define induction by analysis as the process of separating a whole into its parts with a view of deriving a generalization relative to the nature and causal connection of these parts4 ,,illustrations3 7#a7 ,concerning the generalization that 8all birds have wings10 it becomes possible to observe in detail the nature of the wings and advance the hypothesis that these wings are designed for arial navigation4 ,this hypothesis may then be strengthened by observing that the entire structure of the bird is adapted to flying4 7#b7 ,if it were possible to analyze the atmosphere1 water1 and soil of ,mars1 and should such analysis reveal a composition similar to that of the earth1 it would illustrate well not only the method of analysis but also its superiority over the other methods of investigation4 7#c7 ,the physician1 in diagnosing a 8case10 observes that the symptoms resemble those of typhoid2 but to be positive of the truth of his diagnosis1 he takes a blood test4 ,noting the resemblances is induction by analogy2 but the blood test involves induction by analysis4 ,induction by analysis concerns hypothesis1 observation1 and experiment1 including ,mill's experimental methods4 ,these topics will receive due attention in the chapters which follow4 ,it will be sufficient to close this discussion with a brief treatment of perfect induction1 and traduction4 #ad4 ,,perfect ,,induction4 ,as has been indicated under simple enumeration1 a perfect induction is one in which the premises enumerate all the instances denoted by the conclusion4 ,,illustrations3 7#a7 ,a1 ,b1 ,c1 ,d1 and ,e are all ,reactionaries1 7,all7 ,the members of the committee are ,a1 ,b1 ,c1 ,d1 and ,e1 7,all7 ,the members of the committee are ,reactionaries4 7#b7 ,john1 ,james1 ,albert1 and ,peter all have perfect eyesight1 ,john1 ,james1 ,albert1 and ,peter are all the boys of my family1 ,all the boys of my family have perfect eyesight4 7#c7 ,the first1 second1 and third groups are up to grade1 ,the first1 second1 and third groups include all of the children in my room1 ,hence all the children in my room are up to grade4 ,because the conclusion of a perfect induction gives nothing newnothing but what is found in the premises1 some claim that the process is practically valueless4 ,from the viewpoint of the discoverer this position is well taken2 yet to universalize particular observations puts the knowledge in compact1 usable form1 and saves one the trouble of returning each time to the consideration of each particular4 ,thus as a process which leads to verified universals1 perfect induction is a time saver4 ,in the second place it was the method used by ,socrates when he desired to lead up to a definition or some other general truth4 ,the ,sophists were given to a careless use of the 8inductive hazard02 they were prone to generalize from one or two particulars1 or what is worse1 to establish a generalization and then attempt to fit the particular instances to it4 ,this led to a superficiality which the ,great ,pagan ,educator abhorred4 ,the fact that perfect induction was the method used by ,socrates to counteract the teachings of the ,sophists1 is sufficient vindication for its use in discouraging the indefensible assumptions of to-day1 and in inspiring warrantable generalizations based on accurate observation4 ,in the school room with classes addicted to careless1 inaccurate work1 to accept nothing but a perfectly induced generalization1 when this is feasible1 is a most valuable lesson4 ,for example1 the teacher may not accept the generalization that all of the 8first class0 cities of the ,u4 ,s4 are located on navigable waterways1 until the pupils have investigated the waterway conditions of every city belonging to the class4 ,on the other hand1 there may be individual cases of 8cocksureness0 which need attention4 ,the teacher can do little for the 8know-it-all youngster0 until he pricks the bubble of conceit4 ,this may be accomplished by allowing the youth to draw a generalization1 which seems to meet all the requirements of truth arrived at by means of an imperfect induction2 then without warning let the teacher give an instance which will show the generalization to be false4 ,this involves what ,socrates termed the 8torpedo's shock40 ,to illustrate3 ,consider the 8prime number0 formula given by ,jevons4 ,in deriving this1 direct the class to add #b to its square1 and to this sum add #da4 ,give similar directions relative to numbers #c1 #d1 #g and #aj4 ,indicating the work as directed1 would give the following3 7#a7 #b #b #da #dg 7#b7 #c #c #da #ec 7#c7 #d #d #da #fa 7#d7 #g #g #da #ig 7#e7 #aj #aj #da #aea ,a question or two will make apparent the fact that all the results are prime numbers1 and then the generalization may be drawn2 namely1 ,x ,x #da prime number4 ,now without warning1 but under the assumption that you desire to test deductively the general formula1 let ,x #dj4 ,this gives 7#dj #dj #da7 #afha1 which is the square of #da and is1 therefore1 not a prime number4 #ae4 ,,traduction4 ,it may have been noted by the student that 8perfect induction0 is not induction at all according to the definition2 viz43 ,inductive reasoning is reasoning from less general premises to a more general conclusion4 ,referring to the first illustration of the previous section it is apparent that the conclusion is no broader than the premises4 ,ostensibly1 the conclusion is a mere summary1 or a generalization of the facts mentioned in the premises4 ,moreover perfect induction does not readily conform to the definition of deductive reasoning1 as in this the movement must be from the more general to the less4 ,we are thus forced to the conclusion that perfect induction is a form of a third type of reasoning which is known under the cognomen of traduction4 ,this is from the ,latin trans1 and ducere meaning to lead across4 ,definition3 ,traductive reasoning is reasoning to a conclusion which is neither less general nor more general than the premises4 ,aside from the case of perfect induction there are other types which well illustrate traduction4 ,these are3 ,first4 ,reasoning from particular 7or individuals7 to particular 7or individuals74 ,,illustration3 ,highland ,street is the longest street in ,jamaica1 ,highland ,street is not so long as ,broadway of ,new ,york ,city1 ,the longest street of ,jamaica is not so long as ,broadway of ,new ,york ,city4 ,second4 ,reasoning from general to general4 ,,illustration3 ,all growing things die1 ,all living things are growing things1 ,all living things die4 ,it may be observed that all of the propositions in traduction are co-extensive 8,a's0 or 8,e's02 hence all the terms are distributed4 ,this eliminates any possibility of committing fallacies of distribution4 ,further1 the propositions may be interchanged at will1 without invalidating the particular conclusion selected4 ,to illustrate we may change the last argument to this3 ,all growing things are living things1 ,all things that die are growing things1 ,all things that die are living things4 ,from the viewpoint of authenticity traduction is the most1 and induction the least dependable2 whereas the certitude of deductive reasoning lies somewhere between the two4 ,on the other hand1 when looked at from the ground of serviceableness the order is reversed1 induction being the most useful form of inference and traduction the least4 #af4 ,,outline4 ,,inductive ,,reasoning4 7#a7 ,inductive and ,deductive ,reasoning ,distinguished4 7#b7 ,the 8,inductive ,hazard40 ,essential in world's progress4 ,cultivated and regulated in school4 7#c7 ,complexity of the ,problem of ,induction4 7#d7 ,various ,conceptions of ,induction4 ,quotations from prominent authorities4 7#e7 ,induction and ,deduction ,contiguous ,processes4 7#f7 ,induction an ,assumption4 ,a mode of inference2 ,a method4 7#g7 ,universal ,causation4 ,law stated and illustrated4 ,conditions all induction4 7#h7 ,uniformity of ,nature4 ,defined and illustrated4 ,conditions all induction4 ,empirical4 7#i7 ,inductive ,assumptions ,justified4 7#aj7 ,three ,forms of ,inductive ,research4 7#a7 ,enumeration 7#b7 ,analogy 7#c7 ,analysis4 ,illustrated4 ,conditions determine form followed4 7#aa7 ,induction by ,simple ,enumeration4 ,defined and illustrated4 ,outcome threefoldthese illustrated4 7#ab7 ,induction by ,analogy4 ,two conceptions4 ,analogy by type or example4 ,illustrations representative4 ,error of analogy4 ,suggestiveness of analogy4 ,value of analogy4 ,requirements of a true analogy4 ,three4 7#ac7 ,induction by ,analysis4 ,importance4 ,defined and illustrated4 7#ad7 ,perfect ,induction4 ,defined and illustrated4 ,its use4 ,method of ,socrates4 7#ae7 ,traduction4 ,defined and illustrated4 ,three methods compared4 #ag4 ,,summary4 7#a7 ,reasoning is the process of deriving a judgment from two antecedent judgments4 ,the syllogism is a common form of expressing the process of reasoning4 ,inductive reasoning is reasoning from less general premises to a more general conclusion4 ,deductive reasoning is reasoning from more general premises to a less general conclusion4 ,the inductive syllogism is not supposed to conform to the canons of the deductive syllogism4 7#b7 ,positing in the conclusion more than is indicated in the premises involves what is known as the 8inductive hazard40 ,the inductive hazard which is another expression for the spirit of discovery1 should be fostered in the school room since it has been one of the great forces in human progress2 but this venturesome spirit must be regulated by rules1 principles1 and systematic procedure1 or low ideals of recklessness and inaccuracy will result4 7#c7 ,the problem of induction is more complex than that of deduction2 because the former is a comparatively new subject1 and also is more closely related to the activities of life4 7#d7 ,the opinion relative to the exact nature of induction1 though varied1 may be summed up in the thought of its being the process which leads to general truths1 derived from the observation of individual facts4 7#e7 ,induction and deduction are contiguous processes which go to make up the more general process of thinking4 ,where induction ceases1 deduction naturally commences2 induction discovers new knowledge1 deduction clarifies it4 7#f7 ,induction as a general process may be treated as a mode of inference or as a method4 ,in either case the conclusion comprehends more than is contained in the premises4 ,since no imperfect induction is absolutely free from doubt1 on what ground are we justified in making any inductive assumptions8 ,the answer follows3 7#g and #h7 8,nothing can occur without a cause and every cause has its effect10 is the law of universal causation2 while the law of the uniformity of nature is 8the same antecedents are universally followed by the same consequents40 ,these two laws justify inductive assumptions1 and1 in a sense1 condition all thinking4 7#i7 ,uniformity of nature gives man confidence1 while universal causation arouses his curiosity4 ,with these two weapons he is willing to 8march into the unknown40 7#aj7 ,as the process of universalizing individual experiences1 induction assumes the three forms of simple enumeration1 analogy and analysis4 ,the form adopted is not always elective but is controlled largely by the exigency of the case4 ,some topics lend themselves to all three modes4 7#aa7 ,induction by simple enumeration consists in observing many instances which exemplify the uniformity under consideration4 ,complete enumeration gives the so called perfect inductive inference2 incomplete but uncontradicted enumeration leads to empirical truths2 while incomplete and contradictive enumeration involves a mere calculation of chances4 7#ab7 ,induction by analogy assumes that if two 7or more7 things resemble each other in certain respects1 they belong to the same type1 and1 therefore1 any fact known of the one1 may be affirmed of the other4 ,a most common form of analogy is reasoning by type or example4 ,in this it is assumed that if two or more things are of the same type1 they resemble each in every essential property4 ,the type must be truly representative4 ,a second form of analogy is reasoning by marks of resemblance4 ,this second form often leads to egregious error4 ,analogy is especially valuable in suggesting hypotheses and in giving training in originality and initiative4 ,a true analogy demands that the points of resemblance be representative2 that they outweigh the points of difference1 and that no disagreement be incompatible4 7#ac7 ,induction by analysis is the process of dividing a whole into its parts with a view of deriving a generalization relative to the nature and causal connection of these parts4 ,induction by analysis makes use of the hypothesis1 of observation and experiment1 including ,mill's five methods4 7#ad7 ,a perfect induction is one in which the premises enumerate all of the instances denoted by the conclusion4 ,it is serviceable in inspiring care and accuracy in the establishment of generalizations4 7#ae7 ,traduction is the process of reasoning to a conclusion which is neither less general nor more general than the premises4 ,traduction includes reasoning from particular to particular or from general to general4 ,perfect induction is in reality a form of traduction4 ,induction1 though the most useful form of inference1 is the most untrustworthy2 whereas traduction is just the reverse of this4 #ah4 ,,review ,,questions4 7#a7 ,define and illustrate reasoning4 7#b7 ,distinguish by definition and illustration between inductive and deductive reasoning4 7#c7 ,explain the 8inductive hazard0 and show its use to man4 7#d7 8,for twenty centuries ,aristotle's ,deductive ,logic was the logician's bible40 ,explain this4 7#e7 ,show that induction and deduction are contiguous processes4 7#f7 ,distinguish between induction as a mode of inference and induction as a method4 7#g7 ,state and explain the law of universal causation4 ,illustrate fully4 7#h7 ,make evident that a cause may involve many antecedents4 7#i7 ,state and explain by illustration the law of uniformity of nature4 7#aj7 ,verify by illustration the notion that the 8fact of causation0 conditions all induction4 7#aa7 ,which of the two laws is empirical1 8causation0 or 8uniformity08 ,why8 7#ab7 ,show that induction is a form of thinking4 7#ac7 ,why should the law of uniformity of nature convince man that nature is honest8 ,illustrate4 7#ad7 ,show that the law of universal causation stirs the spirit of discovery4 7#ae7 ,name and illustrate the three forms of induction4 7#af7 ,why is it that the tendencies of the investigator often determine the inductive form which he adopts8 7#ag7 ,explain by illustration the three-fold outcome of induction by simple enumeration4 7#ah7 ,selecting some class room experience1 illustrate analogy by example or type4 7#ai7 ,define and exemplify types as used in logic4 7#bj7 ,remark upon the errors incident to analogy4 7#ba7 ,summarize the advantages which induction by analogy offers4 7#bb7 ,state and exemplify the requirements of true analogies4 7#bc7 ,indicate the superiority of induction by analysis over the other two forms4 ,illustrate4 7#bd7 ,define and illustrate perfect induction4 7#be7 ,under what circumstances is perfect induction justified8 7#bf7 ,define and illustrate traduction4 7#bg7 ,indicate the various forms of traduction4 #ai4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,show the connection between illicit minor and the 8inductive hazard40 7#b7 ,show by illustration that time tends to universalize truth4 7#c7 8,induction and not deduction is the natural method of the child mind40 ,prove the correctness of this statement4 7#d7 8,induction is the process of inference by which we get at general truths from particular facts or cases40 ,prove that this is not strictly correct according to definition4 7#e7 ,as related to establishing general truths1 what are the special functions of induction and deduction8 7#f7 ,show that an inductive inference must of necessity be more or less uncertain4 7#g7 ,is there any distinction between the laws of universal causation and sufficient reason8 ,hyslop's ,elements of ,logic1 page #cbi4 7#h7 ,show that universal causation and uniformity of nature are complementary laws4 ,hyslop1 p4 #ccj4 7#i7 ,relate the 8fact of causation0 to the laws of thought4 7#aj7 ,distinguish between empirical and 8a priori0 laws4 7#aa7 ,when ,harvey discovered the circulation of the blood1 what form of induction did he use8 7#ab7 ,what form of reasoning did ,columbus follow in proving that the earth is spherical8 7#ac7 8,it is said that the greatness of ,darwin was due largely to his habit of never ignoring an exception40 ,justify by illustration the truth of this assertion4 7#ad7 ,in analogical reasoning by example1 under what conditions would one illustration be as convincing as many8 7#ae7 8,considering the similarities and differences1 the weight of the argument favors ,mars' habitability40 ,suppose the proportion of probability were something like this,resemblances3 ,differences #h3g2 wherein might the conclusion be erroneous8 7#af7 ,mention a mark or characteristic which would make the habitability of ,mars incompatible8 7#ag7 ,select a topic for investigation which is peculiarly adapted to enumeration2 to analogy2 to analysis4 7#ah7 8,the uniformities we expect to find in the world take two main aspects1 one of which is indicated by the term thing and the other by the term circumstance40 ,aikin's ,principles of ,logic1 #aije2 p4 #bcc4 ,in the light of the two fundamental laws of universal causation and uniformity of nature explain and illustrate the quotation4 7#ai7 ,explain the principle of teleology as related to analogy4 ,hibben1 #aijh2 p4 #cag4 ,,chapter #ah4 ,,the ,,five ,,special ,,methods ,,of ,,observation ,,and ,,experiment4#ac #a4 ,,the ,,aim ,,of ,,the ,,five ,,methods4 ,the primary forms of induction have been divided into simple enumeration1 analogy and analysis 4 ,conditioning these forms are the two laws1 uniformity of nature and universal causation4 ,since these laws are always concerned with causes1 we may refer to them as together expressing the fundamental 8fact of causation40 ,wherever there is a causal connection1 no matter how slight1 these laws obtain4 ,though 8the fact of causation0 probably conditions all forms of induction1 it is most conspicuous in the third form2 namely1 ,analysis4 ,here the main aim is to establish a causal connection of some kind2 an aim which may be accomplished through the medium of observation and experiment4 ,incident to this notion1 ,john ,stewart ,mill formulated five experimental methods of induction4 ,these are known according to the following distinctive titles3 #a4 ,the ,method of ,agreement4 #b4 ,the ,method of ,difference4 #c4 ,the ,joint ,method of ,agreement and ,difference4 #d4 ,the ,method of ,concomitant ,variations4 #e4 ,the ,method of ,residues4 #b4 ,,method ,,of ,,agreement4 7#a7 ,principle stated4 ,as stated by ,mill the principle of the ,method of ,agreement is this3 8,if two or more instances of the phenomenon under investigation have only one circumstance in common1 the circumstances in which alone all the instances agree is the cause 7or effect7 of the given phenomenon40 ,this notion is given in clearer terms by ,jevons and ,creighton4 ,viz43 8,the sole invariable antecedent of a phenomenon is probably its cause02 and 8,the sole invariable consequent of a phenomenon is probably its effect40 ,it is known that an antecedent is anything which precedes2 while a consequent is anything which follows4 ,to be regarded as a cause1 an antecedent must be invariable1 and to be regarded as an effect1 a consequent must likewise be invariable4 ,antecedents and consequents which are in no way constant could hardly have any causal connection4 7#b7 ,method symbolized4 ,let ,p1 ,p1 ,p1 ,p1 etc41 represent the phenomenon as it may appear the first1 second1 third1 fourth1 etc41 times1 and let ,a1 ,b1 ,c1 etc41 stand for the various antecedents1 or the various consequents as the case may demand4 ,these two forms may now be used to illustrate the two statements which summarize ,agreement3 ,first statement4 ,antecedents4 ,consequents4 ,a ,b ,c ,d ,p ,a ,d ,e ,f ,p ,a ,l ,m ,n ,p ,a ,o ,p ,q ,p ,second statement4 ,p ,a ,b ,c ,d ,p ,a ,d ,e ,f ,p ,a ,l ,m ,n ,p ,a ,o ,p ,q ,in the first case1 the sole invariable antecedent is ,a1 and1 therefore1 we infer that ,a is probably the cause of ,p4 ,in the second case1 the invariable consequent being ,a1 is probably the effect of ,p4 7#c7 ,concrete examples illustrating first statement4 ,the ,problem3 ,cause of ,john's tardiness4 ,on investigation the various antecedents are these3 7#a7 ,john has his breakfast at seven2 7#b7 after breakfast he carries his father's dinner to him and 7#c7 feeds the hens2 and then 7#d7 goes to school by the path through the woods and around the mill pond4 ,phenomenon as a consequent4 ,john is tardy4 ,determining to do away with the tardiness1 the teacher brings about a variation in the antecedents1 varying one at a time taken in the order indicated above4 ,to wit3 7#a7 ,varying the first antecedent4 ,john breakfasts at #f3cj2 ,other antecedents the same2 7,phenomenon7 ,but ,john is tardy4 7#b7 ,varying the second antecedent4 ,the younger brother carries the dinner2 ,other antecedents the same2 7,phenomenon7 ,john is tardy4 7#c7 ,varying the third antecedent4 ,another brother cares for the hens2 ,other antecedents the same2 7,phenomenon7 ,john is still tardy4 ,the teacher is now quite certain that the tardiness is due to the route through the woods and around the pond4 ,using1 as symbols1 the initial letters of the italicized 8key-words0 of the antecedents as stated above1 the case of tardiness may be symbolized as follows3 ,key words ,symbols seven s dinner d hens h woods w tardy t1 t1 t ,antecedents ,phenomenon s d h w t e d h w t s b h w t s d a w t 8w0 standing for route through the woods1 is seen to be the invariable antecedent4 7#d7 ,concrete example illustrating the second statement4 ,the ,problem3 ,to determine the effect of direct primaries4 ,first trial4 ,antecedent ,consequents #a4 ,greater expense to candidate1 ,direct #b4 ,greater interest shown1 primary #c4 ,better men nominated1 #d4 8,bumper0 crops4 ,second trial4 #a4 ,greater expense to candidate1 ,direct #b4 ,greater interest shown1 primary #c4 ,better men nominated1 #d4 ,crops below average4 ,third trial4 #a4 ,no greater expense1 ,direct #b4 ,greater interest