,,the ,,art ,,of    ,,logical ,,thinking
      ,,or      ,,the ,,laws ,,of       
,,reasoning      ,by ,,william ,,walker 
,,atkinson        ,l4,n4 ,,fowler       
,,company    #g1 ,imperial ,arcade1     
,ludgate ,circus    ,london1 ,e4,c41    
,england      #aiji    ,,the ,,progress 
,,company    ,,chicago1 ,,ill4          
,copyright #aiji    ,by    ,,the        
,,progress ,,company    ,chicago1 ,ill41
 ,u4,s4,a4          ,,contents          
,i4 ,reasoning                          
#i         ,,ii4 ,the ,process of       
,reasoning            #ag        ,,iii4 
,the ,concept                           
#be         ,,iv4 ,the ,use of ,concepts
                 #cg          ,v4       
,concepts and ,images                   
#dh         ,,vi4 ,terms                
#ef        ,,vii4 ,the ,meaning of      
,terms                #gc       ,,viii4 
,judgments                           #hb
         ,,ix4 ,propositions            
#ij          ,x4 ,immediate ,reasoning  
#ii         ,,xi4 ,inductive ,reasoning 

#ajg        ,,xii4 ,reasoning by        
,induction             #aaf             
,,xiii4 ,theory and ,hypotheses         
#abe        ,,xiv4 ,making and ,testing 
,hypotheses      #acb         ,,xv4     
,deductive ,reasoning                   
#add        ,,xvi4 ,the ,syllogism      
#aef       ,,xvii4 ,varieties of        
,syllogisms            #afg             
,,xviii4 ,reasoning by ,analogy         
#agi        ,,xix4 ,fallacies           
#ahf          ,,chapter ,i4             
,,reasoning      ,reasoning is defined  
as3 ,the act1 process or art of         
exercising the  faculty of reason2 the  
act or faculty of employing reason in   
argument2  argumentation1 ratiocination2
 reasoning power2 disputation1          
discussion1  argumentation4 ,stewart    
says3 ,the word reason itself is far    
from  being precise in its meaning4 ,in 
common and popular discourse it denotes 
that power by which we distinguish truth
 from falsehood1 and right from  wrong1 
and by which we are enabled to combine  

means for the attainment  of particular 
ends4    ,by the employment of the      
reasoning faculties of the mind we      
compare  objects presented to the mind  
as percepts or concepts1 taking up the  
raw materials of thought and weaving    
them into more complex and  elaborate   
mental fabrics which we call abstract   
and general ideas of  truth4 ,brooks    
says3 ,it is the thinking power of the  
mind2 the faculty  which gives us what  
has been called thought-knowledge1 in   
distinction  from sense-knowledge4 ,it  
may be regarded as the mental architect 
among  the faculties2 it transforms the 
material furnished by the senses 444    
into new products1 and thus builds up   
the temples of science and  philosophy4 
,the last-mentioned authority adds3 ,its
 products are  twofold1 ideas and       
thoughts4 ,an idea is a mental product  
which  when expressed in words does not 
give a proposition2 a thought is a      
mental product which embraces the       
relation of two or more ideas4 ,the     

ideas of the understanding are of two   
general classes2 abstract ideas  and    
general ideas4 ,the thoughts are also of
 two general classes2 those  pertaining 
to contingent truth and those pertaining
 to necessary truth4  ,in contingent    
truth1 we have facts1 or immediate      
judgments1 and  general truths including
 laws and causes1 derived from          
particular  facts2 in necessary truth we
 have axioms1 or self-evident truths1   
and  the truths derived from them by    
reasoning1 called theorems4    ,in      
inviting you to consider the processes  
of reasoning1 we are  irresistibly      
reminded of the old story of one of     
,moliere's plays in  which one of the   
characters expresses surprise on        
learning that he had  been talking prose
 for forty years without knowing it4 ,as
 ,jevons says  in mentioning this3      
,ninety-nine people out of a hundred    
might be  equally surprised on hearing  
that they had been converting           
propositions1  syllogizing1 falling into

 paralogisms1 framing hypotheses and    
making  classifications with genera and 
species4 ,if asked whether they were    
logicians1 they would probably answer1  
,no6 ,they would be partly right2  for  
,i believe that a large number even of  
educated persons have no clear  idea of 
what logic is4 ,yet1 in a certain way1  
every one must have been a  logician    
since he began to speak4    ,so1 in     
asking you to consider the processes of 
reasoning we are not  assuming that you 
never have reasoned--on the contrary we 
are fully  aware that you in connection 
with every other person1 have reasoned  
all  your mature life4 ,that is not the 
question4 ,while everyone reasons1 the  
fact is equally true that the majority  
of persons reason incorrectly4  ,many   
persons reason along lines far from     
correct and scientific1 and  suffer     
therefor and thereby4 ,some writers have
 claimed that the majority  of persons  
are incapable of even fairly correct    
reasoning1 pointing to  the absurd ideas

 entertained by the masses of people as 
a proof of the  statement4 ,these       
writers are probably a little radical in
 their views  and statements1 but one is
 often struck with wonder at the        
evidences of  incapacity for            
interpreting facts and impressions on   
the part of the  general public4 ,the   
masses of people accept the most absurd 
ideas as  truth1 providing they are     
gravely asserted by some one claiming   
authority4 ,the most illogical ideas are
 accepted without dispute or            
examination1 providing they are stated  
solemnly and authoritatively4           
,particularly in the respective fields  
of religion and politics do we  find    
this blind acceptance of illogical ideas
 by the multitude4 ,mere  assertion by  
the leaders seems sufficient for the    
multitude of followers  to acquiesce4   
,in order to reason correctly it is not 
merely necessary to have a good         
intellect4 ,an athlete may have the     
proper proportions1 good framework1  and

 symmetrical muscles1 but he cannot     
expect to cope with others of his  kind 
unless he has learned to develop those  
muscles and to use them to  the best    
advantage4 ,and1 in the same way1 the   
man who wishes to reason  correctly must
 develop his intellectual faculties and 
must also learn  the art of using them  
to the best advantage4 ,otherwise he    
will waste his  mental energy and will  
be placed at a disadvantage when        
confronted with  a trained logician in  
argument or debate4 ,one who has        
witnessed a debate  or argument between 
two men equally strong intellectually1  
one of whom  is a trained logician and  
the other lacking this advantage1 will  
never  forget the impression produced   
upon him by the unequal struggle4 ,the  
conflict is like that of a powerful     
wrestler1 untrained in the little       
tricks and turns of the science1 in the 
various principles of applying  force in
 a certain way at a certain time1 at a  
certain place1 with a  trained and      

experienced wrestler4 ,or of a conflict 
between a muscular  giant untrained in  
the art of boxing1 when confronted with 
a trained and  experienced exponent of  
the manly art4 ,the result of any such  
conflict  is assured in advance4        
,therefore1 everyone should refuse to   
rest content  without a knowledge of the
 art of reasoning correctly1 for        
otherwise he  places himself under a    
heavy handicap in the race for success1 
and  allows others1 perhaps less        
well-equipped mentally1 to have a       
decided  advantage over him4    ,jevons 
says in this connection3 ,to be a good  
logician is1 however1 far  more valuable
 than to be a good athlete2 because     
logic teaches us to  reason well1 and   
reasoning gives us knowledge1 and       
knowledge1 as ,lord  ,bacon said1 is    
power4 ,as athletes1 men cannot for a   
moment compare with  horses or tigers or
 monkeys4 ,yet1 with the power of       
knowledge1 men tame  horses and shoot   
tigers and despise monkeys4 ,the weakest

 framework with  the most logical mind  
will conquer in the end1 because it is  
easy to  foresee the future1 to         
calculate the result of actions1 to     
avoid  mistakes which might be fatal1   
and to discover the means of doing      
things  which seemed impossible4 ,if    
such little creatures as ants had better
  brains than men1 they would either    
destroy men or make them into slaves4   
,it is true that we cannot use our eyes 
and ears without getting some  kind of  
knowledge1 and the brute animals can do 
the same4 ,but what gives  power is the 
deeper knowledge called ,science4       
,people may see1 and hear1  and feel all
 their lives without really learning the
 nature of things  they see4 ,but reason
 is the mind's eye1 and enables us to   
see why things  are1 and when and how   
events may be made to happen or not to  
happen4 ,the  logician endeavors to     
learn exactly what this reason is which 
makes the  power of men4 ,we all1 as ,i 
have said1 must reason well or ill1 but 

logic  is the science of reasoning and  
enables us to distinguish between the   
good reasoning which leads to truth1 and
 the bad reasoning which every  day     
betrays people into error and           
misfortune4    ,in this volume we hope  
to be able to point out the methods and 
principles of correctly using the       
reasoning faculties of the mind1 in a   
plain1 simple manner1 devoid of useless 
technicalities and academic  discussion4
 ,we shall adhere1 in the main1 to the  
principles established  by the best of  
the authorities of the old school of    
psychology1 blending  the same with     
those advanced by the best authorities  
of the ,new  ,psychology4 ,no attempt to
 make of this book a school text-book   
shall be  made1 for our sole object and 
aim is to bring this important subject  
before the general public composed of   
people who have neither the time  nor   
inclination to indulge in technical     
discussion nor academic  hair-splitting1
 but who desire to understand the       

underlying working  principles of the   
,laws of ,reasoning4          ,,chapter 
,,ii4    ,,the ,,process ,,of           
,,reasoning      ,the processes of      
,reasoning may be said to comprise four 
general stages  or steps1 as follows3   
,i4 ,abstraction1 by which is meant the 
process of drawing off and  setting     
aside from an object1 person or thing1 a
 quality or  attribute1 and making of it
 a distinct object of thought4 ,for     
instance1  if ,i perceive in a lion the 
quality of strength1 and am able to     
think of this quality abstractly and    
independently of the animal--if the     
term strength has an actual mental      
meaning to me1 independent of the       
lion--then ,i have abstracted that      
quality2 the thinking thereof is an  act
 of abstraction2 and the thought-idea   
itself is an abstract idea4  ,some      
writers hold that these abstract ideas  
are realities1 and not mere  figments of
 fancy4 ,as ,brooks says3 ,the rose     
dies1 but my idea of its  color and     

fragrance remains4 ,other authorities   
regard ,abstraction as  but an act of   
attention concentrated upon but the     
particular quality  to the exclusion of 
others1 and that the abstract idea has  
no existence  apart from the general    
idea of the object in which it is       
included4 ,sir  ,william ,hamilton says3
 ,we can rivet our attention on some    
particular  mode of a thing1 as its     
smell1 its color1 its figure1 its size1 
etc41  and abstract it from the others4 
,this may be called ,modal ,abstraction4
  ,the abstraction we have now been     
considering is performed on individual  
objects1 and is consequently particular4
 ,there is nothing necessarily          
connected with generalization in        
abstraction2 generalization is indeed   
dependent on abstraction1 which it      
supposes2 but abstraction does not      
involve generalization4    ,,ii4        
,generalization1 by which is meant the  
process of forming ,concepts  or        
,general ,ideas4 ,it acts in the        

direction of apprehending the common    
qualities of objects1 persons and       
things1 and combining and uniting them  
into a single notion or conception which
 will comprehend and include  them all4 
,a ,general ,idea or ,concept differs   
from a particular idea in  that it      
includes within itself the qualities of 
the particular and other  particulars1  
and accordingly may be applied to any   
one of these  particulars as well as to 
the general class4 ,for instance1 one   
may  have a particular idea of some     
particular horse1 which applies only  to
 that particular horse4 ,he may also    
have a ,general ,idea of horse1 in  the 
generic or class sense1 which idea      
applies not only to the general  class  
of horse but also to each and every     
horse which is included in  that class4 
,the expression of ,generalization or   
,conception is called a  ,concept4      
,,iii4 ,judgment1 by which is meant the 
process of comparing two objects1       
persons or things1 one with another1 and

 thus perceiving their agreement  or    
disagreement4 ,thus we may compare the  
two concepts horse and  animal1 and     
perceiving a certain agreement between  
them we form the  judgment that3 ,a     
horse is an animal2 or comparing horse  
and  cow1 and perceiving their          
disagreement1 we form the judgment3 ,a  
horse is not a cow4 ,the expression of a
 judgment is called a  ,proposition4    
,,iv4 ,reasoning1 by which is meant the 
process of comparing two objects1       
persons or things1 through their        
relation to a third object1 person or   
thing4 ,thus we may reason 7a7 that all 
mammals are animals2 7b7 that a  horse  
is a mammal2 7c7 that1 therefore1 a     
horse is an animal2 the  result of the  
reasoning being the statement that3 ,a  
horse is an  animal4 ,the most          
fundamental principle of reasoning1     
therefore1  consists in the comparing of
 two objects of thought through and by  
means  of their relation to a third     
object4 ,the natural form of expression 

of  this process of ,reasoning is called
 a ,syllogism4    ,it will be seen that 
these four processes of reasoning       
necessitate the  employment of the      
processes of ,analysis and ,synthesis1  
respectively4  ,analysis means a        
separating of an object of thought into 
its constituent  parts1 qualities or    
relations4 ,synthesis means the         
combining of the  qualities1 parts or   
relations of an object of thought into a
 composite  whole4 ,these two processes 
are found in all processes of           
,reasoning4  ,abstraction is principally
 analytic2 ,generalization or           
,conception  chiefly synthetic2         
,judgment is either or both analytic or 
synthetic2  ,reasoning is either a      
synthesis of particulars in ,induction1 
or an  evolution of the particular from 
the general in ,deduction4    ,there are
 two great classes of ,reasoning2 viz41 
7#a7 ,inductive  ,reasoning1 or the     
inference of general truths from        
particular truths2  and 7#b7 ,deductive 

,reasoning1 or the inference of         
particular truths from  general truths4 
,inductive ,reasoning proceeds by       
discovering a general truth from        
particular truths4 ,for instance1 from  
the particular truths that  individual  
men die we discover the general truth   
that ,all men must  die2 or from        
observing that in all observed instances
 ice melts at a  certain temperature1 we
 may infer that ,all ice melts at a     
certain  temperature4 ,inductive        
,reasoning proceeds from the known to   
the  unknown4 ,it is essentially a      
synthetic process4 ,it seeks to discover
  general laws from particular facts4   
,deductive ,reasoning proceeds by       
discovering particular truths from      
general truths4 ,thus we reason that as 
all men die1 ,john ,smith1 being a  man1
 must die2 or1 that as all ice melts at 
a certain temperature1 it  follows that 
the particular piece of ice under       
consideration will melt  at that certain
 temperature4 ,deductive ,reasoning is  

therefore seen to be  essentially an    
analytical process4    ,mills says of   
,inductive ,reasoning3 ,the inductive   
method of the ancients  consisted in    
ascribing the character of general      
truths to all  propositions which are   
true in all the instances of which we   
have  knowledge4 ,bacon exposed the     
insufficiency of this method1 and       
physical  investigation has now far     
outgrown the ,baconian conception4444   
,induction1 then1 is that operation by  
which we infer that what we know  to be 
true in a particular case or cases1 will
 be true in all cases  which resemble   
the former in certain assignable        
respects4 ,in other  words1 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 in similar circumstances at    
all times4    ,regarding ,deductive     
,reasoning1 a writer says3 ,deductive   
,reasoning is  that process of reasoning

 by which we arrive at the necessary    
consequences1 starting from admitted or 
established premises4 ,brooks  says3    
,the general truths from which we reason
 to particulars are  derived from       
several distinct sources4 ,some are     
intuitive1 as the axioms  of mathematics
 or logic4 ,some of them are derived    
from induction4444  ,some of them are   
merely hypothetical1 as in the          
investigation of the  physical sciences4
 ,many of the hypotheses and theories of
 the physical  sciences are used as     
general truth for deductive reasoning2  
as the  theory of gravitation1 the      
theory of light2 etc4 ,reasoning from   
the  theory of universal gravitation1   
,leverrier discovered the position of a 
new planet in the heavens before it had 
been discovered by human eyes4          
,halleck points out the interdependence 
of ,inductive and ,deductive  ,reasoning
 in the following words3 ,man has to    
find out through his own  experience1 or
 that of others1 the major premises from

 which he argues  or draws his          
conclusions4 ,by induction we examine   
what seems to us a  sufficient number of
 individual cases4 ,we then conclude    
that the rest of  these cases1 which we 
have not examined1 will obey the same   
general  laws4444 ,the premise1 ',all   
cows chew the cud1' was laid down after 
a  certain number of cows had been      
examined4 ,if we were to see a cow      
twenty  years hence1 we should expect   
that she chewed her cud4444 ,after      
,induction has classified certain       
phenomena and thus given us a major     
premise1 we proceed deductively to apply
 the inference to any new  specimen that
 can be shown to belong to that class4  
,the several steps of ,deductive        
,reasoning shall now be considered in   
turn  as we proceed4          ,,chapter 
,,iii4    ,,the ,,concept      ,in      
considering the process of thinking1 we 
must classify the several  steps or     
stages of thought that we may examine   
each in detail for the  purpose of      

comprehending them combined as a whole4 
,in actual thinking  these several steps
 or stages are not clearly separated in 
consciousness1 so that each stands out  
clear and distinct from the  preceding  
and succeeding steps or stages1 but1 on 
the contrary1 they  blend and shade into
 each other so that it is often         
difficult to draw a  clear dividing     
line4 ,the first step or stage in the   
process of thinking  is that which is   
called a concept4    ,a concept is a    
mental representation of anything4      
,prof4 ,wm4 ,james says3  ,the function 
by which we mark off1 discriminate1 draw
 a line around1  and identify a         
numerically distinct subject of         
discourse is called  conception4 ,there 
are five stages or steps in each        
concept1 as  follows3    ,i4            
,presentation4 ,before a concept may be 
formed there must first be a            
presentation of the material from which 
the concept is to be formed4 ,if  we    
wish to form the concept1 animal1 we    

must first have perceived an  animal1   
probably several kinds of               
animals--horses1 dogs1 cats1 cows1      
pigs1 lions1 tigers1 etc4 ,we must also 
have received impressions from  the     
sight of these animals which may be     
reproduced by the  memory--represented  
to the mind4 ,in order that we may have 
a full  concept of animal we should have
 perceived every kind of animal1 for    
otherwise there would be some elements  
of the full concept lacking4            
,accordingly it is practically          
impossible to have a full concept of    
anything4 ,the greater the opportunities
 for perception the greater will  be the
 opportunity for conception4 ,in other  
books of this series we have  spoken of 
the value and importance of the         
attention and of clear and  full        
perception4 ,without an active          
employment of the attention1 it is      
impossible to receive a clear perception
 of anything2 and unless the  perception
 has been clear1 it is impossible for   

the mind to form a clear  concept of the
 thing perceived4 ,as ,sir ,wm4         
,hamilton has said3 ,an act  of         
attention1 that is an act of            
concentration1 seems thus necessary to  
every exertion of consciousness1 as a   
certain contraction of the pupil  is    
requisite to every exertion of          
vision4444 ,attention1 then1 is to      
consciousness what the contraction of   
the pupil is to sight1 or to the  eye of
 the mind what the microscope or        
telescope is to the bodily  eye4444 ,it 
constitutes the half of all intellectual
 power4 ,and ,sir ,b4  ,brodie said3 ,it
 is attention1 much more than in the    
abstract power of  reasoning1 which     
constitutes the vast difference which   
exists between  minds of different      
individuals4 ,and as ,dr4 ,beattie says3
 ,the force  with which anything strikes
 the mind is generally in proportion to 
the  degree of attention bestowed upon  
it4    ,,ii4 ,comparison4 ,following the
 stage of ,presentation is the stage of 

,comparison4 ,we separate our general   
concept of animal into a number of      
sub-concepts1 or concepts of various    
kinds of animals4 ,we compare the  pig  
with the goat1 the cow with the horse1  
in fact each animal with all  other     
animals known to us4 ,by this process we
 distinguish the points of  resemblance 
and the points of difference4 ,we       
perceive that the wolf  resembles the   
dog to a considerable degree2 that it   
has some points of  resemblance to the  
fox2 and a still less distinct          
resemblance to the  bear2 also that it  
differs materially from the horse1 the  
cow or the  elephant4 ,we also learn    
that there are various kinds of wolves1 
all  bearing a great resemblance to each
 other1 and yet having marked points  of
 difference4 ,the closer we observe the 
various individuals among the  wolves1  
the more points of difference do we     
find4 ,the faculty of  ,comparison      
evidences itself in inductive reasoning2
 ability and  disposition to analyze1   

classify1 compare1 etc4 ,fowler says    
that those  in whom it is largely       
developed ,reason clearly and correctly 
from  conclusions and scientific facts  
up to the laws which govern them2       
discern the known from the unknown2     
detect error by its incongruity with    
facts2 have an excellent talent for     
comparing1 explaining1 expounding1      
criticising1 exposing1 etc4 ,prof4      
,william ,james says3 ,any personal or  
practical interest in the results to be 
obtained by distinguishing1  makes one's
 wits amazingly sharp to detect         
differences4 ,and long  training and    
practice in distinguishing has the same 
effect as personal  interest4 ,both of  
these agencies give to small amounts of 
objective  difference the same          
effectiveness upon the mind that1 under 
other  circumstances1 only large ones   
would make4    ,,iii4 ,abstraction4     
,following the stage of ,comparison is  
that of  ,abstraction4 ,the term        
,abstraction as used in psychology      

means3 ,the  act or process of          
separating from the numerous qualities  
inherent in any  object1 the particular 
one which we wish to make the subject of
  observation and reflection4 ,or1 the  
act of withdrawing the consciousness    
from a number of objects with a view to 
concentrate it on some  particular one4 
,the negative act of which ,attention is
 the positive4 ,to  abstract is to      
separate or set apart4 ,in the process  
of ,abstraction  in our consideration of
 animals1 after having recognized the   
various  points of difference and       
resemblance between the various species 
and  individuals1 we proceed to consider
 some special quality of animals1  and1 
in doing so1 we abstract1 set aside1 or 
separate the particular  quality which  
we wish to consider4 ,if we wish to     
consider the size of  animals1 we       
abstract the quality of size from the   
other qualities1 and  consider animals  
with reference to size alone4 ,thus we  
consider the  various degrees of size of

 the various animals1 classifying them  
accordingly4 ,in the same way we may    
abstract the quality of shape1 color  or
 habits1 respectively1 setting aside    
this quality for special  observation   
and classification4 ,if we wish to      
study1 examine or consider  certain     
qualities in a thing we abstract that   
particular quality from  the other      
qualities of the thing2 or we abstract  
the other qualities  until nothing is   
left but the particular quality under   
consideration4 ,in  examining or        
considering a class or number of things1
 we first abstract  the qualities       
possessed in common by the class or     
number of things2  and also abstract or 
set aside the qualities not common to   
them4    ,for instance2 in considering  
classes of animals1 we abstract the     
combined quality of milk-giving and     
pouch-possessing which is possessed  in 
common by a number of animals2 then we  
group these several animals in  a class 
which we name the ,marsupialia1 of which

 the opossum and  kangaroo are members4 
,in these animals the young are brought 
forth in an  imperfect condition1       
undeveloped in size and condition1 and  
are then  kept in the pouch and         
nourished until they are able to care   
for  themselves4 ,likewise1 we may      
abstract the idea of the placenta1 the  
appendage which connects the young      
unborn animal with the mother1 and by   
means of which the foetus is nourished4 
,the animals distinguished by  this     
quality are grouped together as the     
,placental ,mammals4 ,the  ,placental   
,mammals are divided into various       
groups1 by an ,abstraction of  qualities
 or class resemblance or difference1 as 
follows3 ,the  ,edentata1 or toothless  
creatures1 such as the sloths1          
ant-eaters1  armadillos1 etc42 the      
,sirenia1 so-named from their fancied   
resemblance  to the fabled sirens1 among
 which class are the sea-cows1 manatees1
  dugongs1 etc42 the ,cetacea1 or whale 
family1 which although fish-like  in    

appearance1 are really mammals1 giving  
birth to living young which  they       
nourish with breast-milk1 among which   
are the whales1 porpoises1  dolphins1   
etc42 the ,ungulata1 or hoofed animals1 
such as the horse1  the tapir1 the      
rhinoceros1 the swine1 the hippopotamus1
 the camel1 the  deer1 the sheep1 the   
cow1 etc42 the ,hyracoidea1 having teeth
  resembling both the hoofed animals and
 the gnawing animals1 of which the      
coney or rock-rabbit is the principal   
example2 the ,proboscidea1 or  trunked  
animals1 which family is represented by 
the various families of  elephants2 the 
,carnivora1 or flesh-eaters1 represented
 by various  sub-families and species2  
the ,rodentia1 or gnawers2 the          
,insectivora1  or insect feeders2 the   
,cheiroptera1 or finger-winged2 the     
,lemuroidea1 or lemurs1 having the      
general appearance of the monkey1  but  
also the long bushy tail of the fox2 the
 ,primates1 including the  monkeys1     
baboons1 man-apes1 gibbons1 gorillas1   

chimpanzees1  orang-outangs and ,man4   
,in all of these cases you will see that
 each class or general family  possesses
 a certain common quality which gives it
 its classification1  and which quality 
is the subject of the ,abstraction in   
considering the  particular group of    
animals4 ,further and closer            
,abstraction divides  these classes into
 sub-classes2 for instance1 the family  
or class of the  ,carnivora1 or         
flesh-eaters1 may be divided by further 
,abstraction  into the classes of seals1
 bears1 weasels1 wolves1 dogs1 lions1   
tigers1  leopards1 etc4 ,in this        
process1 we must first make the more    
general  ,abstraction of the wolf and   
similar animals into the dog-family2 and
 the  lion1 tiger and similar forms into
 the cat-family4    ,halleck says of    
,abstraction3 ,in the process of        
,abstraction1 we draw our  attention    
away from a mass of confusing details1  
unimportant at the  time1 and attend    
only to qualities common to the class4  

