pg-i ,,symbolic ,,logic ,by ,lewis ,carroll pg-ii pg-iii pg-iv ,a ,syllogism worked out4 ,that story of yours1 about your once meeting the sea-serpent1 always sets me off yawning2 ,i never yawn1 unless when ,i'm listening to something totally devoid of interest4 ,the ,premisses1 separately4 --------------- --------------- 7 7 7 7 ------ ------ 77 7 7 ------------ ------------ 7 7 ------ ------ --------------- --------------- ,the ,premisses1 combined4 --------------- 7 7 7 7 ------ 777 7 ------------ 7 7 ------ --------------- ,the ,conclusion4 ------- 777 7 ------ ------- ,that story of yours1 about your once meeting the sea-serpent1 is totally devoid of interest4 pg-v ,,symbolic ,,logic ,,part ,i ,,elementary ,,by ,,lewis ,,carroll ,,second ,,thousand ,,fourth ,,edition ,,price ,,two ,,shillings ,london ,,macmillan ,,and ,,co41 ,,limited ,,new ,,york3 ,,the ,,macmillan ,,company #ahig ,all rights reserved pg-vi ,,richard ,,clay ,,and ,,sons1 ,,limited1 ,,london ,,and ,,bungay pg-vii ,,advertisement4 ,an envelope1 containing two blank ,diagrams 7,biliteral and ,triliteral7 and #i counters 7#d ,red and #e ,grey71 may be had1 from ,messrs4 ,macmillan1 for #c;d41 by post #d;d4 99 99 99 99 99 ,i shall be grateful to any ,reader of this book who will point out any mistakes or misprints he may happen to notice in it1 or any passage which he thinks is not clearly expressed4 99 99 99 99 99 ,i have a quantity of ,,ms4 in hand for ,parts ,,ii and ,,iii1 and hope to be able----should life1 and health1 and opportunity1 be granted to me1 to publish them in the course of the next few years4 ,their contents will be as follows3-- ,,part ,,ii4 ,,advanced4 ,further investigations in the subjects of ,part ,i4 ,propositions of other forms 7such as ,not-all x are y74 ,triliteral and ,multiliteral ,propositions 7such as ,all abc are de74 ,hypotheticals4 ,dilemmas4 c4 c4 ,part ,,iii4 ,,transcendental4 ,analysis of a ,proposition into its ,elements4 ,numerical and ,geometrical ,problems4 ,the ,theory of ,inference4 ,the ,construction of ,problems4 ,and many other ,curiosa ,logica4 pg-viii ,,preface ,,to ,,the ,,fourth ,,edition4 ,the chief alterations1 since the ,first ,edition1 have been made in the ,chapter on ',classification' 7pp4 #b1 #c7 and the ,book on ',propositions' 7pp4 #aj to #ai74 ,the chief additions have been the questions on words and phrases1 added to the ,examination-,papers at p4 #id1 and the ,notes inserted at pp4 #afd1 #aid4 ,in ,book ,i1 ,chapter ,,ii1 ,i have adopted a new definition of ',classification'1 which enables me to regard the whole ,universe as a ',class1' and thus to dispense with the very awkward phrase 'a ,set of ,things4' ,in the ,chapter on ',propositions of ,existence' ,i have adopted a new 'normal form1' in which the ,class1 whose existence is affirmed or denied1 is regarded as the ,predicate1 instead of the ,subject1 of the ,proposition1 thus evading a very subtle difficulty which besets the other form4 ,these subtle difficulties seem to lie at the root of every ,tree of ,knowledge1 and they are far more hopeless to grapple with than any that occur in its higher branches4 ,for example1 the difficulties of the ,forty-,seventh ,proposition of ,euclid are mere child's play compared with the mental torture endured in the effort to think out the essential nature of a straight ,line4 ,and1 in the present work1 the difficulties of the #e ,liars ,problem1 at p4 #aib1 are trifles1 light as air1 compared with the bewildering question ,what is a ,thing8 ,in the ,chapter on ',propositions of ,relation' ,i have inserted a new ,section1 containing the proof that a ,proposition1 beginning with ,all1 is a ,double ,proposition 7a fact that is quite independent of the arbitrary rule1 laid down in the next ,section1 that such a ,proposition is to be understood as implying the actual existence of its ,subject74 ,this proof was given1 in the earlier editions1 incidentally1 in the course of the discussion of the ,biliteral ,diagram3 but its proper place1 in this treatise1 is where ,i have now introduced it4 pg-ix ,in the ,sorites-,examples1 ,i have made a good many verbal alterations1 in order to evade a difficulty1 which ,i fear will have perplexed some of the ,readers of the first three ,editions4 ,some of the ,premisses were so worded that their ,terms were not ,specieses of the ,univ4 named in the ,dictionary1 but of a larger ,class1 of which the ,univ4 was only a portion4 ,in all such cases1 it was intended that the ,reader should perceive that what was asserted of the larger ,class was thereby asserted of the ,univ41 and should ignore1 as superfluous1 all that it asserted of its other portion4 ,thus1 in ,ex4 #ae1 the ,univ4 was stated to be ducks in this village1 and the third ,premiss was ,mrs4 ,bond has no gray ducks1 i4e4 ,no gray ducks are ducks belonging to ,mrs4 ,bond4 ,here the ,terms are not ,specieses of the ,univ41 but of the larger ,class ducks1 of which the ,univ4 is only a portion3 and it was intended that the ,reader should perceive that what is here asserted of ducks is thereby asserted of ducks in this village4 and should treat this ,premiss as if it were ,mrs4 ,bond has no gray ducks in this village1 and should ignore1 as superfluous1 what it asserts as to the other portion of the ,class ducks1 viz4 ,mrs4 ,bond has no gray ducks out of this village4 ,in the ,appendix ,i have given a new version of the ,problem of the ,five ,liars4 ,my object1 in doing so1 is to escape the subtle and mysterious difficulties which beset all attempts at regarding a ,proposition as being its own ,subject1 or a ,set of ,propositions as being ,subjects for one another4 ,it is certainly1 a most bewildering and unsatisfactory theory3 one cannot help feeling that there is a great lack of substance in all this shadowy host----that1 as the procession of phantoms glides before us1 there is not one that we can pounce upon1 and say ,here is a ,proposition that must be either true or false6----that it is but a ,barmecide ,feast1 to which we have been bidden----and that its prototype is to be found in that mythical island1 whose inhabitants earned a precarious living by taking in each others' washing6 ,by simply translating telling #b ,truths into taking both of #b condiments 7salt and mustard71 telling #b ,lies into taking neither of them and telling a ,truth and a ,lie 7order not specified7 into taking only one condiment 7it is not specified which71 ,i have escaped all those metaphysical puzzles1 and have produced a ,problem which1 when translated into a ,set of symbolized ,premisses1 furnishes the very same ,data as were furnished by the ,problem of the ,five ,liars4 pg-x ,the coined words1 introduced in previous editions1 such as ,eliminands and ,retinends1 perhaps hardly need any apology3 they were indispensable to my system3 but the new plural1 here used for the first time1 viz4 ,soriteses1 will1 ,i fear1 be condemned as bad ,english1 unless ,i say a word in its defence4 ,we have three singular nouns1 in ,english1 of plural form1 series1 species1 and ,sorites3 in all three1 the awkwardness1 of using the same word for both singular and plural1 must often have been felt3 this has been remedied1 in the case of series by coining the plural serieses1 which has already found its way into the dictionaries3 so ,i am no rash innovator1 but am merely following suit1 in using the new plural ,soriteses4 ,in conclusion1 let me point out that even those1 who are obliged to study ,formal ,logic1 with a view to being able to answer ,examination-,papers in that subject1 will find the study of ,symbolic ,logic most helpful for this purpose1 in throwing light upon many of the obscurities with which ,formal ,logic abounds1 and in furnishing a delightfully easy method of testing the results arrived at by the cumbrous processes which ,formal ,logic enforces upon its votaries4 ,this is1 ,i believe1 the very first attempt 7with the exception of my own little book1 ,the ,game of ,logic1 published in #ahhf1 a very incomplete performance7 that has been made to popularise this fascinating subject4 ,it has cost me years of hard work3 but if it should prove1 as ,i hope it may1 to be of real service to the young1 and to be taken up1 in ,high ,schools and in private families1 as a valuable addition to their stock of healthful mental recreations1 such a result would more than repay ten times the labour that ,i have expended on it4 ,l4 ,c4 #bi1 ,,bedford ,,street1 ,,strand4 ,christmas1 #ahif4 pg-xi ,,introduction4 ,,to ,,learners4 ,n4,b4 ,some remarks1 addressed to ,teachers1 will be found in the ,appendix1 at p4 #afe4 ,the ,learner1 who wishes to try the question fairly1 whether this little book does1 or does not1 supply the materials for a most interesting mental recreation1 is earnestly advised to adopt the following ,rules3-- 7#a7 ,begin at the beginning1 and do not allow yourself to gratify a mere idle curiosity by dipping into the book1 here and there4 ,this would very likely lead to your throwing it aside1 with the remark ,this is much too hard for me61 and thus losing the chance of adding a very large item to your stock of mental delights4 ,this ,rule 7of not dipping7 is very desirable with other kinds of books----such as novels1 for instance1 where you may easily spoil much of the enjoyment you would otherwise get from the story1 by dipping into it further on1 so that what the author meant to be a pleasant surprise comes to you as a matter of course4 ,some people1 ,i know1 make a practice of looking into ,vol4 ,,iii first1 just to see how the story ends3 and perhaps it is as well just to know that all ends happily----that the much-persecuted lovers do marry after all1 that he is proved to be quite innocent of the murder1 that the wicked cousin is completely foiled in his plot and gets the punishment he deserves1 and that the rich uncle in ,india 7,qu4 ,why in ,india8 ,ans4 ,because1 somehow1 uncles never can get rich anywhere else7 dies at exactly the right moment----before taking the trouble to read ,vol4 ,i4 ,this1 ,i say1 is just permissible with a novel1 where ,vol4 ,,iii has a meaning1 even for those who have not read the earlier part of the story2 but1 with a scientific book1 it is sheer insanity3 you will find the latter part hopelessly unintelligible1 if you read it before reaching it in regular course4 pg-xii 7#b7 ,don't begin any fresh ,chapter1 or ,section1 until you are certain that you thoroughly understand the whole book up to that point1 and that you have worked1 correctly1 most if not all of the examples which have been set4 ,so long as you are conscious that all the land you have passed through is absolutely conquered1 and that you are leaving no unsolved difficulties behind you1 which will be sure to turn up again later on1 your triumphal progress will be easy and delightful4 ,otherwise1 you will find your state of puzzlement get worse and worse as you proceed1 till you give up the whole thing in utter disgust4 7#c7 ,when you come to any passage you don't understand1 read it again3 if you still don't understand it1 read it again3 if you fail1 even after three readings1 very likely your brain is getting a little tired4 ,in that case1 put the book away1 and take to other occupations1 and next day1 when you come to it fresh1 you will very likely find that it is quite easy4 7#d7 ,if possible1 find some genial friend1 who will read the book along with you1 and will talk over the difficulties with you4 ,talking is a wonderful smoother-over of difficulties4 ,when ,i come upon anything----in ,logic or in any other hard subject----that entirely puzzles me1 ,i find it a capital plan to talk it over1 aloud1 even when ,i am all alone4 ,one can explain things so clearly to one's self6 ,and then1 you know1 one is so patient with one's self3 one never gets irritated at one's own stupidity6 ,if1 dear ,reader1 you will faithfully observe these ,rules1 and so give my little book a really fair trial1 ,i promise you1 most confidently1 that you will find ,symbolic ,logic to be one of the most1 if not the most1 fascinating of mental recreations6 ,in this ,first ,part1 ,i have carefully avoided all difficulties which seemed to me to be beyond the grasp of an intelligent child of 7say7 twelve or fourteen years of age4 ,i have myself taught most of its contents1 viv voce1 to many children1 and have found them take a real intelligent interest in the subject4 ,for those1 who succeed in mastering ,part ,i1 and who begin1 like ,oliver1 asking for more1 ,i hope to provide1 in ,part ,,ii1 some tolerably hard nuts to crack----nuts that will require all the nut-crackers they happen to possess6 pg-xiii ,mental recreation is a thing that we all of us need for our mental health2 and you may get much healthy enjoyment1 no doubt1 from ,games1 such as ,back-gammon1 ,chess1 and the new ,game ,halma4 ,but1 after all1 when you have made yourself a first-rate player at any one of these ,games1 you have nothing real to show for it1 as a result6 ,you enjoyed the ,game1 and the victory1 no doubt1 at the time3 but you have no result that you can treasure up and get real good out of4 ,and1 all the while1 you have been leaving unexplored a perfect mine of wealth4 ,once master the machinery of ,symbolic ,logic1 and you have a mental occupation always at hand1 of absorbing interest1 and one that will be of real use to you in any subject you may take up4 ,it will give you clearness of thought----the ability to see your way through a puzzle----the habit of arranging your ideas in an orderly and get-at-able form----and1 more valuable than all1 the power to detect fallacies1 and to tear to pieces the flimsy illogical arguments1 which you will so continually encounter in books1 in newspapers1 in speeches1 and even in sermons1 and which so easily delude those who have never taken the trouble to master this fascinating ,art4 ,try it4 ,that is all ,i ask of you6 ,l4 ,c4 #bi1 ,,bedford ,,street1 ,,strand4 ,february #ba1 #ahif4 pg-xiv pg-xv ,,contents4 ,,book ,i4 ,,things ,,and ,,their ,,attributes4 ,,chapter ,i4 ,,introductory4 ,,page ',things' #a ',attributes' ',adjuncts' ,,chapter ,,ii4 ,,classification4 ',classification' #a ',class' ',peculiar' ,attributes ',genus' ',species' ',differentia' ',real' and ',unreal'1 or ',imaginary'1 ,classes #b ',individual' ,a ,class regarded as a single ,thing #b pg-xvi ,,chapter ,,iii4 ,,division4 #a4 ,introductory4 ',division' #c ',codivisional' ,classes #b4 ,dichotomy4 ',dichotomy' #c ,arbitrary limits of ,classes ,subdivision of ,classes #d ,,chapter ,,iv4 ,,names4 ',name' #d ',real' and ',unreal' ,names ,three ways of expressing a ,name ,two senses in which a plural ,name may be used #e ,,chapter ,v4 ,,definitions4 ',definition' #f ,examples worked as models pg-xvii ,,book ,,ii4 ,,propositions4 ,,chapter ,i4 ,,propositions ,,generally4 #a4 ,introductory4 ,technical meaning of some #h ',proposition' ',normal form' of a ,proposition ',subject'1 ',predicate'1 and ',terms' #i #b4 ,normal form of a ,proposition4 ,its four parts3-- 7#a7 ',sign of ,quantity' #i 7#b7 ,name of ,subject 7#c7 ',copula' 7#d7 ,name of ,predicate #c4 ,various kinds of ,propositions4 ,three kinds of ,propositions3-- 7#a7 ,begins with ,some4 ,called a ',particular' ,proposition3 also a ,proposition 'in ,i' #aj 7#b7 ,begins with ,no4 ,called a ',universal ,negative' ,proposition3 