shown1 primary #c4 ,better men nominated1 #d4 ,crops average4 ,fourth trial4 #a4 ,no greater expense1 ,direct #b4 ,no greater interest1 primary #c4 ,better men nominated1 #d4 ,crops average4 ,it is seen that the invariable consequent is1 8,better men nominated40 ,we may1 therefore1 conclude that this is a probable effect of 8,direct primaries40 7#e7 ,distinguishing features of method of agreement4 ,the essential characteristics of the method of agreement are three3 ,first1 ,the phenomenon always occurs4 ,second1 ,there is at least one invariable antecedent4 ,third1 ,the other antecedents vary4 ,giving attention to the attending symbolized illustrations it may be noted that 8,p10 the phenomenon1 always happens2 while in the case of the first symbolization1 8,d0 is the invariable antecedent and 8,a1 ,b1 ,c1 ,e1 ,g1 ,l1 ,m1 ,f1 ,i0 are the variable antecedents4 8,k0 is the invariable antecedent of the second and 8,h1 ,i1 ,l1 ,t1 ,m1 ,w1 ,x1 ,y1 ,z1 ,s0 are the variable antecedents4 ,antecedents ,consequents #a4 ,a ,b ,c ,d ,e ,p ,a ,b ,c ,d ,g ,p ,l ,b ,c ,d ,m ,p ,a ,f ,g ,d ,m ,p ,l ,b ,c ,d ,i ,p #b4 ,h ,i ,k ,l ,t ,p ,k ,l ,m ,t ,w ,p ,m ,t ,l ,k ,w ,p ,x ,h ,k ,y ,z ,p ,t ,w ,l ,k ,s ,p 7#f7 ,a ,matter of ,observation and ,experiment4 ,on studying the problem relative to the tardiness of ,john1 it appears that in obtaining the various antecedents the work would be largely a matter of observation4 ,carrying the father's dinner1 the route through the woods1 etc41 are facts which observation would make evident4 ,however1 when it becomes necessary to vary these antecedents with a view to finding the invariable one1 the procedure is experimental as well as a matter of casual observation4 ,moreover1 in connection with the direct primary problem the question would be largely a matter of experiment2 though observation would obtain as a subsidiary condition4 ,we may conclude from this that the method of agreement involves both observation and experiment2 and since the student will discover that the other methods impose similar demands1 we are justified in designating these five special methods of induction as those of observation as well as of experiment4 7#g7 ,advantages and ,disadvantages of the ,method of ,agreement4 ,the concrete cases given to illustrate the method of agreement present a simple combination of antecedents and consequents4 ,in life1 however1 such simplicity does not usually obtain and in consequence the method of agreement gives rise to a few serious difficulties4 ,these may be summarized as 7a7 ,plurality of causes2 7b7 ,immaterial antecedents2 7c7 ,complexity of phenomena2 7d7 ,uncertainty of conclusion4 7a7 ,plurality of causes is mentioned by ,mill as constituting the 8characteristic imperfection0 of the method of agreement4 ,as the term signifies1 plurality of causes represents a condition where a given phenomenon has more than one cause1 or where different causes produce the same effect4 ,for example1 8,a poor crop0 may be due to drought1 neglect1 pests1 etc42 heat may be caused by friction1 electricity1 combustion4 ,unfavorable home conditions2 ill health2 dislike for teacherany one of these might be followed by irregular attendance4 7b7 ,immaterial antecedents are those which precede a given phenomenon and yet1 under the most favorable situations1 have no causal connection with said phenomenon4 ,for example1 the various antecedents of the heavy rain may have been a south wind1 forgetting to take an umbrella1 missing the car and having to walk1 etc4 ,clearly these antecedents1 with the exception of the first1 are immaterial4 7c7 ,the law of agreement demands that all the material antecedents receive consideration1 but often the situation is too complex to make this possible2 a fair illustration of such would be an attempt to ascertain all of the antecedents of 8the high cost of living40 7d7 ,the law of agreement never precludes the possibility of error2 as it is quite impossible to carry the analysis to the point of absolute certainty4 ,of all the methods1 8agreement0 is the least reliable4 ,despite the foregoing objections1 however1 the method is of positive value because of its suggestiveness2 opening the door to plausible hypotheses it gives the investigators a working basis4 #c4 ,,method ,,of ,,difference4 7#a7 ,principle stated4 ,says ,mill1 8,if an instance in which the phenomenon under investigation occurs1 and an instance in which it does not occur1 have every circumstance in common save one1 that one occurring only in the former2 the circumstance in which alone the two instances differ is the effect or the cause of an indispensable part of the cause1 of the phenomenon40 ,to put this in simple terms3 ,whatever is invariably present when the phenomenon occurs and invariably absent when the phenomenon does not occur1 other circumstances remaining the same1 is probably the cause or the effect of the phenomenon4 7#b7 ,method symbolized4 ,using the same symbols as were used in 8,agreement40 ,antecedents ,consequents ,a ,b ,c ,d ,p ,b ,c ,d or ,p ,a ,b ,c ,d ,b ,c ,d ,in the first instance ,a is probably the cause of the phenomenon1 since it is present when the phenomenon occurs and absent when it does not occur4 ,for a similar reason1 ,a is the effect in the second case4 7#c7 ,concrete illustrations4 7,a7 ,a wise teacher in ascertaining the cause of ,john's tardiness would have suggested at once a change of route4 ,using as symbols the initial letters of the key-words of the antecedents in the case1 the following results3 s d h w t s d h 7,b7 ,first trial4 ,problem3 ,unprepared home work4 ,antecedents ,consequents #a4 ,length of lesson1 #b4 ,definiteness of lesson1 ,work not properly #c4 ,amount of interest shown1 prepared4 #d4 ,physical condition the same4 ,second trial4 #a4 ,length of lesson the same1 #b4 ,lesson made more definite1 ,work properly prepared4 #c4 ,interest the same1 #d4 ,physical condition the same4 ,the foregoing symbolized3 ,l ,d ,i ,c ,w ,l ,i ,c ,it is seen that indefiniteness of lesson assignment is the cause of the unprepared home work4 7#d7 ,advantages and disadvantages of the ,method of ,difference4 ,the main difficulty attending the use of the method of difference is the complexity of phenomenon4 ,the very nature of the method insists as an essential requirement that only one material antecedent shall be varied at a time4 ,in life the variations are more or less confused1 and it is often not only impossible to observe cases of a single variation1 but frequently error comes through overlooking antecedents which are material to the case under investigation4 ,for these reasons the ,method of ,difference is more a method of experiment than it is a method of observation4 ,by controlling the circumstances it becomes possible to vary but one antecedent at a time1 and also to bring into prominence all of the material antecedents4 ,bacon claims that all 8crucial instances0 are merely applications of the ,method of ,difference4 ,by crucial instance he means any fact which will enable us to determine at once which supposition is the correct one4 ,for example1 the physician may not know whether it is malaria or typhoid fever till he takes a blood test2 such a test typifies 8crucial instances40 ,the various tests in chemistry are likewise cases of crucial instances1 and1 in consequence1 this science makes use of 8,difference0 more than any other method4 7#e7 ,characteristic features of ,method of ,difference4 ,there are three distinguishing marks of the ,method of ,difference3 these are1 7#a7 ,the phenomenon does not always happen2 7#b7 ,one antecedent is variable2 7#c7 ,the other antecedents are more or less invariable4 ,the following symbolizations will make these three characteristics evident3 ,antecedents ,consequents 7#a7 ,a ,b ,c ,p ,a ,c 7#b7 ,b ,c ,x ,b ,c ,p 7#c7 ,l ,m ,t ,k ,p ,l ,m ,k ,,agreement ,,and ,,difference ,,compared4 7a7 ,the methods of ,agreement and ,difference are complementary as may be discerned by comparing their characteristic features3 ,in ,agreement the phenomenon always occurs2 in ,difference the phenomenon does not always occur3 ,in ,agreement there is one invariable antecedent2 whereas in ,difference there is one variable antecedent3 ,in ,agreement the other antecedents are more or less variable2 but in ,difference the other antecedents are more or less invariable4 7b7 ,according to ,mill the ,method of ,agreement insists that what can be eliminated is not connected2 whereas the ,method of ,difference implies that what cannot be eliminated is connected4 7c7 ,the ,method of ,agreement is more a method of observation1 since it is chiefly concerned with the discovery of causes4 ,the ,method of ,difference is distinctly a method of experiment1 because its usual aim is to discover effects4 7d7 ,the ,method of ,agreement is so called because the object is to compare several instances to determine in what respect they agree2 but in the case of ,difference instances are compared to determine in what respects they differ4 7e7 ,the conclusions of the ,method of ,difference involve greater certainty than those of ,agreement and1 therefore1 the former method should be adopted when there is a choice4 #d4 ,,the ,,joint ,,method ,,of ,,agreement ,,and ,,difference4 7#a7 ,principle stated4 ,the uncertainty of the conclusions of ,agreement and the impossibility at times of employing directly the ,method of ,difference1 give rise to the use of the combination of ,agreement and ,difference known as the ,joint ,method4 ,as stated by ,mill1 the principle conditioning the ,joint ,method is this3 8,if two or more instances in which the phenomenon occurs have only one circumstance in common1 while two or more instances in which it does not occur have nothing in common save the absence of that circumstance1 the circumstance in which alone the two sets of instances differ is the effect or the cause or an indispensable part of the cause1 of the phenomenon40 ,more briefly the notion may be stated in this wise3 ,among many instances1 if one circumstance is invariably present when the phenomenon occurs1 and invariably absent when the phenomenon does not occur this circumstance is probably the cause or the effect of the phenomenon4 ,this principle differs from the one underlying the ,method of ,difference in that the instances considered are more varied and more numerous4 ,the principle of ,difference requires but two sets of instances1 while the ,joint ,method demands at least three2 two when the phenomenon occurs and one when it does not occur4 ,a study of the symbolizations and illustrations will clarify this distinction4 7#b7 ,joint ,method symbolized4 ,if we use circumstances and phenomenon in place of antecedents and consequent1 then one symbolization may be made to stand for ascertaining either the invariable antecedent1 or the invariable consequent4 ,circumstances ,phenomenon #a4 ,a ,b ,c ,d ,p #b4 ,a ,d ,e ,f ,p #c4 ,a ,l ,m ,n ,p #d4 ,a ,o ,p ,q ,p #e4 ,o ,p ,q #f4 ,l ,m ,n #g4 ,d ,e ,f #h4 ,b ,c ,d ,it is obvious that the first1 second1 third and fourth groups of instances illustrate the principle of ,agreement2 whereas the first and eighth1 the second and seventh1 the third and sixth1 and the fourth and fifth illustrate in each case1 the principle of ,difference4 7#c7 ,concrete ,examples illustrating ,joint ,method4 ,the problem3 ,too much whispering4 ,antecedents ,consequent #a4 ,insufficient work1 ,lack of interest1 ,much whispering4 ,seated near a friend4 #b4 ,more work1 ,lack of interest1 ,much whispering4 ,seated near a friend4 #c4 ,more work1 ,more interest1 ,much whispering4 ,seated near a friend4 #d4 ,more work1 ,more interest1 ,not much whispering4 ,not seated near a friend4 #e4 ,more work1 ,lack of interest1 ,not much whispering4 ,not seated near a friend4 #f4 ,insufficient work1 ,lack of interest1 ,not much whispering4 ,not seated near a friend4 ,from this it may be concluded that the undue amount of whispering is caused by seating particular friends near each other4 ,the problem3 ,poor recitations4 ,antecedents ,consequent #a4 ,long lesson1 ,faulty assignment of lesson1 ,poor recitation4 ,fear of teacher4 #b4 ,lesson made shorter1 ,faulty assignment of lesson1 ,poor recitation4 ,fear of teacher4 #c4 ,lesson made shorter1 ,a more careful assignment1 ,poor recitation4 ,fear of teacher4 #d4 ,lesson made shorter1 ,a more careful assignment1 ,good recitation4 ,removal of fear of teacher4 #e4 ,lesson made shorter1 ,faulty assignment1 ,good recitation4 ,no fear of teacher4 #f4 ,lesson long1 ,faulty assignment1 ,good recitation4 ,no fear of teacher4 ,fear of teacher is the cause of the poor recitation4 7#d7 ,distinguishing features4 ,being a combination of ,agreement and ,difference the ,joint ,method possesses the characteristics of each1 though more or less modified4 ,the distinguishing marks may be summarized as follows3 7#a7 ,of the first group of instances3 7#a7 ,the phenomenon must always occur1 7#b7 ,one antecedent must be invariable1 7#c7 ,the other antecedents must be more or less variable4 7#b7 ,of the second group of instances3 7#a7 ,the phenomenon must never occur1 7#b7 ,one antecedent must be variable1 7#c7 ,the other antecedents must be more or less invariable4 ,briefly1 the one principle concerned is this3 ,there must be an invariable conjunction between the phenomenon involved and the antecedent suspected of being the cause4 7#e7 ,advantages and ,disadvantages of the ,joint ,method4 ,since the ,joint ,method permits a consideration of the negative aspect of the question as well as the affirmative1 the opportunities for testing the many instances concerned are doubled4 ,in consequence1 the conclusions of the ,joint ,method are more positive than those of the other methods4 ,it follows that this same opportunity to multiply the instances would tend to lessen the other objections raised against the ,method of ,agreement2 viz41 plurality of causes1 immaterial antecedents1 complexity of phenomenon4 ,the student must regard the given illustrative symbolizations and concrete examples as being of the simplest form2 in life such are the exceptions rather than the rule4 ,when investigating questions1 like the cause of the high cost of living1 the effect of high tariff1 the reason for the typhoid epidemic1 etc41 there is often a confusion of circumstances which makes the ,joint ,method unsatisfactory1 even though it furnishes a larger opportunity for the multiplication of instances4 ,the strongest case which the ,joint ,method is able to present is when the negative instances repeat the positive in every detail1 with the one exception of the variable antecedent4 ,to wit3 ,strong ,argument3 ,circumstances ,phenomenon ,a ,b ,c ,p ,a ,l ,m ,p ,l ,m ,b ,c ,weak ,argument3 ,a ,b ,c ,p ,a ,l ,m ,p ,r ,s ,t ,k ,despite the disadvantages1 the conditions of the ,joint ,method are more or less ideal2 since the positive branch of the argument suggests the hypothesis1 while the negative branch proves the accuracy or inaccuracy of such4 #e4 ,,method ,,of ,,concomitant ,,variations4 7#a7 ,principle stated4 ,mill's statement is this3 8,whatever phenomenon varies in any manner whenever another phenomenon varies in a particular manner1 is either a cause or an effect of that phenomenon1 or is connected with it through some fact of causation40 ,to put it differently3 ,if when one phenomenon varies alone1 another also varies alone1 the one is either the cause or the effect of the other4 7#b7 ,concomitant ,variations symbolized4 ,circumstances ,phenomenon ,a ,p ,a a ,p p 7,a a7 a 7,p p7 p ,it is evident from this that little 8a0 is the cause or the effect of little 8p40 ,to put it in concrete form3 ,let ,a ,x number of calories of heat1 ,and ,p #fh ,f41 the original temperature of room1 ,and a candle burning in room for hour1 ,and p #b ,f4 ,then ,antecedents ,consequent ,x no4 of cal4 of heat in room #fh ,f4 temp4 of room ,x no4 of cal4 of heat burning candle #fh #b #gj ,x 7no4 of cal4 of heat burning candle7 7#fh #b7 #b #fh burning candle ,as large 8,a0 is increased and decreased by little 8a0 so large 8,p0 appears to be increased and decreased by little 8p40 ,this strongly suggests a causal connection between little 8a0 and little 8p40 7#c7 ,other concrete illustrations4 ,problem3 ,to ascertain nature of sound4 ,antecedent ,consequent ,bell rung when within a glass jar filled ,loud sound4 with air1 ,some of the air pumped out of the jar1 ,sound not so loud4 ,more air pumped into jar again1 ,sound louder again4 ,the conclusion must be that air has something to do with the production of sound4 ,problem3 ,to find best feed for egg production4 #ajj lbs4 beef scraps1 #ajj lbs4 wheat1 #cj doz4 eggs4 #ajj lbs4 oats1 #ajj lbs4 corn1 #ej lbs4 beef scraps1 #ajj lbs4 wheat1 #bg doz4 eggs4 #ajj lbs4 oats1 #ajj lbs4 corn1 #ij lbs4 beef scraps1 #ajj lbs4 wheat1 #bh doz4 eggs4 #ajj lbs4 oats1 #ajj lbs4 corn1 ,since the variation in the amount of beef scraps is accompanied by a like variation in the number of eggs produced1 it may be assumed that beef scraps are essential to large egg production4 7#d7 ,distinguishing features4 ,the phenomenon always occurs but in varying degrees2 ,one antecedent varies in degree2 ,the other antecedents are invariable4 7#e7 ,advantages and disadvantages4 ,concomitant ,variations is applicable in cases when it is impossible to use ,difference4 ,recourse is made to the latter when the phenomenon can be made to appear or disappear at will1 but there are times when it is impossible to cause the phenomenon to disappear altogether4 ,for example1 in the case of the varying degrees of heat in the room it would be scientifically impossible to take all of the heat out of the room2 or in experimenting with gravitation1 to do away with its influence entirely1 is beyond the power of man4 ,it is thus evident that ,concomitant ,variations may be used in cases where the conditions forbid doing away entirely with the phenomenon4 ,the special function of ,concomitant ,variations seems to be to establish the exact quantitative relation between the varying cause and the varying effect4 ,to illustrate3 ,as a general law it is known that bodies attract each other in varying degrees according to their distances apart and according to their relative sizes2 by ,concomitant ,variations this law has been given definite quantitative value and reads like this3 8,bodies attract each other directly as the product of their masses1 and inversely as the square of the distance between them40 ,this illustration suggests that the variation between antecedent and consequent may be direct or inverse4 ,the error most common in this method is the assumption that the quantitative relation between two varying phenomena will always be according to a constant ratio4 ,for example1 when being reduced from a high temperature to #ci ,f41 water steadily contracts2 but at #ci ,f4 it commences to expand until it becomes ice4 ,thus the ratio of contraction of water is constant only within certain limits4 ,in any event the established ratio of variation can with absolute safety be applied only to the instances investigated4 ,another disadvantage incident to this method1 is the situation of two elements varying together constantly1 and yet having no causal connection whatever4 #f4 ,,the ,,method ,,of ,,residues4 7#a7 ,principle stated4 ,as stated by ,mill the principle of residue is this3 8,subtract from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents1 and the residue of the phenomenon is the effect of the remaining antecedents40 ,in simpler form the notion is this3 ,subtract from any phenomenon those parts of it which are known to be the effect of certain antecedents1 and what is left of the phenomenon is the effect of the remaining antecedents4 7#b7 ,principle symbolized4 ,antecedent ,consequent ,a x ,b y ,c z ,the total cause of the phenomenon xyz is ,,abc4 ,but it is known that the cause of x is the antecedent ,a2 whereas the cause of y is the antecedent ,b2 hence it is concluded that the cause of z is the antecedent ,c4 7#c7 ,concrete illustrations4 ,problem3 ,to find the weight of coal4 ,antecedents ,consequents ,weight of driver1 ,weight of wagon1 #dbjj lbs4 ,weight of coal4 ,weight of driver1 #bjj lbs4 #bbjj lbs4 ,weight of wagon1 #bjjj lbs4 ,hence we may conclude that the weight of coal is #dbjj lbs4 #bbjj lbs41 or #bjjj lbs4 ,perhaps the most noted instance in history of the application of this method1 was the one which resulted in the discovery of ,neptune4 ,in calculating the orbit of ,uranus1 it was found that the combined attractions of the sun and the known planets did not account for the path which ,uranus took4 ,there was some unknown influence at work4 ,assuming that this unaccountable attraction was due to the presence of another planet beyond the orbit of ,uranus1 an ,englishman by the name of ,adams1 and later the ,frenchman ,leverrier1 were able to indicate by the principle of ,residues1 the spot where this planet should be4 ,by directing the telescope toward this point1 ,neptune was discovered4 7#d7 ,distinguishing features3 ,the phenomenon always occurs1 ,the antecedents are usually invariable1 ,some of the antecedents are known to be the cause of a part of the phenomenon4 7#e7 ,advantages and disadvantages4 ,the ,method of ,residues gives three distinct results3 ,first1 it tells what is left over after all the other parts of the phenomenon have been explained4 ,second1 it tells how much is left over1 and third1 it calls attention to the unexplained parts of the phenomenon4 ,for example1 in the first concrete illustration1 by subtracting the known quantities from the total quantity1 what is left over is found to be coal2 not only so but we are able to calculate the exact amount of coal4 ,this illustrates the first and second results of the ,method of ,residues4 7,like concomitant variations it is seen that residues is serviceable in given definite quantitative values47 ,the discovery of ,neptune illustrates well the third result of this method2 i4 e41 after accounting for every other force1 it was found that there was yet a force at work which had never been explained4 ,it is this third feature of unexplained residues which has placed 8,science in its present advanced state40 8,most of the phenomena which nature presents are complicated2 and when the effects of all known causes are estimated with exactness1 and subducted1 the residual facts are constantly appearing in the form of phenomena altogether new1 and leading to the most