,abstraction is  little else than       
centering the power of attention on some
 qualities to  the exclusion of others4 
,,iv4 ,generalization4 ,arising from the
 stage of ,abstraction is the stage  of 
,generalization4 ,generalization is3    
,the act or process of  generalizing or 
making general2 bringing several objects
 agreeing in  some point under a common 
or general name1 head or class2 an      
extending  from particulars to generals2
 reducing or arranging in a genus2      
bringing  a particular fact or series of
 facts into a relation with a wider     
circle  of facts4 ,as ,bolingbroke says3
 ,the mind1 therefore1 makes its utmost 
endeavors to generalize its ideas1      
beginning early with such as are  most  
familiar and coming in time to those    
which are less so4 ,under the  head of  
,abstraction we have seen that through  
,abstraction we may  ,generalize the    
various species into the various        
families1 and thus1 in  turn1 into the  
various sub-families4 ,following the    

same process we may  narrow down the    
sub-families into species composed of   
various  individuals2 or into greater   
and still greater families or groups4   
,generalization is really the act of    
,classification1 or forming into        
classes all things having certain       
qualities or properties in common4  ,the
 corollary is that all things in a      
certain generalized class must  possess 
the particular quality or property      
common to the class4 ,thus we  know that
 all animals in the class of the        
,carnivora must eat flesh2  and that all
 ,mammals possess breasts from which    
they feed their young4  ,as ,halleck    
says3 ,we put all objects having like   
qualities into a  certain genus1 or     
class4 ,when the objects are in that    
class1 we know  that certain qualities  
will have a general application to them 
all4    ,v4 ,denomination4 ,following   
closely upon the step of ,generalization
 or  ,classification1 is the step of    
,denomination4 ,by ,denomination we mean

  the act of naming or designating by a 
name4 ,a name is the symbol by  which we
 think of a familiar thing without the  
necessity for making a  distinct mental 
image upon each occasion of thought4    
,or1 it may be  considered as akin to a 
label affixed to a thing4 ,as in the    
case of  the algebraic symbols1 a1 b1 c1
 x1 and y1 by the use of which  we are  
able to make intricate calculations     
easily and rapidly1 so may we  use these
 word symbols much more readily than we 
could the lengthy  descriptions or even 
the mental images of the thing          
symbolized4 ,it is  much easier for us  
to think horse than it would be to think
 the full  definition of that animal1 or
 to think of it by recalling a mental   
picture of the horse each time we wished
 to think of it4 ,or1 it is much  better
 for us to be able to glance at a label 
on a package or bottle  than to examine 
the contents in detail4 ,as ,hobbes     
says3 ,a word taken at  pleasure to     
serve for a mark1 which may raise in our

 minds a thought  like to some thought  
we had before1 and which being          
pronounced to  others1 may be to them a 
sign of what thought the speaker had or 
had  not1 before in his mind4 ,mill     
says3 ,a name is a word 7or set of      
words7 serving the double purpose of a  
mark to recall to ourselves the         
likeness of a former thought and as a   
sign to make it known to others4  ,some 
philosophers regard names as symbols of 
our ideas of things1  rather than of the
 things themselves2 others regard them  
as symbols of  the things themselves4   
,it will be seen that the value of a    
name depends  materially upon the       
correct meaning and understanding       
regarding it  possessed by the person   
using it4          ,,chapter ,,iv4      
,,the ,,use ,,of ,,concepts      ,having
 observed the several steps or stages of
 a concept1 let us now  consider the use
 and misuse of the latter4 ,at first    
glance it would  appear difficult to    
misuse a concept1 but a little          

consideration will  show that people    
very commonly fall into error regarding 
their concepts4    ,for instance1 a     
child perceives a horse1 a cow or a     
sheep and hears its  elders apply the   
term animal to it4 ,this term is        
perfectly correct1  although symbolizing
 only a very general classification or  
generalization4 ,but1 the child knowing 
nothing of the more limited and         
detailed classification begins to       
generalize regarding the animal4 ,to    
it1 accordingly1 an animal is identical 
with the dog or the cow1 the  sheep or  
the horse1 as the case may be1 and when 
the term is used the  child thinks that 
all animals are similar to the          
particular animal  seen4 ,later on1 when
 it hears the term animal applied to a  
totally  different looking creature1 it 
thinks that a mistake has been made and 
a state of confusion occurs4 ,or1 even  
when a term is applied within  narrower 
limits1 the same trouble occurs4 ,the   
child may hear the term  dog applied to 

a mastiff1 and it accordingly forms a   
concept of dog  identical with the      
qualities and attributes of the mastiff4
 ,later1  hearing the same term applied 
to a toy-terrier1 it becomes indignant  
and  cries out that the latter is no dog
 but is something entirely  different4  
,it is not until the child becomes      
acquainted with the fact  that there are
 many kinds of creatures in the general 
category of dog  that the latter term   
becomes fully understood and its        
appropriate  concept is intelligently   
formed4 ,thus we see the importance of  
the step  of ,presentation4    ,in the  
same way the child might imagine that   
because some particular  man had red    
hair and long whiskers1 all men were    
red-haired and  long-whiskered4 ,such a 
child would always form the concept of  
man as a  creature possessed of the     
personal qualities just mentioned4 ,as a
 writer  once said1 readers of current  
,french literature might imagine that   
all  ,englishmen were short1 dumpy1     

red-cheeked and irascible1 and that all 
,englishwomen had great teeth and       
enormous feet2 also that readers of     
,english literature might imagine that  
all ,frenchmen were like monkeys1  and  
all ,frenchwomen were sad coquettes4 ,in
 the same way many ,american  young     
people believe that all ,englishmen say 
,don't you know and all  ,englishwomen  
constantly ejaculate3 ,fancy6 ,also that
 every ,englishman  wears a monocle4 ,in
 the same way1 the young ,english       
person1 from reading  the cheap novels  
of his own country1 might well form the 
concept of all  ,americans as           
long-legged1 chin-whiskered and         
big-nosed1 saying ,waal1 ,i  want to    
know2 ,i reckon2 and ,du tell2 while    
they tilted themselves  back in a chair 
with their feet on the mantelpiece4 ,the
 concept of a  ,western man1 entertained
 by the average ,eastern person who has 
never  traveled further ,west than      
,buffalo1 is equally amusing4 ,in the   
same way1  we have known ,western people

 who formed a concept of ,boston people 
as  partaking of a steady and continuous
 diet of baked beans and studiously     
reading ,browning and ,emerson between  
these meals4    ,halleck says3 ,a       
certain ,norwegian child ten years old  
had the quality  white firmly imbedded  
in his concept man4 ,happening one day  
to see a  negro for the first time1 the 
child refused to call him a man until   
the  negro's other qualities compelled  
the child to revise his concept and to  
eliminate whiteness4 ,if that child     
should ever see an ,indian or a         
,chinaman1 the concept would undergo    
still further revision4 ,a girl of  six1
 reared with an intemperate father and  
brothers1 had the quality of            
drunkenness firmly fixed in her concept 
of man4 ,a certain boy kept1  until the 
age of eleven1 trustworthiness in his   
concept of man4  ,another boy1 until    
late in his teens thought that man was a
 creature who  did wrong not from       
determination but from ignorance1 that  

any man would  change his course to the 
right path if he could but understand   
that he  was going wrong4 ,happening one
 day to hear of a wealthy man who was   
neglecting to provide comforts for his  
aged mother in her last sickness1  the  
boy concluded that the man did not know 
his mother's condition4 ,when  he       
informed the man1 the boy was told to   
mind his own business4 ,the same  day he
 heard of some politicians who had      
intentionally cheated the city  in      
letting a contract and he immediately   
revised his concept4 ,it must be  borne 
in mind that most of our concepts are   
subject to change during our  entire    
life2 that at first they are made only  
in a tentative way2 that  experience may
 show us1 at any time1 that they have   
been erroneously  formed1 that we have1 
abstracted too little or too much1 made 
this class  too wide or too narrow1 or  
that here a quality must be added or    
there  one taken away4    ,let us now   
consider the mental processes involved  

in the formation and  use of a concept4 
,we have first1 as we have seen1 the    
presentation of  the crude material from
 which the concept must be formed4 ,our 
attention  being attracted to or        
directed toward an object1 we notice its
 qualities  and properties4 ,then we    
begin a process of comparison of the    
object  perceived or of our perception  
of it4 ,we compare the object with other
  objects or ideas in our mind1 noting  
similarities and differences and        
thereby leading towards classification  
with similar objects and opposed        
dissimilar ones4 ,the greater the range 
of other objects previously  perceived1 
the greater will be the number of       
relations established  between the new  
object or idea and others4 ,as we       
advance in experience  and knowledge1   
the web of related objects and ideas    
becomes more  intricate and complex4    
,the relations attaching to the child's 
concept of  horse is very much simpler  
than the concept of the experienced     

adult4  ,then we pass on to the step of 
analysis1 in which we separate the      
qualities of the object and consider    
them in detail4 ,the act of  abstraction
 is an analytical process4 ,then we pass
 on to the step of  synthesis1 in which 
we unite the materials gathered by      
comparison and  analysis1 and thus form 
a general idea or concept regarding the 
object4  ,in this process we combine the
 various qualities discerned by         
comparison  and analysis1 and grouping  
them together as in a bundle1 we tie    
them  together with the string of       
synthesis and thus have a true general  
conception4 ,thus from the first general
 conception of horse as a  simple thing1
 we notice first that the animal has    
certain qualities  lacking in other     
things and certain others similar to    
other things2 then  we analyze the      
various qualities of the horse1         
recognized through  comparison1 until we
 have a clear and distinct idea of the  
various  parts1 qualities and properties

 of the horse2 then we synthesize1 and  
joining together these various          
conceptions of the said qualities1 we at
  last form a clear general concept of  
the horse as he is1 with all his        
qualities4 ,of course1 if we later      
discover other qualities attached to    
the horse1 we add these to our general  
synthesized concept--our concept  of    
horse is enlarged4    ,of course these  
various steps in the formation and use  
of a concept are  not realized as       
distinct acts in the consciousness1 for 
the processes  are largely instinctive  
and subconscious1 particularly in the   
case of  the experienced individual4    
,the subconscious1 or habit mind1       
usually  attends to these details for   
us1 except in instances in which we     
deliberately apply the will to the task1
 as in cases of close study1 in  which  
we take the process from the region of  
the involuntary and place  it in the    
voluntary category4 ,so closely related 
and blended are these  various steps of 

the process1 that some authorities have 
disputed  vigorously upon the question  
as to which of the two steps1 comparison
  or analysis1 precedes the other4 ,some
 have claimed that analysis must        
precede comparison1 else how could one  
compare without having first  analyzed  
the things to be compared4 ,others hold 
that comparison must  precede analysis1 
else how could one note a quality unless
 he had his  attention drawn to it by   
its resemblance to or difference from   
qualities  in other objects4 ,the truth 
seems to lie between the two ideas1 for 
in  some cases there seems to be a      
perception of some similarity or        
difference before any analysis or       
abstraction takes place2 while in       
others there seems to be an analysis or 
abstraction before comparison is        
possible4 ,in this book we have followed
 the arrangement favored by the  latest 
authorities1 but the question is still  
an open one to many minds4    ,as we    
have seen1 the general concept once     

having been formed1 the mind  proceeds  
to classify the concept with others     
having general qualities in  common4    
,and1 likewise1 it proceeds to          
generalize from the  classification1    
assuming certain qualities in certain   
classes4 ,then we  proceed to make still
 further generalizations and            
classifications on an  ascending and    
widening scale1 including seeming       
resemblances less  marked1 until finally
 we embrace the object with other       
objects in as  large a class as possible
 as well as in as close and limited a   
sub-class  as possible4 ,as ,brooks     
says3 ,generalization is an ascending   
process4  ,the broader concept is       
regarded as higher than the narrower    
concept2 a  concept is considered higher
 than a percept2 a general idea stands  
above  a particular idea4 ,we thus go up
 from particulars to generals2 from     
percepts to concepts2 from lower        
concepts to higher concepts4 ,beginning 
down with particular objects1 we rise   

from them to the general idea of  their 
class4 ,having formed a number of lower 
classes1 we compare them as  we did     
individuals and generalize them into    
higher classes4 ,we perform  the same   
process with these higher classes1 and  
thus proceed until we  are at last      
arrested in the highest class1 ,being4  
,having reached the  pinnacle of        
generalization1 we may descend the      
ladder by reversing the  process through
 which we ascend4    ,from this process 
of generalization1 or synthesis1 we     
create from our  simple concepts our    
general concepts4 ,some of the older    
authorities  distinguished between these
 two classes by terming the former      
conceptions1 and reserving the term     
concepts for the general  concepts4     
,brooks says of this3 ,the products of  
generalization are  general ideas called
 concepts4 ,we have already discussed   
the method of  forming conceptions and  
now consider the nature of the concept  
itself4444 ,a concept is a general idea4

 ,it is a general notion which has  in  
it all that is common to its own class4 
,it is a general scheme which  embraces 
all the individuals of the class while  
it resembles in all  respects none of   
its class4 ,thus my conception of a     
quadruped has in  it all four-footed    
animals1 but it does not correspond in  
all respects  to any particular animals2
 my conception of a triangle embraces   
all  triangles1 but does not agree in   
details with any particular triangle4   
,the general conception cannot be made  
to fit exactly any particular  object1  
but it teems with many particulars4     
,these points may be  illustrated with  
the concepts horse1 bird1 color1 animal1
 etc4    ,so we may begin to perceive   
the distinction and difference between a
  concept and a mental image4 ,this     
distinction1 and the fact that a        
concept cannot be imaged1 is generally  
difficult for the beginner4 ,it  is     
important that one should have a clear  
and distinct understanding  regarding   

this point1 and so we shall consider it 
further in the  following chapter4      
,,chapter ,v4    ,,concepts ,,and       
,,images      ,as we have said1 a       
concept cannot be imaged--cannot be used
 as the  subject of a mental image4     
,this statement is perplexing to the    
student  who has been accustomed to the 
idea that every conception of the mind  
is  capable of being reproduced in the  
form of a mental image4 ,but the        
apparently paradoxical statement is seen
 as quite simple when a little          
consideration is given to it4    ,for   
instance1 you have a distinct general   
concept of animal4 ,you know  what you  
mean when you say or think1 animal4 ,you
 recognize an animal  when you see one  
and you understand what is meant when   
another uses the  word in conversation4 
,but you cannot form a mental image of  
the concept1  animal4 ,why8 ,because any
 mental image you might form would be   
either a  picture of some particular    
animal or else a composite of the       

qualities  of several animals4 ,your    
concept is too broad and general to     
allow of a  composite picture of all    
animals4 ,and1 in truth1 your concept is
 not  a picture of anything that        
actually exists in one particular1 but  
an  abstract idea embracing the         
qualities of all animals4 ,it is like   
the  algebraic x--a symbol for something
 that exists1 but not the thing  itself4
    ,as ,brooks says3 ,a concept cannot 
be represented by a concrete image4     
,this is evident from its being general 
rather than particular4 ,if its  color1 
size or shape is fixed by an image1 it  
is no longer general but  particular4   
,and ,halleck says3 ,it is impossible to
 image anything  without giving that    
image individual marks4 ,the best mental
 images are  so definite that a picture 
could be painted from them4 ,a being    
might  come under the class man and have
 a snub nose1 blonde hair1 scanty       
eyebrows1 and no scar on his face4 ,the 
presence of one of these  individual    

peculiarities in the concept man would  
destroy it4 ,if we  form an image of an 
apple1 it must be either of a yellow1   
red1 green1 or  russet apple1 either as 
large as a pippin or as small as a      
crab-apple4 ,a  boy was asked what he   
thought of when 'apple' was mentioned4  
,he  replied that he thought of 'a big1 
dark-red1 apple with a bad spot on  one 
side1 near the top4' ,that boy could    
image distinctly1 but his power  of     
forming concepts was still in its       
infancy4    ,so we see that while a     
mental image must picture the particular
 and  individual qualities1 properties  
and appearances of some particular unit 
of a class1 a concept can and must      
contain only the class  qualities--that 
is1 the qualities belonging to the      
entire class4 ,the  general concept is  
as has been said a general idea 444 a   
general notion  which has in it all that
 is common to its own class4 ,and it    
follows  that a general idea of this    
kind cannot be pictured4 ,a picture must

 be  of some particular thing1 while a  
concept is something above and higher   
than particular things4 ,we may picture 
a man1 but we cannot picture  ,man the  
concept of the race4 ,a concept is not a
 reproduction of the  image of a thing1 
but on the contrary is an idea of a     
class of  things4 ,we trust that the    
student will consider this point until  
he  arrives at a clear understanding of 
the distinction1 and the reason         
thereof4    ,but1 while a concept is    
incapable of being pictured mentally as 
an  image1 it is true that some         
particular representative of a class may
  be held in the mind or imagination as 
an idealized object1 as a  general      
representative of the class1 when we    
speak or think of the  general term or  
concept1 providing that its real        
relation to the concept  is recognized4 
,these idealized objects1 however1 are  
not concepts--they  are percepts        
reproduced by the memory4 ,it is        
important1 however1 to  all who wish to 

convey their thought plainly1 that they 
be able to  convert their concepts into 
idealized representative objects4       
,otherwise1  they tend to become too    
idealistic and abstract for common      
comprehension4 ,as ,halleck well says3  
,we should in all cases be ready to     
translate our concepts1 when occasion   
requires1 into the images of those      
individuals which the concept           
represents4 ,a concept means nothing    
except  in reference to certain         
individuals4 ,without them it could     
never have  had existence and they are  
entitled to representation4 ,a man who  
cannot  translate his concepts into     
definite images of the proper objects1  
is  fitted neither to teach1 preach1 nor
 practice any profession4444 ,there     
was1 not long ago1 a man very fond of   
talking about fruit in the  abstract2   
but he failed to recognize an individual
 cranberry when it  was placed before   
him4 ,a humorist remarked that a certain
 metaphysician  had such a love for     

abstractions1 and such an intense       
dislike for  concrete things1 as to     
refuse to eat a concrete peach when     
placed before  him4    ,in the beginning
 many students are perplexed regarding  
the difference  between a percept and a 
concept4 ,the distinction is simple when
  properly considered4 ,a percept is3   
the object of an act of perception2     
that which is perceived4 ,a concept is3 
a mental representation4  ,brooks makes 
the following distinction3 ,a percept is
 the mental  product of a real thing2 a 
concept is a mere idea or notion of the 
common attributes of things4 ,a percept 
represents some particular  object2 a   
concept is not particular1 but general4 
,a percept can be  described by         
particulars2 a concept can be described 
only by generals4  ,the former can      
usually be represented by an image1 the 
latter cannot be  imagined1 it can only 
be thought4 ,thus one is able to image  
the  percept of a particular horse which
 has been perceived2 but he is  unable  

to image correctly the concept of horse 
as a class or generic  term4    ,in     
connection with this distinction between
 perception and  conception1 we may as  
well consider the subject of            
apperception1 a  term favored by many   
modern psychologists1 although others   
steadfastly  decline to recognize its   
necessity or meaning and refuse to      
employ it4  ,apperception may be defined
 as3 perception accompanied by          
comprehension2 perception accompanied by
 recognition4 ,the thing  perceived is  
held to be comprehended or              
recognized--that is1 perceived  in a new
 sense1 by reason of certain previously 
acquired ideas in the  mind4 ,halleck   
explains it as3 the perception of things
 in relation to  the ideas which we     
already possess4 ,it follows that all   
individuals  possessed of equally active
 organs of perception1 and equally      
active  attention1 will perceive the    
same thing in the same way and in the   
same  degree4 ,but the apperception of  

each individual will differ and vary    
according to his previous experience and
 training1 temperament and  taste1 habit
 and custom4 ,for instance1 the familiar
 story of the boy who  climbed a tree   
and watched the passers-by1 noting their
 comments4 ,the  first passer-by        
noticing the tree1 says aloud3 ,that    
would make a good  stick of timber4     
,good morning1 ,mr4 ,carpenter1 said the
 boy4 ,the next  man said3 ,that tree   
has fine bark4 ,good morning1 ,mr4      
,tanner1 said  the boy4 ,another said1  
,i bet there's a squirrel's nest up in  
that  tree4 ,good morning1 ,mr4 ,hunter1
 said the boy4    ,the woman sees in a  
bird something pretty and cunning4 ,the 
hunter sees  in it something to kill4   
,the ornithologist sees it as something 
of a  certain genus and species1 and    
perhaps also as something appropriate   
for  his collection4 ,the farmer        
perceives it to be something destructive
 of  either insects or crops4 ,a thief  
sees a jail as something to be dreaded2 

an ordinary citizen1 something useful   
for confining objectionable  people2 a  
policeman1 something in the line of his 
business4 ,and so on1  the apperception 
differing upon the previous experience  
of the  individual4 ,in the same way the
 scientist sees in an animal or rock    
many  qualities of which the ordinary   
person is ignorant4 ,our training1      
experience1 prejudices1 etc41 affect our
 apperception4    ,and so1 we see that  
in a measure our concepts are determined
 not only  by our simple perceptions1   
but also materially by our              
apperceptions4 ,we  conceive things not 
only as they are apparent to our senses1
 but also as  colored and influenced by 
our previous impressions and ideas4 ,for
 this  reason we find widely varying    
concepts of the same things among       
different individuals4 ,only an absolute
 mind could form an absolute  concept4  
,,chapter ,,vi4    ,,terms      ,in     
logic the words concept and term are    
practically identical1 but  in the      

popular usage of the terms there is a   
distinct difference4 ,this  difference  
is warranted1 if we depart from the     
theoretical phase of  logic1 for the    
word concept really denotes an idea in  
the mind1  while the word term really   
denotes a word or name of an idea or    
concept--the symbol of the latter4 ,in a
 previous chapter we have seen  that    
,denomination1 or the act of naming or  
designating by a name is  the final step
 or stage in forming a concept4 ,and it 
is a fact that the  majority of the     
words in the languages of civilized     
people denote  general ideas or         
concepts4 ,as ,brooks says3 ,to give    
each individual or  particular idea a   
name peculiar to itself would be        
impracticable and  indeed impossible2   
the mind would soon become overwhelmed  
with its  burden of names4 ,nearly all  
the ordinary words of our language are  
general rather than particular4 ,the    
individuals distinguished by  particular
 names1 excepting persons and places1   

are comparatively few4  ,most objects   
are named only by common nouns2 nearly  
all of our verbs  express general       
actions2 our adjectives denote common   
qualities1 and our  adverbs designate   
classes of actions and qualities4 ,there
 are very few  words in the language1   
besides the names of persons and places1
 that do  not express general ideas4    
,in logic the word term is employed to  
denote any word or words which          
constitute a concept4 ,the word concept 
is employed strictly in the  sense of a 
subject of thought1 without reference to
 the words  symbolizing it4 ,the        
concept1 or subject of thought1 is the  
important  element or fact and the term 
denoting it is merely a convenient      
symbol  of expression4 ,it must be      
remembered that a term does not         
necessarily  consists of but a single   
word1 for often many words are employed 
to  denote the concept1 sometimes even  
an entire clause or phrase being  found 
necessary for the current term4 ,for the

 purpose of the  consideration of the   
subjects to be treated upon in this     
book1 we may  agree that3 ,a term is the
 outward symbol of a concept2 and that3 
,the  concept is the idea expressed by  
the term4    ,there are three general   
parts or phases of ,deductive ,logic1   
namely3  ,terms1 ,propositions and      
,syllogisms4 ,therefore1 in considering 
,terms we  are entering into a          
consideration of the first phase of     
,deductive ,logic4  ,unless we have a   
correct understanding of ,terms1 we     
cannot expect to  understand the        
succeeding stages of ,deductive         
,reasoning4 ,as ,jevons says3  ,when we 
join terms together we make a           
,proposition2 when we join              
,propositions together1 we make an      
argument or piece of reasoning4444 ,we  
should generally get nothing but        
nonsense if we were to put together any 
terms and any propositions and to       
suppose that we were reasoning4 ,to     
produce a good argument we must be      

careful to obey certain rules1 which  it
 is the purpose of ,logic to make known4
 ,but1 in order to understand  the      
matter perfectly1 we ought first to     
learn exactly what a term is1  and how  
many kinds of terms there may be2 we    
have next to learn the  nature of a     
proposition and the different kinds of  
propositions4  ,afterwards we shall     
learn how one proposition may by        
reasoning be drawn  from other          
propositions in the kind of argument    
called the syllogism4    ,now1 having   
seen that terms are the outward symbols 
or expression of  concepts1 and are the 
names of things which we join together  
in a  proposition1 let us proceed to    
consider the different kinds of terms1  
following the classifications adopted by
 the authorities4    ,a term may contain
 any number of nouns1 substantive or    
adjective or it  may contain but a      
single noun4 ,thus in1 ,tigers are      
ferocious1 the  first term is the single
 substantive tigers2 the second term is 

the  single adjective ferocious4 ,and in
 the proposition1 ,the ,king of         
,england is the ,emperor of ,india1     
there are two terms1 each composed of   
two nouns1 ,king of ,england being the  
first term and ,emperor of ,india  being
 the second term4 ,the proposition1 ,the
 library of the ,british  ,museum is the
 greatest collection of books in the    
world1 contains  fifteen words but only 
two terms2 the first term being ,the    
library of  the ,british ,museum1 in    
which are two substantives1 one         
adjective1 two  definite articles and   
one preposition2 the second term being1 
the  greatest collection of books in the
 world1 which contains three            
substantives1 one adjective1 two        
articles1 and two prepositions4 ,the    
above illustration is supplied by       
,jevons1 who adds3 ,a logical term1     
then1 may consist of any number of      
nouns1 substantive or adjective1 with   
the articles1 prepositions and          
conjunctions required to join them      

together2 still it is only one term if  
it points out1 or makes us think  of a  
single object1 or collection1 or class  
of objects4 7,a  substantive1 is3 the   
part of speech which expresses something
 that  exists1 either material or       
immaterial47    ,the first              
classification of terms divides them    
into two general classes1  viz41 7#a7   
,singular ,terms2 and 7#b7 ,general     
,terms4    ,a ,singular ,term is a term 
denoting a single object1 person or     
thing4  ,although denoting only a single
 object1 person or thing1 it may be     
composed of several words2 or it may be 
composed of but one word as in  the case
 of a proper name1 etc4 ,the following  
are ,singular ,terms1  because they are 
terms denoting but a single object1     
person or thing3  ,europe2 ,minnesota2  
,socrates2 ,shakespeare2 the first man2 
the highest  good2 the first cause2 the 
,king of ,england2 the ,british ,museum2
 the  ,commissioner of ,public ,works2  
the main street of the ,city of ,new    