also a ,proposition 'in ,e' 7#c7 ,begins with ,all4 ,called a ',universal ,affirmative' ,proposition3 also a ,proposition 'in ,a' pg-xviii ,a ,proposition1 whose ,subject is an ,individual1 is to be regarded as ,universal ,two kinds of ,propositions1 ',propositions of ,existence'1 and ',propositions of ,relation' ,,chapter ,,ii4 ,,propositions ,,of ,,existence4 ',proposition of ,existence ' #aa ,,chapter ,,iii4 ,,propositions ,,of ,,relation4 #a4 ,introductory4 ',proposition of ,relation' #ab ',universe of ,discourse1' or ',univ4' #b4 ,reduction of a ,proposition of ,relation to ,normal form4 ,rules #ac ,examples worked #c4 ,a ,proposition of ,relation1 beginning with ,all1 is a ,double ,proposition4 ,its equivalence to two ,propositions #ag pg-xix #d4 ,what is implied1 in a ,proposition of ,relation1 as to the ,reality of its ,terms8 ,propositions beginning with ,some #ai ,no ,all #e4 ,translation of a ,proposition of ,relation into one or more ,propositions of ,existence4 ,rules #bj ,examples worked ,,book ,,iii4 ,,the ,,biliteral ,,diagram4 ,,chapter ,i4 ,,symbols ,,and ,,cells4 ,the ,diagram assigned to a certain ,set of ,things1 viz4 our ,univ4 #bb ,univ4 divided into 'the x-,class' and 'the x'-,class' #bc ,the ,north and ,south ,halves assigned to these two ,classes ,the x-,class subdivided into 'the xy-,class' and 'the xy'-,class' ,the ,north-,west and ,north-,east ,cells assigned to these two ,classes ,the x'-,class similarly divided ,the ,south-,west and ,south-,east ,cells similarly assigned ,the ,west and ,east ,halves have thus been assigned to 'the y-,class' and 'the y'-,class' #bd ,table ,i4 ,attributes of ,classes1 and ,compartments1 or ,cells1 assigned to them #be pg-xx ,,chapter ,,ii4 ,,counters4 ,meaning of a ,red ,counter placed in a ,cell #bf on a ,partition ,american phrase sitting on the fence ,meaning of a ,grey ,counter placed in a ,cell ,,chapter ,,iii4 ,,representation ,,of ,,propositions4 #a4 ,introductory4 ,the word ,things to be henceforwards omitted #bg ',uniliteral' ,proposition ',biliteral' do4 ,proposition 'in terms of' certain ,letters #b4 ,representation of ,propositions of ,existence4 ,the ,proposition ,some x exist #bh ,three other similar ,propositions ,the ,proposition ,no x exist ,three other similar ,propositions #bi ,the ,proposition ,some xy exist ,three other similar ,propositions ,the ,proposition ,no xy exist ,three other similar ,propositions ,the ,proposition ,no x exist is ,double1 and is equivalent to the two ,propositions ,no xy exist and ,no xy' exist #cj pg-xxi #c4 ,representation of ,propositions of ,relations4 ,the ,proposition ,some x are y ,three other similar ,propositions ,the ,proposition ,some y are x #ca ,three other similar ,propositions ,trio of equivalent ,propositions1 viz4 ,some xy exist ,some x are y ,some y are x ',converse' ,propositions1 and ',conversion' ,three other similar ,trios #cb ,the ,proposition ,no x are y ,three other similar ,propositions ,the ,proposition ,no y are x ,three other similar ,propositions ,trio of equivalent ,propositions1 viz4 ,no xy exist ,no x are y ,no y are x #cc ,three other similar ,trios ,the ,proposition ,all x are y is ,double1 and is equivalent to the two ,propositions ,some x are y and ,no x are y' ,seven other similar ,propositions #cd ,tables ,,ii1 ,,iii4 ,representation of ,propositions of ,existence and ,relation #cd1 #ce ,,chapter ,,iv4 ,,interpretation ,,of ,,biliteral ,,diagram1 ,,when ,,marked ,,with ,,counters4 ------- 747 ,interpretation of ------ #cf ------- ,and of three other similar arrangements pg-xxii ------- 7 7 ,interpretation of ------ ------- ,and of three other similar arrangements ------- 747 ,interpretation of ------ #cg ------- ,and of three other similar arrangements ------- 747747 ,interpretation of ------ ------- ,and of three other similar arrangements ------- 7 77 7 ,interpretation of ------ ------- ,and of three other similar arrangements ------- 7477 7 ,interpretation of ------ ------- ,and of seven other similar arrangements #ch ,,book ,,iv4 ,,the ,,triliteral ,,diagram4 ,,chapter ,i4 ,,symbols ,,and ,,cells4 ,change of ,biliteral into ,triliteral ,diagram #ci ,the xy-,class subdivided into 'the xym-,class' and 'the xym'-,class' #dj pg-xxiii ,the ,inner and ,outer ,cells of the ,north-,west ,quarter assigned to these ,classes ,the xy'-,class1 the x'y-,class1 and the x'y'-,class similarly subdivided ,the ,inner and ,outer ,cells of the ,north-,east1 the ,south-,west1 and the ,south-,east ,quarter similarly assigned ,the ,inner ,square and the ,outer ,border have thus been assigned to 'the m-,class' and 'the m'-,class' ,rules for finding readily the ,compartment1 or ,cell1 assigned to any given ,attribute or ,attributes ,table ,,iv4 ,attributes of ,classes1 and ,compartments1 or ,cells1 assigned to them #db ,,chapter ,,ii4 ,,representation ,,of ,,propositions ,,in ,,terms ,,of x ,,and m1 ,,or ,,of y ,,and m4 #a4 ,representation of ,propositions of ,existence in terms of x and m1 or of y and m4 ,the ,proposition ,some xm exist #dc ,seven other similar ,propositions ,the ,proposition ,no xm exist #dd ,seven other similar ,propositions #b4 ,representation of ,propositions of ,relation in terms of x and m1 or of y and m4 ,the ,pair of ,converse ,propositions ,some x are m ,some m are x ,seven other similar ,pairs ,the ,pair of ,converse ,propositions ,no x are m ,no m are x ,seven other similar ,pairs ,the ,proposition ,all x are m #de ,fifteen other similar ,propositions ,tables ,v1 ,,vi1 ,,vii1 ,,viii4 ,representations of ,propositions in terms of x and m1 or of y and m #df to #di pg-xxiv ,,chapter ,,iii4 ,,representation ,,of ,,two ,,propositions ,,of ,,relation1 ,,one ,,in ,,terms ,,of x ,,and m1 ,,and ,,the ,,other ,,in ,,terms ,,of y ,,and m1 ,,on ,,the ,,same ,,diagram4 ,the ,digits ,i and ,o to be used instead of ,red and ,grey ,counters #ej ,rules ,examples worked ,,chapter ,,iv4 ,,interpretation1 ,,in ,,terms ,,of x ,,and y1 ,,of ,,triliteral ,,diagram1 ,,when ,,marked ,,with ,,counters ,,or ,,digits4 ,rules #ec ,examples worked #ed ,,book ,v4 ,,syllogisms4 ,,chapter ,i4 ,,introductory4 ',syllogism' #ef ',premisses' ',conclusion' ',eliminands' #eg ',retinends' ',consequent' ,the ,symbol 4'4 ,specimen-,syllogisms pg-xxv ,,chapter ,,ii4 ,,problems ,,in ,,syllogisms4 #a4 ,introductory4 ',concrete' and ',abstract' ,propositions #ei ,method of translating a ,proposition from concrete into abstract form ,two forms of ,problems #b4 ,given a ,pair of ,propositions of ,relation1 which contain between them a ,pair of codivisional ,classes1 and which are proposed as ,premisses3 to ascertain what ,conclusion1 if any1 is consequent from them4 ,rules #fj ,examples worked fully ,the same worked briefly1 as models #fd #c4 ,given a ,trio of ,propositions of ,relation1 of which every two contain a ,pair of codivisional ,classes1 and which are proposed as a ,syllogism3 to ascertain whether the proposed ,conclusion is consequent from the proposed ,premisses1 and1 if so1 whether it is complete4 ,rules #ff ,examples worked briefly1 as models pg-xxvi ,,book ,,vi4 ,,the ,,method ,,of ,,subscripts4 ,,chapter ,i4 ,,introductory4 ,meaning of x#a1 xy#a1 c4 #gj ',entity' ,meaning of x#j1 xy#j1 c4 ',nullity' ,the ,symbols and ',like' and 'unlike' ,signs ,,chapter ,,ii4 ,,representation ,,of ,,propositions ,,of ,,relation4 ,the ,pair of ,converse ,propositions ,some x are y ,some y are x #ga ,three other similar ,pairs ,the ,pair of ,converse ,propositions ,no x are y ,no y are x ,three other similar ,pairs ,the ,proposition ,all x are y #gb ,the ,proposition ,all x are y is ,double1 and is equivalent to the two ,propositions ,some x exist and ,no x and y' ,seven other similar ,propositions ,rule for translating ,all x are y from abstract into subscript form1 and vice vers pg-xxvii ,,chapter ,,iii4 ,,syllogisms4 #a4 ,representation of ,syllogisms4 ,rules #gc #b4 ,formul for ,syllogisms4 ,three ,formul worked out3-- ,fig4 ,i4 xm#j ym'#j xy#j #ge its two ,variants 7a7 and 7b7 ,fig4 ,,ii4 xm#j ym#a x'y#a #gf ,fig4 ,,iii4 xm#j ym#j m#a x'y'#a #gg ,table ,,ix4 ,formul and ,rules #gh ,examples worked briefly1 as models #c4 ,fallacies4 ',fallacy' #ha ,method of finding ,forms of ,fallacies #hb ,forms best stated in words ,three ,forms of ,fallacies3-- 7#a7 ,fallacy of ,like ,eliminands not asserted to exist 7#b7 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss #hc 7#c7 ,fallacy of two ,entity-,premisses #d4 ,method of proceeding with a given ,pair of ,propositions4 ,rules #hd pg-xxviii ,,book ,,vii4 ,,soriteses4 ,,chapter ,i4 ,,introductory4 ',sorites' #he ',premisses' ',partial ,conclusion' ',complete ,conclusion' 7or ',conclusion'7 ',eliminands' ',retinends' 'consequent' ,the ,symbol 4'4 ,specimen-,soriteses #hf ,,chapter ,,ii4 ,,problems ,,in ,,soriteses4 #a4 ,introductory4 ,form of ,problem #hg ,two ,methods of ,solution #b4 ,solution by ,method of ,separate ,syllogisms4 ,rules #hh ,example worked pg-xxix #c4 ,solution by ,method of ,underscoring4 ',underscoring' #ia ,subscripts to be omitted ,example worked fully #ib ,example worked briefly1 as model #ic ,seventeen ,examination-,papers #id ,,book ,,viii4 ,,examples1 ,,with ,,answers ,,and ,,solutions4 ,,chapter ,i4 ,,examples4 #a4 ,propositions of ,relation1 to be reduced to normal form #ig #b4 ,pairs of ,abstract ,propositions1 one in terms of x and m1 and the other in terms of y and m1 to be represented on the same ,triliteral ,diagram #ih #c4 ,marked ,triliteral ,diagrams1 to be interpreted in terms of x and y #ii #d4 ,pairs of ,abstract ,propositions1 proposed as ,premisses3 ,conclusions to be found #ajj pg-xxx #e4 ,pairs of ,concrete ,propositions1 proposed as ,premisses3 ,conclusions to be found #aja #f4 ,trios of ,abstract ,propositions1 proposed as ,syllogisms3 to be examined #ajf #g4 ,trios of ,concrete ,propositions1 proposed as ,syllogisms3 to be examined #ajg #h4 ,sets of ,abstract ,propositions1 proposed as ,premisses for ,soriteses3 ,conclusions to be found #aaj #i4 ,sets of ,concrete ,propositions1 proposed as ,premisses for ,soriteses3 ,conclusions to be found #aab ,,chapter ,,ii4 ,,answers4 ,answers to #a #abe #b #abf #c1 #d #abg #e #abh #f #acj #g #aca #h1 #i #acb pg-xxxi ,,chapter ,,iii4 ,,solutions4 #a4 ,propositions of ,relation reduced to normal form4 ,solutions for #a #acd #b4 ,method of ,diagrams4 ,solutions for #d ,nos4 #a to #ab #acf #e #a to #ab #ach #f #a to #aj #ada #g #a to #f #add #c4 ,method of ,subscripts4 ,solutions for #d #adf #e ,nos4 #ac to #bd #adg #f1 #g1 #h1 #i #adh to #aeg ,,notes #afd ,,appendix1 ,,addressed ,,to ,,teachers #afe ,,notes ,,to ,,appendix #aie ,,index4 #a4 ,tables #aig #b4 ,words c4 explained pg-xxxii pg#jja ,,book ,i4 ,,things ,,and ,,their ,,attributes4 ,,chapter ,i4 ,,introductory4 ,the ,universe contains ',things4' ,for example1 ,i1 ,london1 roses1 redness1 old ,english books1 the letter which ,i received yesterday4 ,things have ',attributes4' ,for example1 large1 red1 old1 which ,i received yesterday4 ,one ,thing may have many ,attributes2 and one ,attribute may belong to many ,things4 ,thus1 the ,thing a rose may have the ,attributes red1 scented1 full-blown1 c42 and the ,attribute red may belong to the ,things a rose1 a brick1 a ribbon1 c4 ,any ,attribute1 or any ,set of ,attributes1 may be called an ',adjunct4' ,this word is introduced in order to avoid the constant repetition of the phrase ,attribute or ,set of ,attributes4 ,thus1 we may say that a rose has the ,attribute red 7or the ,adjunct red1 whichever we prefer72 or we may say that it has the ,adjunct red1 scented and full-blown4 pg#jja ,,chapter ,,ii4 ,,classification4 ',classification1' or the formation of ,classes1 is a ,mental ,process1 in which we imagine that we have put together1 in a group1 certain ,things4 ,such a group is called a ',class4' ,this ,process may be performed in three different ways1 as follows3-- 7#a7 ,we may imagine that we have put together all ,things4 ,the ,class so formed 7i4e4 the ,class ,things7 contains the whole ,universe4 7#b7 ,we may think of the ,class ,things1 and may imagine that we have picked out from it all the ,things which possess a certain ,adjunct not possessed by the whole ,class4 ,this ,adjunct is said to be 'peculiar' to the ,class so formed4 ,in this case1 the ,class ,things is called a ',genus' with regard to the ,class so formed3 the ,class1 so formed1 is called a ',species' of the ,class ,things3 and its peculiar ,adjunct is called its ',differentia'4 pg#jjb ,as this ,process is entirely ,mental1 we can perform it whether there is1 or is not1 an existing ,thing which possesses that ,adjunct4 ,if there is1 the ,class is said to be ',real'2 if not1 it is said to be ',unreal'1 or ',imaginary4' ,for example1 we may imagine that we have picked out1 from the ,class ,things1 all the ,things which possess the ,adjunct material1 artificial1 consisting of houses and streets2 and we may thus form the ,real ,class towns4 ,here we may regard ,things as a ,genus1 ,towns as a ,species of ,things1 and material1 artificial1 consisting of houses and streets as its ,differentia4 ,again1 we may imagine that we have picked out all the ,things which possess the ,adjunct weighing a ton1 easily lifted by a baby2 and we may thus form the ,imaginary ,class ,things that weigh a ton and are easily lifted by a baby4 7#c7 ,we may think of a certain ,class1 not the ,class ,things1 and may imagine that we have picked out from it all the ,members of it which possess a certain ,adjunct not possessed by the whole ,class4 ,this ,adjunct is said to be 'peculiar' to the smaller ,class so formed4 ,in this case1 the ,class thought of is called a ',genus' with regard to the smaller ,class picked out from it3 the smaller ,class is called a ',species' of the larger3 and its peculiar ,adjunct is called its ',differentia'4 ,for example1 we may think of the ,class towns1 and imagine that we have picked out from it all the towns which possess the ,attribute lit with gas2 and we may thus form the ,real ,class towns lit with gas4 ,here we may regard ,towns as a ,genus1 ,towns lit with gas as a ,species of ,towns1 and lit with gas as its ,differentia4 ,if1 in the above example1 we were to alter lit with gas into paved with gold1 we should get the ,imaginary ,class towns paved with gold4 ,a ,class1 containing only one ,member is called an ',individual4' ,for example1 the ,class towns having four million inhabitants1 which ,class contains only one ,member1 viz4 ,london4 pg#jjb ,hence1 any single ,thing1 which we can name so as to distinguish it from all other ,things1 may be regarded as a one-,member ,class4 ,thus ,london may be regarded as the one-,member ,class1 picked out from the ,class towns1 which has1 as its ,differentia1 having four million inhabitants4 ,a ,class1 containing two or more ,members1 is sometimes regarded as one single ,thing4 ,when so regarded1 it may possess an ,adjunct which is not possessed by any ,member of it taken separately4 ,thus1 the ,class ,the soldiers of the ,tenth ,regiment1 when regarded as one single ,thing1 may possess the ,attribute formed in square1 which is not possessed by any ,member of it taken separately4 pg#jjc ,,chapter ,,iii4 ,,division4 #a4 ,introductory4 ',division' is a ,mental ,process1 in which we think of a certain ,class of ,things1 and imagine that