important conclusions40 ,so says ,john ,herschel4 ,almost all of the discoveries in astronomy have come about in this way4 ,if a heavenly body does not behave as it should according to the established theory1 then either the theory is wrong or there is some residual phenomenon which needs to be explained4 ,its suggestiveness is1 therefore1 the most important function of this method1 though this very feature is the one which makes evident its greatest disadvantage4 ,the unexplained residual phenomenon may be very complex and1 therefore1 a careless observer is apt to overlook a lurking element which in reality is the true cause4 #g4 ,,the ,,general ,,purpose ,,and ,,unity ,,of ,,the ,,five ,,methods4 ,thinking has been defined as the deliberative process of affirming and denying connections4 ,it is obvious that these five methods are a matter of affirming and denying connections between antecedents and consequents4 ,as soon as the looked for connections are established1 the antecedents and consequents are known to be related to each other as causes and effects4 ,in this attempt to find and prove connections the ,method of ,agreement is chiefly valuable in suggesting workable hypotheses1 and the method of difference in verifying1 through experiment1 the correctness or incorrectness of these hypotheses4 ,in substance the principle conditioning both methods is this3 8,if a single antecedent is invariably present when the phenomenon is present and invariably absent when the phenomenon is absent then this antecedent is the cause of the phenomenon40 ,to put it still more briefly3 ,between two phenomena there is a causal connection1 if the conjunction between the two is invariable4 ,it is the business of ,agreement to single out the one antecedent and of ,difference to show1 by presenting the negative as well as the affirmative side of the case1 that the conjunction of the one antecedent and the particular phenomenon is invariable4 ,the ,joint ,method is merely a combination of ,agreement and ,difference carried into more varied and complex situations4 ,the methods of ,concomitant ,variations and ,residues are merely modifications of ,difference2 the former being used when the chief feature is the fluctuation of the phenomenon1 and the latter when it is desired to find what is left over4 ,agreement suggests the hypothesis1 8difference0 proves it2 the joint method is 8difference0 more or less complicated1 concomitant variations is 8difference0 applied to fluctuating phenomena1 residues is 8difference0 used to find what and how much is left over4 ,agreement is the method of observation and belongs to the physician and nature student4 ,difference and the ,joint ,method are experimental devices which are used by the physicist and chemist4 ,concomitant ,variations is the method of unstable phenomena and naturally attaches itself to the economist and statistician4 ,residues is the method of 8lurking exceptions0 and is favored by the astronomer and mathematician4 ,residues1 being the method of 8what is left over10 is the most common in daily affairs4#ad ,all the five methods are forms of inductive thinking which lead to the establishment of causal connections by means of the principle of the invariable conjunction of phenomena4 #h4 ,,outline4 ,,the ,,five ,,special ,,methods ,,of ,,observation ,,and ,,experiment4 7#a7 ,aim of ,five ,methods4 ,fundamental fact of causation4 ,aim of analysis4 agreement difference ,methods of joint concomitant variations residues 7#b7 ,method of ,agreement4 ,principle stated ,method symbolized ,method illustrated ,distinguishing features of method ,a matter of observation and experiment ,advantages and disadvantages 7#c7 ,method of ,difference4 ,principle stated ,method symbolized ,method illustrated ,advantages and disadvantages ,characteristic features ,agreement and ,difference compared 7#d7 ,the ,joint ,method of ,agreement and ,difference ,principle stated ,method symbolized ,concrete illustrations ,distinguishing features ,advantages and disadvantages 7#e7 ,method of ,concomitant ,variations ,principle stated ,method symbolized ,concrete illustrations ,distinguishing features ,advantages and disadvantages 7#f7 ,the ,method of ,residues ,principle stated ,method symbolized ,concrete illustrations ,distinguishing features ,advantages and disadvantages 7#g7 ,general ,purpose and ,unity of ,five ,methods ,one fundamental principle #i4 ,,summary4 7#a7 ,the fundamental fact of causation underlies the three forms of induction1 but is most conspicuous in the method of analysis and may be ascertained by recourse to one of the experimental methods4 7#b7 ,the principle of the method of agreement may be summed up in the two statements3 ,the sole invariable antecedent of a phenomenon is probably its cause and the sole invariable consequent of a phenomenon is probably its effect4 ,these two statements may be symbolized and illustrated4 ,the essential characteristics of the method of agreement are the phenomenon always occurs2 there is at least one invariable antecedent2 the other antecedents vary4 ,the method of agreement together with the other four methods may justly be termed methods of experiment as well as methods of observation4 ,the difficulties of the method of agreement are in the main plurality of causes1 immaterial antecedents1 complexity of phenomenon and uncertainty of conclusion4 ,these difficulties may be summarized as involving a phenomenon which may have several causes2 may be preceded by conditions of no causal consequence2 may be so involved as to prevent exhaustive examination2 and may give unreliable conclusions4 ,agreement is valuable chiefly in furnishing to the investigator plausible hypotheses4 7#c7 ,the principle of difference is this3 8,whatever is invariably present when the phenomenon occurs and invariably absent when the phenomenon does not occur1 other circumstances remaining the same1 is probably the cause or the effect of the phenomenon40 ,like agreement1 difference admits of symbolization and illustration by concrete examples4 ,the chief difficulties attending difference are3 in nature varying one antecedent at a time is infrequent1 and it is easy to overlook antecedents which are closely related to the case under investigation4 ,difference is the most common method of the experimental sciences4 ,the characteristic features of difference are1 the phenomenon does not always occur1 one antecedent is variable1 while the others are invariable4 ,the methods of agreement and difference are complementary processes4 ,agreement attempts to eliminate all the antecedents but one1 while difference aims to eliminate one only4 ,agreement is a method of observation1 while difference is a method of experiment4 ,the conclusion of the method of difference gives greater certainty than that of the method of agreement4 7#d7 ,the joint method may be stated in this way3 ,among many instances if one circumstance is invariably present when the phenomenon occurs and invariably absent when the phenomenon does not occur1 this circumstance is probably the cause or the effect of the phenomenon4 ,the instances of the joint method are more numerous and more varied than those of either agreement or difference4 ,the joint method has the distinguishing characteristics of both agreement and difference4 ,because it furnishes greater opportunities for multiplying and varying the instances involved1 the joint method presents fewer objections than either of the two separate methods4 ,the positive branch of the joint method suggests the hypothesis1 while the negative branch proves it4 ,this makes the method somewhat ideal4 7#e7 ,the principle of concomitant variations may be stated as follows3 ,if when one phenomenon varies alone1 and another also varies alone1 the one is either the cause or the effect of the other4 ,this is the method of fluctuation1 and is used when it is impossible to make the phenomenon disappear altogether1 as in the case of difference4 ,the chief function of concomitant variations is to establish exact quantitative relations between cause and effect4 7#f7 ,the principle of residues is this3 ,subtract from any phenomenon those parts of it which are known to be the effect of certain antecedents1 and what is left of the phenomenon is the effect of the remaining antecedent4 ,the most valuable feature of residues is its suggestiveness2 an attempt to explain the 8residual phenomenon0 has led to many important scientific discoveries4 7#g7 ,the five methods are concerned with the establishment of causal connections between phenomena4 ,agreement suggests the connection while difference proves it4 ,the other methods are modified applications of difference1 necessitated by some peculiar form which the phenomenon may take4 ,a statement of the one principle involved is3 8,if the conjunction between two phenomena is invariable then there is a causal connection40 ,all of the methods are forms of inductive thinking4 #aj4 ,,review ,,questions4 7#a7 ,explain 8the fundamental fact of causation40 7#b7 ,show that the fact of causation is most conspicuous in induction by analysis4 7#c7 ,name the five special inductive methods of observation and experiment4 7#d7 ,state1 symbolize1 and illustrate the method of agreement4 7#e7 ,give examples of antecedents which do not function as causes4 7#f7 ,show that the 8special methods0 are a matter of both observation and experiment4 7#g7 ,give the distinguishing features of the method of agreement2 illustrate by reference to the symbols4 7#h7 ,exemplify the plurality of causes2 immaterial antecedents2 complexity of phenomenon4 7#i7 ,show that the conclusions of agreement are largely hypothetical4 7#aj7 ,state1 symbolize1 and illustrate the method of difference4 7#aa7 ,show by illustration that1 in the method of difference1 only one antecedent should be varied at a time4 7#ab7 ,show that difference is naturally a method of experiment4 7#ac7 ,explain ,bacon's use of the term 8crucial instances40 7#ad7 ,name and explain the characteristic features of the method of difference4 7#ae7 ,show that agreement and difference are complementary4 7#af7 ,explain and illustrate the joint method4 7#ag7 ,what inference may be drawn from the following instances3 ,antecedents ,consequents ,a ,l ,m ,t p q r g ,b ,l ,m ,e z q r x ,b ,c ,m ,e r z x y ,a ,m ,t ,h p q g o 7#ah7 8,mr4 ,darwin1 in his experiment on cross and self fertilization in the vegetable kingdom1 placed a net about one hundred flower heads1 thus protecting them from the bees4 ,he at the same time placed one hundred other flower heads of the same variety of plant where they would be exposed to the bees4 ,he obtained the following result3 ,the protected flowers failed to yield a single seed4 ,the others yielded about #b1gbj seeds4 ,thus cross-fertilization was proved40 7,hibben74 ,what method did ,darwin employ8 ,symbolize the experiment4 7#ai7 ,summarize the distinguishing marks of the joint method4 7#bj7 ,show that the joint method is more ideal than either agreement or difference4 7#ba7 ,state and give concrete illustrations of the law of concomitant variations4 7#bb7 ,what is the chief function of concomitant variations8 ,illustrate4 7#bc7 ,give instances where it would be impossible to use difference1 but easy to use concomitant variations4 7#bd7 ,explain this3 8,the quantitative variation between antecedent and consequent may be either direct or inverse40 7#be7 ,state and explain by illustration the method of residues4 7#bf7 ,what are the advantages and disadvantages of the principle of residues8 7#bg7 ,state the principle which virtually sums up the five methods4 7#bh7 ,write briefly on the practical applications of the five methods to the ordinary walks of life4 #aa4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 ,trace the connection between the method of agreement and induction by simple enumeration4 7#b7 ,show that ,mill's methods may properly be termed 8,inductive ,methods of ,scientific ,investigation40 7#c7 ,how may it be shown by 8agreement0 that the high cost of living is due to the tendency to spend more than we earn8 7#d7 ,assume that you are a member of the ,board of ,health1 and that you desire to ascertain the cause of the diphtheria epidemic by means of the principle of agreement4 7#e7 ,what is the error involved in coming to the conclusion that to sit at table where there are thirteen1 may mean the death of one of the thirteen before the end of the year4 7#f7 ,indicate how it could be shown1 by the method of difference1 that the mosquito is responsible for the propagation of yellow fever4 7#g7 8,another experiment similar to this was tried by ,plateau1 who put some food of which cockroaches are fond on a table and surrounded it with a low circular wall of cardboard4 ,he then put some cockroaches on the table2 they evidently scented the food1 and made straight for it4 ,he then removed their antennae40 7,hibben74 ,complete and give with explanations the method used4 7#h7 8,in some cases it is impossible to remove an element which is supposed to be the cause of an effect under investigation40 ,explain and illustrate4 7#i7 8,extreme care must be taken that1 in the withdrawing of any element1 no other element is inadvertently introduced40 ,tyndale supposed he had proved spontaneous generation1 when1 after sealing in a jar of boiled water a wisp of baked hay1 he found1 after many days1 indications of life within the bottle4 ,in transferring the hay to the bottle1 he carried the former across the room4 ,what element was inadvertently introduced8 7#aj7 8,the attempt to determine the numerical relations according to which two phenomena vary1 requires the utmost caution as soon as our inference outsteps the limits of our observations40 7,fowler74 ,explain this in connection with the law of concomitant variations4 7#aa7 8,when the effects of all known causes are estimated with exactness and subducted1 the residual facts are constantly appearing in the form of phenomena altogether new1 and leading to the most important conclusions40 ,make clear by illustration this quotation which has reference to the principle of residues4 7#ab7 ,explain 8invariable conjunction of phenomena40 7#ac7 ,investigate by means of one of the five methods the following problems3 7#a7 8,all vegetables which grow to root should be planted during the last two days of the waxing moon40 7#b7 8,in this section the south wind is the storm wind40 7#c7 8,mischief is the outcome of misdirected energy40 7#d7 8,bad boys usually receive unjust treatment40 7#e7 8,an ounce of prevention is worth a pound of cure40 ,,chapter #ai4 ,,the ,,auxiliary ,,elements ,,of ,,induction4 ,,observation,,experiment,,hypothesis4 #a4 ,,the ,,foundation ,,of ,,inductive ,,generalizations4 ,induction is the process of universalizing particular facts4 ,the starting point is the fact4 ,through observation the investigator gathers facts1 and then works them over with a view of finding uniformities4 ,the mind cannot build inductive generalizations without facts any more than a mason can build a brick wall without the bricks4 ,a fact is any particular thing made or done or is that which may be acquired by means of the presentative 7perception and imagination7 powers of the mind4 ,the state of awareness which results from the observation of facts is an individual notion4 ,this presents another aspect of the inductive process2 namely1 8,it is a matter of building general notions from individual notions1 acquired by the observation of facts40 ,to illustrate3 ,i note that ,a1 ,b1 ,c and ,d are honest in their dealings with me1 hence ,i come to the conclusion that some men are honest4 ,a fact is something done1 consequently the actual doing of the honest things by ,a1 ,b1 ,c and ,d are facts4 ,each state of awareness of each fact is an individual notion4 ,the mind now discerns a uniformity in these facts and derives the general notion that 8some men are honest40 #b4 ,,observation4 ,facts are acquired by means of observation4 ,when the mind fixes the attention upon any phenomenon it observes it4 ,the term observation means 8to watch for0 and may be defined as the act of watching for phenomena as they may occur4 ,the observation may be only casual1 or it may be willed or rational4 ,it is the latter aspect which most concerns the logician4 ,in this sense observation means careful1 painstaking1 systematic perception4 ,it involves the concentration of consciousness upon the case in hand1 or the actual giving of attention4 ,the thing observed may be external1 when the observation takes the form of sense-perception2 or it may be internal1 when the observation becomes a matter of introspection4 #c4 ,,experiment4 ,in observation we simply watch the phenomenon2 in experiment we make it4 ,in experiment we not only observe1 but we manipulate the circumstances so as to present the phenomenon under the most favorable conditions for observation4 8,in observation10 says ,mill1 8we find an instance in nature suited to our purposes02 whilst in experiment1 by an artificial arrangement of circumstances1 we make an instance suited to our purpose4 ,in observation we watch for causes2 in experiment we work for effects4 ,we may thus define experiment as the act of making phenomena occur for the purpose of watching for effects4 ,in experiment there is much which is merely observation4 ,in fact experiment is observation in which the phenomenon is artificially produced4 ,for the sake of definiteness1 however1 any observation which involves a manipulation of circumstances1 may be designated as experimental4 #d4 ,,rules ,,for ,,logical ,,observation ,,and ,,experiment4 ,to the uninitiated1 the matter of observation seems an easy task1 and yet when one hears two honest men swear to diametrically opposite facts which have come to them from observing the same phenomenon1 his faith is shaken4 8,eyes have they but see not0 is a logical truth as well as a moral one4 ,only the observation of the trained can be depended upon2 and yet this should not discourage the layman1 for even he1 by a little conscientious effort towards careful observation1 may greatly increase his store of accurate knowledge and add to the joy of living4 ,the attending rules are usually heeded by the trained scientist in matters of observation and experiment3 ,first ,rule4 ,the observations should be precise4 ,the time1 the place1 the surrounding conditions must be accurately noted4 ,many artificial contrivances have been devised because of the desire of the scientist to be precise4 ,instruments like the balance1 the thermometer1 the microscope1 etc41 has he invented1 and various devices and methods has he adopted for the sake of precision4 ,a common method is to take an average of observations4 ,for example1 to estimate justly the class work of a student1 the teacher should not be content with the ratings of one or two recitations1 but must average the ratings of many recitations4 ,again1 a child may be led to discover approximately the value of the sum of the interior angles of a triangle by measuring the angles of many triangles and then striking an average2 assume that the following results are obtained by such a procedure3 7#a7 #agh1 7#b7 #aha1 7#c7 #agi1 7#d7 #ahj1 7#e7 #ahb2 adding these and dividing by #e gives #ahj4 ,second ,rule4 ,the observations should concern only the material circumstances of the case in hand4 ,all the non essentials may be ignored1 as they serve only to distract attention4 ,for example1 7#a7 in order to get the 8right count0 all other sounds must be ignored save that of the fire gong2 7#b7 in finding the depth of the water for the building of a dam1 soundings ten miles away from the objective point could be of little value4 ,on the other hand1 it is easy to overlook certain lurking essentials4 ,to observe such1 it is necessary to resort to what the psychologist terms a 8preadjustment of attention40 ,we must know with exactness what we are looking for4 ,we must have a mental image of what we wish to see4 ,the astronomer in the discovery of a new planet must know the exact spot where it ought to be1 and have a clear mental image of its appearance4 ,this expectant attention is a necessity in the case of the physician who is anxious to make no mistakes in his diagnosis4 ,if he is looking for pneumonia1 he must have a very distinct auditory image of the sound of an affected lung4 ,it should be remarked1 however1 that this very preadjustment of attention1 with the untrained1 frequently leads to illusion4 ,we are so anxious to see what we are looking for that nine-tenths of what we believe we see is only inference4 ,how easy it is to read into a phenomenon something that is entirely foreign to it2 to read between the lines2 to see only the reflection of our own ideas4 8,verily the mental picture of what we wish to see becomes so vivid that we are positive of the thing being external40 ,thus the drunkard sees snakes and the superstitious see ghosts4 ,reading into the external what is only vividly internal is probably the most common error with the untrained observer4 ,third ,rule4 ,the observed circumstances should be varied as much as possible4 ,to observe a fact from a different viewpoint may not only broaden the original notion1 but it may change it entirely4 ,in order to gain a true notion of the effect of a particular nostrum on the human organism1 it becomes necessary to experiment with persons of different ages1 living under different environments1 and inheriting different constitutions4 ,those who are noted for pronouncing broad1 safe and sane judgments upon momentous questions are those who are 8all-angled observers40 ,fourth ,rule4 ,the observed phenomenon should1 if possible1 be isolated from all interfering phenomena4 ,in studying the action of a drug or a food1 all other drugs or foods must be eliminated4 ,the effect of gravitation on a body cannot be recorded accurately unless the experiments are made in a vacuum4 ,when studying the deflections of the compass1 all magnetic substances must be removed from the field4 #e4 ,,common ,,errors ,,of ,,observation ,,and ,,experiment4 ,the rules for scientific observation have suggested certain common errors which may now be considered4 7#a7 ,preconceived ideas4 ,there is not an unholy belief nor an unwholesome theory which cannot be bolstered up by means of apparent facts4 ,for example1 that monstrosity of ,puritan thought known as 8,salem ,witchcraft0 was substantiated by facts honestly observed4 ,again1 having made up his