,york4  ,it will be noted that in all of
 the examples given1 the ,singular ,term
  denotes a particular something1 a     
specific thing1 a something of which    
there is but one1 and that one possesses
 particularity and  individuality4 ,as  
,hyslop says3 ,oneness of kind is not   
the only or  distinctive feature of     
,singular ,terms1 but individuality1 or 
singularity1 as representing a concrete 
individual whole4    ,a ,general ,term  
is a term which applies1 in the same    
sense1 to each and  every individual    
object1 person or thing in a number of  
objects1 persons  or things of the same 
kind1 or to the entire class composed of
 such  objects persons or things of the 
same kind4 ,for instance1 horse2 man2   
biped2 mammal2 trees2 figures2 grain of 
sand2 matter1 etc4 ,hyslop says1        
regarding ,general ,terms3 ,in these    
instances the terms denote more than    
one object1 and apply to all of the same
 kind4 ,their meaning is  important in  
the interpretation of what are called   

universal  propositions4    ,another    
general classification of ,terms divides
 them into two  respective classes1 as  
follows3 7#a7 ,collective ,terms2 and   
7#b7  ,distributive ,terms4 ,hyslop says
 of this classification3 ,this division 
is based upon the distinction between   
aggregate wholes of the same kind  and  
class terms4 ,it partly coincides with  
the division into ,singular and         
,general ,terms1 the latter always being
 distributive4    ,a ,collective ,term  
is one which denotes an aggregate or    
collected whole  of objects1 persons or 
things of the same or similar kind1     
which  collective whole is considered as
 an individual1 although composed of a  
totality of separate individual objects1
 persons or things4 ,thus the  following
 terms3 regiment2 congregation2 army2   
family2 crowd2 nation2  company2        
battalion2 class2 congress2 parliament2 
convention2 etc4 are  ,collective       
,terms1 because they denote collective1 
aggregate or composite  wholes1         

considered as an individual4    ,a      
,distributive ,term is a term which     
denotes each and every individual       
object1 person or thing in a given      
class4 ,for example1 are the terms3     
man2 quadruped2 biped2 mammal2 book2    
diamond2 tree4 ,as ,hyslop says3        
,general terms are always distributive4 
,also3 ,it is important also to  keep   
clear the distinction between class     
wholes and collective  wholes4444 ,they 
are often confused so as to call a term 
denoting a  class a ,collective ,term4  
,another general classification of      
,terms divides them into the following  
two respective classes2 7#a7 ,concrete  
,terms2 and 7#b7 ,abstract ,terms4    ,a
 ,concrete ,term is a term denoting     
either a definite object1 person or     
thing which is subject to perception and
 experience1 and may be  considered as  
actually existent concretely1 as for    
instance3 horse2 man2  mountain2 dollar2
 knife2 table2 etc41 or else an         
attribute thought of  and used solely as

 an attribute1 as for instance3         
beautiful1 wise1  noble1 virtuous1 good1
 etc4    ,an ,abstract ,term is a term  
denoting the attribute1 quality or      
property  considered as apart from the  
object1 person or thing and as having an
  abstract existence1 as for instance3  
beauty2 wisdom2 nobility2  goodness2    
virtue1 etc4 ,as we have seen elsewhere1
 these qualities have  no real existence
 in themselves1 but are known and       
thought of only in  connection with     
concrete objects1 persons and things4   
,thus we cannot  know ,beauty1 but may  
know beautiful things2 we cannot know   
,virtue1  but we may know virtuous      
people1 etc4    ,an attribute or quality
 is concrete when expressed as an       
adjective2 and abstract when expressed  
as a noun2 as for instance1  beautiful  
and beauty1 respectively1 or virtuous   
and virtue1  respectively4 ,the         
distinction may be summed up as follows3
 ,a ,concrete  ,term is the name of a   
thing or of a quality of a thing        

expressed as an  adjective and as merely
 a quality2 while an ,abstract ,term is 
the name  of a quality of a thing1      
expressed as a noun and as a thing in   
itself4    ,certain terms may be used as
 either ,concrete ,terms or as ,abstract
 ,terms1  and certain authorities have  
seen fit to classify them as ,mixed     
,terms1  as for instance the terms3     
government2 religion2 philosophy2 etc4  
,another general classification of      
,terms divides them into two respective 
classes as follows3 7#a7 ,positive      
,terms2 and 7#b7 ,negative ,terms4    ,a
 ,positive ,term is a term which denotes
 its own qualities1 as for  instance3   
good1 human1 large1 square1 black1      
strong1 etc4 ,these terms  indicate the 
presence of the quality denoted by the  
term itself4    ,a ,negative ,term is a 
term denoting the absence of a quality1 
as for  instance3 inhuman1 inorganic1   
unwell1 unpleasant1 non-conducive1 etc4 
,these terms deny the presence of       
certain qualities1 rather than          

asserting the presence of an opposite   
quality4 ,they are essentially  negative
 in nature and in form4 ,jevons says3   
,we may usually know a  ,negative ,term 
by its beginning with one of the little 
syllables un-1  in-1 a-1 an-1 non-1 or  
by its ending with -less4 ,hyslop says3 
,the  usual symbols of ,negative ,terms 
are in1 un1 less1 dis1 a1 or  an1 anti1 
mis1 and sometimes de1 and non and not4 
,jevons  adds3 ,if the ,english language
 were a perfect one1 every term ought to
  have a ,negative ,term exactly        
corresponding to it1 so that all        
adjectives  and nouns would be in pairs4
 ,just as convenient has its negative   
inconvenient2 metallic1 non-metallic2   
logical1 illogical2 and so on2  so blue 
should have its negative1 non-blue2     
literary1 non-literary2  paper1         
non-paper4 ,but many of these ,negative 
,terms would be seldom or  never used1  
and if we happen to want them1 we can   
make them for the  occasion by putting  
not-1 or non-1 before the ,positive     

,term4  ,accordingly1 we find in the    
dictionary only those ,negative ,terms  
which  are much employed4    ,the last  
named authority also says3 ,sometimes   
the same word may seem to  have two or  
even more distinct negatives4 ,there is 
much difference  between undressed and  
not-dressed1 that is 'not in evening    
dress4'  ,both seem to be negatives of  
'dressed1' but this is because the word 
has  two distinct meanings4    ,some    
authorities insist upon closer and      
further classification1 as for          
instance1 in the case of what they call 
a ,privative ,term1 denoting the        
absence of qualities once possessed by  
the object1 person or thing1 as3  deaf1 
dead1 blind1 dark1 etc4 ,hyslop says    
that these terms are  ,positive in form 
and ,negative in matter or meaning4     
,also in the case of  what they call a  
,nego-positive ,term1 denoting the      
presence of a  positive quality         
expressed in a negative manner1 as3     
disagreeable1  inhuman1 invaluable1 etc4

 ,these last mentioned classes however  
are  regarded by some as the result of  
carrying too far the tendency  toward   
classification1 and the two general     
classes1 ,positive and  ,negative1 are  
thought sufficient for the purpose of   
the general student4  ,the same         
objection applies to a classification   
occasionally made i4e41  that which is  
called an ,infinitated ,term1 denoting a
 term the intent  of which is to place  
in a distinct category every object1    
person or  thing other than that        
expressed in the corresponding ,positive
 ,term4 ,the  intent of the term is to  
place the positive idea in one class1   
and all  else into a separate one4      
,examples of this class of terms are    
found in3  not-,i1 not-animal1 not-tree1
 unmoral1 etc4 ,hyslop says of these    
terms3  ,they are not always1 if ever1  
recognized as rhetorically elegant1 but 
are valuable often to make clear the    
really negative1 or infinitatively      
negative nature of the idea in mind4    

,another general classification of      
,terms divides them into two respective 
classes1 as follows3 7#a7 ,absolute     
,terms2 and 7#b7 ,relative ,terms4      
,an ,absolute ,term is a term denoting  
the presence of qualities  intrinsic to 
the object1 and not depending upon any  
relation to any  other object1 as for   
instance3 man2 book2 horse2 gun2 etc4   
,these  terms may be related to many    
other terms1 but are not necessarily    
related to any other4    ,a ,relative   
,term is a term denoting certain        
necessary relations to  other terms1 as 
for instance3 father2 son2 mother2      
daughter2 teacher2  pupil2 master2      
servant2 etc4 ,thus it is impossible to 
think of child  except in relation to   
parent1 or vice versa4 ,the one term    
implies  the existence of its related   
term4    ,hyslop says of the above      
classification3 ,relative ,terms suggest
 the  thought of other individuals with 
the relation involved as a part of the  
term's meaning1 while ,absolute ,terms  

suggest only the qualities in the       
subject without a relation to others    
being necessarily involved4    ,some    
authorities also classify terms as      
higher and lower2 also as  broad and    
narrow4 ,this classification is meant to
 indicate the content  and extent of the
 term4 ,for instance1 when we classify1 
we begin with  the individuals which we 
then group into a small class4 ,these   
classes we  then group into a larger    
class1 according to their resemblances4 
,these  larger classes then go to form a
 part of still larger classes1 and so   
on4 ,as these classes advance they form 
broader terms2 and as we  retreat from  
the general class into the less general 
and more  particular1 the term becomes  
narrower4 ,by some1 the broader term    
which includes the narrower is called   
the higher term1 and the  narrower are  
called the lower terms4 ,thus animal    
would be a higher  and broader term than
 dog1 cat or tiger because it includes  
the latter4  ,brooks says3 ,since a     

concept is formed by the union of the   
common  attributes of individuals1 it   
thus embraces both attributes and       
individuals4 ,the attributes of a       
concept constitute what is called its   
content2 the individuals it embraces    
constitute its extent4    ,accordingly1 
the feature of including objects in a   
concept or term is  called its          
extension2 while the feature of         
including attributes or  qualities is   
called its intension4 ,it follows as a  
natural consequence  that the greater   
the extension of a term1 the less its   
intension2  the greater its intension1  
the less its extension4 ,we will        
understand this more clearly when we    
consider that the more individuals      
contained in a term1 the fewer common   
properties or qualities it can  contain2
 and the more common properties1 the    
fewer individuals4 ,as  ,brooks says3   
,the concept man has more extension than
 poet1  orator or statesman1 since it   
embraces more individuals2 and less     

intension1 since we must lay aside the  
distinctive attributes of poet1  orator 
and statesman in order to unite them in 
a common class man4 ,in  the same way   
the general term animal is quite        
extended for it includes  a large number
 of individual varieties of very        
different and varied  characteristics   
and qualities2 as for instance1 the     
lion1 camel1 dog1  oyster1 elephant1    
snail1 worm1 snake1 etc4 ,accordingly   
its intension  must be small for it can 
include only the qualities common to all
  animals1 which are very few indeed4   
,the definition of the term shows how   
small is its intension1 as3 ,animal4 ,an
 organic being1 rising above  a         
vegetable in various respects1          
especially in possessing sensibility1   
will and the power of voluntary motion4 
,another narrows the intension  still   
further when he defines animal as3 a    
creature which possesses1  or has       
possessed1 life4 ,halleck says3 ,animal 
is very narrow in  intension1 very broad

 in extension4 ,there are few qualities 
common to  all animals1 but there is a  
vast number of animals4 ,to give the    
full  meaning of the term in extension1 
we should have to name every animal1    
from the microscopic infusoria to the   
tiger1 from the angleworm to the  whale4
 ,when we decrease the extension to one 
species of animal1 horse1  the          
individuals are fewer1 the qualities    
more numerous4    ,the importance of    
forming clear and distinct concepts and 
of grouping1  classifying and           
generalizing these into larger and      
broader concepts and  terms is          
recognized by all authorities and is    
generally regarded as  forming the real 
basis of all constructive thought4 ,as  
,brooks says3  ,generalization lies at  
the basis of language3 only as man can  
form  general conceptions is it possible
 for him to form a language4444 ,nearly 
all the ordinary words in our language  
are general rather than  particular4444 
,this power of generalization lies also 

at the basis of  science4 ,had we no    
power of forming general ideas1 each    
particular  object would be a study by  
itself1 and we should thus never pass   
beyond  the very alphabet of knowledge4 
,judgments1 except in the simplest form1
  would be impossible2 and it is        
difficult to see how even the simplest  
form of the syllogism could be          
constructed4 ,no general conclusion     
could  be drawn from particulars1 nor   
particular conclusions from generals2   
and  thus neither inductive nor         
deductive reasoning would be possible4  
,the  classifications of science could  
not be made2 and knowledge would end at 
the very threshold of science4          
,,chapter ,,vii4    ,,the ,,meaning ,,of
 ,,terms      ,every term has its       
meaning1 or content1 as some authorities
 prefer  to call it4 ,the word or words 
of which the term is composed are merely
  vocal sounds1 serving as a symbol for 
the real meaning of the term1  which    
meaning exists only in the mind of the  

person understanding it4  ,to one not   
understanding the meaning of the term1  
the latter is but as a  meaningless     
sound1 but to one understanding it the  
sound awakens mental  associations and  
representation and thus serves its      
purpose as a symbol  of thought4        
,each concrete general term has two     
meanings1 7#a7 the actual concrete      
thing1 person or object to which the    
term is applied2 and 7#b7 the           
qualities1 attributes or properties of  
those objects1 persons or things  in    
consequence of which the term is        
applied4 ,for instance1 in the case  of 
the concrete term book1 the first       
meaning consists of the general  idea of
 the thing which we think of as a book1 
and the second meaning  consists of the 
various qualities which go to make that 
thing a book1 as  the printed pages1 the
 binding1 the form1 the cover1 etc4 ,not
 only is  that particular thing a book1 
but every other thing having the same or
  similar properties also must be a     

book4 ,and so1 whenever ,i call a  thing
 a book it must possess the said        
qualities4 ,and1 whenever ,i  combine   
the ideas of these qualities in thought1
 ,i must think of a  book4 ,as ,jevons  
says3 ,in reality1 every ordinary       
general term has a  double meaning3 it  
means the things to which it is applied1
 444 it also  means1 in a totally       
different way1 the qualities and        
peculiarities  implied as being in the  
things4 ,logicians say that the number  
of  things to which a term applies is   
the extension of the term2 while the    
number of qualities or peculiarities    
implied is the intension4    ,the       
extension and intension of terms has    
been referred to in the  previous       
chapter4 ,the general classification of 
the degrees of  extension of a general  
term is expressed by the two terms1     
,genus and  ,species1 respectively4 ,the
 classification of the character of the 
intension of a term is expressed by the 
term1 ,difference1  ,property and       

,accident1 respectively4    ,genus is a 
term indicating3 a class of objects     
containing several  species2 a class    
more extensive than a species2 a        
universal which is  predicable of       
several things of different species4    
,species is a term denoting3 a smaller  
class of objects than a genus1  and of  
two or more of which a genus is         
composed2 a predicable that  expresses  
the whole essence of its subject in so  
far as any common term  can express it4 
,an authority says3 ,the names species  
and genus are merely relative  and the  
same common term may1 in one case1 be   
the species which is  predicated of an  
individual1 and in another case the     
individual of which  a species is       
predicated4 ,thus the individual1       
,george1 belongs to the  logical species
 ,man1 while ,man is an individual of   
the logical species  ,animal4 ,jevons   
says3 ,it is desirable to have names by 
which to show  that one class is        
contained in another1 and accordingly we

 call the  class which is divided into  
two or more smaller ones1 the genus1 and
  the smaller ones into which it is     
divided1 the species4 ,animal is  a     
genus of which man is a species2 while  
man1 in turn1 is a  genus of which      
,caucasian is a species2 and ,caucasian1
 in turn1  becomes a genus of which     
,socrates becomes a species4 ,the       
student  must avoid confusing the       
logical meaning of the terms genus and  
species with the use of the same terms  
in ,natural ,history4 ,each class  is a 
genus to the class below it in          
extension2 and each class is a  species 
to the class above it in extension4 ,at 
the lowest extreme of  the scale we     
reach what is called the infima species1
 which cannot be  further subdivided1 as
 for instance ,socrates--this lowest    
species must  always be an individual   
object1 person or thing4 ,at the highest
 extreme  of the scale we reach what is 
summum genus1 or highest genus1 which is
  never a species of anything1 for there

 is no class higher than it1 as  for    
instance1 being1 existence1 reality1    
truth1 the absolute1 the  infinite1 the 
ultimate1 etc4 ,hyslop says3 ,in reality
 there is but one  summum genus1 while  
there may be an indefinite number of    
infimae  species4 ,all intermediate     
terms between these extremes are        
sometimes  called subalterns1 as being  
either genera or species1 according to  
the relation in which they are viewed4  
,passing on to the classification of the
 character of the intension of  terms1  
we find3    ,difference1 a term         
denoting3 ,the mark or marks by which   
the species  is distinguished from the  
rest of the genus2 the specific         
characteristic4 ,thus the color of the  
skin is a difference between  the ,negro
 and the ,caucasian2 the number of feet 
the difference between  the biped and   
the quadruped2 the form and shape of    
leaves the  difference between the oak  
and the elm trees1 etc4 ,hyslop says3   
,whatever distinguishes one object from 

another can be called the  differentia4 
,it is some characteristic in addition  
to the common  qualities and determines 
the species or individual under the     
genus4    ,property1 a term denoting3 ,a
 peculiar quality of anything2 that     
which  is inherent in or naturally      
essential to anything4 ,thus a property 
is  a distinguishing mark of a class4   
,thus black skin is a property of the   
,negro race2 four feet a property of    
quadrupeds2 a certain form of leaf  a   
property of the oak tree4 ,thus a       
difference between two species  may be a
 property of one of the species4        
,accident1 a term denoting3 ,any quality
 or circumstance which may or  may not  
belong to a class1 accidentally as it   
were2 or1 whatever does  not really     
constitute an essential part of an      
object1 person or thing4  ,as1 for      
instance1 the redness of a rose1 for a  
rose might part with its  redness and   
still be a rose--the color is the       
accident of the rose4  ,or1 a brick may 

be white and still be a brick1 although 
the majority of  bricks are red--the    
redness or whiteness of the brick are   
its  accidents and not its essential    
properties4 ,whately says3  ,accidents  
in ,logic are of two kinds--separable   
and inseparable4 ,if  walking be the    
accident of a particular man1 it is a   
separable one1  for he would not cease  
to be that man though he stood still2   
while1 on  the contrary1 if ,spaniard is
 the accident connected with him1 it is 
an  inseparable one1 since he never can 
cease to be1 ethnologically  considered1
 what he was born4    ,arising from the 
classification of the meaning or content
 of terms1 we  find the process termed  
,definition4    ,definition is a term   
denoting3 ,an explanation of a word or  
term4 ,in  ,logic the term is used to   
denote the process of analysis in which 
the  properties and differences of a    
term are clearly stated4 ,there are  of 
course several kinds of definitions4    
,for instance1 there is what is  called 

a ,real ,definition1 which ,whately     
defines as3 ,a definition  which        
explains the nature of the thing by a   
particular name4 ,there is  also what is
 called a ,physical ,definition1 which  
is3 ,a definition  made by enumerating  
such parts as are actually separable1   
such as the  hull1 masts1 etc41 of a    
ship4 ,also a ,logical ,definition1     
which is3 ,a  definition consisting of  
the genus and the difference4 ,thus if a
 planet  be defined as 'a wandering     
star1' star is the genus1 and wandering 
points out the difference between a     
planet and an ordinary star4 ,an        
,accidental ,definition is3 ,a          
definition of the accidental qualities  
of a thing4 ,an ,essential ,definition  
is3 a definition of the  essential      
properties and differences of an object1
 person or thing4    ,crabbe            
discriminates between a ,definition and 
an ,explanation1 as  follows3 ,a        
definition is correct or precise2 an    
explanation is  general or ample4 ,the  

definition of a word defines or limits  
the  extent of its signification2 it is 
the rule for the scholar in the use  of 
any word2 the explanation of a word may 
include both definition and             
illustration2 the former admits of no   
more words than will include the        
leading features in the meaning of any  
term2 the latter admits of an  unlimited
 scope for diffuseness on the part of   
the explainer4    ,hyslop gives the     
following excellent explanation of the  
,logical  ,definition1 which as he      
states is the proper meaning of the term
 in  ,logic4 ,he states3    ,the rules  
which regulate ,logical ,definition are 
as follows3    #a4 ,a definition should 
state the essential attributes of the   
species  defined4    #b4 ,a definition  
must not contain the name of word       
defined4 ,otherwise the  definition is  
called a circulus in definiendo4    #c4 
,the definition must be exactly         
equivalent to the species defined4      
#d4 ,a definition should not be         

expressed in obscure1 figurative1 or    
ambiguous language4    #e4 ,a definition
 must not be negative when it can be    
affirmative4    ,a correct definition   
necessarily requires the manifestation  
of the two  respective processes of     
,analysis and ,synthesis4    ,analysis  
is a term denoting3 ,the separation of  
anything into its  constituent elements1
 qualities1 properties and attributes4  
,it is seen  at once that in order to   
correctly define an object1 person or   
thing1 it  is first necessary to analyze
 the latter in order to perceive its    
essential and accidental properties or  
differences4 ,unless the  qualities1    
properties and attributes are clearly   
and fully perceived1 we  cannot properly
 define the object itself4    ,synthesis
 is a term denoting3 ,the act of joining
 or putting two or  more things         
together2 in ,logic3 the method by      
composition1 in opposition  to the      
method of resolution or analysis4 ,in   
stating a definition we  must           

necessarily join together the various   
essential qualities1  properties and    
attributes1 which we have discovered by 
the process of  analysis2 and the       
synthesized combination1 considered as a
 whole1 is the  definition of the object
 expressed by the term4                 
,,chapter ,,viii4    ,,judgments        
,the first step in the process of       
reasoning is that of ,conception or the 
forming of ,concepts4 ,the second step  
is that of ,judgment1 or the process  of
 perceiving the agreement or            
disagreement of two conceptions4        
,judgment in ,logic is defined as3 ,the 
comparing together in the mind  of two  
notions1 concepts or ideas1 which are   
the objects of  apprehension1 whether   
complex or incomplex1 and pronouncing   
that they  agree or disagree with each  
other1 or that one of them belongs or   
does  not belong to the other4 ,judgment
 is therefore affirmative or negative4  
,when we have in our mind two concepts1 
we are likely to compare them one  with 

the other1 and to thus arrive at a      
conclusion regarding their  agreement or
 disagreement4 ,this process of         
comparison and decision is  what1 in    
,logic1 is called ,judgment4    ,in     
every act of ,judgment there must be at 
least two concepts to be  examined and  
compared4 ,this comparison must lead to 
a ,judgment  regarding their agreement  
or disagreement4 ,for instance1 we have 
the two  concepts1 horse and animal4 ,we
 examine and compare the two concepts1  
and find that there is an agreement     
between them4 ,we find that the  concept
 horse is included in the higher concept
 of animal and  therefore1 we assert    
that3 ,the horse is an animal4 ,this is 
a  statement of agreement and is1       
therefore1 a ,positive ,judgment4 ,we   
then compare the concepts horse and cow 
and find a disagreement  between them1  
which we express in the statement of the
 ,judgment that3  ,the horse is not a   
cow4 ,this ,judgment1 stating a         
disagreement is  what is called a       