we have divided it into two or more smaller ,classes4 ,thus1 we might think of the ,class books1 and imagine that we had divided it into the two smaller ,classes bound books and unbound books1 or into the three ,classes1 books priced at less than a shilling1 shilling-books1 books priced at more than a shilling1 or into the twenty-six ,classes1 books whose names begin with ,a1 books whose names begin with ,b1 c4 ,a ,class1 that has been obtained by a certain ,division1 is said to be 'codivisional' with every ,class obtained by that ,division4 ,thus1 the ,class bound books is codivisional with each of the two ,classes1 bound books and unbound books4 ,similarly1 the ,battle of ,waterloo may be said to have been contemporary with every event that happened in #ahae4 ,hence a ,class1 obtained by ,division1 is codivisional with itself4 ,thus1 the ,class bound books is codivisional with itself4 ,similarly1 the ,battle of ,waterloo may be said to have been contemporary with itself4 pg#jjc #b4 ,dichotomy4 ,if we think of a certain ,class1 and imagine that we have picked out from it a certain smaller ,class1 it is evident that the ,remainder of the large ,class does not possess the ,differentia of that smaller ,class4 ,hence it may be regarded as another smaller ,class1 whose ,differentia may be formed1 from that of the ,class first picked out1 by prefixing the word not2 and we may imagine that we have divided the ,class first thought of into two smaller ,classes1 whose ,differenti are contradictory4 ,this kind of ,division is called ',dichotomy'4 ,for example1 we may divide books into the two ,classes whose ,differenti are old and not-old4 ,in performing this ,process1 we may sometimes find that the ,attributes we have chosen are used so loosely1 in ordinary conversation1 that it is not easy to decide which of the ,things belong to the one ,class and which to the other4 ,in such a case1 it would be necessary to lay down some arbitrary rule1 as to where the one ,class should end and the other begin4 ,thus1 in dividing books into old and not-old1 we may say ,let all books printed before ,a4,d4 #ahja1 be regarded as 'old1' and all others as 'not-old'4 ,henceforwards let it be understood that1 if a ,class of ,things be divided into two ,classes1 whose ,differenti have contrary meanings1 each ,differentia is to be regarded as equivalent to the other with the word not prefixed4 ,thus1 if books be divided into old and new the ,attribute old is to be regarded as equivalent to not-new1 and the ,attribute new as equivalent to not-old4 pg#jjd ,after dividing a ,class1 by the ,process of ,dichotomy1 into two smaller ,classes1 we may sub-divide each of these into two still smaller ,classes2 and this ,process may be repeated over and over again1 the number of ,classes being doubled at each repetition4 ,for example1 we may divide books into old and new 7i4e4 not-old73 we may then sub-divide each of these into ,english and foreign 7i4e4 not-,english71 thus getting four ,classes1 viz4 7#a7 old ,english2 7#b7 old foreign2 7#c7 new ,english2 7#d7 new foreign4 ,if we had begun by dividing into ,english and foreign1 and had then sub-divided into old and new1 the four ,classes would have been 7#a7 ,english old2 7#b7 ,english new2 7#c7 foreign old2 7#d7 foreign new4 ,the ,reader will easily see that these are the very same four ,classes which we had before4 pg#jjd ,,chapter ,,iv4 ,,names4 ,the word ,thing1 which conveys the idea of a ,thing1 without any idea of an ,adjunct1 represents any single ,thing4 ,any other word 7or phrase71 which conveys the idea of a ,thing1 with the idea of an ,adjunct represents any ,thing which possesses that ,adjunct2 i4e41 it represents any ,member of the ,class to which that ,adjunct is peculiar4 ,such a word 7or phrase7 is called a ',name'2 and1 if there be an existing ,thing which it represents1 it is said to be a ,name of that ,thing4 ,for example1 the words ,thing1 ,treasure1 ,town1 and the phrases valuable ,thing1 material artificial ,thing consisting of houses and streets1 ,town lit with gas1 ,town paved with gold1 old ,english ,book4 ,just as a ,class is said to be ,real1 or ,unreal1 according as there is1 or is not1 an existing ,thing in it1 so also a ,name is said to be ,real1 or ,unreal1 according as there is1 or is not1 an existing ,thing represented by it4 ,thus1 ,town lit with gas is a ,real ,name3 ,town paved with gold is an ,unreal ,name4 ,every ,name is either a ,substantive only1 or else a phrase consisting of a ,substantive and one or more ,adjectives 7or phrases used as ,adjectives74 ,every ,name1 except ,thing1 may usually be expressed in three different forms3-- 7a7 ,the ,substantive ,thing1 and one or more ,adjectives 7or phrases used as ,adjectives7 conveying the ideas of the ,attributes2 pg#jje 7b7 ,a ,substantive1 conveying the idea of a ,thing with the ideas of some of the ,attributes1 and one or more ,adjectives 7or phrases used as ,adjectives7 conveying the ideas of the other ,attributes2 7c7 ,a ,substantive conveying the idea of a ,thing with the ideas of all the ,attributes4 ,thus1 the phrase material living ,thing1 belonging to the ,animal ,kingdom1 having two hands and two feet is a ,name expressed in ,form 7a74 ,if we choose to roll up together the ,substantive ,thing and the ,adjectives material1 living1 belonging to the ,animal ,kingdom1 so as to make the new ,substantive ,animal1 we get the phrase ,animal having two hands and two feet1 which is a ,name 7representing the same ,thing as before7 expressed in ,form 7b74 ,and1 if we choose to roll up the whole phrase into one word1 so as to make the new ,substantive ,man1 we get a ,name 7still representing the very same ,thing7 expressed in ,form 7c74 ,a ,name1 whose ,substantive is in the plural number1 may be used to represent either 7#a7 ,members of a ,class1 regarded as separate ,things2 or 7#b7 a whole ,class1 regarded as one single ,thing4 ,thus1 when ,i say ,some soldiers of the ,tenth ,regiment are tall1 or ,the soldiers of the ,tenth ,regiment are brave1 ,i am using the ,name soldiers of the ,tenth ,regiment in the first sense2 and it is just the same as if ,i were to point to each of them separately1 and to say ,this soldier of the ,tenth ,regiment is tall1 ,that soldier of the ,tenth ,regiment is tall1 and so on4 ,but1 when ,i say ,the soldiers of the ,tenth ,regiment are formed in square1 ,i am using the phrase in the second sense2 and it is just the same as if ,i were to say ,the ,tenth ,regiment is formed in square4 pg#jjf ,,chapter ,v4 ,,definitions4 ,it is evident that every ,member of a ,species is also a ,member of the ,genus out of which that ,species has been picked1 and that it possesses the ,differentia of that ,species4 ,hence it may be represented by a ,name consisting of two parts1 one being a ,name representing any ,member of the ,genus1 and the other being the ,differentia of that ,species4 ,such a ,name is called a ',definition' of any ,member of that ,species1 and to give it such a ,name is to 'define' it4 ,thus1 we may define a ,treasure as a valuable ,thing4 ,in this case we regard ,things as the ,genus1 and valuable as the ,differentia4 ,the following ,examples1 of this ,process1 may be taken as models for working others4 ,note that1 in each ,definition1 the ,substantive1 representing a ,member 7or ,members7 of the ,genus1 is printed in ,capitals4 #a4 ,define a ,treasure4 ,ans4 a valuable ,,thing4 #b4 ,define ,treasures4 ,ans4 valuable ,,things4 #c4 ,define a ,town4 ,ans4 a material artificial ,,thing1 consisting of houses and streets4 pg#jjg #d4 ,define ,men4 ,ans4 material1 living ,,things1 belonging to the ,animal ,kingdom1 having two hands and two feet2 or else ,,animals having two hands and two feet4 #e4 ,define ,london4 ,ans4 the material artificial ,,thing1 which consists of houses and streets1 and has four million inhabitants2 or else the ,,town which has four million inhabitants4 ,note that we here use the article the instead of a1 because we happen to know that there is only one such ,thing4 ,the ,reader can set himself any number of ,examples of this ,process1 by simply choosing the ,name of any common ,thing 7such as house1 tree1 knife71 making a ,definition for it1 and then testing his answer by referring to any ,english ,dictionary4 pg#jjh ,,book ,,ii4 ,,propositions4 ,,chapter ,i4 ,,propositions ,,generally4 #a4 ,introductory4 ,note that the word some is to be regarded1 henceforward1 as meaning one or more4 ,the word ',proposition1' as used in ordinary conversation1 may be applied to any word1 or phrase1 which conveys any information whatever4 ,thus the words yes and no are ,propositions in the ordinary sense of the word2 and so are the phrases you owe me five farthings and ,i don't6 ,such words as oh6 or never61 and such phrases as fetch me that book6 which book do you mean8 do not seem1 at first sight1 to convey any information2 but they can easily be turned into equivalent forms which do so1 viz4 ,i am surprised1 ,i will never consent to it1 ,i order you to fetch me that book1 ,i want to know which book you mean4 ,but a ',proposition1' as used in this ,first ,part of ,symbolic ,logic1 has a peculiar form1 which may be called its ',normal form'2 and if any ,proposition1 which we wish to use in an argument1 is not in normal form1 we must reduce it to such a form1 before we can use it4 pg#jji ,a ',proposition1' when in normal form1 asserts1 as to certain two ,classes1 which are called its ',subject' and ',predicate1' either 7#a7 that some ,members of its ,subject are ,members of its ,predicate2 or 7#b7 that no ,members of its ,subject are ,members of its ,predicate2 or 7#c7 that all ,members of its ,subject are ,members of its ,predicate4 ,the ,subject and the ,predicate of a ,proposition are called its ',terms4' ,two ,propositions1 which convey the same information1 are said to be 'equivalent'4 ,thus1 the two ,propositions1 ,i see ,john and ,john is seen by me1 are equivalent4 #b4 ,normal form of a ,proposition4 ,a ,proposition1 in normal form1 consists of four parts1 viz4-- 7#a7 ,the word some1 or no1 or all4 7,this word1 which tells us how many ,members of the ,subject are also ,members of the ,predicate1 is called the ',sign of ,quantity4'7 7#b7 ,name of ,subject4 7#c7 ,the verb are 7or is74 7,this is called the ',copula4'7 7#d7 ,name of ,predicate4 pg#jaj #c4 ,various kinds of ,propositions4 ,a ,proposition1 that begins with ,some1 is said to be ',particular4' ,it is also called 'a ,proposition in ,i4' ,note1 that it is called ',particular1' because it refers to a part only of the ,subject4 ,a ,proposition1 that begins with ,no1 is said to be ',universal ,negative4' ,it is also called 'a ,proposition in ,e4' ,a ,proposition1 that begins with ,all1 is said to be ',universal ,affirmative4' ,it is also called 'a ,proposition in ,a4' ,note1 that they are called ',universal'1 because they refer to the whole of the ,subject4 ,a ,proposition1 whose ,subject is an ,individual1 is to be regarded as ,universal4 ,let us take1 as an example1 the ,proposition ,john is not well4 ,this of course implies that there is an ,individual1 to whom the speaker refers when he mentions ,john1 and whom the listener knows to be referred to4 ,hence the ,class men referred to by the speaker when he mentions ',john' is a one-,member ,class1 and the ,proposition is equivalent to ,all the men1 who are referred to by the speaker when he mentions ',john'1 are not well4 ,propositions are of two kinds1 ',propositions of ,existence' and ',propositions of ,relation4' ,these shall be discussed separately4 pg#jaa ,,chapter ,,ii4 ,,propositions ,,of ,,existence4 ,a ',proposition of ,existence'1 when in normal form1 has1 for its ,subject1 the ,class existing ,things4 ,its ,sign of ,quantity is ,some or ,no4 ,note that1 though its ,sign of ,quantity tells us how many existing ,things are ,members of its ,predicate1 it does not tell us the exact number3 in fact1 it only deals with two numbers1 which are1 in ascending order1 #j and #a or more4 ,it is called a ,proposition of ,existence because its effect is to assert the ,reality 7i4e4 the real existence71 or else the ,imaginariness1 of its ,predicate4 ,thus1 the ,proposition ,some existing ,things are honest men asserts that the ,class honest men is ,real4 ,this is the normal form2 but it may also be expressed in any one of the following forms3-- 7#a7 ,honest men exist2 7#b7 ,some honest men exist2 7#c7 ,the ,class 'honest men' exists2 7#d7 ,there are honest men2 7#e7 ,there are some honest men4 ,similarly1 the ,proposition ,no existing ,things are men fifty feet high asserts that the ,class men #ej feet high is ,imaginary4 ,this is the normal form2 but it may also be expressed in any one of the following forms3-- 7#a7 ,men #ej feet high do not exist2 7#b7 ,no men #ej feet high exist2 7#c7 ,the ,class 'men #ej feet high' does not exist2 7#d7 ,there are not any men #ej feet high2 7#e7 ,there are no men #ej feet high4 pg#jab ,,chapter ,,iii4 ,,propositions ,,of ,,relation4 #a4 ,introductory4 ,a ,proposition of ,relation1 of the kind to be here discussed1 has1 for its ,terms1 two ,specieses of the same ,genus1 such that each of the two ,names conveys the idea of some ,attribute not conveyed by the other4 ,thus1 the ,proposition ,some merchants are misers is of the right kind1 since merchants and misers are ,specieses of the same ,genus men2 and since the ,name merchants conveys the idea of the ,attribute mercantile1 and the name misers the idea of the ,attribute miserly1 each of which ideas is not conveyed by the other ,name4 ,but the ,proposition ,some dogs are setters is not of the right kind1 since1 although it is true that dogs and setters are ,specieses of the same ,genus animals1 it is not true that the ,name dogs conveys the idea of any ,attribute not conveyed by the ,name setters4 ,such ,propositions will be discussed in ,part ,,ii4 ,the ,genus1 of which the two ,terms are ,specieses1 is called the ',universe of ,discourse1' or 7more briefly7 the ',univ4' ,the ,sign of ,quantity is ,some or ,no or ,all4 ,note that1 though its ,sign of ,quantity tells us how many ,members of its ,subject are also ,members of its ,predicate1 it does not tell us the exact number3 in fact1 it only deals with three numbers1 which are1 in ascending order1 #j1 #a or more1 the total number of ,members of the ,subject4 ,it is called a ,proposition of ,relation because its effect is to assert that a certain relationship exists between its ,terms4 pg#jac #b4 ,reduction of a ,proposition of ,relation to ,normal form4 ,the ,rules1 for doing this1 are as follows3-- 7#a7 ,ascertain what is the ,subject 7i4e41 ascertain what ,class we are talking about72 7#b7 ,if the verb1 governed by the ,subject1 is not the verb are 7or is71 substitute for it a phrase beginning with are 7or is72 7#c7 ,ascertain what is the ,predicate 7i4e41 ascertain what ,class it is1 which is asserted to contain some1 or none1 or all1 of the ,members of the ,subject72 7#d7 ,if the ,name of each ,term is completely expressed 7i4e4 if it contains a ,substantive71 there is no need to determine the ',univ4'2 but1 if either ,name is incompletely expressed1 and contains ,attributes only1 it is then necessary to determine a ',univ4'1 in order to insert its ,name as the ,substantive4 7#e7 ,ascertain the ,sign of ,quantity2 7#f7 ,arrange in the following order3-- ,sign of ,quantity1 ,subject1 ,copula1 ,predicate4 ,let us work a few ,examples1 to illustrate these ,rules4 7#a7 ,some apples are not ripe4 7#a7 ,the ,subject is apples4 7#b7 ,the ,verb is are4 7#c7 ,the ,predicate is not-ripe 99 99 994 7,as no ,substantive is expressed1 and we have not yet settled what the ,univ4 is to be1 we are forced to leave a blank47 7#d7 ,let ,univ4 be fruit4 7#e7 ,the ,sign of ,quantity is some4 7#f7 ,the ,proposition now becomes ,some apples are not-ripe fruit4 pg#jad 7#b7 ,none of my speculations have brought me as much as #e per cent4 7#a7 ,the ,subject is my speculations4 7#b7 ,the ,verb is have brought1 for which we substitute the phrase are 99 99 99 that have brought4 7#c7 ,the ,predicate is 99 99 99 that have brought c4 7#d7 ,let ,univ4 be transactions4 7#e7 ,the ,sign of ,quantity is none of4 7#f7 ,the ,proposition now becomes ,none of my speculations are transactions that have brought me as much as #e per cent4 7#c7 ,none but the brave deserve the fair4 ,to begin with1 we note that the phrase none but the brave is equivalent to no not-brave4 7#a7 ,the ,subject has for its ,attribute not-brave4 ,but no ,substantive is supplied4 ,so we express the ,subject as not-brave 99 99 994 7#b7 ,the ,verb is deserve1 for which we substitute the phrase are deserving of4 7#c7 ,the ,predicate is 99 99 99 deserving of the fair4 7#d7 ,let ,univ4 be persons4 7#e7 ,the ,sign of ,quantity is no4 7#f7 ,the ,proposition now becomes ,no not-brave persons are persons deserving of the fair4 7#d7 ,a lame puppy would not say thank you if you offered to lend it a skipping-rope4 7#a7 ,the ,subject is evidently lame puppies1 and all the rest of the sentence must somehow be packed into the ,predicate4 7#b7 ,the ,verb is would not say1 c41 for which we may substitute the phrase are not grateful for4 7#c7 ,the ,predicate may be expressed as 99 99 99 not grateful for the loan of a skipping-rope4 7#d7 ,let ,univ4 be puppies4 7#e7 ,the ,sign of ,quantity is all4 7#f7 ,the ,proposition now becomes ,all lame puppies are puppies not grateful for the loan of a skipping-rope4 pg#jae 7#e7 ,no one takes in the ,times1 unless he is well-educated4 7#a7 ,the ,subject is evidently persons who are not well-educated 7no one evidently means no person74 7#b7 ,the ,verb is takes in1 for which we may substitute the phrase are persons taking in4 7#c7 ,the ,predicate is persons taking in the ,times4 7#d7 ,let ,univ4 be persons4 7#e7 ,the ,sign of ,quantity is no4 7#f7 ,the ,proposition now becomes ,no persons who are not well-educated are persons taking in the ,times4 7#f7 ,my carriage will meet you at the station4 7#a7 ,the ,subject is my carriage4 ,this1 being an ',individual1' is equivalent to the ,class my carriages4 7,note that this ,class contains only one ,member47 7#b7 ,the ,verb is will meet1 for which we may substitute the phrase are 99 99 99 that will meet4 7#c7 ,the ,predicate is 99 99 99 that will meet you at the station4 7#d7 ,let ,univ4 be things4 7#e7 ,the ,sign of ,quantity is all4 7#f7 ,the ,proposition now becomes ,all my carriages are things that will meet you at the station4 7#g7 ,happy is the man who does not know what 'toothache' means6 7#a7 ,the ,subject is evidently the man c4 7,note that in this sentence1 the ,predicate comes first47 ,at first sight1 the ,subject seems to be an ',individual'2 but on further consideration1 we see that the article the does not imply that there is only one such man4 ,hence the phrase the man who is equivalent to all men who4 7#b7 ,the ,verb is are4 7#c7 ,the ,predicate is happy 99 99 994 7#d7 ,let ,univ4 be men4 7#e7 ,the ,sign of ,quantity is all4 7#f7 ,the ,proposition now becomes ,all men who do not know what 'toothache' means are happy men4 pg#jaf 7#h7 ,some farmers always grumble at the weather1 whatever it may be4 7#a7 ,the ,subject is farmers4 7#b7 ,the ,verb is grumble1 for which we substitute the phrase are 99 99 99 who grumble4 7#c7 ,the ,predicate is 99 99 99 who always grumble c4 7#d7 ,let ,univ4 be persons4 7#e7 ,the ,sign of ,quantity is some4 7#f7 ,the ,proposition now becomes ,some farmers are persons who always grumble at the weather1 whatever it may be4 7#i7 ,no lambs are accustomed to smoke cigars4 7#a7 ,the ,subject is lambs4 7#b7 ,the ,verb is are4 7#c7 ,the ,predicate is 99 99 99 accustomed c4 7#d7 ,let ,univ4 be animals4 7#e7 ,the ,sign of ,quantity is no4 7#f7 ,the ,proposition now becomes ,no lambs are animals accustomed to smoke cigars4 7#aj7 ,i ca'n't understand examples that are not arranged in regular order1 like those ,i am used to4 7#a7 ,the ,subject is examples that1 c4 7#b7 ,the ,verb is ,i ca'n't understand1 which we must alter1 so as to have examples1 instead of ,i1 as the nominative case4 ,it may be expressed as are not understood by me4 7#c7 ,the ,predicate is 99 99 99 not understood by me4 7#d7 ,let ,univ4 be examples4 7#e7 ,the ,sign of ,quantity is all4 7#f7 ,the ,proposition now becomes ,all examples that are not arranged in regular order like those ,i am used to are examples not understood by me4 pg#jag #c4 ,a ,proposition of ,relation1 beginning with ,all1 is a ,double ,proposition4 ,a ,proposition of ,relation1 beginning with ,all1 asserts 7as we already know7 that ,all ,members of the ,subject are ,members of the ,predicate4 ,this evidently contains1 as a part of what it tells us1 the smaller ,proposition ,some ,members of the ,subject are ,members of the ,predicate4 ,thus1 the ,proposition ,all bankers are rich men evidently contains the smaller ,proposition ,some bankers are rich men4 ,the question now arises ,what is the rest of the information which this ,proposition gives us8 ,in order to answer this question1 let us begin with the smaller ,proposition1 ,some ,members of the ,subject are ,members of the ,predicate1 and suppose that this is all we have been told2 and let us proceed to inquire what else we need to be told1 in order to know that ,all ,members of the ,subject are ,members of the ,predicate4 ,thus1 we may suppose that the ,proposition ,some bankers are rich men is all the information we possess2 and we may proceed to inquire what other ,proposition needs to be added to it1 in order to make up the entire ,proposition ,all bankers are rich men4 ,let us also suppose that the ',univ4' 7i4e4 the ,genus1 of which both the ,subject and the ,predicate are ,specieses7 has been divided 7by the ,process of ,dichotomy7 into two smaller ,classes1 viz4 7#a7 the ,predicate2 7#b7 the ,class whose ,differentia is contradictory to that of the ,predicate4 ,thus1 we may suppose that the ,genus men1 7of which both bankers and rich men are ,specieses7 has been divided into the two smaller ,classes1 rich men1 poor men4 pg#jah ,now we know that every ,member of the ,subject is 7as shown at p4 #f7 a ,member of the ,univ4 ,hence every ,member of the ,subject is either in ,class 7#a7 or else in ,class 7#b74 ,thus1 we know that every banker is a ,member of the ,genus men4 ,hence1 every banker is either in the ,class rich men1 or else in the ,class poor men4 ,also we have been told that1 in the case we are discussing1 some ,members of the ,subject are in ,class 7#a74 ,what else do we need to be told1 in order to know that all of them are there8 ,evidently we need to be told that none of them are in ,class 7#b72 i4e4 that none of them are ,members of the ,class whose ,differentia is contradictory to that of the ,predicate4 ,thus1 we may suppose we have been told that some bankers are in the ,class rich men4 ,what else do we need to be told1 in order to know that all of them are there8 ,evidently we need to be told that none of them are in the ,class poor men4 ,hence a ,proposition of ,relation1 beginning with ,all1 is a ,double ,proposition1 and is 'equivalent' to 7i4e4 gives the same information as7 the two ,propositions 7#a7 ,some ,members of the ,subject are ,members of the ,predicate2 7#b7 ,no ,members of the ,subject are ,members of the ,class whose ,differentia is contradictory to that of the ,predicate4 ,thus1 the ,proposition ,all bankers are rich men is a ,double ,proposition1 and is equivalent to the two ,propositions 7#a7 ,some bankers are rich men2 7#b7 ,no bankers are poor men4 pg#jai #d4 ,what is implied1 in a ,proposition of ,relation1 as to the ,reality of its ,terms8 ,note that the rules1 here laid down1 are arbitrary1 and only apply to ,part ,i of my ,symbolic ,logic4 ,a ,proposition of ,relation1 beginning with ,some1 is henceforward to be understood as asserting that there are some existing ,things1 which1 being ,members of the ,subject1 are also ,members of the ,predicate2 i4e4 that some existing ,things are ,members of both ,terms at once4 ,hence it is to be understood as implying that each ,term1 taken by itself1 is ,real4 ,thus1 the ,proposition ,some rich men are invalids is to be understood as asserting that some existing ,things are rich invalids4 ,hence it implies that each of the two ,classes1 rich men and invalids1 taken by itself1 is ,real4 ,a ,proposition of ,relation1 beginning with ,no1 is henceforward to be understood as asserting that there are no existing ,things which1 being ,members of the ,subject1 are also ,members of the ,predicate2 i4e4 that no existing ,things are ,members of both ,terms at once4 ,but this implies nothing as to the ,reality of either ,term taken by itself4 ,thus1 the ,proposition ,no mermaids are milliners is to be understood as asserting that no existing ,things are mermaid-milliners4 ,but this implies nothing as to the ,reality1 or the ,unreality1 of either of the two ,classes1 mermaids and milliners1 taken by itself4 ,in this case as it happens1 the ,subject is ,imaginary1 and the ,predicate ,real4 ,a ,proposition of ,relation1 beginning with ,all1 contains 7see #c7 a similar ,proposition beginning with ,some4 ,hence it is to be understood as implying that each ,term1 taken by itself1 is ,real4 ,thus1 the ,proposition ,all hynas are savage animals contains the ,proposition ,some hynas are savage animals4 ,hence it implies that each of the two ,classes1 hynas and savage animals1 taken by itself1 is ,real4 pg#jbj #e4 ,translation of a ,proposition of ,relation into one or more ,propositions of ,existence4 ,we have seen that a ,proposition of ,relation1 beginning with ,some1 asserts that some existing ,things1 being ,members of its ,subject1 are also ,members of its ,predicate4 ,hence1 it asserts that some existing ,things are ,members of both2 i4e4 it asserts that some existing ,things are ,members of the ,class of ,things which have all the ,attributes of the ,subject and the ,predicate4 ,hence1 to translate it into a ,proposition of ,existence1 we take existing ,things as the new ,subject1 and ,things1 which have all the ,attributes of the ,subject and the ,predicate1 as the new ,predicate4 ,similarly for a ,proposition of ,relation beginning with ,no4 ,a ,proposition of ,relation1 beginning with ,all1 is 7as shown in #c7 equivalent to two ,propositions1 one beginning with ,some and the other with ,no1 each of which we now know how to translate4 ,let us work a few ,examples1 to illustrate these ,rules4 7#a7 ,some apples are not ripe4 ,here we arrange thus3-- ,some ,sign of ,quantity4 existing ,things ,subject4 are ,copula4 not-ripe apples ,predicate4 or thus3-- ,some existing ,things are not-ripe apples4 pg#jba 7#b7 ,some farmers always grumble at the weather1 whatever it may be4 ,here we arrange thus3-- ,some existing ,things are farmers who always grumble at the weather1 whatever it may be4 7#c7 ,no lambs are accustomed to smoke cigars4 ,here we arrange thus3-- ,no existing ,things are lambs accustomed to smoke cigars4 7#d7 ,none of my speculations have brought me as much as #e per cent4 ,here we arrange thus3-- ,no existing ,things are speculations of mine1 which have brought me as much as #e per cent4 7#e7 ,none but the brave deserve the fair4 ,here we note1 to begin with1 that the phrase none but the brave is equivalent to no not-brave men4 ,we then arrange thus3-- ,no existing ,things are not-brave men deserving of the fair4 7#f7 ,all bankers are rich men4 ,this is equivalent to the two ,propositions ,some bankers are rich men and ,no bankers are poor men4 ,here we arrange thus3-- ,some existing ,things are rich bankers2 and ,no existing ,things are poor bankers4 ,work ,examples #a1 #a-d 7p4 #ig74 pg#jbb ,,book ,,iii4 ,,the ,,biliteral ,,diagram4 ------------- xy xy' ------------ x'y x'y' ------------- ,,chapter ,i4 ,,symbols ,,and ,,cells4 ,first1 let us suppose that the above ,diagram is an enclosure assigned to a certain ,class of ,things1 which we have selected as our ',universe of ,discourse4' or1 more briefly1 as our ',univ'4 ,for example1 we might say ,let ,univ4 be 'books'2 and we might imagine the ,diagram to be a large table1 assigned to all books4 ,the ,reader is strongly advised1 in reading this ,chapter1 not to refer to the above ,diagram1 but to draw a large one for himself1 without any letters1 and to have it by him while he reads1 and keep his finger on that particular part of it1 about which he is reading4 pg#jbc ,secondly1 let us suppose that we have selected a certain ,adjunct1 which we may call x1 and have divided the large ,class1 to which we have assigned the whole ,diagram1 into the two smaller ,classes whose ,differenti are x and not-x 7which we may call x'71 and that we have assigned the ,north ,half of the ,diagram to the one 7which we may call the ,class of x-,things1 or the x-,class71 and the ,south ,half to the other 7which we may call the ,class of x'-,things1 or the x'-,class74 ,for example1 we might say ,let x mean 'old1' so that x' will mean 'new'1 and we might suppose that we had divided books into the two ,classes whose ,differenti are old and new1 and had assigned the ,north ,half of the table to old books and the ,south ,half to new books4 ,thirdly1 let us suppose that we have selected another ,adjunct1 which we may call y1 and have subdivided the x-,class into the two ,classes whose ,differenti are y and y'1 and that we have assigned the ,north-,west ,cell to the one 7which we may call the xy-,class71 and the ,north-,east ,cell to the other 7which we may call the xy'-,class74 ,for example1 we might say ,let y mean ',english1' so that y' will mean 'foreign'1 and we might suppose that we had subdivided old books into the two ,classes whose ,differenti are ,english and foreign1 and had assigned the ,north-,west ,cell to old ,english books1 and the ,north-,east ,cell to old foreign books4 ,fourthly1 let us suppose that we have subdivided the x'-,class in the same manner1 and have assigned the ,south-,west ,cell to the x'y-,class1 and the ,south-,east ,cell to the x'y'-,class4 ,for example1 we might suppose that we had subdivided new books into the two ,classes new ,english books and new foreign books1 and had assigned the ,south-,west ,cell to the one1 and the ,south-,east ,cell to the other4 ,it is evident that1 if we had begun by dividing for y and y'1 and had then subdivided for x and x'1 we should have got the same four ,classes4 ,hence we see that we have assigned the ,west ,half to the y-,class1 and the ,east ,half to the y'-,class4 pg#jbd ,thus1 in the above ,example1 we should find that we had assigned the ,west ,half of the table to ,english books and the ,east ,half to foreign books4 ------------------- old old ,english foreign books books ------------------ new new ,english foreign books books ------------------- ,we have1 in fact1 assigned the four ,quarters of the table to four different ,classes of books1 as here shown4 ,the ,reader should carefully remember that1 in such a phrase as the x-,things1 the word ,things means that particular kind of ,things1 to which the whole ,diagram has been assigned4 ,thus1 if we say ,let ,univ4 be 'books'1 we mean that we have assigned the whole ,diagram to books4 ,in that case1 if we took x to mean old1 the phrase the x-,things would mean the old books4 ,the ,reader should not go on to the next ,chapter until he is quite familiar with the blank ,diagram ,i have advised him to draw4 ,he ought to be able to name1 instantly1 the ,adjunct assigned to any ,compartment named in the right-hand column of the following ,table4 ,also he ought to be able to name1 instantly1 the ,compartment assigned to any ,adjunct named in the left-hand column4 ,to make sure of this1 he had better put the book into the hands of some genial friend1 while he himself has nothing but the blank ,diagram1 and get that genial friend to question him on this ,table1 dodging about as much as possible4 ,the ,questions and ,answers should be something like this3-- pg#jbe ,,table ,i4 ---------------------------------------- ,adjuncts ,compartments1 or ,cells1 of assigned to them4 ,classes4 --------------------------------------- x ,north ,half4 x' ,south y ,west y' ,east --------------------------------------- xy ,north-,west ,cell4 xy' ,east x'y ,south-,west x'y' ,east ---------------------------------------- ,q4 ,adjunct for ,west ,half8 ,a4 y4 ,q4 ,compartment for xy'8 ,a4 ,north-,east ,cell4 ,q4 ,adjunct for ,south-,west ,cell8 ,a4 x'y4 c41 c4 ,after a little practice1 he will find himself able to do without the blank ,diagram1 and will be able to see it mentally 7in my mind's eye1 ,horatio67 while answering the questions of his genial friend4 ,when this result has been reached1 he may safely go on to the next ,chapter4 pg#jbf ,,chapter ,,ii4 ,,counters4 ,let us agree that a ,red ,counter1 placed within a ,cell1 shall mean ,this ,cell is occupied 7i4e4 ,there is at least one ,thing in it74 ,let us also agree that a ,red ,counter1 placed on the partition between two ,cells1 shall mean ,the ,compartment1 made up of these two ,cells1 is occupied2 but it is not known whereabouts1 in it1 its occupants are4 ,hence it may be understood to mean ,at least one of these two ,cells is occupied3 possibly both are4 ,our ingenious ,american cousins have invented a phrase to describe the condition of a man who has not yet made up his mind which of two political parties he will join3 such a man is said to be sitting on the fence4 ,this phrase exactly describes the condition of the ,red ,counter4 ,let us also agree that a ,grey ,counter1 placed within a ,cell1 shall mean ,this ,cell is empty 7i4e4 ,there is nothing in it74 ,the ,reader had better provide himself with #d ,red ,counters and #e ,grey ones4 pg#jbg ,,chapter ,,iii4 ,,representation ,,of ,,propositions4 #a4 ,introductory4 ,henceforwards1 in stating such ,propositions as ,some x-,things exist or ,no x-,things are y-,things1 ,i shall omit the word ,things1 which the ,reader can supply for himself1 and shall write them as ,some x exist or ,no x are y4 ,note that the word ,things is here used with a special meaning1 as explained at p4 #bc4 ,a ,proposition1 containing only one of the ,letters used as ,symbols for ,attributes1 is said to be ',uniliteral'4 ,for example1 ,some x exist1 ,no y' exist1 c4 ,a ,proposition1 containing two ,letters1 is said to be ',biliteral'4 ,for example1 ,some xy' exist1 ,no x' are y1 c4 ,a ,proposition is said to be 'in terms of' the ,letters it contains1 whether with or without accents4 ,thus1 ,some xy' exist1 ,no x' are y1 c41 are said to be in terms of x and y4 pg#jbh #b4 ,representation of ,propositions of ,existence4 ,let us take1 first1 the ,proposition ,some x exist4 ,note that this ,proposition is 7as explained at p4 #ab7 equivalent to ,some existing ,things are x-,things4 ,this tells us that there is at least one ,thing in the ,north ,half2 that is1 that the ,north ,half is occupied4 ,and this we can evidently represent by placing a ,red ,counter 7here represented by a dotted circle7 on the partition which divides the ,north ,half4 ------- 747 ------ ------- ,in the books example1 this ,proposition would be ,some old books exist4 ,similarly we may represent the three similar ,propositions ,some x' exist1 ,some y exist1 and ,some y' exist4 ,the ,reader should make out all these for himself4 ,in the books example1 these ,propositions would be ,some new books exist1 c4 ,let us take1 next1 the ,proposition ,no x exist4 ,this tells us that there is nothing in the ,north ,half2 that is1 that the ,north ,half is empty2 that is1 that the ,north-,west ,cell and the ,north-,east ,cell are both of them empty4 ,and this we can represent by placing two ,grey ,counters in the ,north ,half1 one in each ,cell4 ------- 7 77 7 ------ ------- ,the ,reader may perhaps think that it would be enough to place a ,grey ,counter on the partition in the ,north ,half1 and that1 just as a ,red ,counter1 so placed1 would mean ,this ,half is occupied1 so a ,grey one would mean ,this ,half is empty4 ,this1 however1 would be a mistake4 ,we have seen that a ,red ,counter1 so placed1 would mean ,at least one of these two ,cells is occupied3 possibly both are4 ,hence a ,grey one would merely mean ,at least one of these two ,cells is empty3 possibly both are4 ,but what we have to represent is1 that both ,cells are certainly empty3 and this can only be done by placing a ,grey ,counter in each of them4 ,in the books example1 this ,proposition would be ,no old books exist4 pg#jbi ,similarly we may represent the three similar ,propositions ,no x' exist1 ,no y exist1 and ,no y' exist4 ,the ,reader should make out all these for himself4 ,in the books example1 these three ,propositions would be ,no new books exist1 c4 ,let us take1 next1 the ,proposition ,some xy exist4 ,this tells us that there is at least one ,thing in the ,north-,west ,cell2 that is1 that the ,north-,west ,cell is occupied4 ,and this we can represent by placing a ,red ,counter in it4 ------- 747 ------ ------- ,in the books example1 this ,proposition would be ,some old ,english books exist4 ,similarly we may represent the three similar ,propositions ,some xy' exist1 ,some x'y exist1 and ,some x'y' exist4 ,the ,reader should make out all these for himself4 ,in the books example1 these three ,propositions would be ,some old foreign books exist1 c4 ,let us take1 next1 the ,proposition ,no xy exist4 ,this tells us that there is nothing in the ,north-,west ,cell2 that is1 that the ,north-,west ,cell is empty4 ,and this we can represent by placing a ,grey ,counter in it4 ------- 7 7 ------ ------- ,in the books example1 this ,proposition would be ,no old ,english books exist4 ,similarly we may represent the three similar ,propositions ,no xy' exist1 ,no x'y exist1 and ,no x'y' exist4 ,the ,reader should make out all these for himself4 ,in the books example1 these three ,propositions would be ,no old foreign books exist1 c4 pg#jcj ,we have seen that the ,proposition ,no x exist may be represented by placing two ,grey ,counters in the ,north ,half1 one in each ,cell4 ------- 7 77 7 ------ ------- ,we have also seen that these two ,grey ,counters1 taken separately1 represent the two ,propositions ,no xy exist and ,no xy' exist4 ,hence we see that the ,proposition ,no x exist is a ,double ,proposition1 and is equivalent to the two ,propositions ,no xy exist and ,no xy' exist4 ,in the books example1 this ,proposition would be ,no old books exist4 ,hence this is a ,double ,proposition1 and is equivalent to the two ,propositions ,no old ,english books exist and ,no old foreign books exist4 #c4 ,representation of ,propositions of ,relation4 ,let us take1 first1 the ,proposition ,some x are y4 ,this tells us that at least one ,thing1 in the ,north ,half1 is also in the ,west ,half4 ,hence it must be in the space common to them1 that is1 in the ,north-,west ,cell4 ,hence the ,north-,west ,cell is occupied4 ,and this we can represent by placing a ,red ,counter in it4 ------- 747 ------ ------- ,note that the ,subject of the ,proposition settles which ,half we are to use2 and that the ,predicate settles in which portion of it we are to place the ,red ,counter4 ,in the books example1 this ,proposition would be ,some old books are ,english4 ,similarly we may represent the three similar ,propositions ,some x are y'1 ,some x' are y1 and ,some x' are y'4 ,the ,reader should make out all these for himself4 ,in the books example1 these three ,propositions would be ,some old books are foreign1 c4 pg#jca ,let us take1 next1 the ,proposition ,some y are x4 ,this tells us that at least one ,thing1 in the ,west ,half1 is also in the ,north ,half4 ,hence it must be in the space common to them1 that is1 in the ,north-,west ,cell4 ,hence the ,north-,west ,cell is occupied4 ,and this we can represent by placing a ,red ,counter in it4 ------- 747 ------ ------- ,in the books example1 this ,proposition would be ,some ,english books are old4 ,similarly we may represent the three similar ,propositions ,some y are x'1 ,some y' are x1 and ,some y' are x'4 ,the ,reader should make out all these for himself4 ,in the books example1 these three ,propositions would be ,some ,english books are new1 c4 ,we see that this one ,diagram has now served to represent no less than three ,propositions1 viz4 7#a7 ,some xy exist2 7#b7 ,some x are y2 7#c7 ,some y are x4 ------- 747 ------ ------- ,hence these three ,propositions are equivalent4 ,in the books example1 these ,propositions would be 7#a7 ,some old ,english books exist2 7#b7 ,some old books are ,english2 7#c7 ,some ,english books are old4 ,the two equivalent ,propositions1 ,some x are y and ,some y are x1 are said to be ',converse' to each other2 and the ,process1 of changing one into the other1 is called ',converting'1 or ',conversion'4 ,for example1 if we were told to convert the ,proposition ,some apples are not ripe1 we should first choose our ,univ4 7say fruit71 and then complete the ,proposition1 by supplying the ,substantive fruit in the ,predicate1 so that it would be ,some apples are not-ripe fruit2 and we should then convert it by interchanging its ,terms1 so that it would be ,some not-ripe fruit are apples4 pg#jcb ,similarly we may represent the three similar ,trios of equivalent ,propositions2 the whole ,set of four ,trios being as follows3-- 7#a7 ,some xy exist ,some x are y ,some y are x4 7#b7 ,some xy' exist ,some x are y' ,some y' are x4 7#c7 ,some x'y exist ,some x' are y ,some y are x'4 7#d7 ,some x'y' exist ,some x' are y' ,some y' are x'4 ,let us take1 next1 the ,proposition ,no x are y4 ,this tell us that no ,thing1 in the ,north ,half1 is also in the ,west ,half4 ,hence there is nothing in the space common to them1 that is1 in the ,north-,west ,cell4 ,hence the ,north-,west ,cell is empty4 ,and this we can represent by placing a ,grey ,counter in it4 ------- 7 7 ------ ------- ,in the books example1 this ,proposition would be ,no old books are ,english4 ,similarly we may represent the three similar ,propositions ,no x are y'1 and ,no x' are y1 and ,no x' are y'4 ,the ,reader should make out all these for himself4 ,in the books example1 these three ,propositions would be ,no old books are foreign1 c4 ,let us take1 next1 the ,proposition ,no y are x4 ,this tells us that no ,thing1 in the ,west ,half1 is also in the ,north ,half4 ,hence there is nothing in the space common to them1 that is1 in the ,north-,west ,cell4 ,that is1 the ,north-,west ,cell is empty4 ,and this we can represent by placing a ,grey ,counter in it4 ------- 7 7 ------ ------- ,in the books example1 this ,proposition would be ,no ,english books are old4 ,similarly we may represent the three similar ,propositions ,no y are x'1 ,no y' are x1 and ,no y' are x'4 ,the ,reader should make out all these for himself4 ,in the books example1 these three ,propositions would be ,no ,english books are new1 c4 pg#jcc ------- 7 7 ------ ------- ,we see that this one ,diagram has now served to present no less than three ,propositions1 viz4 7#a7 ,no xy exist2 7#b7 ,no x are y2 7#c7 ,no y are x4 ,hence these three ,propositions are equivalent4 ,in the books example1 these ,propositions would be 7#a7 ,no old ,english books exist2 7#b7 ,no old books are ,english2 7#c7 ,no ,english books are old4 ,the two equivalent ,propositions1 ,no x are y and ,no y are x1 are said to be ',converse' to each other4 ,for example1 if we were told to convert the ,proposition ,no porcupines are talkative1 we should first choose our ,univ4 7say animals71 and then complete the ,proposition1 by supplying the ,substantive animals in the ,predicate1 so that it would be ,no porcupines are talkative animals1 and we should then convert it1 by interchanging its ,terms1 so that it would be ,no talkative animals are porcupines4 ,similarly we may represent the three similar ,trios of equivalent ,propositions2 the whole ,set of four ,trios being as follows3-- 7#a7 ,no xy exist ,no x are y ,no y are x4 7#b7 ,no xy' exist ,no x are y' ,no y' are x4 7#c7 ,no x'y exist ,no x' are y ,no y are x'4 7#d7 ,no x'y' exist ,no x' are y' ,no y' are x'4 ,let us take1 next1 the ,proposition ,all x are y4 ,we know 7see p4 #ag7 that this is a ,double ,proposition1 and equivalent to the two ,propositions ,some x are y and ,no x are y'1 each of which we already know how to represent4 ------- 7477 7 ------ ------- ,note that the ,subject of the given ,proposition settles which ,half we are to use2 and that its ,predicate settles in which portion of that ,half we are to place the ,red ,counter4 pg#jcd ,,table ,,ii4 ---------------------------------------- ------------- ------- ------- 747 7 77 7 ,some x exist ------ ,no x exist ------ ------- ------- ---------------------------------------- ---------- ------- ------- ,some x' exist ------ ,no x' exist ------ 747 7 77 7 ------- ------- ---------------------------------------- ---------- ------- ------- 7 7 ,some y exist 747--- ,no y exist ------ 7 7 ------- ------- ---------------------------------------- ---------- ------- ------- 7 7 ,some y' exist ---747 ,no y' exist ------ 7 7 ------- ------- ---------------------------------------- ------------- ,similarly we may represent the seven similar ,propositions ,all x are y'1 ,all x' are y1 ,all x' are y'1 ,all y are x1 ,all y are x'1 ,all y' are x1 and ,all y' are x'4 ,let us take1 lastly1 the ,double ,proposition ,some x are y and some are y'1 each part of which we already know how to represent4 ------- 747747 ------ ------- ,similarly we may represent the three similar ,propositions1 ,some x' are y and some are y'1 ,some y are x and some are x'1 ,some y' are x and some are x'4 ,the ,reader should now get his genial friend to question him1 severely1 on these two ,tables4 ,the ,inquisitor should have the ,tables before him3 but the ,victim should have nothing but a blank ,diagram1 and the ,counters with which he is to represent the various ,propositions named by his friend1 e4g4 ,some y exist1 ,no y' are x1 ,all x are y1 c4 c4 pg#jce ,,table ,,iii4 ---------------------------------------- --------------------- ------- ------- ,some xy exist 747 7477 7 ,some x are y ------ ,all x are y ------ ,some y are x ------- ------- ---------------------------------------- ------------------ ------- ------- ,some xy' exist 747 7 7747 ,some x are y' ------ ,all x are y' ------ ,some y' are x ------- ------- ---------------------------------------- ------------------ ------- ------- ,some x'y exist ,some x' are y ------ ,all x' are y ------ ,some y are x' 747 7477 7 ------- ------- ---------------------------------------- ------------------ ------- ------- ,some x'y' exist ,some x' are y' ------ ,all x' are y' ------ ,some y' are x' 747 7 7747 ------- ------- ---------------------------------------- --------------------- ---------------------------------------- --------------------- ------- ------- ,no xy exist 7 7 747 ,no x are y ------ ,all y are x ------ ,no y are x 7 7 ------- ------- ---------------------------------------- ------------------ ------- ------- ,no xy' exist 7 7 7 7 ,no x are y' ------ ,all y are x' ------ ,no y' are x 747 ------- ------- ---------------------------------------- ------------------ ------- ------- ,no x'y exist 747 ,no x' are y ------ ,all y' are x ------ ,no y are x' 7 7 7 7 ------- ------- ---------------------------------------- ------------------ ------- ------- ,no x'y' exist 7 7 ,no x' are y' ------ ,all y' are x' ------ ,no y' are x' 7 7 747 ------- ------- ---------------------------------------- --------------------- ---------------------------------------- --------------------- ------- ------- 747747 747 ,some x are y1 ------ ,some y are x ------ and some are y' and some are x' 747 ------- ------- ---------------------------------------- ------------------ ------- ------- 747 ,some x' are y1 ------ ,some y' are x ------ and some are y' 747747 and some are x' 747 ------- ------- ---------------------------------------- --------------------- pg#jcf ,,chapter ,,iv4 ,,interpretation ,,of ,,biliteral ,,diagram ,,when ,,marked ,,with ,,counters4 ,the ,diagram is supposed to be set before us1 with certain ,counters placed upon it2 and the problem is to find out what ,proposition1 or ,propositions1 the ,counters represent4 ,as the process is simply the reverse of that discussed in the previous ,chapter1 we can avail ourselves of the results there obtained1 as far as they go4 ,first1 let us suppose that we find a ,red ,counter placed in the ,north-,west ,cell4 ------- 747 ------ ------- ,we know that this represents each of the ,trio of equivalent ,propositions ,some xy exist ,some x are y ,some y are x4 ,similarly we may interpret a ,red ,counter1 when placed in the ,north-,east1 or ,south-,west1 or ,south-,east ,cell4 ,next1 let us suppose that we find a ,grey ,counter placed in the ,north-,west ,cell4 ------- 7 7 ------ ------- ,we know that this represents each of the ,trio of equivalent ,propositions ,no xy exist ,no x are y ,no y are x4 ,similarly we may interpret a ,grey ,counter1 when placed in the ,north-,east1 or ,south-,west1 or ,south-,east ,cell4 pg#jcg ,next1 let us suppose that we find a ,red ,counter placed on the partition which divides the ,north ,half4 ------- 747 ------ ------- ,we know that this represents the ,proposition ,some x exist4 ,similarly we may interpret a ,red ,counter1 when placed on the partition which divides the ,south1 or ,west1 or ,east ,half4 99 99 99 99 99 ,next1 let us suppose that we find two ,red ,counters placed in the ,north ,half1 one in each ,cell4 ------- 747747 ------ ------- ,we know that this represents the ,double ,proposition ,some x are y and some are y'4 ,similarly we may interpret two ,red ,counters1 when placed in the ,south1 or ,west1 or ,east ,half4 99 99 99 99 99 ,next1 let us suppose that we find two ,grey ,counters placed in the ,north ,half1 one in each ,cell4 ------- 7 77 7 ------ ------- ,we know that this represents the ,proposition ,no x exist4 ,similarly we may interpret two ,grey ,counters1 when placed in the ,south1 or ,west1 or ,east ,half4 99 99 99 99 99 ,lastly1 let us suppose that we find a ,red and a ,grey ,counter placed in the ,north ,half1 the ,red in the ,north-,west ,cell1 and the ,grey in the ,north-,east ,cell4 ------- 7477 7 ------ ------- ,we know that this represents the ,proposition1 ,all x are y4 ,note that the ,half1 occupied by the two ,counters1 settles what is to be the ,subject of the ,proposition1 and that the ,cell1 occupied by the ,red ,counter1 settles what is to be its ,predicate4 pg#jch ,similarly we may interpret a ,red and a ,grey counter1 when placed in any one of the seven similar positions ,red in ,north-,east1 ,grey in ,north-,west2 ,red in ,south-,west1 ,grey in ,south-,east2 ,red in ,south-,east1 ,grey in ,south-,west2 ,red in ,north-,west1 ,grey in ,south-,west2 ,red in ,south-,west1 ,grey in ,north-,west2 ,red in ,north-,east1 ,grey in ,south-,east2 ,red in ,south-,east1 ,grey in ,north-,east4 ,once more the genial friend must be appealed to1 and requested to examine the ,reader on ,tables ,,ii and ,,iii1 and to make him not only represent ,propositions1 but also interpret ,diagrams when marked with ,counters4 ,the ,questions and ,answers should be like this3-- ,q4 ,represent ,no x' are y'4 ,a4 ,grey ,counter in ,s4,e4 ,cell4 ,q4 ,interpret ,red ,counter on ,e4 partition4 ,a4 ,some y' exist4 ,q4 ,represent ,all y' are x4 ,a4 ,red in ,n4,e4 ,cell2 ,grey in ,s4,e4 ,q4 ,interpret ,grey ,counter in ,s4,w4 ,cell4 ,a4 ,no x'y exist ,no x' are y ,no y are x'4 c41 c4 ,at first the ,examinee will need to have the ,board and ,counters before him2 but he will soon learn to dispense with these1 and to answer with his eyes shut or gazing into vacancy4 ,work ,examples #a1 #e-h 7p4 #ig74 pg#jci ,,book ,,iv4 ,,the ,,triliteral ,,diagram4 ----------------- ----------------- xy xy' m' m' xy xy' -------- xy xy' m m ---------------- -------------- x'y x'y' m m x'y x'y' -------- x'y x'y' m' m' ----------------- ----------------- ,,chapter ,i4 ,,symbols ,,and ,,cells4 ,first1 let us suppose that the above left-hand ,diagram is the ,biliteral ,diagram that we have been using in ,book ,,iii41 and that we change it into a ,triliteral ,diagram by drawing an ,inner ,square1 so as to divide each of its #d ,cells into #b portions1 thus making #h ,cells altogether4 ,the right-hand ,diagram shows the result4 ,the ,reader is strongly advised1 in reading this ,chapter1 not to refer to the above ,diagrams1 but to make a large copy of the right-hand one for himself1 without any letters1 and to have it by him while he reads1 and keep his finger on that particular part of it1 about which he is reading4 pg#jdj ,secondly1 let us suppose that we have selected a certain ,adjunct1 which we may call m1 and have subdivided the xy-,class into the two ,classes whose ,differenti are m and m'1 and that we have assigned the ,n4,w4 ,inner ,cell to the one 7which we may call the ,class of xym-,things1 or the xym-,class71 and the ,n4,w4 ,outer ,cell to the other 7which we may call the ,class of xym'-,things1 or the xym'-,class74 ,thus1 in the books example1 we might say ,let m mean 'bound'1 so that m' will mean 'unbound'1 and we might suppose that we had subdivided the ,class old ,english books into the two ,classes1 old ,english bound books and old ,english unbound books1 and had assigned the ,n4,w4 ,inner ,cell to the one1 and the ,n4,w4 ,outer ,cell to the other4 ,thirdly1 let us suppose that we have subdivided the xy'-,class1 the x'y-,class1 and the x'y'-,class in the same manner1 and have1 in each case1 assigned the ,inner ,cell to the ,class possessing the ,attribute m1 and the ,outer ,cell to the ,class possessing the ,attribute m'4 ,thus1 in the books example1 we might suppose that we had subdivided the new ,english books into the two ,classes1 new ,english bound books and new ,english unbound books1 and had assigned the ,s4,w4 ,inner ,cell to the one1 and the ,s4,w4 ,outer ,cell to the other4 ,it is evident that we have now assigned the ,inner ,square to the m-,class1 and the ,outer ,border to the m'-,class4 ,thus1 in the books example1 we have assigned the ,inner ,square to bound books and the ,outer ,border to unbound books4 ,when the ,reader has made himself familiar with this ,diagram1 he ought to be able to find1 in a moment1 the ,compartment assigned to a particular pair of ,attributes1 or the ,cell assigned to a particular trio of ,attributes4 ,the following ,rules will help him in doing this3-- 7#a7 ,arrange the ,attributes in the order x1 y1 m4 pg#jda 7#b7 ,take the first of them and find the ,compartment assigned to it4 7#c7 ,then take the second1 and find what portion of that compartment is assigned to it4 7#d7 ,treat the third1 if there is one1 in the same way4 ,for example1 suppose we have to find the ,compartment assigned to ym4 ,we say to ourselves y has the ,west ,half2 and m has the ,inner portion of that ,west ,half4 ,again1 suppose we have to find the ,cell assigned to x'ym'4 ,we say to ourselves x' has the ,south ,half2 y has the ,west portion of that ,south ,half1 i4e4 has the ,south-,west ,quarter2 and m' has the ,outer portion of that ,south-,west ,quarter4 ,the ,reader should now get his genial friend to question him on the ,table given on the next page1 in the style of the following specimen-,dialogue4 ,q4 ,adjunct for ,south ,half1 ,inner ,portion8 ,a4 x'm4 ,q4 ,compartment for m'8 ,a4 ,the ,outer ,border4 ,q4 ,adjunct for ,north-,east ,quarter1 ,outer ,portion8 ,a4 xy'm'4 ,q4 ,compartment for ym8 ,a4 ,west ,half1 ,inner ,portion4 ,q4 ,adjunct for ,south ,half8 ,a4 x'4 ,q4 ,compartment for x'y'm8 ,a4 ,south-,east ,quarter1 ,inner ,portion4 c4 c4 pg#jdb ,,table ,,iv4 ---------------------------------------- ------- ,adjunct of ,compartments1 or ,cells1 assigned ,classes4 to them4 ---------------------------------------- ------ x ,north ,half4 x' ,south y ,west y' ,east m ,inner ,square4 m' ,outer ,border4 ---------------------------------------- ------ xy ,north-,west ,quarter4 xy' ,east x'y ,south-,west x'y' ,east xm ,north ,half1 ,inner ,portion4 xm' ,outer x'm ,south ,inner x'm' ,outer ym ,west ,inner ym' ,outer y'm ,east ,inner y'm' ,outer ---------------------------------------- ------ xym ,north-,west ,quarter1 ,inner ,portion4 xym' ,outer xy'm ,east ,inner xy'm' ,outer x'ym ,south-,west ,inner x'ym' ,outer x'y'm ,east ,inner x'y'm' ,outer ---------------------------------------- ------- pg#jdc ,,chapter ,,ii4 ,,representation ,,of ,,propositions ,,in ,,terms ,,of x ,,and m1 ,,or ,,of y ,,and m4 #a4 ,representation of ,propositions of ,existence in terms of x and m1 or of y and m4 ,let us take1 first1 the ,proposition ,some xm exist4 ,note that the full meaning of this ,proposition is 7as explained at p4 #ab7 ,some existing ,things are xm-,things4 ,this tells us that there is at least one ,thing in the ,inner portion of the ,north ,half2 that is1 that this ,compartment is occupied4 ,and this we can evidently represent by placing a ,red ,counter on the partition which divides it4 --------------- ------ 747 ------------ ------ --------------- ,in the books example1 this ,proposition would mean ,some old bound books exist 7or ,there are some old bound books74 ,similarly we may represent the seven similar ,propositions1 ,some xm' exist1 ,some x'm exist1 ,some x'm' exist1 ,some ym exist1 ,some ym' exist1 ,some y'm exist1 and ,some y'm' exist4 pg#jdd ,let us take1 next1 the ,proposition ,no xm exist4 ,this tells us that there is nothing in the ,inner portion of the ,north ,half2 that is1 that this ,compartment is empty4 ,and this we can represent by placing two ,grey ,counters in it1 one in each ,cell4 --------------- ------ 7 77 7 ------------ ------ --------------- ,similarly we may represent the seven similar ,propositions1 in terms of x and m1 or of y and m1 viz4 ,no xm' exist1 ,no x'm exist1 c4 99 99 99 99 99 ,these sixteen ,propositions of ,existence are the only ones that we shall have to represent on this ,diagram4 #b4 ,representation of ,propositions of ,relation in terms of x and m1 or of y and m4 ,let us take1 first1 the ,pair of ,converse ,propositions ,some x are m ,some m are x4 ,we know that each of these is equivalent to the ,proposition of ,existence ,some xm exist1 which we already know how to represent4 --------------- ------ 747 ------------ ------ --------------- ,similarly for the seven similar ,pairs1 in terms of x and m1 or of y and m4 ,let us take1 next1 the ,pair of ,converse ,propositions ,no x are m ,no m are x4 ,we know that each of these is equivalent to the ,proposition of ,existence ,no xm exist1 which we already know how to represent4 --------------- ------ 7 77 7 ------------ ------ --------------- ,similarly for the seven similar ,pairs1 in terms of x and m1 or of y and m4 pg#jde ,let us take1 next1 the ,proposition ,all x are m4 --------------- 7 7 7 7 ------ 747 ------------ ------ --------------- ,we know 7see p4 #ah7 that this is a ,double ,proposition1 and equivalent to the two ,propositions ,some x are m and ,no x are m' 1 each of which we already know how to represent4 ,similarly for the fifteen similar ,propositions1 in terms of x and m1 or of y and m4 ,these thirty-two ,propositions of ,relation are the only ones that we shall have to represent on this ,diagram4 ,the ,reader should now get his genial friend to question him on the following four ,tables4 ,the ,victim should have nothing before him but a blank ,triliteral ,diagram1 a ,red ,counter1 and #b ,grey ones1 with which he is to represent the various ,propositions named by the ,inquisitor1 e4g4 ,no y' are m1 ,some xm' exist1 c41 c4 pg#jdf ,,table ,v4 ---------------------------------------- ----------------- --------------- ,some xm exist --------------- ,some x are m ------ ,some m are x ------ 747 7 77 7 ------------ ----------------- ------------ ,no xm exist ------ ,no x are m ------ ,no m are x --------------- --------------- ---------------------------------------- ----------------- --------------- ,some xm' exist --------------- 747 ,some x are m' 7 7 7 7 ------ ,some m' are x ------ ------------ ----------------- ------------ ,no xm' exist ------ ,no x are m' ------ ,no m' are x --------------- --------------- ---------------------------------------- ----------------- --------------- ,some x'm exist --------------- ,some x' are m ------ ,some m are x' ------ ------------ ----------------- ------------ 747 ,no x'm exist 7 77 7 ------ ,no x' are m ------ ,no m are x' --------------- --------------- ---------------------------------------- ----------------- --------------- ,some x'm' exist --------------- ,some x' are m' ------ ,some m' are x' ------ ------------ ----------------- ------------ ,no x'm' exist ------ ,no x' are m' ------ 747 ,no m' are x' 7 7 7 7 --------------- --------------- ---------------------------------------- ----------------- pg#jdg ,,table ,,vi4 ---------------------------------------- ----------------- --------------- ,some ym exist --------------- ,some y are m ------ ,some m are y ------ 7 7 ---747------ ----------------- ------------ ,no ym exist 7 7 ------ ,no y are m ------ ,no m are y --------------- --------------- ---------------------------------------- ----------------- --------------- ,some ym' exist --------------- ,some y are m' 7 7 ------ ,some m' are y ------ 747--------- ----------------- ------------ ,no