mind that it is going to be 8so and so10 the statistician goes out into the highways and byways and gathers the facts which vindicate his judgment4 ,further1 the democrat finds that the majority of the voters are democrats2 while the republican is confident that two-thirds of the voters are for republicanism4 ,here again is the fallacy springing from a preadjustment of attention4 ,we see what we want to see4 ,only the highly trained observer is able1 with impunity1 to make use of preadjusted attention1 and even with him1 it is not easy to remove from the situation belief and prejudice4 ,the true observer undertakes his work with his mind open to anything which the eye may bring him1 though it may topple into the dust his dearest theory and most cherished belief2 he proceedsthe mind a 8clean white page40 7#b7 ,the 8observed0 and the 8inferred0 confused4 ,this error has already received some attention4 ,it may be remarked further1 however1 that1 psychologically considered1 observation is a matter of interpreting the new by means of the old4 ,of necessity the interpretation1 whatever it may be1 will assume the complexion of the particular 8old knowledge0 which the mind is able to use4 ,in short1 a man will see what his previous environment has trained him to see2 the conscientious gardener sees the weeds1 whilst the artist may see nothing but the flowers4 ,it follows1 therefore1 that all observation must be largely a matter of inference based on experience4 ,in looking at the moon1 for example1 all ,i actually see is a patch of color2 the form and distant location of the moon being a matter of experience4 ,the inference referred to in this heading is not that which is necessary for perception1 but that which is suggested by perception4 ,to illustrate3 ,it is icy2 three men are running for a car2 ,smith raises his arm2 ,jones slips to the ground2 and ,brown testifies1 that 8,smith knocked ,jones down40 ,brown observed1 that ,smith assumed the proper attitude and that ,jones conveniently went down at the right time2 and then inferred the rest4 7#c7 ,ignoring the exceptions4 ,this comes through an over anxiety to prove our theory4 ,with this mental attitude1 the observations which are corroborative will so completely fill the mental field1 that the exceptions are made to seem of no consequence4 ,this accounts for the superstition attached to thirteen4 ,as a coincidence some one at some time died who had previously eaten at a table where there were thirteen4 ,perhaps during the life of the superstitious one this happened on two or three occasions1 but the fact so impresses the subject that he ignores the dozen times when death did not follow4 ,other generalizations belonging to this class are 7#a7 people never die at flood tide2 7#b7 there must be three accidents in succession2 7#c7 the first sight of the new moon over the right shoulder is a good omen2 7#d7 seeds which grow to root do best when planted during the last days of the waxing moon2 7#e7 horse chestnut in pocket guards against sore throat1 etc4 7#d7 ,sympathy and undue interest4 ,the influence of the heart over the brain is well known4 ,a physician is liable to this error when he attempts to prescribe for one of his own family4 ,sympathy not only warps the judgment but it may actually interfere with the accuracy of an honest observer's perceptive powers4 7#e7 ,inattention and a fallible memory4 ,these short comings are too apparent to demand discussion4 #f4 ,,the ,,hypothesis4 ,having observed the facts1 the mind naturally seeks for explanation of the same4 ,hence taking the facts as a cue and bringing into play a constructive imagination1 a plausible supposition is advanced1 which is then proved or disproved4 ,such a supposition is known as an hypothesis4 ,definition4 ,an hypothesis is a supposition advanced for purposes of explanation and proof4 ,first illustration4 ,the facts are known that light travels from the sun to the earth1 and at the rate of #ahf thousand miles per second4 ,these facts suggest the problems3 7#a7 ,how does the light reach the earth8 7#b7 ,why this rate of speed2 why so much faster than the rate at which sound travels8 ,to solve these problems1 or to explain the facts1 the 8ether0 hypothesis is advanced3 viz41 8,a rare medium called ether pervades space and transmits the light and heat of the sun40 ,this hypothesis has never been conclusively proved4 ,second illustration4 ,fact3 ,the child leans forward and squints his eyes1 when attempting to read work which has been placed on the black board2 hypothesis3 ,the child is near sighted4 #g4 ,,induction ,,and ,,hypothesis ,,distinguished4 ,induction is a matter of realizing generalizations from the observation of facts4 ,the product of such is an induction1 but we know that an hypothesis is likewise a generalization based upon facts4 ,what is the difference8 ,an induction1 as such1 is a broader term than hypothesis4 ,as soon as the hypothesis is proved or disproved1 it ceases to be an hypothesis1 but still remains an induction4 ,an hypothesis1 being advanced for purposes of explanation ceases to be an hypothesis when1 in the last analysis1 it fails to explain4 ,moreover1 as soon as the hypothesis is shown to be an undoubted truth1 it also loses its distinctive hypothetic marks4 ,an hypothesis is merely a tentative induction4 ,,illustrations3 7#a7 ,the hypothesis is advanced that the fire started from the coal range in the kitchen4 ,after the incendiary is caught1 this supposition ceases to be an hypothesis4 7#b7 ,it is suspected1 that my insomnia is due to the three cups of strong coffee indulged in at the evening meal4 ,as soon as this supposition is proved by experimental means 7law of difference71 it ceases to be an hypothesis and becomes an unpopular inductive truth4 #h4 ,,hypothesis ,,and ,,theory4 ,in common parlance hypothesis and theory are used interchangeably4 ,we refer to the 8nebular hypothesis0 or the 8nebular theory02 to the 8hypothesis of the sun's heat0 or 8the theory of the sun's heat40 ,on the other hand1 we say 8the theory of gravitation10 8the theory of evolution10 etc41 with certain uniformity4 ,from these observations we may infer that hypothesis and theory may be used interchangeably when the facts are of a low probability2 but when the facts have undergone cogent verification1 it is more correct to use theory in their designation rather than hypothesis4 8,a theory is a partially verified hypothesis40 ,it has been remarked that theory has a second signification of being a term which stands for 8any body of acquired truth40 ,it is unfortunate that its use could not be confined to this latter conception4 #i4 ,,the ,,requirements ,,of ,a ,,permissible ,,hypothesis4 ,any hypothesis should be made to conform to the following requisites3 7#a7 ,the hypothesis must be conceivable4 ,the hypothetic generalizations of primeval days were mere fancy4 ,for example1 the loud noise from the clouds on dark days was the angry voice of the ,god of the skies4 ,even in this day when a complex situation cannot be explained there comes the temptation to draw entirely upon the imagination1 and advance an hypothesis which is absurd in every sense of the word4 ,the permissible hypothesis demands that there be some ground for the conjecture4 ,a fact or two at least must be used as the foundation for whatever the constructive imagination may build4 ,on the other hand the past has taught us that we cannot afford to be too exacting in the enforcement of this rule4 ,the ideas of ,copernicus1 ,newton1 ,harvey1 ,darwin1 and many another of the world's best thinkers1 were looked upon at first as being ridiculous4 ,there is always a bare possibility of a 8lurking truth0 in the conjecture1 and no broad minded and sanely educated man can afford to scoff blindly at something which may seem to him mere fancy4 ,prejudice and a willful blindness to truth1 have ever been imminent stumbling blocks in the path of progress4 7#b7 ,the hypothesis must be capable of proof or disproof4 ,this means1 that where it is possible the hypothesis should touch1 in one form or another1 our experience4 ,if the hypothesis is wholly unlike any experience we may have had1 it becomes impossible to ascertain1 whether it agrees or disagrees with the facts1 which it is supposed to explain4 ,a legitimate hypothesis must furnish some opportunity for securing facts to prove or disprove it4 ,for example1 to advance an hypothesis relative to the conditions of the next world is hardly permissible1 as 8spirit-facts0 are entirely without our field of experience4 ,surely1 one returning from ,heaven could give us no conception of it2 because there is nothing in the carnal mind that may be used to interpret the experiences that must function in the ,celestial ,city4 7#c7 ,the hypothesis must be adequate4 ,it should take into consideration all the known facts4 ,it stands to reason that1 if one known fact is ignored1 the entire procedure is thus vitiated4 ,it would be absurd to suppose the moon to be inhabited without giving heed to the fact of its having no atmosphere4 7#d7 ,the hypothesis must be as simple as possible4 ,we must1 of course1 recognize situations which in themselves are too complex to admit of simple conjectures4 ,the purport of the fourth rule is1 that the hypothesis should not be made unnecessarily complex4 7#e7 ,the hypothesis should not contradict any verified truth4 ,any conjecture which opposed the law of gravitation would be out of place4 ,of course it is possible to have only apparent conflicts between the new hypothesis and the old law4 ,further observation should show that no such clash exists4 #aj4 ,,the ,,uses ,,of ,,hypotheses4 ,the hypothesis is serviceable mainly in these particulars3 7#a7 ,as a working basis4 ,when one is confronted with a huge mass of facts it becomes necessary to start somewhere1 and with as little waste of time and energy as possible4 ,almost anything is better than a haphazard floundering which reaches 8nowhere40 ,so the investigator hazards a tentative theory1 which he at once proceeds to verify4 ,if verification fails1 then he may discard this first hypothesis for a better one4 7#b7 ,as a guide to ultimate truth4 ,much might be said relative to the use of rejected hypotheses4 ,by means of these1 science has advanced step by step towards the full light of perfect knowledge4 ,as has been remarked1 no true scientist cares to overlook the opportunity for suggestive inspiration which some forsaken hypothesis may afford him4 ,just as the individual attains the best success by using his failures as stepping stones1 so the true scientific discoverer climbs up to the light on the stairway of discarded hypotheses4 ,by testing and rejecting the false hypotheses1 the situation becomes more definite and the problem more accurately defined4 8,kepler himself tried no less than nineteen different hypotheses before he hit upon the right one1 and his ultimate success was doubtless in no slight degree due to his unsuccessful efforts40 7#c7 ,as a discoverer of immediate truth4 ,often1 moreover1 the hypothesis leads directly to positive verification4 ,the supposition advanced may hit the truth squarely2 and may be of such peculiar nature as to lead easily to clear and conclusive proof4 7#d7 ,as affording a probable explanation of a problem which will not lend itself to an entirely satisfactory solution4 ,the theory of evolution may illustrate this fourth use2 while the history of the discovery of ,neptune illustrates the third4 #aa4 ,,characteristics ,,needed ,,by ,,scientific ,,investigators4 ,the hypothesis is referred to 8as the great instrument of science40 ,the greatest thinkers of time have possessed the courage and the conscience to step from the known to the unknown2 to hazard a guess as to the meaning of what they saw1 and then subject their guess to a rigorous test4 ,this procedure involves three elements on the part of the investigator3 7#a7 ,power of accurate observation4 7#b7 ,constructive imagination4 7#c7 ,a passion for truth4 7#a7 ,an hypothesis formed without an accurate knowledge of facts is not only useless1 but often it may work positive harm4 ,to advance serviceable suppositions which are not grounded on fact1 is as impossible1 as it is to build a house without a foundation4 ,the hypothesis is an image of the constructive imagination1 but the pedestal of this image must rest on the ground of fact4 ,the investigator who would be scientific must exercise scrupulous care in securing his facts through observation and experiment4 ,the rules and errors involved in such a procedure have received sufficient attention4 7#b7 ,after the investigator has his facts to build upon2 and these may be few or manysometimes even a single fact is sufficientthen may he theorize as to a possible explanation of them4 ,here is where the real work of the born genius tells4 ,to some the facts are nothing but words1 to others they mean universal laws and great inventions4 ,who but a ,newton could have seen the law of gravitation in the falling apple8 ,who but an ,edison could have seen the phonograph in the sound wave and wax8 ,it must be recognized that this remarkable imaginative insight is inborn in some cases2 and yet this does not preclude the necessity for cultivating this power1 though it may be only in a rudimentary state4 ,here is another opportunity for the school teacher2 namely1 to train in every legitimate way the constructive imagination4 7#c7 ,having once constructed the hypothesis1 the honest scientific investigator at once proceeds to subject it to a series of most rigorous tests4 ,it is well to see big things in a little fact2 to have a mind as fertile in new ideas as a watered gardenthis is genius6 ,but is it not more incumbent to have a conscience so keen1 that nothing will be allowed to pass for truth which has not received ample verification8 ,intellectual dishonesty is quite as common as moral dishonesty4 ,moreover1 one must maintain an open mind1 absolute candor1 and a willingness to abandon the most cherished theory4 ,often it is much easier to explain away contradictory facts than it is to forsake a pet theory4 #ab4 ,,outline4 ,,the ,,auxiliary ,,elements ,,in ,,induction,,observation,,experiment ,,hypothesis4 7#a7 ,the ,foundation of ,inductive ,generalizations4 7#b7 ,observation4 ,defined4 7#c7 ,experiment4 ,defined4 ,compared with ,observation4 7#d7 ,rules for ,logical ,observation and ,experiment4 ,their need4 ,first ,rule4 ,second ,rule4 ,third ,rule4 ,fourth ,rule4 7#e7 ,common ,errors of ,observation and ,experiment4 7#a7 ,preconceived ,ideas4 7#b7 ,confusing the ,observed with the ,inferred4 7#c7 ,ignoring the ,exceptions4 7#d7 ,sympathy and ,undue ,interest4 7#e7 ,inattention and a ,fallible ,memory4 7#f7 ,the ,hypothesis4 ,defined and ,illustrated4 7#g7 ,induction and ,hypothesis ,distinguished4 7#h7 ,hypothesis and ,theory ,distinguished4 7#i7 ,the ,requirements of a ,permissible ,hypothesis4 7#a7 ,conceivable1 7#b7 ,capable of proof or disproof1 7#c7 ,adequate1 7#d7 ,simple1 7#e7 ,not contradictory4 7#aj7 ,uses of ,hypothesis4 7#a7 ,a working basis1 7#b7 ,guide to ultimate truth1 7#c7 ,discoverer of immediate truth1 7#d7 ,probable explanation4 7#aa7 ,characteristics ,required by ,scientific ,investigators4 7#a7 ,accurate observer1 7#b7 ,constructive imagination1 7#c7 ,passion for truth4 #ac4 ,,summary4 7#a7 ,facts are the foundation of all inductive generalizations4 ,induction is largely a matter of building general notions from individual notions derived from the observation of facts4 7#b7 ,observation is the act of watching the phenomena as they may occur4 ,it involves the voluntary concentration of consciousness on the case in hand4 7#c7 ,experiment is the act of making phenomena occur for the purpose of watching for effects4 ,it is in reality a form of observation which necessitates a manipulation of circumstances4 7#d7 ,the average man is not given to careful observation4 ,the rules adopted by scientific observers are3 7#a7 ,the observation should be precise2 7#b7 should concern only the material circumstances2 7#c7 should be varied2 7#d7 should be isolated4 ,for the sake of precision many instruments have been invented and methods devised2 notably instruments for accurate measurements1 such as the balance and thermometer1 and methods like the method of averages4 ,frequently a situation may be so complicated as to demand a 8preadjustment of attention40 ,with the untrained this very preadjustment may lead to serious error4 ,an 8all-angled observer0 is the most trustworthy4 7#e7 ,errors in observation come from preconceived ideas2 confusing perception with inference2 ignoring the exceptions2 sympathy2 inattention2 and a fallible memory4 7#f7 ,an hypothesis is a supposition advanced for purposes of explanation and proof4 7#g7 ,an hypothesis is a tentative induction4 ,as soon as it is deprived of its tentative nature it ceases to be an hypothesis4 7#h7 ,hypothesis and theory are often used interchangeably when reference is made to phenomena of low probability4 ,theory should be used only in instances of high probability4 7#i7 ,a permissible hypothesis must be 7#a7 conceivable2 7#b7 capable of proof or disproof2 7#c7 adequate2 7#d7 simple2 7#e7 must not contradict any verified truth4 7#aj7 ,the hypothesis is especially serviceable in these four particulars3 7#a7 as a working basis2 7#b7 as a guide to ultimate truth2 7#c7 as a discoverer of immediate truth2 7#d7 as affording probable explanations4 7#aa7 ,there are certain characteristics which an honest and courageous investigator needs to possess4 ,these are3 7#a7 undoubted ability as an accurate observer of facts1 7#b7 a constructive imagination1 7#c7 a passion for truth4 ,to build an acceptable hypothesis without fact is as impossible as it is to build a house without a foundation4 ,the genius1 because of his imaginative insight1 transforms the simple fact into a complex invention or law4 ,a prevailing 8intellectual dishonesty0 suggests the need of 8a greater passion for truth40 #ad4 ,,review ,,questions4 7#a7 ,show that facts are the raw material of induction4 7#b7 ,define and illustrate a fact4 7#c7 ,define induction in terms of the notion4 7#d7 ,define and illustrate observation4 7#e7 ,define and illustrate experiment4 7#f7 ,show the difference between observation and experiment4 7#g7 ,state and exemplify the rules for logical observation and experiment4 7#h7 ,illustrate the method of averaging observations4 7#i7 ,explain 8preadjustment of attention40 7#aj7 ,what is the most common error with the untrained observer8 ,explain and illustrate4 7#aa7 ,explain the expression 8all-angled observer40 7#ab7 ,state and exemplify the errors of observation and experiment4 7#ac7 ,to what error in observation are superstitions generally due8 7#ad7 ,define and illustrate hypothesis4 7#ae7 ,indicate the difference between an hypothesis and an ordinary induction4 7#af7 ,when may theory and hypothesis be used interchangeably8 ,illustrate4 7#ag7 ,show by illustration that the term theory is ambiguous4 7#ah7 ,summarize the requirements of a permissible hypothesis4 ,illustrate4 7#ai7 ,select some school room experience with a view of making it conform to the requirements of a permissible hypothesis4 7#bj7 ,explain and illustrate the uses of hypothesis4 7#ba7 8,the scientific discoverer climbs up to the light on the stairway of discarded hypotheses40 ,explain4 7#bb7 ,write a short theme on 8,characteristics ,required by ,scientific ,investigators40 #ae4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 8,land and sea breezes are due to a difference in temperature40 ,is this a fact or a law8 ,explain your position4 7#b7 ,give three different definitions of induction4 ,which one have you adopted8 ,defend your position4 7#c7 ,define and illustrate observation4 7#d7 ,distinguish between observation and attention4 7#e7 8,in observation we find1 in experiment we make40 ,what is meant by this8 7#f7 ,give illustrations of falsehood due to careless observation4 7#g7 ,argue for and against the use of 8expectant attention0 in observation4 7#h7 8,nine-tenths of what we see comes from within40 ,do you believe this8 ,labor the question4 7#i7 ,offer suggestions which1 if followed1 should lead to scientific observation4 7#aj7 8,one must be just before he is sympathetic40 ,relate this to the fine art of accurate observation4 7#aa7 ,is an hypothesis a generalization8 ,explain4 7#ab7 ,give school room examples of hypotheses which lead to injustice4 7#ac7 8,an hypothesis is merely a tentative induction40 ,make clear this assertion4 7#ad7 ,illustrate inconceivable hypotheses by drawing on your knowledge of ancient history4 7#ae7 8,prejudice and willful blindness to truth have ever been imminent stumbling blocks in the path of progress40 ,expatiate upon this4 7#af7 ,are the hypotheses advanced concerning communications from the spiritual world capable of proof or disproof8 ,give reasons4 7#ag7 ,show by historical examples the use of discarded hypotheses4 7#ah7 8,genius is another name for hard work40 ,do you agree8 ,defend your position4 7#ai7 8,the man to whom nothing ever occurs is unlikely to make any important discoveries40 ,discuss this4 ,,chapter #bj4 ,,logic ,,in ,,the ,,class ,,room4 #a4 ,,thought ,,is ,,king4 8,our habits make or unmake us40 8,in a thoughtless hour a groove is imbedded in the nerve substance1 and thereafter1 nine-tenths of the life flows through that groove40 ,habit is1 indeed1 a most powerful and a most tyrannical master2 and yet it has come within the observation and even the experience of many1 that thought is even more masterful than habit4 ,appearing at the psychological moment and in a pedagogical way1 a thought may be made to possess the mind with force sufficient to break almost any habit4 ,from an ethical point of view1 the exceptions to this are due to an inability to arouse thought of sufficient strength4 ,moreover1 mental reactions which result in habit are originally brought about through some thought process4 ,speaking in general terms1 it may be affirmed that thought makes habit and if sufficiently strong breaks habit4 ,that our habits make or unmake us may be true1 but is it not likewise true that our thoughts make or unmake our habits8 ,thought is king2 thought has made man king of the animal kingdom1 and if thought has figured so largely in the evolution of the human animal in past ages1 may we not assume that it will sway the future ages in like manner8 ,thought is a product