,negative ,judgment4    ,in the above   
illustration of the comparison between  
the concepts horse  and animal we find  
that the second concept animal is       
broader than  the first1 horse1 so broad
 in fact that it includes the latter4   
,the  terms are not equal1 for we cannot
 say1 in truth1 that an animal is the   
horse4 ,we may1 however1 include a part 
of the broader conception with  the     
narrower and say3 some animals are      
horses4 ,sometimes both  concepts are of
 equal rank1 as when we state that3 ,man
 is a rational  animal4    ,in the      
process of ,judgment there is always the
 necessity of the choice  between the   
,positive and the ,negative4 ,when we   
compare the concepts  horse and animal1 
we must of necessity decide either that 
the horse  is an animal1 or else that it
 is not an animal4    ,the importance of
 the process of ,judgment is ably stated
 by ,halleck1 as  follows3 ,were        
isolated concepts possible1 they would  
be of very little  use4 ,isolated facts 

are of no more service than unspun wool4
 ,we might  have a concept of a certain 
class of three-leaved ivy1 as we might  
also  of poisons4 ,unless judgment      
linked these two concepts and decided   
that  this species of ivy is poisonous1 
we might take hold of it and be         
poisoned4 ,we might have a concept of   
bread and also one of meat1 fruit  and  
vegetables4 ,if we also had a concept of
 food1 unrelated to these1 we  should   
starve to death1 for we should not think
 of them as foods4 ,a  vessel1 supposing
 itself to be far out at sea1 signaled  
another vessel  that the crew were dying
 of thirst4 ,that crew certainly had a  
concept of  drinkable things and also of
 water4 ,to the surprise of the first1  
the  second vessel signaled back1 ',draw
 from the sea and drink4 ,you are at    
the mouth of the ,amazon4' ,the thirsty 
crew had not joined the concept         
drinkable to the concept of water over  
the ship's side4 ,a man having  taken an
 overdose of laudanum1 his wife lost    

much valuable time in  sending out for  
antidotes1 because certain of her       
concepts had not been  connected by     
judgment4 ,she had good concepts of     
coffee and of mustard2  she also knew   
that an antidote to opium was needed2   
but she had never  linked these concepts
 and judged that coffee and mustard were
 antidotes  to opium4 ,the moment she   
formed that judgment she was a wiser    
woman for  her knowledge was related and
 usable4444 ,judgment is the power      
revolutionizing the world4 ,the         
revolution is slow because nature's     
forces are so complex1 so hard to be    
reduced to their simplest forms and  so 
disguised and neutralized by the        
presence of other forces4444            
,fortunately judgment is ever silently  
working and comparing things that1  to  
past ages1 have seemed dissimilar2 and  
it is continually abstracting  and      
leaving out of the field of view those  
qualities which have simply  served to  
obscure the point at issue4    ,judgment

 may be both analytic or synthetic in   
its processes2 and it may  be neither4  
,when we compare a narrow concept with a
 broader one1 as a  part with a whole1  
the process is synthetic or an act of   
combination4  ,when we compare a part of
 a concept with another concept1 the    
process is  analytic4 ,when we compare  
concepts equal in rank or extent1 the   
process  is neither synthetic nor       
analytic4 ,thus in the statement that3  
,a horse  is an animal1 the judgment is 
synthetic2 in the statement that3 some  
animals are horses1 the judgement is    
analytic2 in the statement that3  a man 
is a rational animal1 the judgment is   
neither analytic nor  synthetic4        
,brooks says3 ,in one sense all         
judgments are synthetic4 ,a judgment    
consists of the union of two ideas and  
this uniting is a process of  synthesis4
 ,this1 however1 is a superficial view  
of the process4 ,such a  synthesis is a 
mere mechanical synthesis2 below this is
 a  thought-process which is sometimes  

analytic1 sometimes synthetic and       
sometimes neither analytic nor          
synthetic4    ,the same authority       
states3 ,the act of mind described is   
what is known  as logical judgment4     
,strictly speaking1 however1 every      
intelligent act  of the mind is         
accompanied with a judgment4 ,to know is
 to discriminate  and1 therefore1 to    
judge4 ,every sensation or cognition    
involves a  knowledge and so a judgment 
that it exists4 ,the mind cannot think  
at all  without judging2 to think is to 
judge4 ,even in forming the notions     
which judgment compares1 the mind       
judges4 ,every notion or concept        
implies a previous act of judgment to   
form it3 in forming a concept1 we       
compare the common attributes before we 
unite them2 and comparison is  judgment4
 ,it is thus true that ',every concept  
is a contracted judgment2  every        
judgment an expanded concept4' ,this    
kind of judgment1 by which we  affirm   
the existence of states of              

consciousness1 discriminate qualities1  
distinguish percepts and form concepts1 
is called primitive or  psychological   
judgment4    ,in ,logical ,judgment     
there are two aspects2 i4e41 ,judgment  
by ,extension  and ,judgment by         
,intension4 ,when we compare the two    
concepts horse and  animal we find that 
the concept horse is contained in the   
concept  animal and the judgment that a 
horse is an animal may be  considered as
 a ,judgment by ,extension4 ,in the same
 comparison we see  that the concept    
horse contains the quality of animality1
 and in  attributing this quality to the
 horse1 we may also say the horse is  an
 animal1 which judgment may be          
considered as a ,judgment by            
,intension4 ,brooks says3 ,both views of
 ,judgment are correct2 the mind  may   
reach its judgment either by extension  
or by intension4 ,the method  by        
extension is usually the more natural4  
,when a ,judgment is expressed in words 
it is called a ,proposition4 ,there  is 

some confusion regarding the two terms1 
some holding that a ,judgment  and a    
proposition are identical1 and that the 
term proposition may be  properly used  
to indicate the judgment itself4 ,but   
the authorities who  seek for clearness 
of expression and thought now generally 
hold that3  ,a ,proposition is a        
,judgment expressed in words4 ,in the   
next chapter1  in which we consider     
,propositions1 we shall enter into a    
more extended  consideration of the     
subject of ,judgments as expressed in   
,propositions1  which consideration we  
omit at this point in order to avoid    
repetition4  ,just as the respective    
subjects of ,concepts and ,terms        
necessarily blend  into each other1 so  
do the respective subjects of ,judgments
 and  ,propositions4 ,in each case1 too1
 there is the element of the mental     
process on the one hand and the verbal  
expression of it on the other  hand4 ,it
 will be well to keep this fact in mind4
          ,,chapter ,,ix4               

,,propositions      ,we have seen that  
the first step of ,deductive ,reasoning 
is that which we  call ,concepts4 ,the  
second step is that which we call       
,propositions4    ,in ,logic1 a         
,proposition is3 ,a sentence1 or part of
 a sentence1  affirming or denying a    
connection between the terms2 limited to
 express  assertions rather than        
extended to questions and commands4     
,hyslop  defines a ,proposition as3 any 
affirmation or denial of an agreement   
between two conceptions4    ,examples of
 ,propositions are found in the         
following sentences3 ,the  rose is a    
flower2 a horse is an animal2 ,chicago  
is a city2 all of  which are            
affirmations of agreement between the   
two terms involved2 also  in3 ,a horse  
is not a zebra2 pinks are not roses2 the
 whale is not a  fish2 etc41 which are  
denials of agreement between the terms4 
,the ,parts of a ,proposition are3 7#a7 
the ,subject1 or that of which          
something is affirmed or denied2 7#b7   

the ,predicate1 or the  something which 
is affirmed or denied regarding the     
,subject2 and 7#c7  the ,copula1 or the 
verb serving as a link between the      
,subject and the  ,predicate4           
99       99       99       99       99  
,in the ,proposition3 ,man is an animal1
 the term man is the ,subject2  the term
 an animal is the ,predicate2 and the   
word is1 is the ,copula4  ,the ,copula  
is always some form of the verb to be1  
in the present tense  indicative1 in an 
affirmative ,proposition2 and the same  
with the  negative particle affixed1 in 
a negative ,proposition4 ,the ,copula is
 not  always directly expressed by the  
word is or is not1 etc41 but is  instead
 expressed in some phrase which implies 
them4 ,for instance1 we  say he runs1   
which implies he is running4 ,in the    
same way1 it may  appear at times as if 
the ,predicate was missing1 as in3 ,god 
is1 by  which is meant ,god is existing4
 ,in some cases1 the ,proposition is    
inverted1 the ,predicate appearing first

 in order1 and the ,subject last1  as   
in3 ,blessed are the peacemakers2 or    
,strong is ,truth4 ,in such  cases      
judgment must be used in determining the
 matter1 in accordance  with the        
character and meaning of the terms4     
,an ,affirmative ,proposition is one in 
which the ,predicate is affirmed  to    
agree with the ,subject4 ,a ,negative   
,proposition is one in which the        
agreement of the ,predicate and ,subject
 is denied4 ,examples of both of  these 
classes have been given in this chapter4
    ,another classification of          
,propositions divides them in three     
classes1 as  follows 7#a7 ,categorical2 
7#b7 ,hypothetical2 7#c7 ,disjunctive4  
,a ,categorical ,proposition is one in  
which the affirmation or denial is  made
 without reservation or qualification1  
as for instance3 ,man is an  animal2 the
 rose is a flower1 etc4 ,the fact       
asserted may not be  true1 but the      
statement is made positively as a       
statement of reality4    ,a             

,hypothetical ,proposition is one in    
which the affirmation or denial  is made
 to depend upon certain conditions1     
circumstances or  suppositions1 as for  
instance3 ,if the water is boiling-hot1 
it will  scald2 or if the powder be     
damp1 it will not explode1 etc4 ,jevons 
says3 ,hypothetical ,propositions may   
generally be recognized by  containing  
the little word 'if2' but it is doubtful
 whether they really  differ much from  
the ordinary propositions4444 ,we may   
easily say that  'boiling water will    
scald1' and 'damp gunpowder will not    
explode1' thus  avoiding the use of the 
word 'if4'    ,a ,disjunctive           
,proposition is one implying or         
asserting an  alternative1 and usually  
containing the conjunction or1 sometimes
  together with either1 as for instance3
 ,lightning is sheet or forked2  ,arches
 are either round or pointed2 ,angles   
are either obtuse1 right  angled or     
acute4    ,another classification of    
,propositions divides them in two       

classes as  follows3 7#a7 ,universal2   
7#b7 ,particular4    ,a ,universal      
,proposition is one in which the whole  
quantity of the  ,subject is involved in
 the assertion or denial of the         
,predicate4 ,for  instance3 ,all men are
 liars1 by which is affirmed that all of
 the  entire race of men are in the     
category of liars1 not some men but  all
 the men that are in existence4 ,in the 
same way the ,proposition3  ,no men are 
immortal is ,universal1 for it is a     
universal denial4    ,a ,particular     
,proposition is one in which the        
affirmation or denial of  the ,predicate
 involves only a part or portion of the 
whole of the  ,subject1 as for instance3
 ,some men are atheists1 or ,some women 
are not vain1 in which cases the        
affirmation or denial does not involve  
all or the whole of the ,subject4 ,other
 examples are3 ,a few men1  etc42 many  
people1 etc42 certain books1 etc42 most 
people1  etc4    ,hyslop says3 ,the     
signs of the ,universal ,proposition1   

when formally  expressed1 are all1      
every1 each1 any1 and whole or words    
with  equivalent import4 ,the signs of  
,particular ,propositions are also      
certain adjectives of quantity1 such as 
some1 certain1 a few1  many1 most or    
such others as denote at least a part of
 a class4    ,the subject of the        
,distribution of ,terms in ,propositions
 is considered  very important by       
,logicians1 and as ,hyslop says3 has    
much importance in  determining the     
legitimacy1 or at least the             
intelligibility1 of our  reasoning and  
the assurance that it will be accepted  
by others4 ,some  authorities favor the 
term1 ,qualification of the ,terms of   
,propositions1 but the established usage
 favors the term  ,distribution4    ,the
 definition of the ,logical term1       
,distribution1 is3 ,the  distinguishing 
of a universal whole into its several   
kinds of species2  the employment of a  
term to its fullest extent2 the         
application of a  term to its fullest   

extent1 so as to include all            
significations or  applications4 ,a     
,term of a ,proposition is distributed  
when it is  employed in its fullest     
sense2 that is to say1 when it is       
employed so  as to apply to each and    
every object1 person or thing included  
under  it4 ,thus in the proposition1    
,all horses are animals1 the term       
horses is distributed2 and in the       
proposition1 ,some horses are           
thoroughbreds1 the term horses is not   
distributed4 ,both of these  examples   
relate to the distribution of the       
subject of the proposition4  ,but the   
predicate of a proposition also may or  
may not be distributed4  ,for instance1 
in the proposition1 ,all horses are     
animals1 the  predicate1 animals1 is not
 distributed1 that is1 not used in its  
fullest sense1 for all animals are not  
horses--there are some  animals which   
are not horses and1 therefore1 the      
predicate1 animals1  not being used in  
its fullest sense is said to be not     

distributed4  ,the proposition really   
means3 ,all horses are some animals4    
,there is however another point to be   
remembered in the consideration of      
,distribution of ,terms of              
,propositions1 which ,brooks expresses  
as  follows3 ,distribution generally    
shows itself in the form of the         
expression1 but sometimes it may be     
determined by the thought4 ,thus if  we 
say1 ',men are mortal1' we mean all men1
 and the term men is  distributed4 ,but 
if we say ',books are necessary to a    
library1' we mean1  not 'all books' but 
'some books4' ,the test of distribution 
is whether  the term applies to 'each   
and every4' ,thus when we say 'men are  
mortal1' it is true of each and every   
man that he is mortal4    ,the ,rules of
 ,distribution of the ,terms of         
,proposition are as follows3    #a4 ,all
 universals distribute the subject4     
#b4 ,all particulars do not distribute  
the subject4    #c4 ,all negatives      
distribute the predicate4    #d4 ,all   

affirmatives do not distribute the      
predicate4    ,the above rules are based
 upon logical reasoning4 ,the reason for
 the  first two rules is quite obvious1 
for when the subject is universal1  it  
follows that the whole subject is       
involved2 when the subject is           
particular it follows that only a part  
of the subject is involved4  ,in the    
case of the third rule1 it will be seen 
that in every negative  proposition the 
whole of the predicate must be denied   
the subject1 as  for instance1 when we  
say3 ,some animals are not horses1 the  
whole  class of horses is cut off from  
the subject1 and is thus  distributed4  
,in the case of the fourth rule1 we may 
readily see that  in the affirmative    
proposition the whole of the predicate  
is not  denied the subject1 as for      
instance1 when we say that3 ,horses are 
animals1 we do not mean that horses are 
all the animals1 but that  they are     
merely a part or portion of the class   
animal--therefore1 the  predicate1      

animals1 is not distributed4    ,in     
addition to the forms of ,propositions  
given there is another class of         
,propositions known as ,definitive or   
,substitutive ,propositions1 in  which  
the ,subject and the ,predicate are     
exactly alike in extent and  rank4 ,for 
instance1 in the proposition1 ,a        
triangle is a polygon of  three sides   
the two terms are interchangeable2 that 
is1 may be  substituted for each other4 
,hence the term substitutive4 ,the term 
definitive arises from the fact that the
 respective terms of this kind  of a    
proposition necessarily define each     
other4 ,all logical  definitions are    
expressed in this last mentioned form of
 proposition1  for in such cases the    
subject and the predicate are precisely 
equal to  each other4          ,,chapter
 ,x4    ,,immediate ,,reasoning      ,in
 the process of ,judgment we must       
compare two concepts and ascertain      
their agreement of disagreement4 ,in the
 process of ,reasoning we follow a      

similar method and compare two          
judgments1 the result of such comparison
  being the deduction of a third        
judgment4    ,the simplest form of      
reasoning is that known as ,immediate   
,reasoning1 by  which is meant the      
deduction of one proposition from       
another which  implies it4 ,some have   
defined it as3 reasoning without a      
middle  term4 ,in this form of reasoning
 only one proposition is required for   
the premise1 and from that premise the  
conclusion is deduced directly  and     
without the necessity of comparison with
 any other term of  proposition4    ,the
 two principal methods employed in this 
form of ,reasoning are2 7#a7            
,opposition2 7#b7 ,conversion4          
,opposition exists between propositions 
having the same subject and  predicate1 
but differing in quality or quantity1 or
 both4 ,the ,laws of  ,opposition are as
 follows3    ,i4 7#a7 ,if the universal 
is true1 the particular is true4 7#b7   
,if the  particular is false1 the       

universal is false4 7#c7 ,if the        
universal is  false1 nothing follows4   
7#d7 ,if the particular is true1 nothing
 follows4    ,,ii4 7#a7 ,if one of two  
contraries is true1 the other is false4 
7#b7 ,if one  of two contraries is      
false1 nothing can be inferred4 7#c7    
,contraries are  never both true1 but   
both may be false4    ,,iii4 7#a7 ,if   
one of two sub-contraries is false1 the 
other is true4 7#b7  ,if one of two     
sub-contraries is true1 nothing can be  
inferred concerning  the other4 7#c7    
,sub-contraries can never be both false1
 but both may be  true4    ,,iv4 7#a7   
,if one of two contradictories is true1 
the other is false4 7#b7  ,if one of two
 contradictories is false1 the other is 
true4 7#c7  ,contradictories can never  
be both true or both false1 but always  
one is  true and the other is false4    
,in order to comprehend the above laws1 
the student should familiarize  himself 
with the following arrangement1 adopted 
by logicians as a  convenience3         

,universal  ,affirmative 7,a7           
,negative    7,e7    ,propositions      
,affirmative 7,i7                       
,particular ,negative    7,o7           
,examples of the above3 ,universal      
,affirmative 7,a73 ,all men are mortal2 
,universal ,negative 7,e73 ,no man is   
mortal2 ,particular ,affirmative 7,i73  
,some men are mortal2 ,particular       
,negative 7,o73 ,some men are not       
mortal4    ,the following examples of   
abstract propositions are often used by 
logicians as tending toward a clearer   
conception than examples such as  given 
above3    7,a7 ,all ,a is ,b4    7,i7   
,some ,a is ,b4    7,e7 ,no ,a is ,b4   
7,o7 ,some ,a is not ,b4    ,these four 
forms of propositions bear certain      
logical relations to each  other1 as    
follows3    ,a and ,e are styled        
contraries4 ,i and ,o are               
sub-contraries2 ,a and ,i  and also ,e  
and ,o are called subalterns2 ,a and ,o 
and also ,i and ,e are  styled          
contradictories4    ,a close study of   

these relations1 and the symbols        
expressing them1 is  necessary for a    
clear comprehension of the ,laws of     
,opposition stated a  little further    
back1 as well as the principles of      
,conversion which we  shall mention a   
little further on4 ,the following chart1
 called the  ,square of ,opposition1 is 
also employed by logicians to illustrate
 the  relations between the four classes
 of propositions3       ,a              
,,contraries       ,e                   
------------------------                
_/                          _/,s        
,c                 _/,e         ,o      
_/,i           ,n             _/,r      
,t           _/,o         ,s     ,r     
_/,t      ,s    ,u      ,a       _/,c   
,u    ,b             _/,i        ,b     
,a            _/,d         ,a    ,l     
_/           ,l    ,t          _/       
,t    ,e         _/  ,d          ,e     
,r        _/    ,i         ,r    ,n     
_/,a     ,c        ,n    ,s      _/,r   
,t       ,s          _/,t         ,o    

_/,n           ,r             _/,o      
,i           _/,c               ,e      
_/                  ,s       _/         
------------------------     ,i         
,,sub-,,contraries      ,o              
,conversion is the process of immediate 
reasoning by which we infer  from a     
given proposition another proposition   
having the predicate of  the original   
for its subject and the subject of the  
original for its  predicate2 or stated  
in a few words3 ,conversion is the      
transposition of  the subject and       
predicate of a proposition4 ,as ,brooks 
states it3  ,propositions or judgments  
are converted when the subject and      
predicate change places in such a manner
 that the resulting judgment is  an     
inference from the given judgment4 ,the 
new proposition1 resulting  from the    
operation or ,conversion1 is called the 
,converse2 the original  proposition is 
called the ,convertend4    ,the ,law of 
,conversion is that3 ,no term must be   
distributed in the  ,converse that is   

not distributed in the ,convertend4     
,this arises from  the obvious fact that
 nothing should be affirmed in the      
derived  proposition than there is in   
the original proposition4    ,there are 
three kinds of ,conversion2 viz3 7#a7   
,simple ,conversion2 7#b7  ,conversion  
by ,limitation2 7#c7 ,conversion by     
,contraposition4    ,in ,simple         
,conversion there is no change in either
 quality or quantity4  ,in ,conversion  
by ,limitation the quality is changed   
from universal to  particular4 ,in      
,conversion by ,negation the quality is 
changed but not  the quantity4          
,referring to the classification tables 
and symbols given  in the preceding     
pages of this chapter1 we may now       
proceed to consider  the application of 
these methods of ,conversion to each of 
the four kinds  of propositions2 as     
follows3    ,the ,universal ,affirmative
 7symbol ,a7 proposition is converted by
  ,limitation1 or by a change of quality
 from universal to particular4 ,the     

predicate not being distributed in the  
convertend1 we must not  distribute it  
in the converse by saying all4 ,thus in 
this case we  must convert the          
proposition1 all men are mortal 7,a71   
into some  mortals are men 7,i74    ,the
 ,universal ,negative 7symbol ,e7 is    
converted by ,simple ,conversion1  in   
which there is no change in either      
quality or quantity4 ,for since  both   
terms of ,e are distributed1 they may   
both be distributed in the  converse    
without violating the law of conversion4
 ,thus ,no man is  mortal is converted  
into3 ,no mortals are men4 ,e is        
converted into  ,e4    ,the ,particular 
,affirmative 7symbol ,i7 is also        
converted by ,simple  ,conversion in    
which there is no change in either      
quality or quantity4  ,for since neither
 term is distributed in ,i1 neither term
 may be  distributed in the converse1   
and the latter must remain ,i4 ,for     
instance2 the proposition3 ,some men are
 mortal is converted into the           

proposition1 ,some mortals are men4     
,the ,particular ,negative 7symbol ,o7  
is converted by ,conversion by          
,negation1 in which the quality is      
changed but not the quantity4 ,thus in  
converting the proposition3 ,some men   
are not mortal1 we must not say  some   
mortals are not men1 for in so doing we 
would distribute men in  the predicate1 
where it is not distributed in the      
convertend4 ,avoiding  this1 we transfer
 the negative particle from the copula  
to the  predicate so that the convertend
 becomes ,i which is converted by       
,simple ,conversion4 ,thus we transfer  
,some men are not mortal into ,some  men
 are not-mortal from which we easily    
convert 7by simple ,conversion7  the    
proposition3 ,some not-mortals are men4 
,it will be well for students1 at this  
point1 to consider the three  following 
,fundamental ,laws of ,thought as laid  
down by the authorities1  which are as  
follows3    ,the ,law of ,identity1     
which states that3 ,the same quality or 

thing is  always the same quality or    
thing1 no matter how different the      
conditions  in which it occurs4    ,the 
,law of ,contradiction1 which states    
that3 ,no thing can at the same  time   
and place both be and not be4    ,the   
,law of ,excluded ,middle1 which states 
that3 ,everything must either  be or not
 be2 there is no other alternative or   
middle course4    ,of these laws1 ,prof4
 ,jevons1 a noted authority1 says3      
,students are  seldom able to see at    
first their full meaning and importance4
 ,all  arguments may be explained when  
these self-evident laws are granted2 and
  it is not too much to say that the    
whole of logic will be plain to those   
who will constantly use these laws as   
the key4          ,,chapter ,,xi4       
,,inductive ,,reasoning      ,inductive 
,reasoning1 as we have said1 is the     
process of discovering  general truth   
from particular truths1 or inferring    
general laws from  particular facts4    
,thus1 from the experience of the       

individual and the  race regarding the  
particular truth that each and every man
 under  observation has been observed to
 die sooner or later1 it is inferred    
that all men die1 and hence1 the        
induction of the general truth that     
,all men must die4 ,or1 as from         
experience we know that the various     
kinds of metals expand when subjected to
 heat1 we infer that all  metals are    
subject to this law1 and that           
consequently we may arrive by  inductive
 reasoning at the conclusion that3 ,all 
metals expand when  subjected to heat4  
,it will be noticed that the conclusion 
arrived at in  this way by ,inductive   
,reasoning forms the fundamental premise
 in the  process of ,deductive          
,reasoning4 ,as we have seen elsewhere1 
the two  processes1 ,inductive and      
,deductive ,reasoning1 respectively are 
interdependent--resting upon one        
another4    ,jevons says of ,inductive  
,reasoning3 ,in ,deductive ,reasoning we
 inquire  how we may gather the truth   

contained in some propositions called   
,premises1 and put into another         
proposition called the ,conclusion4 ,we 
have not yet undertaken to find out how 
we can learn what propositions  really  
are true1 but only what propositions are
 true when other ones  are true4 ,all   
the acts of reasoning yet considered    
would be called  deductive because we   
deduce1 or lead down the truth from     
premises to  conclusion4 ,it is an      
exceedingly important thing to          
understand  deductive inference         
correctly1 but it might seem to be still
 more  important to understand inductive
 inference1 by which we gather the      
truth of general propositions from facts
 observed as happening in the  world    
around us4 ,halleck says3 ,man has to   
find out through his own  experience1 or
 that of others1 the major premises from
 which he argues  or draws his          
conclusions4 ,by induction we examine   
what seems to us a  sufficient number of
 individual cases4 ,we then conclude    

that the rest of  these cases1 which we 
have not examined1 will obey the same   
general  law4444 ,only after general    
laws have been laid down1 after objects 
have  been classified1 after major      
premises have been formed1 can deduction
 be  employed4    ,strange as may now   
appear1 it is a fact that until a       
comparatively  recent period in the     
history of man1 it was held by          
philosophers that  the only way to      
arrive at all knowledge was by means of 
,deductive  ,reasoning1 by the use of   
the ,syllogism4 ,the influence of       
,aristotle was  great and men preferred 
to pursue artificial and complicated    
methods of  ,deductive ,reasoning1      
rather than to reach the truth by       
obtaining the  facts from ,nature       
herself1 at first hand1 and then        
inferring general  principle from the   
facts so gathered4 ,the rise of modern  
scientific  methods of reasoning1 along 
the lines of ,inductive ,inference1     
dates from  about #abbe-acjj4 ,roger    