ym' exist ------ ,no y are m' ------ ,no m' are y 7 7 --------------- --------------- ---------------------------------------- ----------------- --------------- ,some y'm exist --------------- ,some y' are m ------ ,some m are y' ------ 7 7 ------747--- ----------------- ------------ ,no y'm exist 7 7 ------ ,no y' are m ------ ,no m are y' --------------- --------------- ---------------------------------------- ----------------- --------------- ,some y'm' exist --------------- ,some y' are m' 7 7 ------ ,some m' are y' ------ ---------747 ----------------- ------------ ,no y'm' exist ------ ,no y' are m' ------ ,no m' are y' 7 7 --------------- --------------- ---------------------------------------- ----------------- pg#jdh ,,table ,,vii4 ---------------------------------------- ----------------- --------------- --------------- 7 7 7 7 ,all x are m 747 ------ ------ 747 7 77 7 ------------ ----------------- ------------ ------ ,all x are m' ------ --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- ,all x' are m ------ ------ ------------ ----------------- ------------ 747 7 77 7 ------ ,all x' are m' ------ 7 7 7 7 747 --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- ,all m are x ------ ------ 747 7 77 7 ------------ ----------------- ------------ 7 77 7 747 ------ ,all m are x' ------ --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- 747 ,all m' are x 7 7 7 7 ------ ------ ------------ ----------------- ------------ ------ ,all m' are x' ------ 7 7 7 7 747 --------------- --------------- ---------------------------------------- ----------------- pg#jdi ,,table ,,viii4 ---------------------------------------- ----------------- --------------- --------------- 7 7 ,all y are m ------ ------ 7 7 ---747------ ----------------- 747--------- 7 7 ------ ,all y are m' ------ 7 7 --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- 7 7 ,all y' are m ------ ------ 7 7 ------747--- ----------------- ---------747 7 7 ------ ,all y' are m' ------ 7 7 --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- ,all m are y ------ ------ 7 7 7 7 ---747------ ----------------- ------747--- 7 7 7 7 ------ ,all m are y' ------ --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- 7 7 ,all m' are y 7 7 ------ ------ 747--------- ----------------- ---------747 ------ ,all m' are y' ------ 7 7 7 7 --------------- --------------- ---------------------------------------- ----------------- pg#jej ,,chapter ,,iii4 ,,representation ,,of ,,two ,,propositions ,,of ,,relation1 ,,one ,,in ,,terms ,,of x ,,and m1 ,,and ,,the ,,other ,,in ,,terms ,,of y ,,and m1 ,,on ,,the ,,same ,,diagram4 ,the ,reader had better now begin to draw little ,diagrams for himself1 and to mark them with the ,digits ,i and ,o1 instead of using the ,board and ,counters3 he may put a ,i to represent a ,red ,counter 7this may be interpreted to mean ,there is at least one ,thing here71 and a ,o to represent a ,grey ,counter 7this may be interpreted to mean ,there is nothing here74 ,the ,pair of ,propositions1 that we shall have to represent1 will always be1 one in terms of x and m1 and the other in terms of y and m4 ,when we have to represent a ,proposition beginning with ,all1 we break it up into the two ,propositions to which it is equivalent4 ,when we have to represent1 on the same ,diagram1 ,propositions1 of which some begin with ,some and others with ,no1 we represent the negative ones first4 ,this will sometimes save us from having to put a ,i on a fence and afterwards having to shift it into a ,cell4 ,let us work a few examples4 7#a7 ,no x are m'2 ,no y' are m4 ,let us first represent ,no x are m'4 ,this gives us ,diagram a4 ,then1 representing ,no y' are m on the same ,diagram1 we get ,diagram b4 pg#jea a b --------------- --------------- 7,o7 7,o7 7,o7 7,o7 ------ ------ 7,o7 ------------ ------------ 7,o7 ------ ------ --------------- --------------- 7#b7 ,some m are x2 ,no m are y4 ,if1 neglecting the ,rule1 we were begin with ,some m are x1 we should get ,diagram a4 ,and if we were then to take ,no m are y1 which tells us that the ,inner ,n4,w4 ,cell is empty1 we should be obliged to take the ,i off the fence 7as it no longer has the choice of two ,cells71 and to put it into the ,inner ,n4,e4 ,cell1 as in ,diagram c4 ,this trouble may be saved by beginning with ,no m are y1 as in ,diagram b4 ,and now1 when we take ,some m are x1 there is no fence to sit on6 ,the ,i has to go1 at once1 into the ,n4,e4 ,cell1 as in ,diagram c4 a b c --------------- --------------- --------------- ------ ------ ------ 7,i7 7,o7 7,o77,i7 ------------ ------------ ------------ 7,o7 7,o7 ------ ------ ------ --------------- --------------- --------------- 7#c7 ,no x' are m'2 ,all m are y4 ,here we begin by breaking up the ,second into the two ,propositions to which it is equivalent4 ,thus we have three ,propositions to represent1 viz4-- 7#a7 ,no x' are m'2 7#b7 ,some m are y2 7#c7 ,no m are y'4 ,these we will take in the order #a1 #c1 #b4 ,first we take ,no4 7#a71 viz4 ,no x' are m'4 ,this gives us ,diagram a4 pg#jeb ,adding to this1 ,no4 7#c71 viz4 ,no m are y'1 we get ,diagram b4 ,this time the ,i1 representing ,no4 7#b71 viz4 ,some m are y1 has to sit on the fence1 as there is no ,o to order it off6 ,this gives us ,diagram c4 a b c --------------- --------------- --------------- ------ ------ ------ 7,o7 7,o7 ------------ ------------ ---7,i7------ 7,o7 7,o7 ------ ------ ------ 7,o7 7,o7 7,o7 7,o7 7,o7 7,o7 --------------- --------------- --------------- 7#d7 ,all m are x2 ,all y are m4 ,here we break up both ,propositions1 and thus get four to represent1 viz4-- 7#a7 ,some m are x2 7#b7 ,no m are x'2 7#c7 ,some y are m2 7#d7 ,no y are m'4 ,these we will take in the order #b1 #d1 #a1 #c4 ,first we take ,no4 7#b71 viz4 ,no m are x'4 ,this gives us ,diagram a4 ,to this we add ,no4 7#d71 viz4 ,no y are m'1 and thus get ,diagram b4 ,if we were to add to this ,no4 7#a71 viz4 ,some m are x1 we should have to put the ,i on a fence3 so let us try ,no4 7#c7 instead1 viz4 ,some y are m4 ,this gives us ,diagram c4 ,and now there is no need to trouble about ,no4 7#a71 as it would not add anything to our information to put a ,i on the fence4 ,the ,diagram already tells us that ,some m are x4 a b c --------------- --------------- --------------- 7,o7 7,o7 ------ ------ ------ 7,i7 ------------ ------------ ------------ 7,o77,o7 7,o77,o7 7,o77,o7 ------ ------ ------ 7,o7 7,o7 --------------- --------------- --------------- ,work ,examples #a1 #i-ab 7p4 #ig72 #b1 #a-bj 7p4 #ih74 pg#jec ,,chapter ,,iv4 ,,interpretation1 ,,in ,,terms ,,of x ,,and y1 ,,of ,,triliteral ,,diagram1 ,,when ,,marked ,,with ,,counters ,,or ,,digits4 ,the problem before us is1 given a marked ,triliteral ,diagram1 to ascertain what ,propositions of ,relation1 in terms of x and y1 are represented on it4 ,the best plan1 for a beginner1 is to draw a ,biliteral ,diagram alongside of it1 and to transfer1 from the one to the other1 all the information he can4 ,he can then read off1 from the ,biliteral ,diagram1 the required ,propositions4 ,after a little practice1 he will be able to dispense with the ,biliteral ,diagram1 and to read off the result from the ,triliteral ,diagram itself4 ,to transfer the information1 observe the following ,rules3-- 7#a7 ,examine the ,n4,w4 ,quarter of the ,triliteral ,diagram4 7#b7 ,if it contains a ,i1 in either ,cell1 it is certainly occupied1 and you may mark the ,n4,w4 ,quarter of the ,biliteral ,diagram with a ,i4 7#c7 ,if it contains two ,os1 one in each ,cell1 it is certainly empty1 and you may mark the ,n4,w4 ,quarter of the ,biliteral ,diagram with a ,o4 pg#jed 7#d7 ,deal in the same way with the ,n4,e41 the ,s4,w41 and the ,s4,e4 ,quarter4 ,let us take1 as examples1 the results of the four ,examples worked in the previous ,chapters4 7#a7 --------------- 7,o7 7,o7 ------ 7,o7 ------------ 7,o7 ------ --------------- ,in the ,n4,w4 ,quarter1 only one of the two ,cells is marked as empty3 so we do not know whether the ,n4,w4 ,quarter of the ,biliteral ,diagram is occupied or empty3 so we cannot mark it4 ------- 7,o7 ------ ------- ,in the ,n4,e4 ,quarter1 we find two ,os3 so this ,quarter is certainly empty2 and we mark it so on the ,biliteral ,diagram4 ,in the ,s4,w4 ,quarter1 we have no information at all4 ,in the ,s4,e4 ,quarter1 we have not enough to use4 ,we may read off the result as ,no x are y'1 or ,no y' are x1 whichever we prefer4 7#b7 --------------- ------ 7,o77,i7 ------------ 7,o7 ------ --------------- ,in the ,n4,w4 ,quarter1 we have not enough information to use4 ,in the ,n4,e4 ,quarter1 we find a ,i4 ,this shows us that it is occupied3 so we may mark the ,n4,e4 ,quarter on the ,biliteral ,diagram with a ,i4 ------- 7,i7 ------ ------- ,in the ,s4,w4 ,quarter1 we have not enough information to use4 ,in the ,s4,e4 ,quarter1 we have none at all4 ,we may read off the result as ,some x are y'1 or ,some y' are x1 whichever we prefer4 pg#jee 7#c7 --------------- ------ 7,o7 ---7,i7------ 7,o7 ------ 7,o7 7,o7 --------------- ,in the ,n4,w4 ,quarter1 we have no information4 7,the ,i1 sitting on the fence1 is of no use to us until we know on which side he means to jump down67 ,in the ,n4,e4 ,quarter1 we have not enough information to use4 ,neither have we in the ,s4,w4 ,quarter4 ------- ------ 7,o7 ------- ,the ,s4,e4 ,quarter is the only one that yields enough information to use4 ,it is certainly empty3 so we mark it as such on the ,biliteral ,diagram4 ,we may read off the results as ,no x' are y'1 or ,no y' are x'1 whichever we prefer4 7#d7 --------------- 7,o7 ------ 7,i7 ------------ 7,o77,o7 ------ 7,o7 --------------- ,the ,n4,w4 ,quarter is occupied1 in spite of the ,o in the ,outer ,cell4 ,so we mark it with a ,i on the ,biliteral ,diagram4 ,the ,n4,e4 ,quarter yields no information4 ------- 7,i7 ------ ------- ,the ,s4,w4 ,quarter is certainly empty4 ,so we mark it as such on the ,biliteral ,diagram4 ------- 7,i7 ------ 7,o7 ------- ,the ,s4,e4 ,quarter does not yield enough information to use4 ,we read off the result as ,all y are x4 ,review ,tables ,v1 ,,vi 7pp4 #df1 #dg74 ,work ,examples #a1 #ac-af 7p4 #ig72 #b1 #ba-cb 7p4 #ih72 #c1 #a-bj 7p4 #ii74 pg#jef ,,book ,v4 ,,syllogisms4 ,,chapter ,i4 ,,introductory ,when a ,trio of ,biliteral ,propositions of ,relation is such that 7#a7 all their six ,terms are ,species of the same ,genus1 7#b7 every two of them contain between them a ,pair of codivisional ,classes1 7#c7 the three ,propositions are so related that1 if the first two were true1 the third would be true1 the ,trio is called a ',syllogism'2 the ,genus1 of which each of the six ,terms is a ,species1 is called its ',universe of ,discourse'1 or1 more briefly1 its ',univ4'2 the first two ,propositions are called its ',premisses'1 and the third its ',conclusion'2 also the ,pair of codivisional ,terms in the ,premisses are called its ',eliminands'1 and the other two its ',retinends'4 ,the ,conclusion of a ,syllogism is said to be 'consequent' from its ,premisses3 hence it is usual to prefix to it the word ,therefore 7or the ,symbol 4'474 pg#jeg ,note that the ',eliminands' are so called because they are eliminated1 and do not appear in the ,conclusion2 and that the ',retinends' are so called because they are retained1 and do appear in the ,conclusion4 ,note also that the question1 whether the ,conclusion is or is not consequent from the ,premisses1 is not affected by the actual truth or falsity of any of the ,trio1 but depends entirely on their relationship to each other4 ,as a specimen-,syllogism1 let us take the ,trio ,no x-,things are m-,things2 ,no y-,things are m'-,things4 ,no x-,things are y-,things4 which we may write1 as explained at p4 #bf1 thus3-- ,no x are m2 ,no y are m'4 ,no x are y4 ,here the first and second contain the ,pair of codivisional ,classes m and m'2 the first and third contain the ,pair x and x2 and the second and third contain the ,pair y and y4 ,also the three ,propositions are 7as we shall see hereafter7 so related that1 if the first two were true1 the third would also be true4 ,hence the ,trio is a ,syllogism2 the two ,propositions1 ,no x are m and ,no y are m'1 are its ,premisses2 the ,proposition ,no x are y is its ,conclusion2 the ,terms m and m' are its ,eliminands2 and the ,terms x and y are its ,retinends4 ,hence we may write it thus3-- ,no x are m2 ,no y are m'4 4'4 ,no x are y4 ,as a second specimen1 let us take the ,trio ,all cats understand ,french2 ,some chickens are cats4 ,some chickens understand ,french4 ,these1 put into normal form1 are ,all cats are creatures understanding ,french2 ,some chickens are cats4 ,some chickens are creatures understanding ,french4 ,here all the six ,terms are ,species of the ,genus creatures4 ,also the first and second ,propositions contain the ,pair of codivisional ,classes cats and cats2 the first and third contain the ,pair creatures understanding ,french and creatures understanding ,french2 and the second and third contain the ,pair chickens and chickens4 pg#jeh ,also the three ,propositions are 7as we shall see at p4 #fd7 so related that1 if the first two were true1 the third would be true4 7,the first two are1 as it happens1 not strictly true in our planet4 ,but there is nothing to hinder them from being true in some other planet1 say ,mars or ,jupiter--in which case the third would also be true in that planet1 and its inhabitants would probably engage chickens as nursery-governesses4 ,they would thus secure a singular contingent privilege1 unknown in ,england1 namely1 that they would be able1 at any time when provisions ran short1 to utilise the nursery-governess for the nursery-dinner67 ,hence the ,trio is a ,syllogism2 the ,genus creatures is its ',univ4'2 the two ,propositions1 ,all cats understand ,french and ,some chickens are cats1 are its ,premisses1 the ,proposition ,some chickens understand ,french is its ,conclusion2 the ,terms cats and cats are its ,eliminands2 and the ,terms1 creatures understanding ,french and chickens1 are its ,retinends4 ,hence we may write it thus3-- ,all cats understand ,french2 ,some chickens are cats2 4'4 ,some chickens understand ,french4 pg#jei ,,chapter ,,ii4 ,,problems ,,in ,,syllogisms4 #a4 ,introductory4 ,when the ,terms of a ,proposition are represented by words1 it is said to be 'concrete'2 when by letters1 'abstract4' ,to translate a ,proposition from concrete into abstract form1 we fix on a ,univ41 and regard each ,term as a ,species of it1 and we choose a letter to represent its ,differentia4 ,for example1 suppose we wish to translate ,some soldiers are brave into abstract form4 ,we may take men as ,univ41 and regard soldiers and brave men as ,species of the ,genus men2 and we may choose x to represent the peculiar ,attribute 7say military7 of soldiers1 and y to represent brave4 ,then the ,proposition may be written ,some military men are brave men2 i4e4 ,some x-men are y-men2 i4e4 7omitting men1 as explained at p4 #bf7 ,some x are y4 ,in practice1 we should merely say ,let ,univ4 be men1 x soldiers1 y brave1 and at once translate ,some soldiers are brave into ,some x are y4 ,the ,problems we shall have to solve are of two kinds1 viz4 7#a7 ,given a ,pair of ,propositions of ,relation1 which contain between them a pair of codivisional ,classes1 and which are proposed as ,premisses3 to ascertain what ,conclusion1 