of the class room4 ,here thoughts which make habits1 and thoughts which break habits have full sway4 ,as the children of the ,american schools think to-day1 so will the men of ,american life think on the morrow2 and as ,america thinks so will she ultimately do4 ,this lends vital import to any object which may either inspire or regulate thought4 #b4 ,,special ,,function ,,of ,,induction ,,and ,,deduction4 ,as commonly treated logic is a regulative subject4 ,this implies the two aspects of direction and correction4 ,logic directs by means of the laws and forms of thought1 and corrects by means of the rules of right thinking4 ,to a certain degree both departments of logic are directive as well as corrective2 but it is worthy of remark that inductive logic emphasizes the former1 while deductive logic lays stress upon the latter4 ,it is inductive logic which shows how man has acquired new knowledge2 inductive logic explains the mode of procedure adopted by the discoverer and the inventor4 ,on the other hand1 deductive logic is distinctly a science of criticism4 ,induction directs to new truth2 deduction aims to modify and correct new truth4 #c4 ,,two ,,types ,,of ,,mind4 ,though there are many special forms of thought1 yet there are but two general forms2 namely1 induction and deduction4 ,inductive thought seeks the new2 deductive thought corrects the old4 ,similarly1 there are two types of mind3 the inductive type and the deductive type4 ,the former reaches out for new things1 the latter is satisfied with ordering the old4 ,in politics the man with the inductive type of mind becomes a 8,liberal0 or a 8,progressive02 while the man with the deductive type of mind becomes a 8,conservative0 or a 8,standpatter40 ,it must be conceded that both are needed in the development of the best form of ,democracy4 ,we need an unfettered freedom as advocated by ,jefferson2 but we also need an ordered freedom as taught by ,hamilton4 #d4 ,,too ,,much ,,conservatism ,,in ,,school ,,room4 ,since the beginning these two mental types have been in evidencethe liberal who wants to do things1 and the conservative who wants to weigh things4 ,with the liberal1 it is fight whether or no2 with the conservative1 it is fight provided the enemy is not too formidable4 ,the one dares2 the other cautions3 both are needed to balance the world4 ,liberalism and conservatism may be fostered in the school room1 and to maintain a true balance each must receive its share of attention4 ,is such the case8 ,the passing of 8district-school-individualism0 and the coming of 8graded-school-collectism0 has transferred the emphasis from liberalism to conservatismfrom the inductive type to the deductive type4 ,in this day it seems to be more important to have the child's work orderly1 than to have it original4 ,in the main1 examination papers call for correct knowledge and not for thought2 in the main1 promotions are based on accuracy1 not on initiative4 ,the conservative type being in control1 the schools are sending out too many 8,deductives10 not enough 8,inductives40 ,the world needs more ,columbuses and ,edisons4 #e4 ,,the ,,method ,,of ,,the ,,discoverer4 ,a change must come4 ,the methods of instruction are too didactic and not sufficiently inspirational4 ,greater attention must be given to the spirit of discovery and less to the spirit of correction4 ,the teacher must lead less and follow more2 must correct less and suggest more2 must tell less and direct more4 ,if we are to give greater attention to the training of discoverers1 logic may aid in this crusade by calling attention to the common mode of procedure which the discoverers of the past have adopted4 ,this is a legitimate topic for the logician1 since induction1 deduction1 hypothesis1 and proof have ever been common tools in the discoverer's workshop4 ,with a view to becoming better acquainted with the common mode of procedure of the man who seeks for new truth1 let us study two typical instances3 7#a7 ,the ,discovery of ,neptune4 ,the discovery of ,neptune was a double one4 ,early in the present century it was found that ,uranus was straying widely from his theoretic positions1 and the cause of this deviation was for a long time unsuspected4 ,two astronomers1 ,adams in ,england and ,leverrier in ,france1 the former in #ahdc and the latter in #ahde1 undertook to find out the cause of this perturbation1 on the supposition of an undiscovered planet beyond ,uranus4 ,adams reached his result first1 and the ,english astronomers began to search for the suspected planet with their telescopes1 by first making a careful map of all the stars in that part of the sky4 ,but ,leverrier1 on reaching the conclusion of his search1 sent his result to the ,berlin observatory1 where it chanced that an accurate map had just been formed of all the stars in the suspected region4 ,on comparing this with the sky1 the new planet1 afterward called ,neptune1 was at once discovered1 #bc;d ,september1 #ahdf4 7#b7 ,bees are guided in their flight by a knowledge of their surroundings1 not by a general sense of direction4 8,m4 ,romanes took a score of bees in a box out to sea1 where there could be no landmarks to guide the insects home4 ,none of them returned home4 ,then he liberated a second lot of bees on the seashore and none of these returning1 he liberated another lot on the lawn between the shore and the house4 ,none of these returned1 although the distance from the lawn to the hive was not more than two hundred yards4 ,lastly he liberated bees in different parts of the flower garden on either side of the house1 and these at once returned to the hive40 7,hibben47 ,a multiplication of instances would only give stronger evidence to the fact that the mode of procedure adopted by the discoverer and inventor conforms to these three general steps3 7#a7 antecedent facts1 7#b7 forming an hypothesis1 7#c7 verification4 ,it will be to our advantage to study somewhat in detail these three steps4 7#a7 ,antecedent facts4 ,in the discovery of ,neptune the decisive or crucial fact was the knowledge that ,uranus deviated from his true path about the sun4 ,this knowledge was obtained through observation and mathematical calculation4 ,but the hypothesis of the existence of another planet could not have been formed had it not been for the more fundamental facts of inertia1 gravitation1 falling bodies1 etc4 ,for the sake of definiteness antecedent facts may thus be divided into foundation facts and crucial or decisive facts4 ,the latter are an outgrowth of the former4 ,the foundation fact of the second illustration is ,romanes' knowledge of animal instinct2 while the crucial fact is1 no doubt1 the observation that bees fly in a circle before starting for home4 ,in the case of ,newton's discovery of the law of gravitation1 the falling of the apple was the crucial fact2 while his knowledge of terrestrial gravity proved to be the vital foundation fact4 ,a crucial fact is one which leads immediately to the formation of a reasonable hypothesis4 ,it is not to be inferred from this that the same fact becomes a crucial one to all alike4 ,the falling of the apple was only crucial to a genius like ,newton4 ,with the average only extraordinary facts become crucial2 but with the genius any ordinary fact may become crucial4 ,both the scholar and the genius may have the foundation facts1 but only the latter may be able to read into a dry fact or event1 a new world of truth4 7#b7 ,forming an ,hypothesis4 ,from the viewpoint of logical correctness1 the matter of hypothesis has received due attention in an antecedent chapter2 we need now to look at the subject through the eyes of the discoverer1 not the logician4 ,the crucial fact at first creates an intellectual perplexity which is accompanied with an uneasy1 dissatisfied state of mind4 ,this unsatisfied feeling drives the intellect to protracted thought4 ,as a final result some hypothesis is constructed which seems to explain the crucial fact4 ,here is where analogy functions in a most vital manner4 ,no hypothesis is forthcoming unless it resembles the crucial fact4 ,it has been remarked elsewhere that analogy is the basic element in the forming of hypotheses4 ,so it transpires1 that the protracted thought referred to1 is virtually a mental effort to detect significant resemblances between the well known crucial fact1 and some hypothetical fact which the imagination may picture4 ,to put it differently3 ,the crucial fact arouses a mental state of unrest which in turn drives the mind to a 8still hunt0 for relations4 ,the establishment of the hypothesis is simply a makeshift1 designed to satisfy this 8mental urge40 ,in the discovery of ,neptune the crucial fact1 the deviation of ,uranus1 produced a state of uneasiness in the minds of the astronomers4 ,surely something was wrong4 ,this urged them to further meditation1 which finally resulted in the hypothesis that there must be an unknown planet beyond the orbit of ,uranus4 ,they assumed1 of course1 that the relation between this supposed planet and ,uranus was analogous to the relation between any two of the known planets4 ,in the case of ,newton the falling apple stirred his astute mind to the assumption that the same force which pulled the apple1 likewise pulled the moon towards the earth4 ,here we have again 7#a7 the crucial fact1 7#b7 the mental urge1 7#c7 the analogous hypothesis4 7#c7 ,verification4 ,forming an hypothesis only partly fulfills the demands of an unsatisfied intellect4 ,the true discoverer1 being possessed with a passion for truth1 seeks for 8the truth1 the whole truth1 and nothing but the truth40 ,in consequence the hypothesis is subjected to tests which may lead to its confirmation1 its rejection1 or its modification4 ,the two possible modes of verification are recourse to experience and appeal to reason2 or empirical proofs and rational proofs4 ,in the former the hypothesis is compared with facts by means of further observation and experiment4 ,m4 ,romanes' experience with the bees is a fair illustration of this form4 ,possibly the student has already noted that ,romanes' mode of procedure conforms to the 8joint method of agreement and difference40 ,in the case of rational proofs the hypothesis is subjected to deductive demonstration1 either of the form of syllogistic argument or mathematical calculation4 ,a fair sample of this kind of verification is ,newton's discovery of universal gravitation4 ,when he decided that the moon and the apple might be controlled by the same universal force1 he undertook to establish his hypothesis by mathematical calculation4 ,at first his figures seemed to disprove his theory1 but after a wait of ten years1 new data relative to the diameter of the earth1 removed the apparent discrepancy4 ,in the case of the discovery of ,neptune1 the verification was both rational and empirical4 ,mathematical 7rational7 calculation led to the assumption that the new planet must be at such a point4 ,with this knowledge the observer was enabled to turn his telescope to the spot indicated and there1 true to the calculations1 was ,neptune 7empirical74 ,to summarize3 ,the method of the discoverer involves a knowledge of certain fundamental facts2 the observation of crucial facts2 a mental unrest2 the constructing of an hypothesis through analogy2 and finally verification by either appeal to experience1 or mathematical demonstration4 #f4 ,,the ,,real ,,inductive ,,method ,,or ,,discoverer',s ,,method ,,not ,,in ,,vogue ,,in ,,class ,,room ,,work4 ,it has been remarked elsewhere that there are two general mind types1 the liberal and the conservative4 ,also that the natural method of thought animating the former is inductive2 while the natural method of thought of the latter is deductive4 ,the 8liberal0 is the apostle of new truth2 the 8conservative0 an apostle of safe truth4 ,both types are needed2 the one to balance the other4 ,in consequence both methods are of service in the class room2 here each should be given its proportionate place4 ,that this condition does not obtain may not be apparent1 since much attention is being given to certain inductive forms1 such as 8proceeding from the concrete to the abstract10 8from the particular to the general10 8from the known to the related unknown10 etc4 ,likewise the courses of study and the various text books1 claim to advocate the use of the inductive process4 ,seemingly these facts point toward a very general observance of the inductive tenets4 ,this is true with one vital exception3 ,induction is the natural method of the discoverer4 ,with it he acquires knowledge2 but in the class room induction is used to impart knowledge4 ,in life the discoverer takes the initiative1 thinks his own thoughts first hand2 but in the school room1 above the kindergarten1 the child is not allowed to take the initiative1 not even in his play4 ,all is planned for him1 all doled out1 not in the raw1 but partially made over4 ,the teacher must impart a certain amount of knowledge in a given time1 and consequently she must 8set the pace0 in this race for second hand facts4 ,to allow the child to lead2 to give him the benefit of his own individuality2 to permit him to use the ,god given spirit of discovery which clamors for recognition2 would be suicidal according to our present standards4 ,if the plan of the discoverer were followed1 the course of study could not be covered2 children would fail of promotion2 and criticism would be forthcoming from both principal and parent4 ,in the average class room of the day the inductive ,,form prevails but the ,,spirit is not in evidence4 ,like a wolf in sheep's clothing induction has entered the class room to devour that primal force in the child's make-up1 which has raised his race above his simian ancestors4 ,our class room methods1 being inductive in form but deductive in spirit1 may train the youngster to be a camp follower but never a leader in thought and action4 ,the call of the day is for more initiative2 for more originality2 for more individuality2 for more enthusiasm4 ,there is too much form without the spirit2 so much that bespeaks system and refinement without those native impulses and native abilities which mark one child from another4 ,like the books of a library our children are classified and labeled1 and when more come in the others are dusted and placed on the next higher shelf4 ,how many more centuries must we wait before the schools will adopt1 in spirit as well as in form1 the pedagogical principles of life8 ,will the time ever come when it may be said that all our leaders in thought and action are college graduates8 #g4 ,,as ,a ,,method ,,of ,,instruction ,,deduction ,,is ,,superior ,,to ,,induction4 ,the inductive method is pre-eminently the method of the discoverer only when it involves both the form1 which he follows1 and the spirit1 which he evinces4 ,the so-called method of the school room is inductive in form1 as the procedure is from particular facts to general truths2 but deductive in spirit1 as it is used to impart knowledge4 ,if it were inductive in spirit1 the child would be allowed to acquire knowledge entirely through his own initiative4 ,deduction is the method of instruction1 whereas induction is the method of discovery4 ,that the child of the school is instructed or better 8deducted0 and not generally allowed to discover1 is a situation so apparent that we need not labor the point further4 ,because the inductive process has been made a method of instruction1 it has been robbed of its chief advantage over deduction4 ,indeed1 as a method of instruction1 deduction is really the superior method4 ,it requires less time1 demands greater concentration1 often arouses more interest1 and creates situations which are less involved4 #h4 ,,conquest ,,not ,,knowledge ,,the ,,desideratum4 ,in all great inventions1 man has taken his cue from nature4 ,in inventing the telescope1 his model was the eye2 in building his house1 his inspiration was the cave4 ,in reality man has accepted nature's suggestions1 and then attempted to improve upon them4 ,in this he has met with success4 ,from the crab apple tree1 he has developed the northern spy2 from the wild hen which laid #be eggs a year1 he has evolved the modern hen which produces #bbe eggs a year4 ,moreover1 man has attained his greatest successes by enlarging upon the thoughts of nature and not by unmixed substitutions4 ,burbank1 through a long process of years1 has changed the color of a flower1 but in accomplishing this did he not use some hidden tendency of nature8 ,burbank1 with all his wisdom1 cannot give a flower color unaided by 8,dame ,nature40 ,when man commenced to study nature's mode of education1 he saw that fearful sacrifices were entailed1 both in time and in energy as well as in life itself2 and so he evolved a more economical way of leading the child through the experiences of the race4 ,in consequence1 he has developed the present splendid system of education4 ,in the evolution of all great institutions1 there are in evidence crucial weaknesses1 and in the evolution of man's educational system it appears that he has erred in adopting nature's form of education without her spirit of education4 ,in his anxiety to have the young acquire as much as possible1 man has overshot nature's true purpose4 ,for example1 the big word in man's educational system is knowledge2 but the big word in nature's educational system is conquest4 ,nature gives man knowledge simply to reward him for his effort2 but man would give to his fellow the reward without the effort4 ,according to nature1 the strongest men are those who overcome most2 according to man1 the strongest men are those who know most4 ,the common educational principles1 such as1 8,from the concrete to the abstract and from the known to the related unknown10 etc41 are interpreted by man from the viewpoint of knowledge2 whereas nature would teach that these are a feasible way to develop powerto grow manhood4 ,it is seen that nature uses knowledge only as a means to an end1 and therefore when man uses knowledge as an end only1 he is trying to substitute a plan of his own for nature's plan4 ,the best results can be secured only when man co-operates with nature in developing1 and at the same time regulating1 the spirit of conquest4 #i4 ,,motivation ,,as ,,related ,,to ,,the ,,spirit ,,of ,,discovery4 ,it has been remarked in this chapter1 that the 8crucial fact0 serves to stir the mind of the natural born discoverer to an activity raised to the nth power of effectiveness4 ,naturally1 the intent of such activity is to solve the mysteries which the crucial fact may suggest4 ,this passion of the mind to 8know more about it0 is appropriately termed 8the mental urge40 ,from the viewpoint of the pedagogue1 the 8mental urge0 is simply an intrinsic interest in the situation at hand2 an interest born of an innate or acquired passion to know the truth4 ,with the average child1 the 8mental urge0 is strong only when the situations appeal to some immediate need or vital experience4 ,the attempt to make the school work concrete and vital2 to make it answer the child's natural curiosities and real necessities1 is dignified with the name 8motivation40 ,it is obvious that this is a new term for an old condition4 ,to motivate the work1 means to give to it an attractiveness which any situation might have for the true born discoverer and inventor4 ,if we would use the discoverer's method successfully1 we must learn the art of motivating the work4 ,this may be accomplished by appealing to the play instincts1 to the business instincts1 and to the vital interests of every day life4 #aj4 ,,discoverer',s ,,method ,,or ,,the ,,real ,,inductive ,,method ,,adapted ,,to ,,class ,,room ,,work4 ,a revolt has already set in against this insatiate desire to teach knowledge1 rather than to teach the child4 ,many schools are permitting a study of those topics which vitally concern every day life4 ,less attention is being given to formal discipline1 and more attention to self activity4 ,gradually will the scheme of education be directed toward fitting the school work to the child1 rather than fitting the child to the school work4 ,when this new thought in education is fully upon us1 then will every device and method be directed toward giving full scope to the spirit of inquiry1 which so completely possesses every normal child4 ,it now remains for us to indicate ways in which the spirit of inquiry1 or the 8discoverer's method10 may be adapted to school room work4 ,in the first illustration1 we shall outline the topic as it is generally given in the average school where attention is paid to development work4 ,this will then be followed by a second outline which may be suggestive of the discoverer's mode of procedure4 ,first illustration4 ,school ,room ,method4 ,i4 ,aim3 ,to teach addition of business fractions4 ,,ii4 ,preparation3 7,only type examples given74 7#a7 7#b7 7#c7 #c bushels #c parts ,rule3 ,only like numbers #e bushels #e parts can be added4 #h bushels #h parts ,,iii4 ,presentation3 7#a7 7#b7 7#c7 7#d7 #c ninths #c_/i #b_/c #d_/f #b_/c #h_/ab #e ninths #e_/i #a_/f #a_/f #c_/d #i_/ab #h ninths #h_/i #e_/f #ag_/ab ,,iv4 ,summary3 7#a7 ,only like fractions can be added4 7#b7 ,change unlike fractions to like fractions4 7#c7 ,add the numerators1 placing the sum over the common denominator4 ,v4 ,application3 ,examples and problems involving similar and dissimilar fractions4 ,before undertaking to illustrate the discoverer's method1 it may be well to designate in order the evident steps as they would appear to the pedagogue3 7#a7 ,motivate the topic to be presented4 7#b7 ,bring to mind appropriate 8foundation facts40 7#c7 ,make evident the 8crucial fact40 7#d7 ,lead to the forming of an hypothesis through analogy4 7#e7 ,afford ample opportunity to prove the hypothesis4 ,discoverer's ,method ,adapted4 ,lesson ,plan4 ,i4 ,aim3 7#a7 ,by playing upon the curiosity or by exposing a vital need1 create a strong desire to know how to add business fractions4 7,motivate the topic47 ,curiosity3 8,we all know what a fraction is and we know1 too1 how to change fractions to higher or lower terms40 8,now ,i wonder how many know how to add fractions1 such as #b_/e and #a_/e80 8,don't you tell any one1 ,mary1 but just write your answer on a piece of paper and show it to me40 7,mary's answer shows that she has thought correctly1 but figured incorrectly4 ,john1 after having raised his hand1 shows his answer to the teacher47 8,john has the right answer40 8,that's