,bacon was one of the first to teach    
that we must  arrive at scientific truth
 by a process of observation and        
experimentation on the natural objects  
to be found on all sides4 ,he made  many
 discoveries by following this process4 
,he was ably seconded by  ,galileo who  
lived some three hundred years later1   
and who also taught  that many great    
general truths might be gained by       
careful observation  and intelligent    
inference4 ,lord ,francis ,bacon1 who   
lived about the same  time as ,galileo1 
presented in his ,novum ,organum many   
excellent  observations and facts       
regarding the process of ,inductive     
,reasoning and  scientific thought4 ,as 
,jevons says3 ,inductive logic inquires 
by what  manner of reasoning we can     
gather the laws of nature from the facts
 and  events observed4 ,such reasoning  
is called induction1 or inductive       
inquiry1 and1 as it has actually been   
practiced by all the great  discoverers 
in science1 it consists in four steps4  

,the ,four ,steps in ,inductive         
,reasoning1 as stated by ,jevons1 are as
  follows3    ,first                    
,step4--,preliminary observation4       
,second ,step4--,the making of          
hypotheses4    ,third ,step4--,deductive
 reasoning4    ,fourth                  
,step4--,verification4    ,it will be   
seen that the process of ,inductive     
,reasoning is essentially  a synthetic  
process1 because it operates in the     
direction of combining  and uniting     
particular facts or truths into general 
truths or laws which  comprehend1       
embrace and include them all4 ,as       
,brooks says3 ,the  particular facts are
 united by the mind into the general    
law2 the  general law embraces the      
particular facts and binds them together
 into a  unity of principle and thought4
 ,induction is thus a process of thought
  from the parts to the whole--a        
synthetic process4 ,it will also be seen
  that the process of ,inductive        
,reasoning is essentially an ascending  

process1 because it ascends from        
particular facts to general laws2       
particular truths to universal truths2  
from the lower to the higher1 the       
narrower to the broader1 the smaller to 
the greater4    ,brooks says of         
,inductive ,reasoning3 ,the relation of 
induction to  deduction will be clearly 
seen4 ,induction and ,deduction are the 
converse1 the opposites of each other4  
,deduction derives a particular  truth  
from a general truth2 ,induction derives
 a general truth from  particular       
truths4 ,this antithesis appears in     
every particular4  ,deduction goes from 
generals to particulars2 ,induction goes
 from  particulars to generals4         
,deduction is an analytic process2      
,induction is  a synthetic process4     
,deduction is a descending process--it  
goes from  the higher truth to the lower
 truth2 ,induction is an ascending      
process--it goes from the lower truth to
 the higher4 ,they differ also in  that 
,deduction may be applied to necessary  

truths1 while ,induction is  mainly     
restricted to contingent truths4 ,hyslop
 says3 ,there have been  several ways of
 defining this process4 ,it has been    
usual to contrast it  with ,deduction4  
,now1 deduction is often said to be     
reasoning from  general to particular   
truths1 from the containing to the      
contained  truth1 or from cause to      
effect4 ,induction1 therefore1 by       
contrast is  defined as reasoning from  
the particular to the general1 from the 
contained to the containing1 or from    
effect to cause4 ,sometimes  induction  
is said to be reasoning from the known  
to the unknown4 ,this  would make       
deduction1 by contrast1 reasoning from  
the unknown to the  known1 which is     
absurd4 ,the former ways of representing
 it are much the  better4 ,but there is 
still a better way of comparing them4   
,deduction is  reasoning in which the   
conclusion is contained in the premises4
 ,this is  a ground for its certitude   
and we commit a fallacy whenever we go  

beyond  the premises as shown by the    
laws of the distribution of terms4 ,in  
contrast with this1 then1 we may call   
inductive reasoning the process  by     
which we go beyond the premises in the  
conclusion4444 ,the process  here is to 
start from given facts and to infer some
 other probable facts  more general or  
connected with them4 ,in this we see the
 process of going  beyond the premises4 
,there are1 of course1 certain          
conditions which  regulate the          
legitimacy of the procedure1 just as    
there are conditions  determining       
deduction4 ,they are that the conclusion
 shall represent the  same general kind 
as the premises1 with a possibility of  
accidental  differences4 ,but it goes   
beyond the premises in so far as known  
facts  are concerned4    ,the following 
example may give you a clearer idea of  
the processes of  ,inductive ,reasoning3
    ,first ,step4 ,preliminary          
,observation4 ,example3 ,we notice that 
all the  particular magnets which have  

come under our observation attract      
iron4 ,our mental record of the         
phenomena may be stated as3 ,a1 ,b1 ,c1 
,d1  ,e1 ,f1 ,g1 etc41 and also ,x1 ,y1 
and ,z1 all of which are magnets1 in all
  observed instances1 and at all        
observed times1 attract iron4    ,second
 ,step4 ,the ,making of ,hypotheses4    
,example3 ,upon the basis of  the       
observations and experiments1 as above  
stated1 and applying the  axiom of      
,inductive ,reasoning1 that3 ,what is   
true of the many1 is true  of the whole1
 we feel justified in forming a         
hypothesis or inference of  a general   
law or truth1 applying the facts of the 
particulars to the  general1 whole or   
universal1 thus3 ,all magnets attract   
iron4    ,third ,step4 ,deductive       
,reasoning4 ,example3 ,picking up a     
magnet  regarding which we have had no  
experience and upon which we have made  
no  experiments1 we reason by the       
syllogism1 as follows3 7#a7 ,all magnets
  attract iron2 7#b7 ,this thing is a   

magnet2 therefore 7#c7 ,this thing  will
 attract iron4 ,in this we apply the    
axiom of ,deductive ,reasoning3         
,whatever is true of the whole is true  
of the parts4    ,fourth ,step4         
,verification4 ,example3 ,we then       
proceed to test the  hypothesis upon the
 particular magnet1 so as to ascertain  
whether or not  it agrees with the      
particular facts4 ,if the magnet does   
not attract  iron we know that either   
our hypothesis is wrong and that some   
magnets  do not attract iron2 or else   
that our judgment regarding that        
particular thing being a magnet is at   
fault and that it is not a  magnet4 ,in 
either case1 further examination1       
observation and experiment  is          
necessary4 ,in case the particular      
magnet does attract iron1 we feel  that 
we have verified our hypothesis and our 
judgment4          ,,chapter ,,xii4     
,,reasoning ,,by ,,induction      ,the  
term ,induction1 in its logical usage1  
is defined as follows3 7a7  ,the process

 of investigating and collecting facts2 
and 7b7 the deducing  of an inference   
from these facts2 also 7c7 sometimes    
loosely used in the  sense of an        
inference from observed facts4 ,mill    
says3 ,induction1  then1 is that        
operation of the mind1 by which we infer
 that what we know  to be true in a     
particular case or cases1 will be true  
in all cases  which resemble the former 
in certain assignable respects4 ,in     
other  words1 ,induction is the process 
by which we conclude that what is true  
of certain individuals of a class1 is   
true of the whole class1 or that  what  
is true at certain times will be true in
 similar circumstances at  all times4   
,the ,basis of ,induction is the axiom  
that3 ,what is true of the many  is true
 of the whole4 ,esser1 a well known     
authority1 states this axiom  in rather 
more complicated form1 as follows3 ,that
 which belongs or does  not belong to   
many things of the same kind1 belongs or
 does not belong  to all things of the  

same kind4    ,this basic axiom of      
,induction rests upon the conviction    
that ,nature's  laws and manifestations 
are regular1 orderly and uniform4 ,if we
 assume  that ,nature does not manifest 
these qualities1 then the axiom must    
fall1  and all inductive reason must be 
fallacious4 ,as ,brooks well says3      
,induction has been compared to a ladder
 upon which we ascend from facts  to    
laws4 ,this ladder cannot stand unless  
it has something to rest upon2  and this
 something is our faith in the constancy
 of ,nature's laws4 ,some  authorities  
have held that this perception of the   
uniformity of ,nature's  laws is in the 
nature of an intuitive truth1 or an     
inherent law of our  intelligence4      
,others hold that it is in itself an    
inductive truth1  arrived at by         
experience and observation at a very    
early age4 ,we are  held to have noticed
 the uniformity in natural phenomena1   
and almost  instinctively infer that    
this uniformity is continuous and       

universal4    ,the authorities assume   
the existence of two kinds of           
,induction1 namely3  7#a7 ,perfect      
,induction2 and 7#b7 ,imperfect         
,induction4 ,other1 but similar1  terms 
are employed by different authorities to
 designate these two  classes4          
,perfect ,induction necessitates a      
knowledge of all the particulars        
forming a class2 that is1 all the       
individual objects1 persons1 things  or 
facts comprising a class must be known  
and enumerated in this form of          
,induction4 ,for instance1 if we knew   
positively all of ,brown's  children1   
and that their names were ,john1 ,peter1
 ,mark1 ,luke1 ,charles1  ,william1     
,mary and ,susan1 respectively2 and that
 each and every one of  them were       
freckled and had red hair2 then1 in that
 case1 instead of  simply generalizing  
and stating that3 ,john1 ,peter1 ,mark1 
,luke1  ,charles1 ,william1 ,mary and   
,susan1 who are all of ,brown's         
children1 are  freckled and have red    

hair1 we would save words1 and state the
  inductive conclusion3 ,all ,brown's   
children are freckled and have red      
hair4 ,it will be noticed that in this  
case we include in the process  only    
what is stated in the premise itself1   
and we do not extend our  inductive     
process beyond the actual data upon     
which it is based4 ,this  form of       
,induction is sometimes called ,logical 
,induction1 because the  inference is a 
logical necessity1 without the          
possibility of error or  exception4 ,by 
some authorities it is held not to be   
,induction at all1 in  the strict sense1
 but little more than a simplified form 
of enumeration4  ,in actual practice it 
is seldom available1 for it is almost   
impossible  for us to know all the      
particulars in inferring a general law  
or truth4  ,in view of this difficulty1 
we fall back upon the more practical    
form of  induction known as3            
,imperfect ,induction1 or as it is      
sometimes called ,practical  ,induction1

 by which is meant the inductive process
 of reasoning in  which we assume that  
the particulars or facts actually known 
to us  correctly represent those which  
are not actually known1 and hence the   
whole class to which they belong4 ,in   
this process it will be seen that  the  
conclusion extends beyond the data upon 
which it is based4 ,in this  form of    
,induction we must actually employ the  
principle of the axiom3  ,what is true  
of the many is true of the whole--that  
is1 must assume  it to be a fact1 not   
because we know it by actual experience1
 but  because we infer it from the axiom
 which also agrees with past            
experience4 ,the conclusion arrived at  
may not always be true in its  fullest  
sense1 as in the case of the conclusion 
of ,perfect ,induction1  but is the     
result of an inference based upon a     
principle which gives us  a reasonable  
right to assume its truth in absence of 
better knowledge4    ,in considering the
 actual steps in the process of         

,inductive ,reasoning we  can do no     
better than to follow the classification
 of ,jevons1 mentioned  in the preceding
 chapter1 the same being simple and     
readily  comprehended1 and therefore    
preferable in this case to the more     
technical classification favored by some
 other authorities4 ,let us now         
consider these four steps4    ,first    
,step4 ,preliminary observation4 ,it    
follows that without the  experience of 
oneself or of others in the direction of
 observing and  remembering particular  
facts1 objects1 persons and things1 we  
cannot  hope to acquire the preliminary 
facts for the generalization and        
inductive inference necessary in        
,inductive ,reasoning4 ,it is necessary 
for us to form a variety of clear       
,concepts or ideas of facts1 objects1   
persons and things1 before we may hope  
to generalize from these  particulars4  
,in the chapters of this book devoted to
 the consideration  of ,concepts1 we may
 see the fundamental importance of the  

formation and  acquirement of correct   
,concepts4 ,concepts are the fundamental
 material  for correct reasoning4 ,in   
order to produce a perfect finished     
product1  we must have perfect          
materials1 and a sufficient quantity of 
them4 ,the  greater the knowledge one   
possesses of the facts and objects of   
the  outside world1 the better able is  
he to reason therefrom4 ,concepts are   
the raw material which must feed the    
machinery of reasoning1 and from  which 
the final product of perfected thought  
is produced4 ,as ,halleck  says3 ,there 
must first be a presentation of         
materials4 ,suppose that we  wish to    
form the concept fruit4 ,we must first  
perceive the different  kinds of        
fruit--cherry1 pear1 quince1 plum1      
currant1 apple1 fig1 orange1  etc4      
,before we can take the next step1 we   
must be able to form distinct  and      
accurate images of the various kinds of 
fruit4 ,if the concept is to  be        
absolutely accurate1 not one kind of    

fruit must be overlooked4  ,practically 
this is impossible2 but many kinds      
should be examined4 ,where  perception  
is inaccurate and stinted1 the products 
of thought cannot be  trustworthy4 ,no  
building is firm if reared on insecure  
foundations4    ,in the process of      
,preliminary ,observation1 we find that 
there are two  ways of obtaining a      
knowledge of the facts and things around
 us4 ,these  two ways are as follows3   
,i4 ,by ,simple ,observation1 or the    
perception of the happenings which  are 
manifested without our interference4 ,in
 this way we perceive the  motion of the
 tides2 the movement of the planets2 the
 phenomena of the  weather2 the passing 
of animals1 etc4    ,,ii4 ,by the       
,observation of ,experiment1 or the     
perception of happenings  in which we   
interfere with things and then observe  
the result4 ,an  experiment is3 ,a      
trial1 proof1 or test of anything2 an   
act1  operation1 or process designed to 
discover some unknown truth1 principle  

or effect1 or to test some received or  
reputed truth or principle4  ,hobbes    
says3 ,to have had many experiments is  
what we call  experience4 ,jevons says3 
,experimentation is observation with    
something more2 namely1 regulation of   
the things whose behavior is to be      
observed4 ,the advantages of experiment 
over mere observation are of two  kinds4
 ,in the first place1 we shall generally
 know much more certainly  and          
accurately with what we are dealing1    
when we make experiments than  when we  
simply observe natural events4444 ,it is
 a further advantage of  artificial     
experiments1 that they enable us to     
discover entirely new  substances and to
 learn their properties4444 ,it would be
 a mistake to  suppose that the making  
of an experiment is inductive reasoning1
 and  gives us without further trouble  
the laws of nature4 ,experiments only   
give us the facts upon which we may     
afterward reason4444 ,experiments  then 
merely give facts1 and it is only by    

careful reasoning that we can  learn    
when the same facts will be observed    
again4 ,the general rule is  that the   
same causes will produce the same       
effects4 ,whatever happens in  one case 
will happen in all like cases1 provided 
that they are really  like1 and not     
merely apparently so4444 ,when we have  
by repeated  experiments tried the      
effect which all the surrounding things 
might have  on the result1 we can then  
reason with much confidence as to       
similar  results in similar             
circumstances4444 ,in order that we may1
 from our  observations and experiments1
 learn the law of nature and become able
 to  foresee the future1 we must perform
 the process of generalization4 ,to     
generalize is to draw a general law from
 particular cases1 and to infer  that   
what we see to be true of a few things  
is true of the whole genus  or class to 
which these things belong4 ,it requires 
much judgment and  skill to generalize  
correctly1 because everything depends   

upon the  number and character of the   
instances about which we reason4        
,having seen that the first step in     
,inductive ,reasoning is ,preliminary   
,observation1 let us now consider the   
next steps in which we may see what  we 
do with the facts and ideas which we    
have acquired by this  ,observation and 
,experiment4          ,,chapter ,,xiii4 
,,theory ,,and ,,hypotheses             
,following ,jevons' classification1 we  
find that the ,second ,step in          
,inductive ,reasoning is that called    
,the ,making of ,hypotheses4    ,a      
,hypothesis is3 ,a supposition1         
proposition or principle assumed or     
taken for granted in order to draw a    
conclusion or inference in proof  of the
 point or question2 a proposition       
assumed or taken for granted1  though   
not proved1 for the purpose of deducing 
proof of a point in  question4 ,it will 
be seen that a ,hypothesis is merely    
held to be  possibly or probably true1  
and not certainly true2 it is in the    

nature of a working assumption1 whose   
truth must be tested by observed  facts4
 ,the assumption may apply either to the
 cause of things1 or to  the laws which 
govern things4 ,akin to a hypothesis1   
and by many people  confused in meaning 
with the latter1 is what is called a    
,theory4    ,a ,theory is3 ,a verified  
hypothesis2 a hypothesis which has been 
established as1 apparently1 the true    
one4 ,an authority says ,theory  is a   
stronger word than hypothesis4 ,a theory
 is founded on  principles which have   
been established on independent         
evidence4 ,a  hypothesis merely assumes 
the operation of a cause which would    
account  for the phenomena1 but has not 
evidence that such cause was actually at
  work4 ,metaphysically1 a theory is    
nothing but a hypothesis supported by  a
 large amount of probable evidence4     
,brooks says3 ,when a hypothesis is     
shown to explain all the facts that are 
known1 these facts being varied  and    
extensive1 it is said to be verified1   

and becomes a theory4 ,thus we  have the
 theory of universal gravitation1 the   
,copernican theory of the  solar system1
 the undulatory theory of light1 etc41  
all of which were  originally mere      
hypotheses4 ,this is the manner in which
 the term is  usually employed in the   
inductive philosophy2 though it must be 
admitted  that it is not always used in 
this strict sense4 ,discarded hypotheses
  are often referred to as theories2 and
 that which is actually a theory  is    
sometimes called a hypothesis4    ,the  
steps by which we build up a hypothesis 
are numerous and varied4 ,in  the first 
place we may erect a hypothesis by the  
methods of what we have  described as   
,perfect ,induction1 or ,logical        
,induction4 ,in this case we  proceed by
 simple generalization or simple        
enumeration4 ,the example of  the       
freckled1 red-haired children of ,brown1
 mentioned in a previous  chapter1      
explains this method4 ,it requires the  
examination and knowledge  of every     

object or fact of which the statement or
 hypothesis is made4  ,hamilton states  
that it is the only induction which is  
absolutely  necessitated by the laws of 
thought4 ,it does not extend further    
than the  plane of experience4 ,it is   
akin to mathematical reasoning4    ,far 
more important is the process by which  
hypotheses are erected by  means of     
inferences from ,imperfect ,induction1  
by which we reason from  the known to   
the unknown1 transcending experience1   
and making true  inductive inferences   
from the axiom of ,inductive ,reasoning4
 ,this process  involves the subject of 
,causes4 ,jevons says3 ,the cause of an 
event is  that antecedent1 or set of    
antecedents1 from which the event always
  follows4 ,people often make much      
difficulty about understanding what the 
cause of an event means1 but it really  
means nothing beyond the things  that   
must exist before in order that the     
event shall happen afterward4    ,causes
 are often obscure and difficult to     

determine4 ,the following five          
difficulties are likely to arise3 ,i4   
,the cause may be out of our            
experience1 and is therefore not to be  
understood2 ,,ii4 ,causes often act     
conjointly1 so that it is difficult to  
discover the one predominant  cause by  
reason of its associated causes2 ,,iii4 
,often the presence of a  counteracting1
 or modifying cause may confuse us2     
,,iv4 ,often a certain  effect may be   
caused by either of several possible    
causes2 ,v4 ,that which  appears as a   
cause of a certain effect may be but a  
co-effect of an  original cause4        
,mill formulated several tests for      
ascertaining the causal agency in       
particular cases1 in view of the        
above-stated difficulties4 ,these tests 
are as follows3 7#a7 ,the ,method of    
,agreement2 7#b7 ,the ,method of        
,difference2 7#c7 ,the ,method of       
,residues2 and 7#d7 ,the ,method of     
,concomitant ,variations4 ,the following
 definitions of these various tests  are

 given by ,atwater as follows3          
,method of ,agreement3 ,if1 whenever a  
given object or agency is present       
without counteracting forces1 a given   
effect is produced1 there is a  strong  
evidence that the object or agency is   
the cause of the effect4    ,method of  
,difference3 ,if1 when the supposed     
cause is present the  effect is present1
 and when the supposed cause is absent  
the effect is  wanting1 there being in  
neither case any other agents present to
 effect  the result1 we may reasonably  
infer that the supposed cause is the    
real  one4    ,method of ,residue3 ,when
 in any phenomena we find a result      
remaining  after the effects of all     
known causes are estimated1 we may      
attribute it  to a residual agent not   
yet reckoned4    ,method of ,concomitant
 ,variations3 ,when a variation in a    
given  antecedent is accompanied by a   
variation of a given consequent1 they   
are  in some manner related as cause and
 effect4    ,atwater adds3 ,whenever    

either of these criteria is found free  
from  conflicting evidence1 and         
especially when several of them concur1 
the  evidence is clear that the cases   
observed are fair representatives of    
the whole class1 and warrant a valid    
inductive conclusion4    ,jevons gives  
us the following valuable rules3    ,i4 
,whenever we can alter the quantity of  
the things experimented on1 we  can     
apply a rule for discovering which are  
causes and which are  effects1 as       
follows3 ,we must vary the quantity of  
one thing1 making it  at one time       
greater and at another time less1 and if
 we observe any  other thing which      
varies just at the same times1 it will  
in all  probability be an effect4       
,,ii4 ,when things vary regularly and   
frequently1 there is a simple rule1  by 
following which we can judge whether    
changes are connected together  as      
causes and effects1 as follows3 ,those  
things which change in exactly  equal   
times are in all likelihood connected   

together4    ,,iii4 ,it is very         
difficult to explain how it is that we  
can ever reason  from one thing to a    
class of things by generalization1 when 
we cannot  be sure that the things      
resemble each other in the important    
points4444  ,upon what grounds do we    
argue8 ,we have to get a general law    
from  particular facts4 ,this can only  
be done by going through all the steps  
of inductive reasoning4 ,having made    
certain observations1 we must frame     
hypotheses as to the circumstances1 or  
laws from which they proceed4  ,then we 
must reason deductively2 and after      
verifying the deductions in  as many    
cases as possible1 we shall know how far
 we can trust similar  deductions       
concerning future events4444 ,it is     
difficult to judge when we  may1 and    
when we may not1 safely infer from some 
things to others in  this simple way1   
without making a complete theory of the 
matter4 ,the  only rule that can be     
given to assist us is that if things    

resemble  each other in a few properties
 only1 we must observe many instances   
before inferring that these properties  
will always be joined together in  other
 cases4          ,,chapter ,,xiv4       
,,making ,,and ,,testing ,,hypotheses   
,the older philosophers and logicians   
were often at a loss how to  reasonably 
account for the origin of hypotheses4   
,it will be seen1 after  giving the     
matter a little thought1 that the actual
 formation of the  hypothesis is more   
than a mere grouping together or        
synthesis of facts  or ideas--there is  
another mental process which actually   
evolves the  hypothesis or theory--which
 gives a possible reason4 ,what is this 
mental process8 ,let us consider the    
matter4 ,brooks well says3 ,the         
hypotheses of science originate in what 
is called anticipation4 ,they are  not  
the result of a mere synthesis of facts1
 for no combination of facts  can give  
the law or cause4 ,we do not see the    
law2 we see the facts and  the mind     

thinks the law4 ,by the power of        
anticipation1 the mind often  leaps from
 a few facts to the cause which produces
 them or the law which  governs them4   
,many hypotheses were but a happy       
intuition of the mind4  ,they were the  
result of what ,la ,place calls 'a great
 guess1' or what  ,plato so beautifully 
designates as 'a sacred suspicion of    
truth4' ,the  forming of hypotheses     
requires a suggestive mind1 a lively    
fancy1 a  philosophic imagination1 that 
catches a glimpse of the idea through   
the  form1 or sees the law standing     
behind the fact4    ,the student of ,the
 ,new ,psychology sees in the mental    
operation of the  forming of the        
hypothesis--the mind thinking the       
law--but an instance  of the operation  
of the activities of the ,subconscious  
,mind1 or even the  ,superconscious     
,mind4 7,see the volume on the          
,subconscious ,mind in this  series47   
,not only does this hypothesis give the 
explanation which the  old psychology   

has failed to do1 but it agrees with the
 ideas of others  on the subject as     
stated in the above quotation from      
,brooks2 and  moreover agrees with many 
recorded instances of the formation of  
great  hypotheses4 ,sir ,wm4 ,hamilton  
discovered the very important           
mathematical  law of quaternions while  
walking one day in the ,dublin          
,observatory4 ,he  had pondered long on 
the subject1 but without result4 ,but1  
finally1 on  that eventful day he       
suddenly felt the galvanic circle of    
thought  close1 and the result was the  
realization of the fundamental          
mathematical relations of the problem4  
,berthelot1 the founder of  ,synthetic  
,chemistry1 has testified that the      
celebrated experiments which  led to his
 remarkable discoveries were seldom the 
result of carefully  followed lines of  
conscious thought or pure reasoning     
processes2 but1  instead1 came to him of
 their own accord1 so to speak1 as from 
a  clear sky4 ,in these and many other  

similar instances1 the mental  operation
 was undoubtedly purely subjective and  
subconscious4 ,dr4 ,hudson  has claimed 
that the ,subjective ,mind cannot reason
 inductively1 and  that its operations  
are purely and distinctly deductive1 but
 the  testimony of many eminent         
scientists1 inventors and philosophers  
is  directly to the contrary4    ,in    
this connection the following quotation 
from ,thomson is interesting3  ,the     
system of anatomy which has immortalized
 the name of ,oken is the  consequence  
of a flash of anticipation which glanced
 through his mind  when he picked up in 
a chance walk the skull of a deer1      
bleached and  disintegrated by the      
weather1 and exclaimed after a glance1  
',it is part  of a vertebral column6'   
,when ,newton saw the apple fall1 the   
anticipatory  question flashed through  
his mind1 ',why do not the heavenly     
bodies fall  like this apple8' ,in      
neither case had accident any important 
share2  ,newton and ,oken were prepared 

by the deepest previous study to seize  
upon the unimportant fact offered to    
them1 and to show how important it      
might become2 and if the apple and the  
deer-skull had been wanting1 some  other
 falling body1 or some other skull1     
would have touched the string  so ready 
to vibrate4 ,but in each case there was 
a great step of  anticipation2 ,oken    
thought he saw a type of the whole      
skeleton in a  single vertebra1 while   
,newton conceived at once that the whole
 universe  was full of bodies tending to
 fall4444 ,the discovery of ,goethe1    
which  did for the vegetable kingdom    
what ,oken did for the animal1 that the 
parts of a plant are to be regarded as  
metamorphosed leaves1 is an  apparent   
exception to the necessity of discipline
 for invention1 since it  was the       
discovery of a poet in a region to which
 he seemed to have paid  no especial or 
laborious attention4 ,but ,goethe was   
himself most anxious  to rest the basis 
of this discovery upon his observation  

rather than his  imagination1 and       
doubtless with good reason4444 ,as with 
other great  discoveries1 hints had been
 given already1 though not pursued1 both
 of  ,goethe's and ,oken's principles4  
,goethe left his to be followed up by   
others1 and but for his great fame1     
perhaps his name would never have  been 
connected with it4 ,oken had amassed all
 the materials necessary for  the       
establishment of his theory2 he was able
 at once to discover and  conquer the   
new territory4    ,it must not be       
supposed1 however1 that all hypotheses  
flashing into the  field of             
consciousness from the                  
,subconsciousness1 are necessarily true 
or correct4 ,on the contrary many of    
them are incorrect1 or at least only    
partially correct4 ,the                 
,subconsciousness is not infallible or  
omniscient--it merely produces results  
according to the material  furnished it4
 ,but even these faulty hypotheses are  
often of value in the  later formation  

of a correct one4 ,as ,whewell says3 ,to
 try wrong guesses  is with most persons
 the only way to hit upon right ones4   
,kepler is  said to have erected at     
least twenty hypotheses regarding the   
shape of  the earth's orbit before he   
finally evolved the correct one4 ,as    
,brooks  says3 ,even incorrect          
hypotheses may be of use in scientific  
research1  since they may lead to more  
correct suppositions4 ,the supposition  
of  the circular motions of the heavenly
 bodies around the earth as a  center1  
which lead to the conception of         
epicycles1 etc41 and at last to  the    
true theory is an illustration of this4 
,so the 'theory of  phlogiston' in      
chemistry1 made many facts intelligible1
 before the true  one of 'oxidation'    
superseded it4 ,and so1 as ,thomson     
says1 with the  theory that ',nature    
abhors a vacuum1' which served to bring 
together so  many cognate facts not     
previously considered as related4 ,even 
an  incorrect conception of this kind   

has its place in science1 so long as  it
 is applicable to the facts2 when facts 
occur which it cannot explain1  we      
either correct it or replace it with a  
new one4 ,the pathway of  science1 some 
one remarks1 is strewn with the remains 
of discarded  hypotheses4    ,halleck   
says regarding the danger of hasty      
inference3 ,men must  constantly employ 
imperfect induction in order to advance2
 but great  dangers attend inductive    
inferences made from too narrow         
experience4 ,a  child has experience    
with one or two dogs at his home4       
,because of their  gentleness1 he argues
 that all dogs are gentle4 ,he does not1
 perhaps1  find out the contrary until  
he has been severely bitten4 ,his       
induction  was too hasty4 ,he had not   
tested a sufficiently large number of   
dogs to  form such a conclusion4 ,from  
one or two experiences with a large crop
 in  a certain latitude1 a farmer may   
argue that the crop will generally be   
profitable1 whereas it may not again    

prove so for years4 ,a man may have     
trusted a number of people and found    
them honest4 ,he concludes that  people 
as a rule are honest1 trusts a certain  
dishonest man1 and is  ruined4 ,the     
older people grow1 the more cautious    
they generally become  in forming       
inductive conclusions4 ,many instances  
are noted and compared2  but even the   
wisest sometimes make mistakes4 ,it once
 was a generally  accepted fact that all
 swans were white4 ,nobody had ever seen
 a dark  swan1 and the inference that   
all swans were white was regarded as    
certainly true4 ,black swans were1      
however1 found in ,australia4    ,brooks
 says regarding the probability of      
hypotheses3 ,the probability of  a      
hypothesis is in proportion to the      
number of facts and phenomena it  will  
explain4 ,the larger the number of facts
 and phenomena that it will             
satisfactorily account for1 the greater 
our faith in the correctness of  our    
supposition4444 ,if there is more than  

one hypothesis in respect to  the facts 
under consideration1 that one which     
accounts for the greatest  number of    
facts is the most probable4444 ,in order
 to verify a hypothesis  it must be     
shown that it will account for all the  
facts and phenomena4  ,if these facts   
are numerous and varied1 and the subject
 is so thoroughly  investigated that it 
is quite certain that no important class
 of facts  has been overlooked1 the     
supposition is regarded as true1 and the
  hypothesis is said to be verified4    
,thus the hypothesis of the 'daily      
rotation' of the earth on its axis to   
account for the succession of day  and  
night is accepted as absolutely true4   
,this is the view taken by ,dr4         
,whewell and many other thinkers in     
respect to the verification of a        
hypothesis4 ,some writers1 however1 as  
,mill and his school1 maintain that  in 
order to verify a hypothesis1 we must   
show not only that it explains  all the 
facts and phenomena1 but that there is  

no other possible  hypothesis which will
 account for them4444 ,the former view  
of  verification is regarded as the     
correct one4 ,by the latter view1 it is 
evident that a hypothesis could never be
 verified4    ,jevons says3 ,in the     
fourth step 7verification71 we proceed  
to compare  these deductions with the   
facts already collected1 or when        
necessary and  practicable1 we make new 
observations and plan new experiments1  
so as to  find out whether the          
hypothesis agrees with nature4 ,if we   
meet with  several distinct             
disagreements between our deductions and
 our  observations1 it will become      
likely that the hypothesis is wrong1 and
 we  must then invent a new one4 ,in    
order to produce agreement it will      
sometimes be enough to change the       
hypothesis in a small degree4 ,when we  
get hold of a hypothesis which seems to 
give results agreeing with a few  facts1
 we must not at once assume that it is  
certainly correct4 ,we must  go on      

making other deductions from it under   
various circumstances1 and1  whenever it
 is possible1 we ought to verify these  
results1 that is1  compare them with    
facts observed through the senses4 ,when
 a hypothesis  is shown in this way to  
be true in a great many of its results1 
especially when it enables us to predict
 what we should never otherwise  have   
believed or discovered1 it becomes      
certain that the hypothesis  itself is a
 true one4444 ,sometimes it will happen 
that two or even three  quite different 
hypotheses all seem to agree with       
certain facts1 so that  we are puzzled  
which to select4444 ,when there are thus
 two hypotheses1  one as good as the    
other1 we need to discover some fact or 
thing which  will agree with one        
hypothesis and not with the other1      
because this  immediately enables us to 
decide that the former hypothesis is    
true and  the latter false4    ,in the  
above statements regarding the          
verification of hypotheses we  see      

references made to the testing of the   
latter upon the facts of the  case4     
,these facts may be either the observed 
phenomena or facts  apparent to the     
perception1 or else facts obtained by   
deductive  reasoning4 ,the latter may be
 said to be facts which are held to be  
true  if the hypothesis be true4 ,thus  
if we erect the hypothesis that ,all men
  are mortal1 we may reason deductively 
that it will follow that each and  every
 thing that is a man must die sooner or 
later4 ,then we test our  hypotheses    
upon each and every man whom we may     
subject to observation  and experiment4 
,if we find a single man who does not   
die1 then the test  disproves our       
hypotheses2 if on the contrary all men  
7the facts in the  case7 prove to be    
mortal1 then is our hypotheses proven or
 established4  ,the deductive reasoning 
in this case is as follows3 ,if         
so-and-so is  true regarding            
such-and-such a class2 and if this      
particular thing  belongs to that class2

 then it will follow that so-and-so is  
true  regarding this particular thing4  
,this argument is expressed in what is  
called a ,hypothetical ,proposition 7see
 ,chapter ,,ix71 the consideration of   
which forms a part of the general       
subject of ,deductive ,reasoning4       
,therefore as ,jevons has said1         
,deductive ,reasoning is the ,third     
,step in  ,inductive ,reasoning1 and    
precedes ,verification1 which we have   
already  considered4 ,halleck says3     
,after ,induction has classified certain
  phenomena and thus given us a major   
premise1 we may proceed  deductively to 
apply the inference to any new specimen 
that can be  shown to belong to that    
class4 ,induction hands over to         
deduction a  ready-made major           
premise4444 ,deduction takes that as a  
fact1 making no  inquiry about its      
truth4444 ,only after general laws have 
been laid down1  after objects have been
 classified1 after major premises have  
been  formed1 can deduction be employed4

    ,in view of the above facts1 we     
shall now proceed to a consideration of 
that great class of ,reasoning known    
under the term--,deductive  ,reasoning4 
,,chapter ,,xv4    ,,deductive          
,,reasoning      ,we have seen that     
there are two great classes of          
reasoning1 known  respectively1 as 7#a7 
,inductive ,reasoning1 or the discovery 
of general  truth from particular       
truths2 and 7#b7 ,deductive ,reasoning1 
or the  discovery of particular truths  
from general truths4    ,as we have     
said1 ,deductive ,reasoning is the      
process of discovering  particular      
truths from a general truth4 ,thus from 
the general truth  embodied in the      
proposition ,all horses are animals1    
when it is  considered in connection    
with the secondary proposition that     
,dobbin is  a horse1 we are able to     
deduce the particular truth that3       
,dobbin is an  animal4 ,or1 in the      
following case we deduce a particular   
truth from a  general truth1 as follows3

 ,all mushrooms are good to eat2 this   
fungus  is a mushroom2 therefore1 this  
fungus is good to eat4 ,a deductive     
argument is expressed in a deductive    
syllogism4    ,jevons says regarding the
 last stated illustration3 ,here are    
three  sentences which state three      
different facts2 but when we know the   
two  first facts1 we learn or gather the
 third fact from the other two4 ,when   
we thus learn one fact from other facts1
 we infer or reason1 and we do  this in 
the mind4 ,reasoning thus enables us to 
ascertain the nature of a  thing without
 actual trial4 ,if we always needed to  
taste a thing before  we could know     
whether it was good to eat or not1 cases
 of poisoning  would be alarmingly      
frequent4 ,but the appearance and       
peculiarities of a  mushroom may be     
safely learned by the eye or the nose1  
and reasoning  upon this information and
 the fact already well known1 that      
mushrooms  are good to eat1 we arrive   
without any danger or trouble at the    

conclusion that the particular fungus   
before us is good to eat4 ,to  reason1  
then1 is to get some knowledge from     
other knowledge4    ,the student will   
recognize that ,deductive ,reasoning is 
essentially an  analytic process1       
because it operates in the direction of 
analyzing a  universal or general truth 
into its particulars--into the          
particular  parts which are included    
within it--and asserting of them that   
what is  true of the general is true of 
the particular4 ,thus in the general    
truth that ,all men are mortal1 we see  
included the particular truth  that     
,john ,smith is mortal--,john ,smith    
having been discovered to be a  man4 ,we
 deduce the particular truth about ,john
 ,smith from the general  truth about   
all men4 ,we analyze all men and find   
,john ,smith to be  one of its          
particular parts4 ,therefore1 ,deduction
 is an inference from  the whole to its 
parts2 that is1 an analytic process4    
,the student will also recognize that   

,deductive ,reasoning is essentially  a 
descending process1 because it operates 
in the direction of a  descent from the 
universal to the particular2 from the   
higher to the  lower2 from the broader  
to the narrower4 ,as ,brooks says3      
,deduction  descends from higher truths 
to lower truths1 from laws to facts1    
from  causes to phenomena1 etc4 ,given  
the law1 we can by deduction descend to 
the facts that fall under the law1 even 
if we have never before seen the  facts2
 and so from the cause we may pass down 
to observed and even  unknown phenomena4
    ,the general truths which are used  
as the basis of ,deductive ,reasoning   
are discovered in several ways4 ,the    
majority arise from ,inductive          
,reasoning1 based upon experience1      
observation and experiment4 ,for        
instance in the examples given above1 we
 could not truthfully assert our  belief
 that3 ,all horses are animals unless we
 had previously studied  both the horse 
and animals in general4 ,nor without    

this study could we  state that ,dobbin 
is a horse4 ,nor could we1 without      
previous study1  experience and         
experiment truthfully assert that3 ,all 
mushrooms are  good to eat2 or that this
 fungus is a mushroom2 and that         
therefore1  this fungus is good to eat4 
,even as it is1 we must be sure that the
  fungus really is a mushroom1 else we  
run a risk of poisoning ourselves4      
,general truths of this kind are not    
intuitive1 by any means1 but are  based 
upon our own experience or the          
experience of others4    ,there is a    
class of general truths which are called
 intuitive by some  authorities4        
,halleck says of these3 ,some           
psychologists claim that we  have       
knowledge obtained neither through      
induction nor deduction2 that  we       
recognize certain truths the moment we  
perceive certain objects1  without any  
process of inference4 ,under the head of
 intuitive knowledge  are classified    
such cases as the following3 ,we        

perceive an object and  immediately know
 that it is a time relation1 as existing
 now and then4  ,we are said to have an 
intuitive concept of time4 ,when we are 
told that  the whole is greater than a  
part2 that things equal to the same     
thing  are equal to each other2 that a  
straight line cannot enclose space1 we  
immediately1 or intuitively1 recognize  
the truth of these statements4          
,attempts at proof do not make us feel  
surer of their truth4444 ,we say  that  
it is self-evident1 or that we know the 
fact intuitively4 ,the  axioms of       
mathematics and logic are said to be    
intuitive4    ,another class of         
authorities1 however1 deny the nature of
 intuitive  knowledge of truth1 or      
intuitive truths4 ,they claim that all  
our ideas  arise from sensation and     
reflection1 and that what we call       
intuition  is merely the result of      
sensation and reflection reproduced by  
memory  or heredity4 ,they hold that the
 intuitions of animals and men are      

simply the representation of experiences
 of the race1 or individual1  arising   
from the impressions stored away in the 
subconsciousness of the  individual4    
,halleck states regarding this3 ,this   
school likens intuition  to instinct4   
,it grants that the young duck knows    
water instinctively1  plunges into it1  
and swims without learning4 ,these      
psychologists believe  that there was a 
time when this was not the case with the
 progenitors of  the duck4 ,they had to 
gain this knowledge slowly through      
experience4  ,those that learned the    
proper aquatic lesson survived and      
transmitted  this knowledge through a   
modified structure1 to their progeny4   
,those  that failed in the lesson       
perished in the struggle for            
existence4444  ,this school claims that 
the intuition of cause and effect arose 
in the  same way4 ,generations of human 
beings have seen the cause invariably   
joined to the effect2 hence1 through    
inseparable association came the        

recognition of their necessary sequence4
 ,the tendency to regard all  phenomena 
in these relations was with steadily    
increasing force  transmitted by the    
laws of heredity to posterity1 until the
 recognition  of the relationship has   
become an intuition4    ,another class  
of general truths is merely             
hypothetical4 ,hypothetical  means      
,founded on or including a hypothesis or
 supposition2 assumed or  taken for     
granted1 though not proved1 for the     
purpose of deducing proofs  of a point  
in question4 ,the hypotheses and        
theories of physical science  are used  
as general truths for deductive         
reasoning4 ,hypothetical general  truths
 are in the nature of premises assumed  
in order to proceed with  the process of
 ,deductive ,reasoning1 and without     
which such reasoning  would be          
impossible4 ,they are1 however1 as a    
rule not mere assumptions1  but are     
rather in the nature of assumptions     
rendered plausible by  experience1      

experiment and ,inductive ,reasoning4   
,the ,law of ,gravitation  may be       
considered hypothetical1 and yet it is  
the result of ,inductive  ,reasoning    
based upon a vast multitude of facts and
 phenomena4    ,the ,primary ,basis of  
,deductive ,reasoning may be said to    
rest upon the  logical axiom1 which has 
come down to us from the ancients1 and  
which is  stated as follows3 ,whatever  
is true of the whole is true of its     
parts4 ,or1 as later authorities have   
expressed it3 ,whatever is true  of the 
general is true of the particular4 ,this
 axiom is the basis upon  which we build
 our ,deductive ,reasoning4 ,it         
furnishes us with the  validity of the  
deductive inference or argument4 ,if we 
are challenged  for proof of the        
statement that ,this fungus is good to  
eat1 we are  able to answer that we are 
justified in making the statement by the
  self-evident proposition1 or axiom1   
that ,whatever is true of the  general  
is true of the particular4 ,if the      

general mushroom is good to  eat1 then  
the particular1 this fungus being a     
mushroom1 must also be  good to eat4    
,all horses 7general7 being animals1    
then according to the  axiom1 ,dobbin   
7particular horse7 must also be an      
animal4    ,this axiom has been stated  
in various terms other than those stated
  above4 ,for instance3 ,whatever may be
 affirmed or denied of the whole1  may  
be denied or affirmed of the parts2     
which form is evidently derived  from   
that used by ,hamilton who said3 ,what  
belongs1 or does not belong1  to the    
containing whole1 belongs or does not   
belong1 to each of the  contained parts4
 ,aristotle formulated his celebrated   
,dictum as follows3  ,whatever can be   
predicated affirmatively or negatively  
of any class or  term distributed1 can  
be predicated in like manner of all and 
singular  the classes or individuals    
contained under it4    ,there is another
 form of ,deductive ,reasoning1 that is 
a form based upon  another axiom than   

that of3 ,whatever is true of the whole 
is true of  the parts4 ,this form of    
reasoning is sometimes called           
,mathematical  ,reasoning1 because it is
 the form of reasoning employed in      
mathematics4  ,its axiom is stated as   
follows3 ,things which are equal to the 
same  thing1 are equal to one another4  
,it will be seen that this is the       
principle employed in mathematics4      
,thus3 x equals y2 and y equals #e2     
therefore1 x equals #e4 ,or stated in   
logical terms3 ,a equals ,b2 ,b  equals 
,c2 therefore1 ,a equals ,c4 ,thus it is
 seen that this form of  reasoning1 as  
well as the ordinary form of ,deductive 
,reasoning1 is  strictly mediate1 that  
is1 made through the medium of a third  
thing1  or two things being compared    
through their relation to a third4      
,brooks states3 ,the real reason for the
 certainty of mathematical  reasoning   
may be stated as follows3 ,first1 its   
ideas are definite1  necessary1 and     
exact conceptions of quantity4 ,second1 

its definitions1  as the description of 
these ideas are necessary1 exact1 and   
indisputable  truths4 ,third1 the axioms
 from which we derive conclusions by    
comparison  are all self-evident and    
necessary truths4 ,comparing these exact
 ideas  by the necessary laws of        
inference1 the result must be absolutely
 true4  ,or1 stated in another way1     
using these definitions and axioms as   
the  premises of a syllogism1 the       
conclusion follows inevitably4 ,there is
 no  place or opportunity for error to  
creep in to mar or vitiate our derived  
truths4    ,in conclusion1 we wish to   
call your attention to a passage from   
,jevons  which is worthy of             
consideration and recollection4 ,jevons 
says3 ,there  is a simple rule which    
will enable us to test the truth of a   
great many  arguments1 even of many     
which do not come under any of the rules
  commonly given in books on logic4     
,this rule is that whatever is true of  
one term is true of any term which is   

stated to be the same in meaning  as    
that term4 ,in other words1 we may      
always substitute one term for  another 
if we know that they refer to exactly   
the same thing4 ,there is  no doubt that
 a horse is some animal1 and therefore  
the head of a horse  is the head of some
 animal4 ,this argument cannot be       
brought under the  rules of the         
syllogism1 because it contains four     
distinct logical terms  in two          
propositions2 namely1 horse1 some       
animal2 head of horse1 head of  some    
animal4 ,but it easily comes under the  
rule which ,i have given1  because we   
have simply to put 'some animal' instead
 of 'a horse'4 ,a  great many arguments 
may be explained in this way4 ,gold is a
 metal2  therefore a piece of gold is a 
piece of metal4 ,a negro is a fellow    
creature2 therefore1 he who strikes a   
negro1 strikes a fellow creature4       
,the same eminent authority says3 ,when 
we examine carefully enough the  way in 
which we reason1 it will be found in    

every case to consist in  putting one   
thing or term in place of another1 to   
which we know it to  have an exact      
resemblance in some respect4 ,we use the
 likeness as a  kind of bridge1 which   
leads us from a knowledge of one thing  
to a  knowledge of another2 thus the    
true principle of reasoning may be      
called the substitution of similars1 or 
the passing from like to like4  ,we     
infer the character of one thing from   
the character of something  which acts  
as a go-between1 or third term4 ,when we
 are certain there is  an exact         
likeness1 our inference is certain2 when
 we only believe that  there probably   
is1 or guess that there is1 then our    
inferences are only  probable1 not      
certain4          ,,chapter ,,xvi4      
,,the ,,syllogism      ,the third and   
highest phase or step in reasoning--the 
step which follows  after those styled  
,conception and ,judgment--is generally 
known by the  general term ,reasoning1  
which term1 however1 is used to include 