fine1 but let us keep the secret1 ,john40 8,i wonder how many others there are in this class who will find the right way80 etc41 or ,vital need3 ,discuss with the class the various occupations of life and secure expressions of preference4 ,some may plan to be real estate agents1 others contractors or book keepers1 etc4 8,george1 you plan to be a book keeper40 8,let us suppose that ,i have given you the job of book keeper in my factory40 8,show that you are worth your wages by adding these numbers3 #abd1 #fdg40 8,what6 can't do it80 8,then ,i don't want you60 etc4 ,,ii4 ,preparation3 7#b7 ,bring to the foreground the necessary foundational knowledge4 ,suggestions3 #d bushels #h parts #c bushels #b parts #g bushels #aj parts ,,iii4 ,presentation3 7#c7 ,make evident the crucial fact4 ,suggestions3 ,add #b fifths #c eighths #c_/h #a fifth #a eighth #a_/h #c fifths #d eighths 7#d7 ,without further suggestion1 give the young discoverer suitable opportunity for finding the sum of #c_/h and #a_/h4 ,in the act of discovering1 an implicit hypothesis takes form in the mind through analogous reasoning4 ,this point marks the climax of the lessonthe supreme moment1 when the skill and tact of the teacher is assessed to the limit4 ,just here the child must have a comfortable environment where perfect concentration is possible4 ,nothing must be forced2 and there should be nothing suggestive of disgrace or shame1 if the youthful ,columbus is unsuccessful4 ,the first attempt should be without books4 ,if more help is needed1 access to books may be given4 ,if the investigation is still without definite result1 then as a last resort the teacher may1 in the presence of the child1 add fractions1 solving with deliberation example after example1 until the child believes he has discovered the process4 7#e7 ,stimulate a desire to verify the facts discovered4 ,suggestions leading to verification3 ,afford opportunity for mathematical demonstration4 ,illustrations3 ,the fractions #a_/d and #c_/h have been added in this way #a_/d #b_/h #c_/h #c_/h #e_/h ,use is now made of the crucial fact1 when the example assumes this form #b eighths #c eighths #e eighths ,or if the class has been trained in the use of the diagram the following may be the form of proof3 #a_/d #c_/h ,explanation from diagram4 ,i see that #a_/d equals #b parts and #c_/h equals #c parts2 the sum of #c parts and #b parts are #e parts4 ,but the name of the part is eighths2 hence the answer #e parts may be written #e eighths1 or #e_/h4 ,thus the final form is #b parts #c parts #e parts #e_/h ,give opportunity to consult answers in text books as further verification4 ,the summary and application of adding fractions according to the 8discoverer's method10 are virtually the same as the corresponding steps in the 8school room method40 ,second ,illustration of ,discoverer's ,method4 ,david ,p4 ,page in his ,theory and ,practice of ,teaching well illustrates the discoverer's method in conducting a general exercise in nature study4 ,we cannot do better than to quote from him3 8,it is the purpose of the following remarks to give a specimen of the manner of conducting exercises with reference to waking up the mind in the school and also in the district4 ,let us suppose that the teacher has promised that on the next day1 at ten minutes past ten o'clock1 he shall request the whole school to give their attention five minutes to something that he may have to show them4 ,this very announcement will excite an interest both in school and at home 7playing upon the curiosity72 and when the children come in the morning they will be more wakeful than usual till the fixed time arrives4 ,at the precise time1 the teacher gives the signal agreed upon1 and all the pupils drop their studies and sit erect4 ,when there is perfect silence and strict attention by all1 he takes from his pocket an ear of corn and in silence holds it up before the school4 ,the children smile1 for it is a familiar object 7foundational knowledge already in hand72 and they probably did not suspect they were to be fed with corn40 ,teacher4 8,now1 children10 addressing himself to the youngest1 8,i am going to ask you only one question about this ear of corn4 ,if you can answer it1 ,i shall be very glad4 ,as soon as ,i ask the question1 those who are under seven years old1 and think they can give an answer1 may raise their hand4 ,what is this ear of corn for80 ,several of the children raise their hands1 and the teacher points to one after another in order1 and they rise and give their answers4 ,mary4 ,it is to feed the geese with4 ,john4 ,yes1 and the hens1 too1 and the pigs4 ,sarah4 ,my father gives corn to the cows4 ,laura4 ,it is good to eat4 ,they shell it from the cobs and send it to the mill1 and it is ground into meal4 ,they make bread of the meal and we eat it4 8,i am sorry to tell you that none of you have mentioned the use ,i was thinking of1 though1 ,i confess1 ,i expected it every minute4 ,i shall now put the ear of corn in my desk1 and no one of you must speak to me about it till to-morrow4 ,you may now take your studies40 ,the consequence of this would be that various families1 father1 mother and older brothers and sisters1 would resolve themselves into a committee of the whole on the ear of corn3 and by the next morning several children would have something further to communicate on the subject4 ,the hour would this day be awaited with great interest and the first signal would produce perfect silence4 ,the teacher now takes the ear of corn from the desk and displays it before the school2 and quite a number of hands are instantly raised as if eager to be the first to tell what other use they have discovered for it4 ,the teacher now says pleasantly1 8,the use ,i am thinking of you have all observed1 ,i have no doubt2 it is a very important use1 indeed2 but as it is a little out of the common course 7crucial facts7 ,i shall not be surprised if you cannot give it4 ,however1 you may try40 8,it is good to boil10 says little ,susan1 almost springing from the floor as she speaks4 8,and it is for squirrels to eat10 says little ,samuel4 8,i saw one carry away a whole mouthful yesterday from the cornfield40 ,others still mention other uses4 ,perhaps1 however1 none will name the one the teacher has in his own mind2 he should cordially welcome the answer if perchance it is given4 7,supposing that it has not been given47 8,i have told you that the answer ,i was thinking of was a very simple one2 it is something you have all observed and you may be a little disappointed when ,i tell you4 ,the use ,i have been thinking of for the ear of corn is this3 ,it is to plant4 ,it is for seed1 to propagate that species of plant called corn40 7,verification47 ,here the children may look disappointed as much as to say1 ,we knew that before4 ,the teacher continues3 8,and this is a very important use for the corn2 for if for one year none should be planted1 and all the ears that grew the year before should be consumed1 we should have no more corn4 ,the other uses you have named were merely secondary4 ,but ,i mean to make something more of my ear of corn4 ,my next question is3 ,do other plants have seed80 ,here is a new field of inquiry1 etc41 etc4 ,from the standpoint of 8the greatest amount of knowledge in the shortest possible time10 this mode of presentation consumes an inexcusable amount of time and is1 therefore1 8impracticable40 ,but when viewed from the ground of interest1 originality1 initiative1 and conquestthe watchwords of the 8new thought in education02 there is no real waste in either time or energy4 ,the spirit and method of the discoverer will no doubt be the educational slogan of the future age4 ,epitome of ,discoverer's ,method1 adapted to the class room3 7#a7 ,motivate the topic to be presented4 7#b7 ,bring to mind1 if necessary1 the 8foundational facts40 7#c7 ,make evident the 8crucial fact40 7#d7 ,furnish every opportunity for a first-hand discovery of the 8lesson-point0 7establishing hypothesis through analogy74 7#e7 ,let the hypothesis be verified4 ,the entire situation must be one of freedom1 zeal1 originality1 and initiative4 #aa4 ,,the ,,question ,,and ,,answer ,,method ,,not ,,necessarily ,,one ,,of ,,discovery4 ,no one mode of presentation is more universally used than the 8question and answer40 ,the advantages of this mode are many and the teacher who is an adept in the art of questioning1 from the standpoint of knowledge1 is generally efficient4 ,the common error1 however1 incident to much questioning1 is that of asking 8telling questions40 ,by the use of such1 the class is forced along the desired channel of thought so rigorously as to have a condition where the spirit of inquiry is entirely wanting4 ,it is possible to conform to the rules of good questioning1 and yet rob the class of all originality and initiative4 ,from the teacher's viewpoint1 the discoverer's method demands few questions2 it is the method of suggestion rather than one of questions4 ,avowedly in this method1 the children should ask and answer their own questions4 ,viewed from the ground of discovery there are three modes of presentation which may represent a progressive series4 ,these are 7#a7 the lecture mode1 7#b7 the question and answer mode1 7#c7 the mode by suggestion4 ,in the first there is little of the spirit of the discoverer2 in the second there is a trifle more of the spirit of the discoverer2 while in the third there is much of this spirit4 ,the student is advised to select some class room topic with a view to illustrating these three modes of presentation4 #ab4 ,,outline4 ,,logic ,,in ,,the ,,class ,,room4 7#a7 ,thought is king4 7#b7 ,special functions of induction and deduction4 7#c7 ,two types of mind4 ,inductive or liberal4 ,deductive or conservative4 7#d7 ,too much conservatism in school4 7#e7 ,the method of the discoverer4 ,three steps #a4 ,antecedent #a4 ,foundational facts #b4 ,crucial #b4 ,forming #a4 8,mental urge0 hypothesis #b4 ,analogy #c4 ,verification #a4 ,empirical #b4 ,rational 7#f7 ,the real inductive method or ,discoverer's ,method not in vogue in class room work4 7#g7 ,as a method of instruction1 deduction is superior to induction4 7#h7 ,conquest1 not knowledge1 the desideratum4 7#i7 ,motivation as related to the spirit of discovery4 7#aj7 ,discoverer's method or the real inductive method adapted to class room work4 ,school room method4 ,discoverer's method4 ,epitome4 7#aa7 ,question and answer method not necessarily one of discovery4 #ac4 ,,summary4 7#a7 ,thought is king in that it is the ruling factor in the making and breaking of habit4 ,this lends import to logic1 which is the science of thought4 7#b7 ,the chief function of induction is to discover new truth2 whereas deduction aims at clarifying and correcting new truth4 ,inductive logic makes known the special forms of thought which the discoverer uses2 while deductive logic tends to show how he verifies the truth thus obtained4 7#c7 ,just as there are two general forms of thinking1 inductive and deductive2 so there are two general types of mind1 the inductive and the deductive2 the former leads to liberalism1 the latter to conservatism4 ,both types are needed to maintain a safe balance4 7#d7 ,the schools of the day are emphasizing the deductive phase of work to the sacrifice of the inductive4 ,they are neglecting the ,columbuses and the ,edisons of the class4 ,the course of study makes for a conservatism1 which 8nips in the bud0 any marked tendency to discover and invent4 7#e7 ,logic may aid in the crusade against the ultra conservative tendency of class method1 by giving emphasis to the method of the discoverer and inventor4 ,an analysis of this method reveals these three steps3 antecedent facts1 forming an hypothesis and verification4 ,antecedent facts may be divided into foundational and crucial4 ,a crucial fact leads immediately to the formation of the hypothesis2 whereas the foundational facts represent that body of knowledge which makes it possible to interpret the crucial fact4 ,the crucial fact creates an unsatisfied state of mind1 which1 in turn1 urges the discoverer to construct some satisfactory hypothesis4 ,inference by analogy is the process used in such a construction4 ,the two modes of verification are recourse to experience1 or empirical2 and appeal to reason1 or rational4 7#f7 ,in the class room1 induction is used in form1 not in spirit2 in consequence we are neglecting the generals for the camp followers4 7#g7 ,the inductive method is logically the method of discovery1 while the deductive method is the method of instruction4 ,in the class room1 both methods have been devoted to the matter of instruction4 ,because of this1 induction has been robbed of its chief advantage over deduction4 7#h7 ,man has attained his greatest success by enlarging upon the thoughts of nature and not by an absolute substitution4 ,in enlarging upon nature's way of educating the child1 man has adopted her form of procedure1 but has lost her spirit of work4 ,in his scheme of education1 man's watchword is knowledge1 while nature's is conquest4 ,to seek knowledge without inspiring the spirit of conquest is man's way2 whereas nature's way is to encourage the spirit of conquest by using knowledge as a reward4 ,man must co-operate with nature1 if the best results are to be secured4 7#i7 ,in the case of the true discoverer1 it is not necessary to endow the object of his thought with added attractiveness2 but with the child enthusiasm may need to be stimulated by 8motivating0 the subject in hand4 ,this may be accomplished by appealing directly to the vital needs1 worldly necessities1 and innate cravings of the child mind4 7#aj7 ,a revolt is in evidence against that insatiate desire to teach knowledge1 which has been so marked in the past4 ,already schools are introducing departments of work which look toward conquest rather than knowledge4 ,when adapted to the school room the discoverer's method naturally resolves itself into these five steps3 7#a7 8,motivate0 the topic for presentation4 7#b7 ,bring to mind 8foundational facts40 7#c7 ,vividly make evident the 8crucial fact40 7#d7 ,lead to discovery of 8lesson-point40 7#e7 ,afford opportunity for verification4 7#aa7 ,the question and answer method of presenting work1 does not necessarily give full scope to the spirit of inquiry as emulated by the true born discoverer4 ,as a matter of affording opportunity for the development of the spirit of discovery1 there are three modes of presentation which may be arranged in a progressive series3 7#a7 ,the lecture mode in which there is little opportunity for discovery4 7#b7 ,the question and answer mode which permits some opportunity for discovery4 7#c7 ,the mode by suggestion which permits ample opportunity for discovery4 #ad4 ,,review ,,questions4 7#a7 ,show that thought may be made to make and break habit4 7#b7 8,induction directs to new truth1 deduction aims to modify and correct new truth40 ,explain and illustrate this4 7#c7 ,relate radicalism and conservatism to induction and deduction4 7#d7 ,show that in the present day school situations1 the spirit of deduction prevails4 7#e7 ,describe a discovery which is a typical illustration of the discoverer's method4 7#f7 ,indicate with explanation the general steps in the discoverer's method4 7#g7 ,show by illustration the difference between 8foundational facts0 and 8crucial facts40 7#h7 ,explain how the 8crucial fact0 leads to the construction of an hypothesis4 7#i7 ,explain and illustrate the two ways of verification4 7#aj7 ,distinguish between the inductive method as it is used in the class room1 and the inductive method as used by the discoverer4 7#aa7 ,show that in his inventions1 man enlarges upon the thoughts of nature4 7#ab7 ,explain 8motivation0 and show that it is a new name for an old situation4 7#ac7 ,in adapting the discoverer's method to class work1 what are the successive steps to be followed8 7#ad7 ,show by illustration that the question and answer method is not necessarily one which encourages the spirit of discovery4 #ae4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 8,our pet thoughts control us40 ,discuss this4 7#b7 ,select some class room experience for the purpose of showing that induction is especially directive in nature1 whereas deduction is more or less corrective in nature4 7#c7 8,there are just two kinds of people in the world1 the ,inductives and the ,deductives40 ,explain4 7#d7 ,are the schools sending out too many ,deductives8 ,argue the question4 7#e7 8,it is the business of the teacher to teach himself out of the business40 ,explain4 7#f7 ,look up the discovery of the laws of the pendulum1 with a view of showing that the event well illustrates the fact of the three general steps in the discoverer's method4 7#g7 8,with the average1 only extraordinary facts become crucial2 but with the genius any ordinary fact may become crucial40 ,make this clear4 7#h7 ,explain 8mental urge40 ,illustrate4 7#i7 ,illustrate 8empirical proof10 also 8rational proof40 7#aj7 ,show by illustration that the inductive method as used in the class room1 falls far short of being the method of the discoverer4 7#aa7 ,indicate by citing historical examples1 that conquest rather than knowledge makes for manhood4 7#ab7 ,show how you would motivate a topic in geography4 7#ac7 ,outline a plan for teaching some topic in nature according to the discoverer's method4 7#ad7 ,select a topic in arithmetic1 for the purpose of giving a comparative illustration of the 8question and answer mode0 of presentation1 and the 8mode by suggestion40 ,,chapter #ba4 ,,logic ,,and ,,life4 #a4 ,,logic ,,given ,a ,,place ,,in ,a ,,secondary ,,course4 8,to prepare for complete living0 seems to be the ultimate aim of education1 and any school subject which does not aid to this end must be eliminated from the courses of study4 8,knowledge for the sake of knowledge0 will not do in this age of practical efficiency4 ,a subject in order to survive must show indications of doing its share in this larger business of man building4 ,if it can be made evident that logic lends itself in no undecided terms to such an aim1 then may its incorporation in a secondary course of study be not only justified but more highly appreciated4 #b4 ,,man',s ,,supremacy ,,due ,,to ,,power ,,of ,,thought4 ,that man is the supreme agent of intelligent progress is due to three factors3 ,first1 to the existence of the natural world2 second1 to the existence of man himself2 third1 to man's ability to think4 ,given life and the world as a place to evolve that life1 and it is barely possible that man might have survived1 but without thought he could never have become supreme4 ,man is king of the animal kingdom because of his power of thought4 ,let us illustrate3 ,ages ago when ,england was a part of the main land2 when there was no ,north ,sea nor ,english ,channel2 we are told that there lived in the forest tracts there about many large and ferocious animals2 such as the elephant1 the lion1 and the tiger4 ,there lived also in the region a smaller and apparently a weaker animal4 ,this creature had no tusks to hook with1 no great jaws to crunch with1 and no claws to tear with2 and an eye witness would have said 8,such a weakling has no possible chance against these enemies of his2 he and his descendants will succumb and the species will become extinct40 ,the region was tropical2 but1 of a sudden1 a cataclysmic twist changed the temperature from a torrid to a frigid state4 ,what happened8 ,the large and ferocious animals either migrated to the south or froze to death2 but this weakling put on furs1 built fires1 and remained in the jungle as its king4 ,his name was man1 and though he had no horns to hook with1 he possessed a brain to think with2 this gave him supremacy over the forces of nature4 ,from the beginning the adaptation of the lower animals has been physical2 whereas man's has been more or less intellectual4 ,by means of deliberative thought man made the bow and arrow which could kill at a distance of #bjj yards2 then he invented the repeating rifle which may kill a mile away4 ,thought has taught man to harness the forces of nature in the form of all kinds of invention4 ,thought has given man the power to build bridges and palaces1 to paint pictures1 to chisel angels4 ,thought has pierced the fog of ignorance and brought light to the dark spots of the globe4 ,thought has build nations and established the spirit of good will on earth4 ,through the long years1 thought has been the one tool of conquest which has enabled man to build for himself1 out of the furnishings of nature1 a heaven on earth4 ,can you recall a department of life which thought has not embellished8 ,can you recall a single factor that has been raised to the nth power of efficiency without thought8 ,steam and electricity plus thought lights the world1 unites the world1 feeds and clothes the world4 ,to-day1 as in the olden time1 men who think are ever at a premium4 ,this holds true from the ,shopkeeper to the ,magnate of ,wall ,street2 from ,basil1 the ,blacksmith1 to ,edison1 the ,king ,inventor2 from ,reuben1 the ,farmer1 to ,burbank1 the ,wizard4 #c4 ,,importance ,,of ,,progressive ,,thought4 ,man not only thinks but he thinks progressively4 ,the average horse of to-day1 for example1 is probably no more intelligent than was the average equine of the time of ,alexander the ,great1 whose war horse1 ,bucephalus1 attained historical fame4 ,yet1 intellectually1 the average man of to-day is far above the average man of ,alexander's time4 8,horse-knowledge0 is more or less stationary4 ,through instinct each generation makes use of the knowledge of its ancestors without any noticeable accretions4 ,but 8man-knowledge0 is a growing product of progressive thought4 ,man appropriates all the knowledge of his forbears1 and then adds to this a bit of his own4 ,by being able to think progressively1 man is enabled to stand upon the shoulders of his ancestors and thus to take advantage of a broader vision4 ,we are now led to the conclusion that man's supremacy is due not only to his ability to think1 but to his power of progressive thought4 #d4 ,,necessity ,,of ,,right ,,thinking4 ,in the main1 man's thinking has been for his good1 that is1 in the long run1 it has contributed to his general progress4 ,if this had not been so1 long since would he have dropped back to the level of the non-thinking animals4 ,thinking has been defined as the process of affirming or denying connections4 ,right thinking