the  two precedent steps as well as the 
final step itself4 ,this step or        
process consists of the comparing of two
 objects1 persons or things1  through   
their relation to a third object1 person
 or thing4 ,as1 for  instance1 we reason
 7a7 that all mammals are animals2 7b7  
that a horse  is a mammal2 and 7c7 that1
 therefore1 a horse is an animal4 ,the  
most  fundamental principle of this step
 or reasoning consists in the  comparing
 of two objects of thought through and  
by means of their  relation to a third  
object4 ,the natural form of expression 
of this  process of reasoning is called 
a ,syllogism4    ,the process of        
reasoning which gives rise to the       
expression of the  argument in the form 
of a ,syllogism must be understood if   
one wishes to  form a clear conception  
of the ,syllogism4 ,the process itself  
is very  simple when plainly stated1    
although the beginner is sometimes      
puzzled  by the complicated definitions 
and statements of the authorities4 ,let 

us  suppose that we have three objects1 
,a1 ,b and ,c1 respectively4 ,we wish to
  compare ,c and ,b1 but fail to        
establish a relation between them at    
first4  ,we however are able to         
establish a relation between ,a and ,b2 
and between  ,c and ,a4 ,we thus have   
the two propositions 7#a7 ,a equals ,b2 
and 7#b7 ,c  equals ,a4 ,the next step  
is that of inferring that if ,a equals  
,b1 and ,c  equals ,a1 then it must     
follow1 logically1 that ,c equals ,b4   
,this  process is that of indirect or   
mediate comparison1 rather than         
immediate4 ,c and ,b are not compared   
directly or immediately1 but  indirectly
 and through the medium of ,a4 ,a is    
thus said to mediate  between ,b and ,c4
    ,this process of reasoning embraces 
three ideas or objects of thought1 in   
their expression of propositions4 ,it   
comprises the fundamental or  elemental 
form of reasoning4 ,as ,brooks says3    
,the simplest movement of  the reasoning
 process is the comparing of two objects

 through their  relation to a third4    
,the result of this process is an       
argument  expressed in what is called a 
,syllogism4 ,whately says that3 ,a      
,syllogism  is an argument expressed in 
strict logical form so that its         
conclusiveness is manifest from the     
structure of the expression alone1      
without any regard to the meaning of the
 terms4 ,brooks says3 ,all  reasoning   
can be and naturally is expressed in the
 form of the  syllogism4 ,it applies to 
both inductive and deductive reasoning1 
and is  the form in which these         
processes are presented4 ,its importance
 as an  instrument of thought requires  
that it receive special notice4    ,in  
order that the nature and use of the    
,syllogism may be clearly  understood1  
we can do no better than to at once     
present for your  consideration the     
well-known ,rules of the ,syllogism1 an 
understanding  of which carries with it 
a perfect comprehension of the          
,syllogism  itself4    ,the ,rules of   

the ,syllogism state that in order for a
 ,syllogism to be a  perfect ,syllogism1
 it is necessary3    ,i4 ,that there    
should be three1 and no more than three1
 ,propositions4  ,these three           
propositions are3 7#a7 the ,conclusion1 
or thing to be  proved2 and 7#b and #c7 
the ,premises1 or the means of proving  
the  ,conclusion1 and which are called  
the ,major ,premise and ,minor ,premise1
  respectively4 ,we may understand this 
more clearly if we will examine the     
following example3    ,major ,premise3  
,man is mortal2 7or ,a is ,b74    ,minor
 ,premise3 ,socrates is a man2 7or ,c is
 ,a74 ,therefore3    ,conclusion3       
,socrates is mortal 7or ,c is ,b74      
,it will be seen that the above         
,syllogism1 whether expressed in words  
or  symbols1 is logically valid1 because
 the conclusion must logically  follow  
the premises4 ,and1 in this case1 the   
premises being true1 it must  follow    
that the conclusion is true4 ,whately   
says3 ,a ,syllogism is said  to be valid

 when the conclusion logically follows  
from the premises2 if  the conclusion   
does not so follow1 the ,syllogism is   
invalid and  constitutes a ,fallacy1 if 
the error deceives the reasoner himself2
 but  if it is advanced with the idea of
 deceiving others it constitutes a      
,sophism4    ,the reason for ,rule ,i is
 that only three propositions--a ,major 
,premise1  a ,minor ,premise1 and a     
,conclusion--are needed to form a       
,syllogism4 ,if we  have more than three
 propositions1 then we must have more   
than two  premises from which to draw   
one conclusion4 ,the presence of more   
than  two premises would result in the  
formation of two or more ,syllogisms1 or
  else in the failure to form a         
,syllogism4    ,,ii4 ,that there should 
be three and no more than three ,terms4 
,these  ,terms are 7#a7 ,the ,predicate 
of the ,conclusion2 7#b7 the ,subject of
 the  ,conclusion2 and 7#c7 the ,middle 
,term which must occur in both premises1
  being the connecting link in bringing 

the two other ,terms together in  the   
,conclusion4    ,the ,predicate of the  
,conclusion is called the ,major ,term1 
because it  is the greatest in extension
 compared with its fellow terms4 ,the   
,subject of the ,conclusion is called   
the ,minor ,term because it is the      
smallest in extension compared with its 
fellow terms4 ,the ,major and  ,minor   
,terms are called the ,extremes4 ,the   
,middle ,term operates between  the two 
,extremes4    ,the ,major ,term and the 
,middle ,term must appear in the ,major 
,premise4    ,the ,minor ,term and the  
,middle ,term must appear in the ,minor 
,premise4    ,the ,minor ,term and the  
,major ,term must appear in the         
,conclusion4    ,thus we see that ,the  
,major ,term must be the ,predicate of  
the  ,conclusion2 the ,minor ,term the  
,subject of the ,conclusion2 the ,middle
  ,term may be the ,subject or          
,predicate of either of the premises1   
but  must always be found once in both  
premises4    ,the following example will

 show this arrangement more clearly3    
,in the ,syllogism3 ,man is mortal2     
,socrates is a man2 therefore ,socrates 
is mortal1 we have the following        
arrangement3 ,mortal1 the ,major ,term2 
,socrates1 the ,minor ,term2 and ,man1  
the ,middle ,term2 as follows3    ,major
 ,premise3 ,man 7middle term7 is mortal 
7major term74    ,minor ,premise3       
,socrates 7minor term7 is a man 7major  
term74    ,conclusion3 ,socrates 7minor 
term7 is mortal 7major term74    ,the   
reason for the rule that there shall be 
only three terms is that  reasoning     
consists in comparing two terms with    
each other through the  medium of a     
third term4 ,there must be three terms2 
if there are  more than three terms1 we 
form two syllogisms instead of one4     
,,iii4 ,that one premise1 at least1 must
 be affirmative4 ,this1 because  from   
two negative propositions nothing can be
 inferred4 ,a negative  proposition     
asserts that two things differ1 and if  
we have two  propositions so asserting  

difference1 we can infer nothing from   
them4 ,if  our ,syllogism stated that3  
7#a7 ,man is not mortal2 and 7#b7 that  
,socrates is not a man2 we could form no
 ,conclusion1 either that  ,socrates was
 or was not mortal4 ,there would be no  
logical connection  between the two     
premises1 and therefore no ,conclusion  
could be deduced  therefrom4 ,therefore1
 at least one premise must be           
affirmative4    ,,iv4 ,if one premise is
 negative1 the conclusion must be       
negative4 ,this  because if one term    
agrees and another disagrees with a     
third term1  they must disagree with    
each other4 ,thus if our ,syllogism     
stated that3  7#a7 ,man is not mortal2  
and 7#b7 that3 ,socrates is a man2 we   
must  announce the ,negative ,conclusion
 that3 7#c7 ,socrates is not mortal4    
,v4 ,that the ,middle ,term must be     
distributed2 7that is1 taken            
universally7 in at least one premise4   
,this because1 otherwise1 the  ,major   
,term may be compared with one part of  

the ,middle ,term1 and the  ,minor ,term
 with another part of the latter2 and   
there will be actually  no common       
,middle ,term1 and consequently no      
common ground for an  inference4 ,the   
violation of this rule causes what is   
commonly known as  ,the ,undistributed  
,middle1 a celebrated ,fallacy condemned
 by the  logicians4 ,in the ,syllogism  
mentioned as an example in this chapter1
 the  proposition ,man is mortal1 really
 means ,all men1 that is1 ,man in  his  
universal sense4 ,literally the         
proposition is ,all men are mortal1     
from which it is seen that ,socrates    
being a man 7or some of all  men7 must  
partake of the quality of the universal 
,man4 ,if the ,syllogism1  instead1     
read3 ,some men are mortal1 it would not
 follow that  ,socrates must be         
mortal--he might or might not be so4    
,another form of  this fallacy is shown 
in the statement that 7#a7 ,white is a  
color2 7#b7  ,black is a color2 hence   
7#c7 ,black must be ,white4 ,the two    

premises  really mean ,white is some    
color2 ,black is some color2 and not    
that either is all colors4 ,another     
example is3 ,men are bipeds2  birds are 
bipeds2 hence1 men are birds4 ,in this  
example bipeds is not  distributed as   
all bipeds but is simply not-distributed
 as some  bipeds4 ,these syllogisms1    
therefore1 not being according to rule1 
must  fail4 ,they are not true          
syllogisms1 and constitute fallacies4   
,to be distributed1 the ,middle ,term   
must be the ,subject of a  ,universal   
,proposition1 or the ,predicate of a    
,negative ,proposition2 to be           
undistributed it must be the ,subject of
 a ,particular ,proposition1 or  the    
,predicate of an ,affirmative           
,proposition4 7,see chapter on          
,propositions47    ,,vi4 ,that an       
extreme1 if undistributed in a ,premise1
 may not be  distributed in the         
,conclusion4 ,this because it would be  
illogical and  unreasonable to assert   
more in the conclusion than we find in  

the  premises4 ,it would be most        
illogical to argue that3 7#a7 ,all      
horses are  animals2 7#b7 no man is a   
horse2 therefore 7#c7 no man is an      
animal4 ,the  conclusion would be       
invalid1 because the term animal is     
distributed in  the conclusion1 7being  
the predicate of a negative proposition7
 while it  is not distributed in the    
premise 7being the predicate of an      
affirmative  proposition74    ,as we    
have said before1 any ,syllogism which  
violates any of the above  six          
syllogisms is invalid and a fallacy4    
,there are two additional rules which   
may be called derivative4 ,any          
syllogism which violates either of these
 two derivative rules1 also  violates   
one or more of the first six rules as   
given above in detail4    ,the ,two     
,derivative ,rules of the ,syllogism are
 as follows3    ,,vii4 ,that one        
,premise at least must be ,universal4   
,this because from  two particular      
premises no conclusion can be drawn4    

,,viii4 ,that if one premise is         
,particular1 the ,conclusion must be    
particular also4 ,this because only a   
universal conclusion can be drawn  from 
two universal premises4    ,the         
principles involved in these two        
,derivative ,rules may be tested by     
stating ,syllogisms violating them4     
,they contain the essence of the other  
rules1 and every syllogism which breaks 
them will be found to also break  one or
 more of the other rules given4         
,,chapter ,,xvii4    ,,varieties ,,of   
,,syllogisms      ,the authorities in   
,logic hold that with the four kinds of 
propositions  grouped in every possible 
order of arrangement1 it is possible to 
form  nineteen different kinds of valid 
arguments1 which are called the         
nineteen moods of the syllogism4 ,these 
are classified by division into  what   
are called the four figures1 each of    
which figures may be known  by the      
position of the middle term in the      
premises4 ,logicians have  arranged     

elaborate and curious tables constructed
 to show what kinds of  propositions    
when joined in a particular order of    
arrangement will make  sound and valid  
syllogisms4 ,we shall not set forth     
these tables here1 as  they are too     
technical for a popular presentation of 
the subject before  us1 and because they
 are not necessary to the student who   
will  thoroughly familiarize himself    
with the above stated ,laws of the      
,syllogism and who will therefore be    
able to determine in every case  whether
 any given argument is a correct        
syllogism1 or otherwise4    ,in many    
instances of ordinary thought and       
expression the complete  syllogistic    
form is omitted1 or not stated at full  
length4 ,it is common  usage to omit one
 premise of a syllogism1 in ordinary    
expression1 the  missing premise being  
inferred by the speaker and hearer4 ,a  
syllogism  with one premise unexpressed 
is sometimes called an ,enthymene1 the  
term meaning in the mind4 ,for instance1

 the following3 ,we are a free  people1 
therefore we are happy1 the major       
premise ,all free people are  happy     
being omitted or unexpressed4 ,also in  
,poets are imaginative1  therefore      
,byron was imaginative1 the minor       
premise ,byron was a poet  is omitted or
 unexpressed4 ,jevons says regarding    
this phase of the  subject3 ,thus in the
 ,sermon on the ,mount1 the verses known
 as the  ,beatitudes consist each of one
 premise and a conclusion1 and the      
conclusion is put first4 ',blessed are  
the merciful3 for they shall  obtain    
mercy4' ,the subject and the predicate  
of the conclusion are here  inverted1 so
 that the proposition is really ',the   
merciful are blessed4'  ,it is evidently
 understood that ',all who shall obtain 
mercy are  blessed1' so that the        
syllogism1 when stated at full length1  
becomes3  ',all who shall obtain mercy  
are blessed2 ,all who are merciful shall
  obtain mercy2 ,therefore1 all who are 
merciful are blessed4' ,this is a       

perfectly good syllogism4    ,whenever  
we find any of the words3 because1 for1 
therefore1  since1 or similar terms1 we 
may know that there is an argument1 and 
usually a syllogism4    ,we have seen   
that there are three special kinds of   
,propositions1 namely1  7#a7            
,categorical ,propositions1 or          
propositions in which the affirmation   
or denial is made without reservation or
 qualification2 7#b7 ,hypothetical      
,propositions1 in which the affirmation 
or denial is made to depend upon        
certain conditions1 circumstances1 or   
suppositions2 and 7#c7 ,disjunctive     
,propositions1 in which is implied or   
asserted an alternative4    ,the forms  
of reasoning based upon these three     
several classes of  propositions bear   
the same names as the latter4 ,and1     
accordingly the  respective syllogisms  
expressing these forms of reasoning also
 bear the  class name or term4 ,thus1 a 
,categorical ,syllogism is one          
containing  only categorical            

propositions2 a ,hypothetical ,syllogism
 is one  containing one or more         
hypothetical propositions2 a            
,disjunctive  ,syllogism is one         
containing a disjunctive proposition in 
the major  premise4    ,categorical     
,syllogisms1 which are far more common  
than the other two  kinds1 have been    
considered in the previous chapter1 and 
the majority of  the examples of        
syllogisms given in this book are of    
this kind4 ,in a  ,categorical          
,syllogism the statement or denial is   
made positively1 and  without           
reservation or qualification1 and the   
reasoning thereupon  partakes of the    
same positive character4 ,in            
propositions or syllogisms  of this kind
 it is asserted or assumed that the     
premise is true and  correct1 and1 if   
the reasoning be logically correct it   
must follow that  the conclusion is     
correct1 and the new proposition        
springing therefrom  must likewise be   
,categorical in its nature4             

,hypothetical ,syllogisms1 on the       
contrary1 have as one or more of their  
premises a hypothetical proposition     
which affirms or asserts something      
provided1 or if1 something else be true4
 ,hyslop says of this3 ,often  we wish  
first to bring out1 if only             
conditionally1 the truth upon which  a  
proposition rests1 so as to see if the  
connection between this  conclusion and 
the major premise be admitted4 ,the     
whole question will  then depend upon   
the matter of treating the minor        
premise4 ,this has the  advantage of    
getting the major premise admitted      
without the formal  procedure of proof1 
and the minor premise is usually more   
easily proved  than the major4          
,consequently1 one is made to see more  
clearly the force  of the argument or   
reasoning by removing the question of   
the material  truth of the major premise
 and concentrating attention upon the   
relation  between the conclusion and its
 conditions1 so that we know clearly    

what  we have first to deny if we do not
 wish to accept it4    ,by joining a    
hypothetical proposition with an        
ordinary proposition we  create a       
,hypothetical ,proposition4 ,for        
instance3 ,if ,york contains a          
cathedral it is a city2 ,york does      
contain a cathedral2 therefore1 ,york   
is a city4 ,or3 ,if dogs have four feet1
 they are quadrupeds2 dogs  do have four
 feet2 therefore dogs are quadrupeds4   
,the ,hypothetical  ,syllogism may be   
either affirmative or negative2 that is1
 its  hypothetical proposition may      
either hypothetically affirm or         
hypothetically deny4 ,the part of the   
premise of a ,hypothetical  ,syllogism  
which conditions or questions 7and which
 usually contains the  little word if7  
is called the ,antecedent4 ,the major   
premise is the one  usually thus        
conditioned4 ,the other part of the     
conditioned proposition1  and which part
 states what will happen or is true     
under the conditional  circumstances1 is

 called the ,consequent4 ,thus1 in one  
of the above  examples3 ,if dogs have   
four feet is the ,antecedent2 and the   
remainder  of the proposition3 they are 
quadrupeds is the ,consequent4 ,the     
,antecedent is indicated by the presence
 of some conditional term as3  if1      
supposing1 granted that1 provided that1 
although1 had1  were1 etc41 the general 
sense and meaning of such terms being   
that of  the little word if4 ,the       
,consequent has no special indicating   
term4    ,jevons gives the following    
clear and simple ,rules regarding the   
,hypothetical ,syllogism3    ,i4 ,if the
 ,antecedent be affirmed1 the consequent
 may be affirmed4 ,if  the ,consequent  
be denied1 the ,antecedent may be       
denied4    ,,ii4 ,avoid the fallacy of  
affirming the consequent1 or denying the
  antecedent4 ,this is a fallacy because
 of the fact that the conditional       
statement made in the major premise may 
not be the only one  determining the    
consequent4 ,the following is an example

 of ,affirming  the ,consequent3 ,if it 
is raining1 the sky is overclouded2 the 
sky  is overclouded2 therefore1 it is   
raining4 ,in truth1 the sky may be      
overclouded1 and still it may not be    
raining4 ,the fallacy is still  more    
apparent when expressed in symbols1 as  
follows3 ,if ,a is ,b1 ,c is  ,d2 ,c is 
,d2 therefore1 ,a is ,b4 ,the fallacy of
 denying the ,antecedent  is shown by   
the following example3 ,if ,radium were 
cheap it would be  useful2 ,radium is   
not cheap2 therefore ,radium is not     
useful4 ,or1  expressed in symbols3 ,if 
,a is ,b1 ,c is ,d2 ,a is not ,b2       
therefore ,c  is not ,d4 ,in truth      
,radium may be useful although not      
cheap4 ,jevons  gives the following     
examples of these fallacies3 ,if a man  
is a good  teacher1 he thoroughly       
understands his subject2 but ,john      
,jones  thoroughly understands his      
subject2 therefore1 he is a good        
teacher4  ,also1 ,if snow is mixed with 
salt it melts2 the snow on the ground is

  not mixed with salt2 therefore it does
 not melt4    ,jevons says3 ,to affirm  
the consequent and then to infer that we
 can  affirm the antecedent1 is as bad  
as breaking the third rule of the       
syllogism1 and allowing an undistributed
 middle term4444 ,to deny the           
antecedent is really to break the fourth
 rule of the syllogism1 and to  take a  
term as distributed in the conclusion   
which was not so in the  premises4      
,hypothetical ,syllogisms may usually be
 easily reduced to or converted  into   
,categorical ,syllogisms4 ,as ,jevons   
says3 ,in reality1 hypothetical         
propositions and syllogisms are not     
different from those which we have  more
 fully considered4 ,it is all a matter  
of the convenience of stating  the      
propositions4 ,for instance1 instead of 
saying3 ,if ,radium were  cheap1 it     
would be useful1 we may say ,cheap      
,radium would be useful2  or instead of 
saying3 ,if glass is thin1 it breaks    
easily1 we may say  ,thin glass breaks  

easily4 ,hyslop gives the following     
,rule for  ,conversion in such cases3   
,regard the antecedent of the           
hypothetical  proposition as the subject
 of the categorical1 and the consequent 
of  the hypothetical proposition as the 
predicate of the categorical4 ,in  some 
cases this change is a very simple one2 
in others it can be  effected only by a 
circumlocution4    ,the third class of  
syllogisms1 known as ,the ,disjunctive  
,syllogism1 is  the exception to the law
 which holds that all good syllogisms   
must fit  in and come under the ,rules  
of the ,syllogism1 as stated in the     
preceding  chapter4 ,not only does it   
refuse to obey these ,rules1 but it     
fails to  resemble the ordinary         
syllogism in many ways4 ,as ,jevons     
says3 ,it would  be a great mistake to  
suppose that all good logical arguments 
must obey  the rules of the syllogism1  
which we have been considering4 ,only   
those  arguments which connect two terms
 together by means of a middle term1    

and are therefore syllogisms1 need obey 
these rules4 ,a great many of the       
arguments which we daily use are of this
 nature2 but there are a great  many    
other kinds of arguments1 some of which 
have never been understood  by logicians
 until recent years4 ,one important kind
 of argument is known  as the           
,disjunctive ,syllogism1 though it does 
not obey the rules of the  syllogism1 or
 in any way resemble syllogisms4    ,the
 ,disjunctive ,syllogism is one having a
 disjunctive proposition in its  major  
premise4 ,the disjunctive proposition   
also appears in the  conclusion when the
 disjunction in the major premise       
happens to contain  more than two terms4
 ,a disjunctive proposition1 we have    
seen1 is one  which possesses           
alternative predicates for the subject  
in which the  conjunction or 7sometimes 
accompanied by either7 appears4 ,as for 
instance3 ,lightning is sheet or forked2
 or1 ,arches are either  round or       
pointed2 or1 ,angles are either obtuse1 

or right angled1 or  acute4 ,the        
different things joined together by or  
are called  ,alternatives1 the term     
indicating that we may choose between   
the things1  and that if one will not   
answer our purpose we may take the      
other1 or  one of the others if there be
 more than one other4    ,the ,rule     
regarding the ,use of ,disjunctive      
,syllogisms is that3 ,if one  or more   
alternatives be denied1 the rest may    
still be affirmed4 ,thus if  we say that
 ,a is ,b or ,c1 or that ,a is either ,b
 or ,c1 we may deny  the ,b but still   
affirm the ,c4 ,some authorities also   
hold that ,if we  affirm one            
alternative1 we must deny the remainder1
 but this view is  vigorously disputed  
by other authorities4 ,it would seem to 
be a valid  rule in cases where the term
 either appears as3 ,a is either ,b or  
,c1 because there seems to be an        
implication that one or the other alone 
can be true4 ,but in cases like3 ,a is  
,b or ,c1 there may be a  possibility of

 both being true4 ,jevons takes this    
latter view1 giving  as an example the  
proposition3 ,a ,magistrate is a        
,justice-of-the-,peace1  a ,mayor1 or a 
,stipendiary ,magistrate1 but it does   
not follow that one  who is a           
,justice-of-the-,peace may not be at the
 same time a ,mayor4 ,he  states3 ,after
 affirming one alternative we can only  
deny the others if  there be such a     
difference between them that they could 
not be true at  the same time4 ,it would
 seem that both contentions are at the  
same  time true1 the example given by   
,jevons illustrating his contention1 and
  the proposition ,the prisoner is      
either guilty or innocent illustrating  
the contentions of the other side4    ,a
 ,dilemma is a conditional syllogism    
whose ,major ,premise presents  some    
sort of alternative4 ,whately defines it
 as3 ,a conditional  syllogism with two 
or more antecedents in the major1 and a 
disjunctive  minor4 ,there being two    
mutually exclusive propositions in the  

,major  ,premise1 the reasoner is       
compelled to admit one or the other1 and
 is  then caught between the two horns  
of the dilemma4          ,,chapter      
,,xviii4    ,,reasoning ,,by ,,analogy  
,what is called ,reasoning by ,analogy  
is one of the most elementary forms  of 
reasoning1 and the one which the        
majority of us most frequently  employ4 
,it is a primitive form of hasty        
generalization evidencing in the        
natural expectation that things will    
happen as they have happened  before in 
like circumstances4 ,the term as used in
 logic has been  defined as ,resemblance
 of relations2 ,resemblances of any kind
 on which  an argument falling short of 
induction may be founded4 ,brooks says3 
,analogy is that process of thought by  
which we infer that if two things       
resemble each other in one or more      
particulars1 they will resemble each    
other in some other particular4         
,jevons states the ,rule for ,reasoning 
by ,analogy1 as follows3 ,if two  or    

more things resemble each other in many 
points1 they will probably  resemble    
each other also in more points4 ,others 
have stated the same  principle as      
follows3 ,when one thing resembles      
another in known  particulars1 it will  
resemble it also in the unknown2 and ,if
 two  things agree in several           
particulars1 they will also agree in    
other  particulars4    ,there is a      
difference between generalization by    
induction1 and by  analogy4 ,in         
inductive generalization the rule is3   
,what is true of the  many is true of   
all2 while the rule of analogy is3      
things that have  some things in common 
have other things in common4 ,as ,jevons
 aptly  remarks3 ,reasoning by ,analogy 
differs only in degree from that kind of
  reasoning called ',generalization4'   
,when many things resemble each  other  
in a few properties1 we argue about them
 by ,generalization4 ,when  a few things
 resemble each other in many properties1
 it is a case of  analogy4 ,illustrating

 ,analogy1 we may say that if in ,a we  
find the  qualities1 attributes or      
properties called a1 b1 c1 d1 e1 f1  g1 
respectively1 and if we find that in ,b 
the qualities1 etc41 called  a1 b1 c1 d1
 e1 respectively1 are present1 then we  
may reason  by analogy that the         
qualities f and g must also belong to   
,b4    ,brooks says of this form of     
reasoning3 ,this principle is in        
constant  application in ordinary life  
and in science4 ,a physician1 in        
visiting a  patient1 says this disease  
corresponds in several particulars with 
typhoid fever1 hence it will correspond 
in all particulars1 and is  typhoid     
fever4 ,so1 when the geologist discovers
 a fossil animal with  large1 strong1   
blunt claws1 he infers that it procured 
its food by  scratching or burrowing in 
the earth4 ,it was by analogy that ,dr4 
,buckland constructed an animal from a  
few fossil bones1 and when  subsequently
 the bones of the entire animal were    
discovered1 his  construction was found 

to be correct4 ,halleck says3 ,in       
argument or  reasoning we are much aided
 by the habit of searching for hidden   
resemblances4444 ,the detection of such 
a relation cultivates thought4 ,if  we  
are to succeed in argument1 we must     
develop what some call a sixth  sense of
 such relations4444 ,the study of poetry
 may be made very  serviceable in       
detecting analogies and cultivating the 
reasoning powers4  ,when the poet brings
 clearly to mind the change due to      
death1 using as  an illustration the    
caterpillar body transformed into the   
butterfly  spirit1 moving with winged   
ease over flowering meadows1 he is      
cultivating our apprehension of         
relations1 none the less valuable       
because they are beautiful4    ,but the 
student must be on guard against the    
deceptive conclusions  sometimes arising
 from ,reasoning by ,analogy4 ,as       
,jevons says3 ,in many  cases ,reasoning
 by ,analogy is found to be a very      
uncertain guide4 ,in  some cases        

unfortunate mistakes are made4 ,children
 are sometimes killed  by gathering and 
eating poisonous berries1 wrongly       
inferring that they  can be eaten1      
because other berries1 of a somewhat    
similar appearance1  have been found    
agreeable and harmless4 ,poisonous      
toadstools are  occasionally mistaken   
for mushrooms1 especially by people not 
accustomed  to gathering them4 ,in      
,norway mushrooms are seldom seen1 and  
are not  eaten2 but when ,i once found a
 few there and had them cooked at an    
inn1  ,i was amused by the people of the
 inn1 who went and collected toadstools 
and wanted me to eat them also4 ,this   
was clearly a case of mistaken          
reasoning by analogy4 ,even brute       
animals reason in the same way in some  
degree4 ,the beaten dog fears every     
stick1 and there are few dogs which     
will not run away when you pretend to   
pick up a stone1 even if there be  no   
stone to pick up4 ,halleck says3 ,many  
false analogies are  manufactured1 and  

it is excellent thought training to     
expose them4 ,the  majority of people   
think so little that they swallow these 
false  analogies just as newly fledged  
robins swallow small stones dropped into
  their open mouths4444 ,this tendency  
to think as others do must be  resisted 
somewhere along the line1 or there can  
be no progress4 ,brooks  says3 ,the     
argument from ,analogy is plausible1 but
 often deceptive4 ,thus  to infer that  
since ,american swans are white1 the    
,australian swan is  white1 gives a     
false conclusion1 for it is really      
black4 ,so to infer  that because ,john 
,smith has a red nose and is a drunkard1
 then ,henry  ,jones who also has a red 
nose is also a drunkard1 would be a     
dangerous  inference4444 ,conclusions of
 this kind drawn from analogy are       
frequently  fallacious4    ,regarding   
the ,rule for ,reasoning from ,analogy1 
,jevons says3 ,there is  no way in which
 we can really assure ourselves that we 
are arguing  safely by analogy4 ,the    

only rule that can be given is this2    
that the  more closely two things       
resemble each other1 the more likely it 
is that  they are the same in other     
respects1 especially in points closely  
connected with those observed4444 ,in   
order to be clear about our             
conclusions1 we ought in fact never to  
rest satisfied with mere analogy1  but  
ought to try to discover the general    
laws governing the case4 ,in  analogy we
 seem to reason from one fact to another
 fact without  troubling ourselves      
either with deduction or induction4 ,but
 it is only  by a kind of guess that we 
do so2 it is not really conclusive      
reasoning4  ,we ought properly to       
ascertain what general laws of nature   
are shown to  exist by the facts        
observed1 and then infer what will      
happen according  to these laws4444 ,we 
find that reasoning by analogy is not to
 be  depended upon1 unless we make such 
an inquiry into the causes and laws  of 
the things in question1 that we really  

employ inductive and deductive          
reasoning4    ,along the same lines1    
,brooks says3 ,the inference from       
analogy1 like  that from induction1     
should be used with caution4 ,its       
conclusion must  not be regarded as     
certain1 but merely as reaching a high  
degree of  probability4 ,the inference  
from a part to a part1 no more than from
 a  part to the whole1 is attended with 
any rational necessity4 ,to attain      
certainty1 we must show that the        
principles which lie at the root of the 
process are either necessary laws of    
thought or necessary laws of  nature2   
both of which are impossible4 ,hence    
analogy can pretend to only  a high     
degree of probability4 ,it may even     
reach a large degree of  certainty1 but 
it never reaches necessity4 ,we must1   
therefore1 be  careful not to accept any
 inference from analogy as true until it
 is  proved to be true by actual        
observation and experiment1 or by such  
an  application of induction as to      

remove all reasonable doubt4            
,,chapter ,,xix4    ,,fallacies      ,a 
,fallacy is3 ,an unsound argument or    
mode of arguing1 which1 while  appearing
 to be decisive of a question1 is in    
reality not so2 an  argument or         
proposition apparently sound1 but really
 fallacious2 a  fallacious statement or 
proposition1 in which the error is not  
apparent1  and which is therefore likely
 to mislead or deceive2 sophistry4      
,in ,deductive ,reasoning1 we meet with 
two classes of ,fallacies2 namely1  7#a7
 ,fallacious ,premise2 and 7#b7         
,fallacious ,conclusion4 ,we shall now  
consider each of these in turn4         
,fallacious ,premise is in effect an    
unwarranted assumption of  premises4    
,one of the most common forms of this   
kind of ,fallacy is known  as ,begging  
the ,question1 the principle of which is
 the assumption of  a fundamental       
premise which is not conceded2 the      
unwarrantable  assumption of that which 
is to be proved2 or the assumption of   

that by  which it is to be proved1      
without proving it4 ,its most common    
form is  that of boldly stating some    
unproven fact1 authoritatively and      
positively1 and then proceeding to use  
the statement as the major  premise of  
the argument1 proceeding logically from 
that point4 ,the  hearer perceiving the 
argument proceeding logically often     
fails to  remember that the premise has 
been merely assumed1 without warrant and
  without proof and omitting the        
hypothetical if4 ,one may proceed to    
argue logically from the premise that   
,the moon is made of green  cheese1 but 
the whole argument is invalid and       
fallacious because of the  fact that the
 person making it has begged the        
question upon an  unwarranted premise4  
,hyslop gives a good example of this    
form of fallacy  in the case of the     
proposition ,church and ,state should be
 united4  ,proof being demanded the     
advocate proceeds to beg the question as
  follows3 ,good institutions should be 

united2 ,church and ,state are good     
institutions2 therefore1 ,church and    
,state should be united4 ,the           
proposition that ,good institutions     
should be united is fallacious1  being  
merely assumed and not proven4 ,the     
proposition sounds reasonable1  and few 
will feel disposed to dispute it at     
first1 but a little  consideration will 
show that while some good institutions  
may well be  united1 it is not a general
 truth that all should be so4           
,begging the ,question also often arises
 from giving a name to a  thing1 and    
then assuming that we have explained the
 thing4 ,this is a  very frequent       
practice with many people--they try to  
explain by merely  applying names4 ,an  
example of this kind is had in the case 
of the person  who tried to explain why 
one could see through a pane of glass by
 saying  because it is transparent4 ,or 
when one explains that the reason a     
certain substance breaks easily is      
because it is brittle4 ,moliere  makes  

the father of a dumb girl ask why his   
daughter is dumb4 ,the  physician       
answers3 ,nothing is more easy than to  
explain it2 it comes  from her having   
lost the power of speech4 ,yes1 yes1    
objects the  father1 but the cause1 if  
you please1 why she has lost the power  
of  speech4 ,the physician gravely      
replies3 ,all our best authors will tell
  you that it is the impeding of the    
action of the tongue4    ,jevons says3  
,the most frequent way1 perhaps1 in     
which we commit this  kind of fallacy is
 to employ names which imply that we    
disapprove of  something1 and then argue
 that because it is such and such1 it   
must be  condemned4 ,when two sportsmen 
fall out in some manner relating to the 
subject of game1 one will1 in all       
probability1 argue that the act of the  
other was 'unsportsmanlike1' and        
therefore should not have been done4    
,here is to all appearance a correct    
syllogism3    ,no unsportsmanlike act   
should be done2 ,john ,robinson's act   

was  unsportsmanlike3 ,therefore1 ,john 
,robinson's act should not have been    
done4    ,this is quite correct in form2
 but it is evidently the mere semblance 
of an argument4 ',unsportsmanlike' means
 what a sportsman should not  do4 ,the  
point to be argued was whether the act  
fell within the  customary definition of
 what was unsportsmanlike4    ,arising  
from ,begging the ,question1 and in fact
 a class of the latter1  is what is     
called ,reasoning in a ,circle4 ,in this
 form of fallacy one  assumes as proof  
of a proposition the proposition itself2
 or1 uses the  conclusion to prove the  
premise4 ,for instance3 ,this man is a  
rascal  because he is a rogue2 and he is
 a rogue because he is a rascal4 ,or1   
,it is warm because it is summer2 and it
 is summer because it is warm4  ,or ,he 
never drinks to excess1 because he is   
never intemperate in  drinking4         
,brooks says3 ,thus to argue that a     
party is good because it advocates  good
 measures1 and that certain measures are

 good because they are  advocated by so 
excellent a party1 is to reason in a    
circle4 ,so when  persons argue that    
their church is the true one1 because it
 was  established by ,god1 and then     
argue that since it is the true church  
it  must have been founded by ,god1 they
 fall into this fallacy4 ,to argue  that
 'the will is determined by the         
strongest motive' and to define the     
strongest motive as 'that which         
influences the will1' is to revolve in a
  circle of thought and prove nothing4  
,plato commits this error when he       
argues the immortality of the soul from 
its simplicity1 and afterwards  attempts
 to prove its simplicity from its       
immortality4 ,it needs care to  avoid   
this error1 for it is surprising how    
easily one falls into it4  ,hyslop says3
 ,the fallacy of ,reasoning in a ,circle
 occurs mostly in  long arguments where 
it can be committed without ready       
detection4444  ,when it occurs in a long
 discourse it may be committed without  

easy  discovery4 ,it is likely to be    
occasioned by the use of synonyms which 
are taken to express more than the      
conception involved when they do  not4  
,what is called a ,vicious ,circle is   
caused when the conclusion of  one      
syllogism is used for a proposition in  
another syllogism1 which in  its turn   
comes to be used as a basis for the     
first or original  syllogism4           
,fallacious ,conclusion is in effect an 
unwarranted or irrelevant  assumption of
 a logical conclusion4 ,there are many  
forms of this  fallacy among which are  
the following3    ,shifting ground1     
which consists in the pretence of       
proving one thing  while in reality     
merely a similar or related thing is    
being proved4 ,in  this class is the    
argument that because a man is profane  
he must  necessarily be dishonest2 or   
that because a man denies the           
inspiration  of the ,scriptures he must 
be an atheist4    ,fallacious           
,questioning1 in which two or more      

related questions are  asked1 and the   
answer of one is then applied to the    
other4 ,for  instance3 ,you assert that 
the more civilized a community1 the more
  silk-hats are to be found in it8 ,yes4
 ,then1 you state that silk-hats  are   
the promoters and cause of civilization 
in a community8 ,a question  of this    
kind is often so arranged that an answer
 either in the  affirmative or the      
negative will lead to a false or        
fallacious  inference4 ,for instance1   
the question once asked a respectable   
citizen  on the witness stand3 ,have you
 stopped beating your mother8 ,an answer
  of either ,yes or ,no1 was out of the 
question1 for it would have  placed the 
witness in a false position1 for he had 
never beaten his  mother1 nor been      
accused of the same4    ,partial ,proof1
 in which the proof of a partial or     
related fact is used  to infer a proof  
of the whole fact or a related one4 ,for
 instance1 it is  fallacious to argue   
that a man has been guilty of           

drunkenness by merely  proving that he  
was seen entering a saloon4    ,appeal  
to ,public ,opinion1 in which the       
prejudices of the public are  appealed  
to rather than its judgment or reason4  
,in politics and  theological argument  
this fallacy is frequent4 ,it is no     
argument1 and is  reprehensible4        
,appeal to ,authority1 or ,reverence1 in
 which the reverence and respect  of the
 public for certain persons is used to  
influence their feelings in  place of   
their judgment or reason4 ,for instance3
 ,washington thought  so-and-so1 and    
therefore it must be right2 or ,it is   
foolish to affirm  that ,aristotle      
erred2 or ,it has been believed by men  
for two thousand  years1 that1 etc2 or  
,what our fathers believed must be true4
 ,appeals  of this kind may have their  
proper place1 but they are fallacies    
nevertheless1 and not real argument4    
,appeal to ,profession1 in which an     
appeal is made to practices1  principles
 or professions of the opponent1 rather 

than to reason or  judgment4 ,thus we   
may argue that a certain philosophy or  
religion cannot  be sound or good1      
because certain people who hold it are  
not consistent1  or not worthy1 moral or
 sober4 ,this argument is often used    
effectively  against an opponent1 and is
 valid against him personally4 ,but it  
is no  valid argument against his       
philosophy or belief1 because he may act
 in  violation of them1 or he may change
 his practices and still adhere to  his 
beliefs--the two are not joined4        
,appeal to ,general ,belief1 in which an
 appeal is made to general or  universal
 belief1 although the same may be       
unsupported by proof4 ,this is  quite   
common1 but is no real argument4 ,the   
common opinion may be  erroneous1 as    
history proves4 ,a few centuries ago    
this argument could  have been used in  
favor of the earth being flat1 etc4 ,a  
half-century ago  it was used against   
,darwin4 ,today it is being used against
 other new  ideas4 ,it is a fallacy by  

its very nature4    ,appeal to          
,ignorance1 in which an appeal is made  
to the ignorance of  the opponent that  
his conviction may follow from his      
inability to prove  the contrary4 ,it is
 virtually no argument that3 ,so-and-so 
must be true1  because you cannot prove 
that it is not4 ,as ,brooks says3 ,to   
argue  that there is no material world1 
because we cannot explain how the mind  
knows it to exist1 is the celebrated    
fallacy of ,hume in philosophy4 ,the    
fact that we cannot find a needle in a  
haystack is no proof that it is  not    
there4    ,introduction of ,new ,matter1
 also called ,non ,sequitur1 in which   
matter is introduced into the conclusion
 that is not in the premises4  ,hyslop  
gives the following example of it3 ,all 
men are rational2  ,socrates is a man2  
therefore1 ,socrates is noble4 ,de      
,morgan gives the  following more       
complex example3 ,episcopacy is of      
,scripture origin2 ,the  ,church of     
,england is the only ,episcopal church  

in ,england2 therefore1  the church     
established is the church that ought to 
be supported4    ,other fallacies1      
resembling in some respects those above 
mentioned1 are  as follows3    ,fallacy 
of ,ambiguous ,terms1 in which different
 meanings of the same  word are used to 
produce the fallacious argument4 ,as    
,jevons says3 ,a  word with two distinct
 meanings is really two words4          
,confusion between ,collective and      
,general ,meanings of a ,term1 of which 
,jevons says3 ,it would be obviously    
absurd to argue that because all  the   
books in the ,british ,museum ,library  
are sure to give information  about     
,king ,alfred1 therefore any particular 
book will be sure to give  it4 ,by 'all 
the books in the ,british ,museum       
,library1' we mean all  taken together4 
,there are many other cases where the   
confusion is not  so evident1 and where 
great numbers of people are unable to   
see the  exact difference4    ,arguing  
from the ,collective to the ,general1 in

 which the fallacy  consists of arguing 
that because something is true of the   
whole of a  group of things1 therefore  
it is true of any of those things4      
,jevons  says3 ,all the soldiers in a   
regiment may be able to capture a town1 
but it is absurd to suppose that        
therefore every soldier in the  regiment
 could capture the town single handed4  
,white sheep eat a great  deal more than
 black sheep2 but that is because there 
are so many more  of them4    ,uncertain
 ,meaning of a ,sentence1 from which    
confusion arises and  fallacious        
argument may spring4 ,jevons says3      
,there is a humorous way of  proving    
that a cat must have three tails3       
,because a cat has one tail  more than  
no cat2 and no cat has two tails2       
therefore1 any cat has  three tails4    
,here the fallacy rests upon a punning  
interpretation of  no4    ,proving the  
,wrong ,conclusion1 in which the attempt
 to confuse  conclusions is made1 with  
the result that some people will imagine

 that  the case is established4 ,jevons 
says3 ,this was the device of the       
,irishman1 who was charged with theft on
 the evidence of three witnesses1  who  
had seen him do it2 he proposed to call 
thirty witnesses who had  not seen him  
do it4 ,equally logical was the defense 
of the man who was  called a            
materialist1 and who replied1 ',i am not
 a materialist2 ,i am a  barber4'       
,fallacy of ,unsuccessful ,argument1 in 
which is attempted the illogical        
conclusion that because a certain       
argument has failed the opposite        
conclusion is proven4 ,this fallacy is  
quite common1 especially in cases  of   
juries4 ,one side fails to prove certain
 contentions1 and the jury  leaps to the
 conclusion that the opposite contention
 must be correct4  ,this is clearly     
fallacious1 for there is always the     
possibility of a  third explanation4 ,in
 the case of a claim of alibi juries are
 apt to  fall into this fallacy4 ,the   
failure of the attempt to establish an  

alibi is often held to be in the nature 
of proof of the guilt of the  accused4  
,old trial lawyers assert that a failure
 to establish a claimed  alibi tends to 
injure the chance of the accused more   
than direct  evidence against him4 ,yet1
 as all logical reasoners will see1     
there is  no logical validity in any    
such inference4 ,as ,jevons has well    
said3 ,no  number of failures in        
attempting to prove a proposition really
 disprove  it4 ,at the end of each      
failure the case simply stands in the   
same  position as before the attempt2   
i4e41 not proven4    ,all ,violations of
 the ,rules of the ,syllogism constitute
 fallacies1 as  may be seen by forming a
 syllogism in violation of one or more  
of the  rules4    ,the logicians1       
particularly those of ancient times1    
took great pains to  discover and name  
new variations of fallacies1 many of    
which were  hair-splitting in nature1   
and not worthy of being considered      
seriously4  ,some of those which we have

 enumerated may possibly be open to the 
same  criticism1 but we have omitted    
many of the worst offenders against     
practical common sense4 ,an             
understanding of the fundamental ,laws  
of  ,reasoning is sufficient to expose  
and unmask all fallacies1 and such      
understanding is far more valuable than 
the memorizing of the names of          
hair-splitting fallacies which would not
 deceive a child4    ,in addition to the
 above stated fallacies of ,deductive   
,reasoning1 there  are other fallacies  
which are met with in ,inductive        
,reasoning4 ,let us  briefly consider   
them4    ,hasty and ,false              
,generalization is a common fallacy of  
this class4  ,persons sometimes see     
certain qualities in a few individuals  
of a class1  and mistakenly infer that  
all the individuals in that class must  
possess these same qualities4 ,travelers
 frequently commit this fallacy4        
,englishmen visiting the ,united ,states
 for a few weeks have been known to     

publish books upon their return home    
making the most ridiculous              
generalizations regarding the ,american 
people1 their assertions being  based   
upon the observation of a few scattered 
individuals1 often not at  all          
representative4 ,americans traveling    
abroad commit similar errors4 ,a  flying
 trip through a country does not afford 
the proper opportunity for  correct     
generalization4 ,as ,brooks says3 ,no   
hypothesis should be  accepted as true  
until the facts are so numerous that    
there can be no  doubt of its being     
proved4    ,fallacies of ,observation   
result from incorrect methods of        
observation  among which may be         
mentioned the following3 7#a7 ,careless 
,observation1  or inexact perception and
 conception2 7#b7 ,partial ,observation1
 in  which one observes only a part of  
the thing or fact1 omitting the         
remainder1 and thus forming an          
incomplete and imperfect concept of the 
thing or fact2 7#c7 ,neglect of         

,exceptions and ,contradictory ,facts1  
in  which the exceptions and            
contradictory facts are ignored1 thereby
 giving  undue importance to the        
observed facts2 7#d7 ,assumption of     
,facts which  are not real facts1 or the
 assumption of the truth of things which
 are  untrue2 7#e7 ,confusing of        
,inferences with ,facts1 which is most  
unwarrantable4    ,fallacies of         
,mistaken ,cause result from the        
assumption of a thing as a  cause1 when 
it is not so1 of which the following are
 familiar examples3  ,substituting the  
,antecedent for the ,cause1 which       
consists in assuming  a mere antecedent 
thing for a cause of another thing4     
,thus one might  assume that the crowing
 of the cock was the cause of daybreak1 
because  it preceded it2 or that a comet
 was the cause of the plague which      
followed its appearance2 or in the      
actual case in which a child reasoned   
that doctors caused deaths1 because     
observation had shown that they  always 

visited persons before they died2 or    
that crops failed because a  ,president 
of a certain political party had been   
inaugurated a few months  before4 ,some 
fallacies of everyday reasoning are     
quite as illogical as  those just       
mentioned4 ,substituting the ,symptom   
for the ,cause1 which  consists in      
assuming as a cause some mere symptom1  
sign or incident of  the real cause4 ,to
 assume that the pimples of measles were
 the cause  of the disease1 would be to 
commit a fallacy of this kind4 ,we have 
mentioned elsewhere the fallacy which   
would assume silk-hats to be the  cause 
of ,civilization1 instead of being a    
mere incident of the latter4            
,politicians are fond of assuming       
certain incidents or signs of a period1 
as being the causes of the prosperity1  
culture and advancement of the  period1 
or the reverse4 ,one might argue1 with  
equal force1 that  automobiles were the 
causes of national prosperity1 pointing 
to the fact  that the more automobiles  

to be seen the better the times4 ,or1   
that  straw hats produced hot weather1  
for similar reasons4    ,the ,fallacy of
 ,analogy consists in assuming a        
resemblance or identity1  where none    
exists4 ,we have spoken of this in      
another chapter4 ,brooks  says1 also3   
,it is a fallacy to carry an analogy too
 far2 as to infer  from the parable of  
the praying of the importunate woman    
that ,god  resembles the unjust judge4  
,in conclusion1 we would call your      
attention to the following words from   
,jevons1 in which he expresses the gist 
of the matter3 ,it is impossible  too   
often to remind people that1 on the one 
hand1 all correct reasoning  consists in
 substituting like things for like      
things1 and inferring  that what is true
 of one will be true of all which are   
similar to it in  the points of         
resemblance concerned in the matter4 ,on
 the other hand1  all incorrect         
reasoning consists in putting one thing 
for another where  there is not the     

requisite likeness4 ,it is the purpose  
of the rules of  deductive and inductive
 logic to enable us to judge as far as  
possible  when we are thus rightly or   
wrongly reasoning from some things to   
others4      ,,finis4                   
,,transcriber',s ,,note3      ,obvious  
typos and printer errors have been      
corrected without comment4 ,in  addition
 to obvious errors1 the following       
changes have been made3      ,page #ah3 
,idea changed to ,ideas in the phrase1  
444 forming      ,concepts or ,general  
,ideas4      ,page #ga3 infuoria changed
 to infusoria in the phrase1 444 the    
microscopic infusoria4444      ,page    
#ace3 disciple changed to discipline in 
the phrase1 444      necessity of       
discipline for invention4444    ,other  
than the above changes1 no attempt has  
been made to correct common  spelling1  
punctuation1 grammar1 etc4 ,the author's
 usage is preserved as  printed in the  
original publication4