is1 therefore1 a matter of affirming the right connections or denying the wrong connections4 ,to put it differently3 right thinking is the process of adjusting the best means to a right end2 whereas wrong thinking is a matter of overlooking the best means1 or directing improper means to a wrong end4 ,right thinking involves proper adjustment2 wrong thinking improper adjustment4 ,in the intellectual world as in the physical1 improper adjustment means extinction4 ,illustrations of this3 7#a7 ,a contractor undertakes to build a skyscraper4 ,in the excavation an old wall is discovered4 ,the thought of the contractor is1 8,i must make a pot of money out of this job1 and since this old wall is in the right spot ,i will build on it1 and thus save me #8five hundred'40 ,in the course of ten years1 without warning1 the building topples over and fifty women and children are killed4 ,the contractor is convicted and sent to prison for life4 ,if the builder had thought the right thought2 namely1 8,i want to put up a building that will stand for generations10 he would have survived the competition of his fellows and entered his long home with success etched upon his soul4 7#b7 ,two school teachers1 ,a and ,b1 are working in the same system4 ,a's ambition is to be promoted and she uses 8pull0 as the means4 ,for a time she succeeds in pulling the wires1 and likewise in pulling the 8wool0 over the eyes of the ,board of ,education4 ,b aspires to professional growth1 using as the means every opportunity for genuine improvement4 ,in time both are known as they really are1 not as they seem to be4 ,a is denominated a 8shirk10 a politician1 a mere school keeper2 whereas ,b is looked up to as the best equipped worker in the building1 a real school teacher4 ,there may seem to be many exceptions to this point of view1 and yet in the last analysis we find that these exceptions are only apparent4 ,when we maintain that right thinking means survival and wrong thinking extinction1 we assume that the standard adopted is genuine efficiency and not a certain money basis4 ,high positions may be secured through wrong thinking1 but these cannot be filled creditably without the preponderance of right thinking4 #e4 ,,indifferent ,,and ,,careless ,,thought4 ,it may be advanced as a plausible hypothesis that man1 especially if he is an ,american1 finds much trouble for himself1 and makes much trouble for the world because of his indifference to thought4 ,to leap first and look afterwards is the spirit of youth1 and ,america is young4 ,think twice before you look and look twice before you leap is sound logical doctrine4 ,a logically minded man rationalizes every new proposition before he adopts it4 ,he marshals before the mind the favorable points and then bombards them with every conceivable objection4 ,with the steady eye of an honest1 earnest1 open minded critic1 he weighs the unfavorable against the favorable and then accepts the indications of the balance unequivocally4 ,if logic did nothing else save to inspire young people to thus rationalize every doubtful undertaking1 it would do its share toward world betterment4 #f4 ,,the ,,rationalization ,,of ,,the ,,world ,,of ,,chance4 ,man seems to be a natural born gambler4 ,he loves to 8take a chance0 and herein lies much of his unhappiness4 ,without discussing the evils of the stock exchange1 the horrors of the gambling den1 and the unbusiness like procedure of the race track1 we may merely attempt here to show how the rationalization of the conception of chance may be instrumental in dimming the glare of gambling to the average youth4 7#a7 ,the meaning of the term chance4 ,the term chance implies an inability to find a cause for any particular event4 ,whenever we trust to luck1 we do so through ignorance4 ,in reality every thing in this world is ordered according to law1 and if we possessed infinite knowledge concerning these laws1 then1 for us1 the word 8chance0 would have no meaning4 ,one accomplishment of knowledge has been to rationalize superstition and chance4 8,not a grain of sand lies upon the beach1 but infinite knowledge would account for its lying there2 and the cause of every falling leaf is guided by the same principles of mechanics as rule the motions of the heavenly bodies40,jevon's ,prin4 of ,science1 vol4 ,i1 p4 #bbe4 ,that chance is a literal confession of ignorance1 is a wholesome truth for all to bear in mind4 ,if we were not so ignorant of atmospheric conditions1 we would never be caught in the rain without an umbrella2 if we knew perfectly the laws of mechanics1 we would not speed our car and trust to luck that the car would hold together4 7#b7 ,chance mathematically considered4 ,the principle of the 8calculation of chances0 has been discussed elsewhere4 ,it will be sufficient here to illustrate the principle from a mathematical point of view4 ,suppose that a jeweller desires to dispose of a ten-dollar watch by a raffle4 ,he may place a hundred numbers in a box1 one of which corresponds to the number on the watch4 ,my chance of drawing the right number is one out of a hundred and may be expressed by the fraction #a_/ajj4 ,the fact that ,i may draw the right number on the first trial or on the last trial is immaterial4 ,the real meaning of the ratio 8one out of a hundred0 is1 that in the long run1 ,i shall lose #ii times where ,i gain but once4 ,this implies1 that if ,i pay #be cents for each draw1 ,i shall in the end pay #ii times #be cents for the watch1 or ,i will have paid #bd4ge for a ten dollar watch4 7#c7 ,chance and gambling4 ,in all forms of gambling no wealth is produced4 ,what one man gains the other man loses4 ,in addition to this the institution which projects the gambling scheme must be supported4 ,in consequence1 more money must be lost than can possibly be gained4 ,this leads to the conclusion that on the basis of averages he who would gamble must terminate his career 8behind the game40 ,statistics verify this conclusion4 7#d7 ,chance and investments4 ,interest1 which is money paid for the use of money1 is high when the demand for money exceeds the supply and low when the supply equals or exceeds the demand4 ,the fact that the supply is short is largely due to the lack of confidence on the part of the investor4 ,this means that he is unwilling to take the risk4 ,thus the principle3 8,high rate of interest1 great risk2 low rate of interest1 little risk40 #g4 ,,the ,,rationalization ,,of ,,political ,,and ,,business ,,sophistries4 8,win right or wrong0 is a nut shell statement of modern sophistry4 ,corollaries to this are such aphorisms as 8,of two evils choose the lesser02 8,do evil that good may come10 etc4 ,armed with these platitudes the modern business and political octopus will play the bully and squeeze the life out of the little fellow in the name of economy2 will pay for editorials to elect the 8right man02 will evade bad laws so-called2 institute lobbies2 buy votes2 and perpetrate a thousand other immoral deeds in the name of 8good business0 or of 8party loyalty40 ,half truths are the most atrocious of all kinds of fallacies in that they are the most misleading4 8,do evil that good may come0 is but half of the whole truth 8,do evil that good may come1 provided there is no other way open40 ,again1 8,of two evils choose the lesser1 if a complete enumeration has shown that there is not a third course40 ,a development of a finer ability of discernment under right influence should lead the common citizen to see through these various sophistries practiced by corporate greed1 and should enable him by means of the ballot to 8blaze a better way40 ,the 8public is a blunderbuss0 because the average man either cannot1 or will not1 think his own thoughts4 ,by developing greater skill and arousing greater interest in the thinking process1 the crowd of camp followers will be reduced2 selfish bossism will die2 and a truer and more efficient democracy will reign supreme4 #h4 ,,the ,,rationalization ,,of ,,the ,,spirit ,,of ,,progress4 ,genuine progress comes through a happy combination of the old with the new4 ,a love for the old only1 means ultra conservatism2 whereas a love for the new only1 means ultra radicalism2 a love for both means rational liberalism4 ,that people love the old way may be attributed to two forces which will receive attention here4 7#a7 ,race instinct4 ,it may be said that 8life is a brief space between two eternitiesa path between infinity and infinitude40 8,man is a pedestrian who perambulates along the way40 ,the eternities concern him not so much as the path which stretches between them4 ,in a former day1 one of the striking characteristics of the western plain was the beaten path stretching out along the table-land like an elongated1 dust colored serpent2 and often following this path would be a herd of buffalo winding its way in single file around boulder and ant hill till shut from view by the distant horizon4 ,thus has man travelled along the beaten path1 following the 8foot prints of the ages40 ,here and there and everywhere do we see signs of those who have gone on before2 father1 grandfather1 great grandfather2 yes1 even to the toe marks of those primeval ancestors of ours who shambled along the way1 nobody knows how many years ago4 ,from the dark recesses of the cave1 have our forbears thrown a lasso of blood about our necks1 and it seems as if we must follow the old1 old way4 8,being acorns of the ancestral oak10 we grow similar oak tree tendencies1 living over again the life of our progenitors4 8,there lies in every soul the history of the universe40 7#b7 ,imitation4 ,but there is another reason for this ultra conservative spirit and it is that nature's chief mode of instruction is by means of imitation4 ,to every living thing of wood or field nature seems to say1 8,your parents are always right1 do as they do for this is the best way to learn the lessons of life40 ,a man thinks1 feels and wills his way through life in a certain manner largely because his father did likewise4 ,moreover1 we not only imitate those who have gone on before1 but we counterfeit each other2 fashion is another name for world wide mimicry4 ,we imitate our friends and those whom we admire2 we talk like them1 we walk like them1 we live like them4 ,it now appears that we are held to the path of the past by means of race instinct and the power of imitation1 and we are thus prone to believe that the old way is good enough4 ,it is evident that to get out of the beaten path is dangerous4 ,the wild animal that deserts the habits of the race dies a premature death1 and the man who possesses the temerity to struggle through the thicket of new things must1 of necessity1 shorten his span of life4 ,to follow the 8same old rut0 is easiest for the teacher2 to be loyal to the 8grand old party0 is safest for the politician4 ,but to the contrary1 if every man of every generation had followed the beaten path blindlywithout deviation1 the human race would now be a horde of simians4 ,because man has possessed the power of progressive thought1 he has developed the spirit of radicalism and has thereby made himself supreme4 8,the old way anywaythe old way right or wrong0 has been the world's biggest stumbling block4 ,every innovation must fight for its life4 ,every good thing has to be condemned in its day and generation4 ,it is ,huxley who suggests three stages for the course of a new idea3 ,first1 it is revolutionary2 second1 it will make little difference2 third1 ,i have always believed in it4 ,on the other hand1 the new way anyway2 8we must have a change whether or no02 8we must have something different despite the cost10 have ever been the slogans of waste and destitution4 ,the wars which have not resulted from the prejudice of ultra conservatism have been brought about through the thoughtlessness of ultra radicalism4 ,the revolutionist1 the freak and the anarchist1 products of impulse and the spirit of discontent1 spring from an unwise love of change4 ,the world needs conservatism and radicalism not so much as it needs rationalism4 ,it needs men who can hold to the good of the old and adopt the best of the new2 men who neither 8rust out0 nor 8waste out02 but wear out4 ,that rational progress may obtain1 there must be a perfect dovetailing of the old with the new4 ,man must leave the beaten path not altogether1 but at times4 ,he needs to blaze out a new way not so much as he needs to straighten the bends1 tunnel through the mountains1 and fill in the swamps of the old way4 ,a rational 8liberalism0 implies a willingness to follow the old path with a view to improving the imperfections thereof4 #i4 ,a ,,rationalization ,,of ,,the ,,attitude ,,toward ,,work4 ,on the assumption that true happiness is the ultimate aim of life1 we may conclude that anything which does not contribute to this end functions as a curse and not as a blessing4 ,happiness involves physical comfort and mental joy4 ,to have comfort of the body implies moderate means4 ,the poor cannot be happy because of bodily want4 ,when 8physical-man0 is not given proper nourishment for healthy growth1 then does he goad 8spiritual-man0 with the pricks of appetite and pain till his wants are appeased4 ,this is a law of nature4 ,on the other hand happiness is not attained through acquisition2 neither the millionaires1 nor the scholars1 nor the famous are the happiest4 ,this is a fact apparent to all4 ,over worry and over excitement follow closely the heels of much money and high position4 ,too little brings unhappiness through want2 too much brings unhappiness through worry4 ,therefore man is cursed by his work when the remuneration is not enough for comfort of body1 or when the income is too much for poise of mind4 ,unless the organs of the body are used they atrophy4 ,every cell of the physical makeup demands exercise4 ,work which is not drudgery2 work which causes the organs of the body and the powers of the mind to function normally2 work which gives comfort without luxury2 work which forces one to the highest actualization of his physical and spiritual powers is man's greatest blessing4 ,in and through such work will man attain his highest state of happiness4 #aj4 ,,the ,,logic ,,of ,,success4 ,we may now hope to show that material aggrandizement1 the adopted standard of success1 is one of the illogical factors of modern life4 ,the tree of the forest always grows toward the light4 ,it pushes its way through the darkness of the soil into the shadow of the underbrush and finally out into the unobstructed light of the sun4 ,this parallels the progress of the race4 ,from the darkness of savagery into the shadow of barbarism1 and finally out into the full light of civilization4 ,thus has man grown steadily and continually toward better things4 ,but 8better things0 is a relative term and has changed with the development of the race4 8,a good healthy idea may not live longer than twenty years40 ,in consequence growth toward the light has been in accordance with man's conception of a higher and a better life2 which conception is ever changing4 ,moreover1 growth toward the best is always rewarded by real happiness4 ,it therefore follows that the right road to real happiness extends along the way of better things as conceived by the traveller1 man4 ,any force which tends to lift the world up toward more light is a blessing1 and any personality which contributes to this end is a success4 ,when one drops a pin it falls down toward the earth1 at the same time the earth comes up to meet the pin4 ,this is according to the universal law of gravitation4 ,it is true that the earth moves the pin through a much greater space than the pin moves the earth1 and yet the fact remains that the pin does move the earth4 ,the extent to which the smaller body is able to move the larger1 depends on the two factors of weight and relative position4 ,if the pin were lighter or farther away it would influence the earth so much the less4 ,in like manner does the 8pin-man0 influence the 8human-world40 ,the extent of this influence is controlled by man's weight1 or his 8lifting power10 and the position which he occupies2 just as the attraction of the pin for the earth is controlled by weight and position4 ,the facts of history have proved that man's power to lift depends not so much upon what he has as upon what he is4 ,in short1 lifting power is directly in proportion to personal worth4 ,moreover1 man's ability to draw humanity up may be increased or decreased by the position which he occupies4 ,such a position must function for the best good of the world1 and at the same time must elicit the highest development of the man4 ,,to ,,summarize3 ,individual success involves these three elements3 ,first,a man of personal worth4 ,second,a position which draws out the best in the man4 ,third,a work which definitely contributes to the uplift of the world4 ,a definition is now in order3 ,success is the right man in the right place doing his best for the highest good of the world4 #aa4 ,,outline4 ,,logic ,,and ,,life4 7#a7 ,logic given a place in a secondary course4 7#b7 ,man's supremacy due to power of thought4 7#c7 ,importance of progressive thinking4 7#d7 ,necessity of right thinking4 7#e7 ,indifferent and careless thought4 7#f7 ,the rationalization of the world of chance4 7#a7 ,meaning of the term chance4 7#b7 ,chance mathematically considered4 7#c7 ,chance and gambling4 7#d7 ,chance and investments4 7#g7 ,the rationalization of business and political sophistries4 7#h7 ,the rationalization of the spirit of progress4 7#i7 ,a rationalization of the attitude toward work4 7#aj7 ,the logic of success4 #ab4 ,,summary4 7#a7 ,to justify its having a place in any course of study1 logic must lend itself to character building4 7#b7 ,man is king of the animal kingdom because of his power of thought4 ,from the beginning his adaption has been more or less intellectual and his chief weapon of conquest has ever been his thinking brain4 7#c7 ,man's supremacy has been due not only to his ability to think1 but also to his power of progressive thought4 7#d7 ,right thinking is the process of adjusting the best means to a right end4 ,wrong thinking involves improper adjustment1 which in turn results in extinction4 7#e7 ,a 8logically-minded0 man rationalizes every new proposition before he adopts it4 ,that is1 he analyzes with the utmost care and with unprejudiced frankness all the favorable and unfavorable situations2 he then throws them into the balance of honest judgment and adopts the indications of said balance1 unequivocally4 7#f7 ,chance is a confession of ignorance4 ,if man possessed infinite knowledge1 the term chance would have no place in his vocabulary4 ,the games of chance are money making schemes supported by the gambling fraternity4 ,on the basis of averages1 the gambler1 in the long run1 must terminate his career 8behind the game40 ,high rate of interest implies great risk2 low rate of interest little risk4 7#g7 8,win right or wrong0 epitomizes the teachings of modern sophistry4 ,with the coming of better thinking1 a more efficient democracy will obtain4 7#h7 ,rational progress combines the best of the old with what seems to be the best of the new4 ,blind love for the old1 or ultra conservatism1 is due to the two forces of race instinct and power of imitation4 ,an adherence to the 8old way anyway0 may mean retrogression2 whereas following the new way1 simply because of its newness1 may involve unnecessary waste4 7#i7 ,work which is not drudgery2 work which causes the organs of the body and the powers of the mind to function normally2 work which gives comfort without luxury2 work which forces one to the highest actualization of his physical and spiritual powers is man's greatest blessing4 7#aj7 ,logically considered personal aggrandizement is not a true standard of success4 ,success involves personal worth rather than personal holding4 ,success is measured by man's ability to help the world on toward better things4 ,success is the right man in the right place doing his best for the highest good of the world4 #ac4 ,,review ,,questions4 7#a7 ,what is the ultimate aim of education8 ,show that logic contributes to this end4 7#b7 ,prove that man's power of thought has ever been his best weapon of conquest4 7#c7 ,exemplify the distinction between non-progressive and progressive thinking4 7#d7 ,define right thinking4 ,illustrate4 7#e7 8,a logically-minded man rationalizes every new project before undertaking it40 ,give a concrete instance in explanation of this4 7#f7 8,chance is a literal confession of ignorance40 ,demonstrate this4 7#g7 ,give a mathematical illustration proving that schemes of chance are simply money making devices for the benefit of those who project them4 7#h7 ,the average gambler must terminate his career behind the game4 ,prove this4 7#i7 ,why should high rate of interest imply great risk8 7#aj7 ,show that a half truth is a most misleading fallacy4 7#aa7 ,illustrate a business sophistry4 ,explain4 7#ab7 ,write a brief theme on 8,the ,rationalization of the ,spirit of ,progress40 7#ac7 ,under what conditions may work become man's greatest blessing8 7#ad7 ,define success4 ,illustrate4 7#ae7 ,in the light of your definition of success discuss the following3 8,the only failure is not to try40 #ad4 ,,questions ,,for ,,original ,,thought ,,and ,,investigation4 7#a7 8,to prepare for complete living0 is the end of education4 ,interpret and discuss this quotation from ,spencer4 7#b7 ,mention some discovery or invention which represents the power of progressive thought4 7#c7 8,man's adaptation has been largely intellectual while the adaptation of the camel has been physical40 ,explain4 7#d7 ,interpret the expression1 8,the son stands upon the shoulders of the father40 7#e7 ,illustrate instances where man's thinking has not been for his best interests4 7#f7 ,indicate how wrong thinking led to the ,civil ,war4 7#g7 ,distinguish between legitimate speculation and gambling4 7#h7 ,name and explain the logical elements involved in a low rate of interest4 7#i7 ,how may training in right thinking lead to more efficient citizenship8 7#aj7 8,there lies in every soul a history of the universe40 ,show the truth of this4 7#aa7 ,show by illustration that imitation is one of nature's chief modes of instruction4 7#ab7 ,explain the meaning of drudgery4 7#ac7 ,mention instances where work is a curse4 7#ad7 ,is success possible when the right man is found doing his best in the wrong place8 7#ae7 ,whom do you consider the most successful ,american8 ,give reasons4 ,,general ,,exercises ,,in ,,testing ,,the ,,validity ,,of ,,categorical ,,arguments4 ,let the student give attention to the fallacies in meaning as well as to the fallacies in form4 #a4 ,none but those who are contented with their lot in life can justly be considered happy4 ,but the truly wise man will always make himself contented with his lot in life1 and1 therefore he may justly be considered happy4 ,keynes4 #b4 ,suffering is a title to an excellent inheritance2 for ,god chastens every son whom he receives4 ,keynes4 #c4 ,no young man is wise2 for only experience can give wisdom1 and experience comes only with age4 ,keynes4 #d4 ,dr4 ,johnson remarked that 8a man who sold a penknife was not necessarily an iron-monger40 ,against what logical fallacy was this remark directed8 ,explain4 ,keynes4 #e4 ,this pamphlet contains seditious doctrines1 the spread of which may be dangerous to the state2 hence the pamphlet must be suppressed4 ,keynes4 #f4 ,good workmen do not complain of their tools3 my pupils do not complain of their tools2 therefore1 my pupils are probably good workmen4 ,keynes4 #g4 ,knowledge gives power2 consequently1 since power is desirable1 knowledge is desirable4 ,keynes4 #h4 ,some who are truly wise are not learned2 but the virtuous alone are truly wise2 the learned1 therefore1 are not always virtuous4 ,keynes4 #i4 ,the spread of education among the lower orders will make them unfit for their work2 for it has always had that effect on those among them who happen to have acquired it in previous times4 ,keynes4 #aj4 ,slavery is a natural institution and therefore ought not to be abolished4 ,russell4 #aa4 ,the yardstick of success is the dollar1 and you have made your millions4 #ab4 8,all who talk well are not necessarily intelligent1 and ,a is certainly a spell-binder40 #ac4 ,gold and silver are the wealth of a country2 consequently1 the diminution of gold and silver by exportation must mean the diminution of the wealth of a country4 ,russell4 #ad4 ,a miracle is unbelievable1 because it fails to conform to known laws of nature4 #ae4 ,improbable events happen every day2 now1 what happens every day is a probable event2 therefore1 improbable events are probable events4 #af4 ,what fallacy did ,columbus commit when he made the egg stand on end by breaking one end8 #ag4 ,some holder of a ticket is sure to draw the prize2 and1 as ,i am a ticket holder1 ,i am sure to draw the prize4 ,russell4 #ah4 ,all the members of the jury are just men1 hence you may trust the foreman4 #ai4 ,select the star players of the country and you will have a team which cannot be beaten4 #bj4 ,all the houses on this street present a pretty picture2 this house1 therefore1 which is on this street1 will make a fine picture4 #ba4 ,what is the good of all your teaching1 for every day we hear of wrong doing made possible by education4 #bb4 ,you are not what ,i am2 ,i am a teacher2 hence you are not a teacher4 #bc4 ,the student of history is compelled to admit the law of progress1 for he finds that society has never stood still4 ,russell4 #bd4 ,this bill must have been designed to bleed the people because it is supported by the grafters of the state4 #be4 8,to close the saloons on ,sunday is contrary to the wishes of the people of the city2 hence those #8farmer legislators' should keep hands off40 #bf4 ,success is the right man in the right place doing his best1 and you are working to the limit4 #bg4 ,early to bed and early to rise1 makes one healthy1 wealthy and wise4 ,it is1 therefore1 easy enough to get rich4 #bh4 ,honesty being the best policy1 ,i must tell the truth to my patient1 though to tell him that he cannot live will shorten his life many days4 #bi4 ,a stitch in times saves nine1 hence an ounce of prevention is worth a pound of cure4 #cj4 ,the richest man ,i know used to sweep his office every morning1 hence it pays to commence at the bottom4 #ca4 ,cramming is an injurious habit1 since it makes the building of logical memories practically impossible4 #cb4 ,a strong will means a trained will2 struggle is an indication of weakness4 #cc4 ,there is no such thing as a national or state conscience2 therefore1 no judgments can fall upon a sinful nation4 ,hibben4 #cd4 ,the principles of justice are variable2 the appointments of nature are invariable2 therefore1 the principles of justice are no appointment of nature4 ,aristotle4 #ce4 ,intelligence and not sex should be the standard2 therefore1 let the women have their way4 #cf4 8,war by killing off the men of the country gives the living a better opportunity to succeed because of reduced competition40 #cg4 ,since you deem yourself a misfit1 in the name of common sense1 why do you not change your occupation8 #ch4 ,the conquest of ,america by ,europeans has been a good thing for the world2 since no eminent historian doubts it4 ,,general ,,exercises ,,in ,,testing ,,the ,,validity ,,of ,,hypothetical1 ,,disjunctive ,,and ,,dilemmatic ,,arguments4 ,the student must remember to give attention to the fallacies in meaning as well as to the fallacies in form4 #a4 ,if ,i speak at length1 he is bored2 if ,i speak briefly1 he is offended2 therefore ,i will not speak at all4 #b4 ,if virtue is involuntary1 vice is also involuntary2 but vice is voluntary1 hence virtue is also4 #c4 ,if a man cannot make progress toward perfection1 he must either be a brute or a divinity2 but no man is either2 therefore every man is capable of such progress4 ,fowler4 #d4 ,if education is popular1 compulsion is unnecessary2 if unpopular1 compulsion will not be tolerated4 ,fowler4 #e4 ,if you are to recover from this illness1 then you will4 ,if you are not to recover1 then you will not1 hence what is the use of calling in a physician8 #f4 ,if your act was right1 your conscience will approve it2 if wrong1 your conscience will prick you4 ,either your act was right or wrong1 so you can depend upon your conscience4 #g4 ,if he is intoxicated then he is not responsible1 but he acts like a sober man4 #h4 ,if the ,elixir of ,life is of any value1 those who take it will improve in health2 now my friend who has been taking it has improved in health1 and therefore the elixir is of value as a curative agent4 ,hyslop4 #i4 ,if you will settle down to business1 you may still win out1 because ,i am confident it is not too late for hard work to be effective4 #aj4 ,if the end justifies the means then money used for any object of charity may be secured in any way4 #aa4 ,if might is right then money talks1 but ,i find that occasionally money proves ineffective4 #ab4 ,if the majority of those who use public houses are prepared to close them1 legislation is unnecessary1 but if they are not prepared for such a measure1 then to force it on them by outside pressure is both dangerous and unjust4 ,hyslop4 #ac4 ,if the conscience is infallible in matters of right and wrong1 then sin is just one thing2 namely1 doing that which is contrary to one's conscience4 ,we believe that an educated conscience is infallible4 #ad4 ,if the earth were of equal density throughout1 it would be about #b times as dense as water2 but it is about #e times as dense2 therefore the earth must be of unequal density4 ,hyslop4 #ae4 ,the end of human life is either perfection or happiness2 death is the end of human life1 therefore death is either perfection or happiness4 ,creighton4 #af4 ,that chauffeur either lost his head or was drunk because no sane man would deliberately run down an innocent child4 #ag4 ,if you argue on a subject which you do not understand1 you will prove yourself a fool2 for this is a mistake which fools always make4 ,keynes4 #ah4 ,if you are a man of your word1 you will live up to your agreement1 or if you have any self respect1 you will do the manly thing4 ,now your neighbors tell me that you are a man in the habit of making good your promises4 ,,sets ,,of ,,examination ,,questions ,,for ,,training ,,schools ,,and ,,colleges4 ,answer ten questions4 ,time1 #b hours4 ,set ,i4 #a4 ,define and illustrate obversion and state the principle which conditions the process4 #b4 ,give directions for making the following propositions logical3 7#a7 ,only first class passengers may ride in parlor cars4 7#b7 ,all who claim to be pious are not pious4 7#c7 8,blessed are the merciful40 #c4 ,write a theme of #bjj words on 8,logic and ,life40 #d4 ,put into syllogistic form and test the validity of this argument4 8,we are going to have an open winter because the hornets' nests are near the ground40 #e4 ,justify the teaching of logic in an institution which offers courses in ,educational ,theory4 #f4 ,correct the following definitions1 stating the rules violated3 7#a7 ,a man is an organized entity whose cognitive powers function rationally4 7#b7 ,a bird is an animal that flies4 7#c7 ,a scholar is an educated man with scholarly attainments4 #g4 ,prove that in the first figure the minor premise must be affirmative4 #h4 ,investigate a case of habitual tardiness by making use of the canon of difference4 #i4 ,describe with illustrations the various ways of begging the question4 #aj4 ,why should classification rather than logical division be the mode of procedure in the case of small children8 ,illustrate4 #aa4 ,illustrate the following3 7#a7 non connotative term1 7#b7 undistributed middle1 7#c7 fallacy of accident4 ,set ,,ii4 ,answer ten questions4 ,time1 #b hours4 ,throw the following into the form of a syllogism and criticise1 giving reasons3 #a4 8,i do not know how to teach school as ,i have had no experience40 #b4 8,only the honest should be in business and you are not honest40 #c4 ,why should all teachers study logic8 ,give arguments in full4 #d4 ,describe ,mill's methods of induction and illustrate one4 #e4 ,give and explain the rules of logical definition4 #f4 ,explain the distribution of terms and illustrate by circles the meaning of the four logical propositions4 #g4 ,define the following3 7#a7 teaching1 7#b7 extension of terms1 7#c7 obversion1 7#d7 hypothesis1 7#e7 relative term4 #h4 ,give a class room illustration of the ,complete ,method4 #i4 ,distinguish between 7#a7 distributive and collective terms1 7#b7 analysis and deduction1 7#c7 logical division and classification4 #aj4 ,illustrate the following3 7#a7 contradictory proposition1 7#b7 analogy1 7#c7 law of identity1 7#d7 singular term1 7#e7 univocal term4 #aa4 ,convert1 if possible1 the following3 7#a7 ,some men are honest4 7#b7 ,all that glitters is not gold4 7#c7 ,all kings are fallible4 ,set ,,iii4 ,answer ten questions4 ,time1 #b hours4 #a4 ,investigate by the ,joint ,method of ,induction this question3 8,why is ,john absent so often80 #b4 ,explain and illustrate3 7#a7 contradictory propositions1 7#b7 illicit middle1 7#c7 obversion1 7#d7 contraversion1 7#e7 synthesis4 #c4 ,state and exemplify the rules of logical division4 #d4 ,write a theme of at least #aej words on one of the following3 7#a7 ,induction as the ,discoverer's ,method4 7#b7 ,a ,rational ,view of ,success4 #e4 ,define logically3 7#a7 teaching1 7#b7 deduction1 7#c7 education1 7#d7 analysis1 7#e7 money4 #f4 ,distinguish between the extension and intension of terms4 #g4 ,exemplify3 7#a7 an absolute term1 7#b7 the complete method1 7#c7 non connotative terms1 7#d7 fallacy of accident1 7#e7 hypothesis4 #h4 8,educated among savages1 he could not be expected to know the customs of polite society40 ,is this valid8 ,reasons4 #i4 8,the signs indicate that you are either stupid or unprepared2 but the past proves that you are not the former40 ,test the validity4 #aj4 ,discuss comprehensively one of the following topics3 7#a7 ,the ,fallacies4 7#b7 ,thinking4 7#c7 ,abbreviated ,arguments4 ,set ,,iv4 ,answer ten questions4 ,time1 #b hours4 #a4 ,exemplify3 7#a7 the law of variation in the extension and intension of terms1 7#b7 a distributed predicate4 #b4 ,indicate with explanation the logical errors3 7#a7 ,a teacher assumes that the 8bad boy of the school0 is going to cause trouble in her room4 7#b7 ,all the men of the ,commission are fair minded men1 hence they will render a fair decision4 #c4 ,what experimental method of induction is the most positive in its conclusion8 ,illustrate this method4 #d4 ,state and illustrate the rules of logical definition4 #e4 ,obvert each of the four logical propositions4 ,explain the principle involved4 ,test the validity of the following arguments3 #f4 8,horses1 not being human1 cannot reason40 #g4 8,only the industrious deserve to succeed and you have never done a hard day's work in your life40 #h4 8,if you had been wise1 you would have refused to stoop to the methods of the firm1 but you were not wise40 #i4 ,from this premise construct a valid syllogism3 8,all large cities owe their size to some commercial advantage40 #aj4 ,define and illustrate the following3 analogy1 hypothesis1 thinking1 connotative term1 relative term4 #aa4 ,distinguish between3 7#a7 ,analysis and deduction4 7#b7 ,logical division and classification4 7#c7 ,relative and absolute identity4 ,set ,v4 ,answer ten questions4 ,time1 #b hours4 ,test the validity1 giving reasons3 #a4 ,all successful teachers are industrious1 but you are not industrious because you are not successful4 #b4 ,john was a troublesome boy in the first and second grades1 therefore he is going to make trouble for the third grade teacher4 #c4 ,teaching is the art of imparting knowledge4 ,criticise1 giving reasons4 ,define correctly1 pointing out the essentials4 #d4 ,explain the extensional and intensional use of terms and illustrate the law of variation4 #e4 ,describe ,mill's experimental methods of induction4 ,symbolize the joint method4 #f4 ,define the following3 analysis1 law of identity1 obversion4 #g4 ,illustrate the laws of thought4 #h4 ,write on one of the following topics3 7#a7 ,complete ,method1 7#b7 ,right ,thinking4 #i4 8,the science of logic never made a man reason rightly40 ,discuss this question4 #aj4 ,explain and illustrate the enthymeme4 ,set ,,vi4 ,answer ten questions4 ,time1 #b hours4 #a4 ,exemplify the following3 7#a7 illicit minor1 7#b7 begging the question1 7#c7 law of excluded middle1 7#d7 inductive method4 #b4 ,write a short theme on one of these topics3 7#a7 ,thinking4 7#b7 ,logical ,terms4 ,test the validity of the attending arguments1 giving reasons3 #c4 8,he who talks much usually says little and you are certainly a great talker40 #d4 8,you must be industrious1 since only such truly succeed40 #e4 ,illustrate and give the characteristic marks of the joint method of induction4 #f4 ,summarize the benefits to be derived from a study of logic4 #g4 ,state and illustrate the rules of logical definition4 #h4 ,distinguish between 7#a7 extension and intension1 7#b7 opposite and contradictory terms1 7#c7 analysis and synthesis4 #i4 ,define and illustrate hypothesis1 obversion1 sorites1 hypothetical argument4 #aj4 ,explain and illustrate the three forms of induction4 #aa4 ,distinguish logically between a teacher and an instructor4 ,,bibliography4 ,aikins4 ,the ,principles of ,logic4 ,henry ,holt and ,co41 ,new ,york4 #aije4 ,bain4 ,logic1 ,inductive and ,deductive4 ,longmans1 ,green and ,co4 #aijb4 ,bosanquet4 ,the ,essentials of ,logic4 ,the ,mac,millan ,co41 ,london4 #aiaj4 ,bradley4 ,the ,principles of ,logic4 ,london4 #ahhf4 ,creighton4 ,introductory ,logic4 ,the ,mac,millan ,co41 ,new ,york4 #aije4 ,dewey4 ,studies in ,logical ,theory4 ,the ,university of ,chicago ,press4 #aijc4 ,fowler4 ,the ,elements of ,deductive and ,inductive ,logic4 ,oxford4 #aije4 ,hibben4 ,logic1 ,deductive and ,inductive4 ,chas4 ,scribner's ,sons1 ,new ,york4 #aijf4 ,hyslop4 ,elements of ,logic4 ,chas4 ,scribner's ,sons1 ,new ,york4 #aije4 ,jevons-,hill4 ,elements of ,logic4 ,american ,book ,co41 ,new ,york4 #ahhc4 ,keynes4 ,formal ,logic4 ,the ,mac,millan ,co41 ,london4 #aijf4 ,lotze4 ,logic4 ,translated by ,b4 ,bosanquet1 #b vols4 ,oxford4 #ahhh4 ,mc,cosh4 ,laws of ,discursive ,thought4 ,chas4 ,scribner's ,sons4 #aijf4 ,mill4 ,a ,system of ,logic1 #b vols4 ,longmans1 ,green and ,co41 ,london4 #aijd4 ,russell4 ,elementary ,logic4 ,the ,mac,millan ,co41 ,new ,york4 #aijh4 ,ryland4 ,logic4 ,george ,bell and ,sons1 ,london4 #aijj4 ,sigwart4 ,logic4 ,translated by ,helen ,dendy1 #b vols4 ,the ,mac,millan ,co4 #ahie4 ,swinburne4 ,picture ,logic4 ,longmans1 ,green and ,co41 ,london4 #aijd4 ,taylor4 ,elementary ,logic4 ,chas4 ,scribner's ,sons1 ,new ,york4 #aiaa4 ,venn4 ,the ,logic of ,chance4 ,the ,mac,millan ,co41 ,new ,york4 ,,outline ,,of ,,briefer ,,course4 ,subject ,i4 ,,thought ,,and ,,its ,,laws ,logic ,defined ,the ,thinking ,process4 ,stages in ,thinking ,the ,law of ,identity ,the ,law of ,contradiction ,the ,law of ,excluded ,middle ,,ii4 ,,logical ,,terms ,all of ,chapter #d ,,iii4 ,,extentsion ,,and ,,intension ,,of ,,terms ,all of ,chapter #e ,,iv4 ,,definition ,all of ,chapter #f ,v4 ,,logical ,,division ,,and ,,classification ,all of ,chapter #g ,,vi4 ,,logical ,,propositions ,all of ,chapter #h ,except ,section #g ,,vii4 ,,immediate ,,inference ,all of ,chapter #aj ,,viii4 ,,mediate ,,inference ,all of ,chapter #aa ,except ,section #h ,,ix4 ,,figures ,,and ,,moods ,the ,four ,figures of the ,syllogism ,the ,moods of the ,syllogism ,testing the ,validity of the ,moods ,x4 ,,incomplete ,,syllogisms ,enthymeme ,polysyllogisms ,sorites ,,xi4 ,,categorical ,,arguments ,,tested ,all of ,chapter #ad ,,xii4 ,,hypothetical ,,and ,,disjunctive ,,arguments ,all of ,chapter #ae except ,sections #ac1ad1 #ae and #ag ,,xiii4 ,,logical ,,fallacies ,all of ,chapter #af ,,xiv4 ,,inductive ,,reasoning ,all of ,chapter #ag ,except ,sections #c1 #d1 #g1 #h and #i ,,xv4 ,,mill',s ,,methods ,,of ,,observation ,,and ,,experiment ,all of ,chapter #ah ,,xvi4 ,,observation1 ,,experiment ,,and ,,hypothesis ,all of ,chapter #ai ,,index ,a ,absolute ,terms1 #ef4 ,abstract ,terms1 #ea4 ,accent1 ,fallacy of1 #ccj4 ,accident1 #ha2 ,fallacy of1 #ccd4 ,affirmative ,proposition1 #abg4 ,agreement1 ,method of1 #chg4 ,allnot1 ,some1 ,few1 ,logical ,significance of1 #acc4 ,ambiguous ,middle1 #cbh4 ,amphibology1 #cbi4 ,analogy1 #cfh4 ,analysis1 ,definition of1 #ig2 ,as a 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,classification of1 #abh4 ,cause1 ,fallacy of ,false1 #cdj4 ,chance1 ,rationalization of1 #dfh4 ,child1 ,thinking of1 #bj4 ,circulus in ,probando1 #cdc4 ,classification ,compared with ,division1 #aab2 ,kinds1 #aac2 ,rules of1 #aad2 ,use1 #aad4 ,co-extensive ,propositions1 #adb4 ,collective ,terms1 #ej4 ,comparison1 ,stages in ,thinking1 #be4 ,complete ,method1 ,three ,elements1 #ig4 ,composition1 ,fallacy of1 #cca4 ,concept1 ,definition of1 #ag2 a ,thought ,product1 #ba4 ,concomitant ,variations1 #djb4 ,concrete ,terms1 #ea4 ,connotative ,terms1 ,two-fold ,function of1 #fb2 ,definition of1 #eb2 a ,list of1 #fe4 ,conquest the ,desideratum1 #ddg4 ,consequent1 #bhi2 ,fallacy of ,false1 #cci4 ,contradiction1 ,law of1 #ce4 ,contradictory ,terms1 #ec2 ,propositions1 #afg4 ,contrary ,propositions1 #afe4 ,contraversion1 #aha2 ,fallacies of1 #cbg4 ,converse ,accident1 ,fallacy of1 #cce4 ,conversion1 #agf2 by ,limitation1 #agh2 ,simply1 #agi2 ,fallacies of1 #cbg4 ,copula1 #abc4 ,creighton 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,knowing4 #e - ,hyslop's ,elements of ,logic 7#aija71 page #ajj4 #f - ,hyslop4 #g - ,men do have the power of reason4 #h - ,sometimes called contraposition4 #i - ,from the ,greek meaning to reason with4 #aj - ,the student may be sufficiently interested to complete the list4 #aa - ,the student should prove that the last premise may be affirmative4 #ab - ,this cause1 however1 need not be a single antecedent1 in fact it seldom is4 8,this cause1 philosophically speaking1 is the sum total of the conditions1 positive and negative1 taken together40,mill4 ,the cause of the price of food stuff being high1 involves many conditions1 or antecedents1 so interwoven that it is impossible to designate any one as being the chief factor concerned4 #ac - ,those might be named the ,five ,special ,methods of ,induction by ,analysis4 #ad - ,all cases of finding the net proceeds are examples of the law of residue4 ,transcriber's ,notes4 ,the following corrections have been made in the text3 ,page #bb3 ,sentence starting3 ,first1 ,i may be4444 - #8recignize' replaced with #8recognize' 7able to recognize each7 ,page #fa1 ,question #af3 ,sentence starting3 ,what is the difference4444 - #8differenece' replaced with #8difference' 7the difference in meaning7 ,page #fa1 ,question #bc3 ,sentence starting3 ,argue to the effect4444 - #8non-contotative' replaced with #8non-connotative' 7can be non-connotative47 ,page #hf3 ,sentence starting3 ,a logical definition4444 - #8digerenti' replaced with #8differenti' 7by means of its differenti47 ,page #add3 ,sentence starting3 ,here1 as in the ,i1444 - #8comfined' replaced with #8confined' 7knowledge is confined to7 ,page #bjd3 ,sentence starting3 7#f7 ,if one premise4444 - #8nagtive' replaced with #8negative' 7one premise be negative7 ,page #bdj3 ,sentence starting3 ,since1 however1 the easiest4444 - #8affirmavite' replaced with #8affirmative' 7and a particular affirmative7 ,page #bdf3 ,sentence starting3 7#c7 ,show why it is4444 - ,printer error3 lost end of point 7#c7 and duplicated part of point 7#d7 ,page #bgf3 ,sentence starting3 ,other arguments where4444 - #8agruments' replaced with #8arguments' 7,other arguments where7 ,page #bhf3 ,sentence starting3 7#d7 ,in the practice4444 - #8analagous' replaced with #8analogous' 7custom analogous to giving7 ,page #bhf3 ,sentence starting3 7#d7 8,the man is guilty4444 - #87#d7' missing from text 77#d7 8,the man is guilty7 ,page #cbe3 ,sentence starting3 ,these fallacies arise from4444 - #8abitrary' replaced with #8arbitrary' 7words as arbitrary signs7 ,page #cbf3 ,sentence starting3 ,there is little difference4444 - #8fallicies' replaced with #8fallacies' 7and fallacies of converse7 ,page #cga3 ,sentence starting3 7#a7 ,noting that two4444 - #8sirname' replaced with #8surname' 7have the same surname17 ,page #cgf3 ,sentence starting3 ,in the school room4444 - #8generalziation' replaced with #8generalization' 7perfectly induced generalization17 ,page #chb3 ,sentence starting3 ,complete enumeration gives4444 - #8uncontradiced' replaced with #8uncontradicted' 7incomplete but uncontradicted7 ,page #dje3 ,sentence starting3 ,it is thus evident that4444 - #8prenomenon' replaced with #8phenomenon' 7entirely with the phenomenon47 ,page #dbb3 ,sentence starting3 ,reading into the external4444 - #8vivdly' replaced with #8vividly' 7what is only vividly internal7