if any1 is consequent from them4 7#b7 ,given a ,trio of ,propositions of ,relation1 of which every two contain a pair of codivisional ,classes1 and which are proposed as a ,syllogism3 to ascertain whether the proposed ,conclusion is consequent from the proposed ,premisses1 and1 if so1 whether it is complete4 ,these ,problems we will discuss separately4 pg#jfj #b4 ,given a ,pair of ,propositions of ,relation1 which contain between them a pair of codivisional ,classes1 and which are proposed as ,premisses3 to ascertain what ,conclusion1 if any1 is consequent from them4 ,the ,rules1 for doing this1 are as follows3-- 7#a7 ,determine the ',universe of ,discourse'4 7#b7 ,construct a ,dictionary1 making m and m 7or m and m'7 represent the pair of codivisional ,classes1 and x 7or x'7 and y 7or y'7 the other two4 7#c7 ,translate the proposed ,premisses into abstract form4 7#d7 ,represent them1 together1 on a ,triliteral ,diagram4 7#e7 ,ascertain what ,proposition1 if any1 in terms of x and y1 is also represented on it4 7#f7 ,translate this into concrete form4 ,it is evident that1 if the proposed ,premisses were true1 this other ,proposition would also be true4 ,hence it is a ,conclusion consequent from the proposed ,premisses4 ,let us work some examples4 7#a7 ,no son of mine is dishonest2 ,people always treat an honest man with respect4 ,taking men as ,univ41 we may write these as follows3-- ,no sons of mine are dishonest men2 ,all honest men are men treated with respect4 ,we can now construct our ,dictionary1 viz4 m honest2 x sons of mine2 y treated with respect4 7,note that the expression x sons of mine is an abbreviated form of x the ,differentia of 'sons of mine'1 when regarded as a ,species of 'men'47 ,the next thing is to translate the proposed ,premisses into abstract form1 as follows3-- ,no x are m'2 ,all m are y4 pg#jfa ,next1 by the process described at p4 #ej1 we represent these on a ,triliteral ,diagram1 thus3-- --------------- 7,o7 7,o7 ------ 7,o7 ---7,i7------ 7,o7 ------ --------------- ,next1 by the process described at p4 #ec1 we transfer to a ,biliteral ,diagram all the information we can4 ------- 7,o7 ------ ------- ,the result we read as ,no x are y' or as ,no y' are x1 whichever we prefer4 ,so we refer to our ,dictionary1 to see which will look best2 and we choose ,no x are y'1 which1 translated into concrete form1 is ,no son of mine fails to be treated with respect4 7#b7 ,all cats understand ,french2 ,some chickens are cats4 ,taking creatures as ,univ41 we write these as follows3-- ,all cats are creatures understanding ,french2 ,some chickens are cats4 ,we can now construct our ,dictionary1 viz4 m cats2 x understanding ,french2 y chickens4 ,the proposed ,premisses1 translated into abstract form1 are ,all m are x2 ,some y are m4 ,in order to represent these on a ,triliteral ,diagram1 we break up the first into the two ,propositions to which it is equivalent1 and thus get the three ,propositions 7#a7 ,some m are x2 7#b7 ,no m are x'2 7#c7 ,some y are m4 ,the ,rule1 given at p4 #ej1 would make us take these in the order #b1 #a1 #c4 ,this1 however1 would produce the result ----------------- -------- 7,i77,i7 -------- 7,o7 7,o7 -------- ----------------- pg#jfb ,so it would be better to take them in the order #b1 #c1 #a4 ,nos4 7#b7 and 7#c7 give us the result here shown2 and now we need not trouble about ,no4 7#a71 as the ,proposition ,some m are x is already represented on the ,diagram4 --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- ,transferring our information to a ,biliteral ,diagram1 we get ------- 7,i7 ------ ------- ,this result we can read either as ,some x are y or ,some y are x4 ,after consulting our ,dictionary1 we choose ,some y are x1 which1 translated into concrete form1 is ,some chickens understand ,french4 7#c7 ,all diligent students are successful2 ,all ignorant students are unsuccessful4 ,let ,univ4 be students2 m successful2 x diligent2 y ignorant4 ,these ,premisses1 in abstract form1 are ,all x are m2 ,all y are m'4 ,these1 broken up1 give us the four ,propositions 7#a7 ,some x are m2 7#b7 ,no x are m'2 7#c7 ,some y are m'2 7#d7 ,no y are m4 which we will take in the order #b1 #d1 #a1 #c4 ,representing these on a ,triliteral ,diagram1 we get --------------- 7,o7 7,o7 ------ 7,o77,i7 ------------ 7,o7 ------ 7,i7 --------------- ,and this information1 transferred to a ,biliteral ,diagram1 is ------- 7,o77,i7 ------ 7,i7 ------- ,here we get two ,conclusions1 viz4 ,all x are y'2 ,all y are x'4 pg#jfc ,and these1 translated into concrete form1 are ,all diligent students are 7not-ignorant1 i4e47 learned2 ,all ignorant students are 7not-diligent1 i4e47 idle4 7,see p4 #d47 7#d7 ,of the prisoners who were put on their trial at the last ,assizes1 all1 against whom the verdict 'guilty' was returned1 were sentenced to imprisonment2 ,some1 who were sentenced to imprisonment1 were also sentenced to hard labour4 ,let ,univ4 be the prisoners who were put on their trial at the last ,assizes2 m who were sentenced to imprisonment2 x against whom the verdict 'guilty' was returned2 y who were sentenced to hard labour4 ,the ,premisses1 translated into abstract form1 are ,all x are m2 ,some m are y4 ,breaking up the first1 we get the three 7#a7 ,some x are m2 7#b7 ,no x are m'2 7#c7 ,some m are y4 ,representing these1 in the order #b1 #a1 #c1 on a ,triliteral ,diagram1 we get --------------- 7,o7 7,o7 ------ 7,i7 ---7,i7------ ------ --------------- ,here we get no ,conclusion at all4 ,you would very likely have guessed1 if you had seen only the ,premisses1 that the ,conclusion would be ,some1 against whom the verdict 'guilty' was returned1 were sentenced to hard labour4 ,but this ,conclusion is not even true1 with regard to the ,assizes ,i have here invented4 ,not true6 you exclaim4 ,then who were they1 who were sentenced to imprisonment and were also sentenced to hard labour8 ,they must have had the verdict 'guilty' returned against them1 or how could they be sentenced8 ,well1 it happened like this1 you see4 ,they were three ruffians1 who had committed highway-robbery4 ,when they were put on their trial1 they pleaded 'guilty'4 ,so no verdict was returned at all2 and they were sentenced at once4 ,i will now work out1 in their briefest form1 as models for the ,reader to imitate in working examples1 the above four concrete ,problems4 pg#jfd 7#a7 see p4 #fj ,no son of mine is dishonest2 ,people always treat an honest man with respect4 ,univ4 men2 m honest2 x my sons2 y treated with respect4 --------------- ------- ,no x are m'2 7,o7 7,o7 7,o7 ,all m are y4 ------ ------ 7,o7 ---7,i7------ ------- 7,o7 ------ 4'4 ,no x are y'4 --------------- i4e4 ,no son of mine ever fails to be treated with respect4 7#b7 see p4 #fa ,all cats understand ,french2 ,some chickens are cats4 ,univ4 creatures2 m cats2 x understanding ,french2 y chickens4 --------------- ------- ,all m are x2 7,i7 ,some y are m4 ------ ------ 7,i7 ------------ ------- 7,o77,o7 ------ 4'4 ,some y are x4 --------------- i4e4 ,some chickens understand ,french4 7#c7 see p4 #fb ,all diligent students are successful2 ,all ignorant students are unsuccessful4 ,univ4 students2 m successful2 x diligent2 y ignorant4 --------------- ------- ,all x are m2 7,o7 7,o7 7,o77,i7 ,all y are m'4 ------ ------ 7,o77,i7 7,i7 ------------ ------- 7,o7 ------ 4'4 ,all x are y'2 7,i7 ,all y are x'4 --------------- i4e4 ,all diligent students are learned2 and all ignorant students are idle4 pg#jfe 7#d7 see p4 #fc ,of the prisoners who were put on their trial at the last ,assizes1 all1 against whom the verdict 'guilty' was returned1 were sentenced to imprisonment2 ,some1 who were sentenced to imprisonment1 were also sentenced to hard labour4 ,univ4 prisoners who were put on their trial at the last ,assizes1 m sentenced to imprisonment2 x against whom the verdict 'guilty' was returned2 y sentenced to hard labour4 --------------- ,all x are m2 7,o7 7,o7 ,some m are y4 ------ 7,i7 ---7,i7------ ------ ,there is no ,conclusion4 --------------- ,review ,tables ,,vii1 ,,viii 7pp4 #dh1 #di74 ,work ,examples #a1 #ag-ba 7p4 #ig72 #d1 #a-f 7p4 #ajj72 #e1 #a-f 7p4 #aja74 pg#jff #c4 ,given a ,trio of ,propositions of ,relation1 of which every two contain a ,pair of codivisional ,classes1 and which are proposed as a ,syllogism2 to ascertain whether the proposed ,conclusion is consequent from the proposed ,premisses1 and1 if so1 whether it is complete4 ,the ,rules1 for doing this1 are as follows3-- 7#a7 ,take the proposed ,premisses1 and ascertain1 by the process described at p4 #fj1 what ,conclusion1 if any1 is consequent from them4 7#b7 ,if there be no ,conclusion1 say so4 7#c7 ,if there be a ,conclusion1 compare it with the proposed ,conclusion1 and pronounce accordingly4 ,i will now work out1 in their briefest form1 as models for the ,reader to imitate in working examples1 six ,problems4 7#a7 ,all soldiers are strong2 ,all soldiers are brave4 ,some strong men are brave4 ,univ4 men2 m soldiers2 x strong2 y brave4 pg#jfg --------------- ------- ,all m are x2 7,i7 ,all m are y4 ------ ------ ,some x are y4 7,i77,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,some x are y4 --------------- ,hence proposed ,conclusion is right4 7#b7 ,i admire these pictures2 ,when ,i admire anything ,i wish to examine it thoroughly4 ,i wish to examine some of these pictures thoroughly4 ,univ4 things2 m admired by me2 x these pictures2 y things which ,i wish to examine thoroughly4 --------------- ------- ,all x are m2 7,o7 7,o7 7,i77,o7 ,all m are y4 ------ ------ ,some x are y4 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,all x are y4 --------------- ,hence proposed ,conclusion is incomplete1 the complete one being ,i wish to examine all these pictures thoroughly4 7#c7 ,none but the brave deserve the fair2 ,some braggarts are cowards4 ,some braggarts do not deserve the fair4 ,univ4 persons2 m brave2 x deserving of the fair2 y braggarts4 --------------- ------- ,no m' are x2 7,o7 7,o7 ,some y are m'4 ------ ------ ,some y are x'4 7,i7 ------------ ------- ------ 4'4 ,some y are x'4 7,i7 --------------- ,hence proposed ,conclusion is right4 pg#jfh 7#d7 ,all soldiers can march2 ,some babies are not soldiers4 ,some babies cannot march4 ,univ4 persons2 m soldiers2 x able to march2 y babies4 --------------- ,all m are x2 ,some y are m'4 ------ ,some y are x'4 7,i7 7,i7--------- 7,o77,o7 ------ ,there is no ,conclusion4 --------------- 7#e7 ,all selfish men are unpopular2 ,all obliging men are popular4 ,all obliging men are unselfish4 ,univ4 men2 m popular2 x selfish2 y obliging4 --------------- ------- ,all x are m'2 7,o7 7,i7 7,o77,i7 ,all y are m4 ------ ------ ,all y are x'4 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 ,all x are y'2 7,o7 ,all y are x'4 --------------- ,hence proposed ,conclusion is incomplete1 the complete one containing1 in addition1 ,all selfish men are disobliging4 7#f7 ,no one1 who means to go by the train and cannot get a conveyance1 and has not enough time to walk to the station1 can do without running2 ,this party of tourists mean to go by the train and cannot get a conveyance1 but they have plenty of time to walk to the station4 ,this party of tourists need not run4 ,univ4 persons meaning to go by the train1 and unable to get a conveyance2 m having enough time to walk to the station2 x needing to run2 y these tourists4 pg#jfi --------------- ,no m' are x'2 7,o7 ,all y are m4 ------ ,all y are x'4 ---7,i7------ ------ ,there is no 7,o7 7,o7 ,conclusion4 --------------- ,here is another opportunity1 gentle ,reader1 for playing a trick on your innocent friend4 ,put the proposed ,syllogism before him1 and ask him what he thinks of the ,conclusion4 ,he will reply ,why1 it's perfectly correct1 of course6 ,and if your precious ,logic-book tells you it isn't1 don't believe it6 ,you don't mean to tell me those tourists need to run8 ,if ,i were one of them1 and knew the ,premisses to be true1 ,i should be quite clear that ,i needn't run--and ,i should walk6 ,and you will reply ,but suppose there was a mad bull behind you8 ,and then your innocent friend will say ,hum6 ,ha6 ,i must think that over a bit6 ,you may then explain to him1 as a convenient test of the soundness of a ,syllogism1 that1 if circumstances can be invented which1 without interfering with the truth of the ,premisses1 would make the ,conclusion false1 the ,syllogism must be unsound4 ,review ,tables ,v-,,viii 7pp4 #df-di74 ,work ,examples #d1 #g-ab 7p4 #ajj72 #e1 #g-ab 7p4 #aja72 #f1 #a-aj 7p4 #ajf72 #g1 #a-f 7pp4 #ajg1 #ajh74 pg#jgj ,,book ,,vi4 ,,the ,,method ,,of ,,subscripts4 ,,chapter ,i4 ,,introductory4 ,let us agree that x#a shall mean ,some existing ,things have the ,attribute x1 i4e4 7more briefly7 ,some x exist2 also that xy#a shall mean ,some xy exist1 and so on4 ,such a ,proposition may be called an ',entity4' ,note that1 when there are two letters in the expression1 it does not in the least matter which stands first3 xy#a and yx#a mean exactly the same4 ,also that x#j shall mean ,no existing ,things have the ,attribute x1 i4e4 7more briefly7 ,no x exist2 also that xy#j shall mean ,no xy exist1 and so on4 ,such a ,proposition may be called a ',nullity'4 ,also that shall mean and4 ,thus ab#a cd#j means ,some ab exist and no cd exist4 ,also that shall mean would1 if true1 prove4 ,thus1 x#j xy#j means ,the ,proposition ',no x exist' would1 if true1 prove the ,proposition ',no xy exist'4 ,when two ,letters are both of them accented1 or both not accented1 they are said to have ',like ,signs'1 or to be ',like'3 when one is accented1 and the other not1 they are said to have ',unlike ,signs'1 or to be ',unlike'4 pg#jga ,,chapter ,,ii4 ,,representation ,,of ,,propositions ,,of ,,relation4 ,let us take1 first1 the ,proposition ,some x are y4 ,this1 we know1 is equivalent to the ,proposition of ,existence ,some xy exist4 7,see p4 #ca47 ,hence it may be represented by the expression xy#a4 ,the ,converse ,proposition ,some y are x may of course be represented by the same expression1 viz4 xy#a4 ,similarly we may represent the three similar ,pairs of ,converse ,propositions1 viz4-- ,some x are y' ,some y' are x1 ,some x' are y ,some y are x'1 ,some x' are y' ,some y' are x'4 ,let us take1 next1 the ,proposition ,no x are y4 ,this1 we know1 is equivalent to the ,proposition of ,existence ,no xy exist4 7,see p4 #cc47 ,hence it may be represented by the expression xy#j4 ,the ,converse ,proposition ,no y are x may of course be represented by the same expression1 viz4 xy#j4 ,similarly we may represent the three similar ,pairs of ,converse ,propositions1 viz4-- ,no x are y' ,no y' are x1 ,no x' are y ,no y are x'1 ,no x' are y' ,no y' are x'4 pg#jgb ,let us take1 next1 the ,proposition ,all x are y4 ,now it is evident that the ,double ,proposition of ,existence ,some x exist and no xy' exist tells us that some x-,things exist1 but that none of them have the ,attribute y'3 that is1 it tells us that all of them have the ,attribute y3 that is1 it tells us that ,all x are y4 ,also it is evident that the expression x#a xy'#j represents this ,double ,proposition4 ,hence it also represents the ,proposition ,all x are y4 ,the ,reader will perhaps be puzzled by the statement that the ,proposition ,all x are y is equivalent to the ,double ,proposition ,some x exist and no xy' exist1 remembering that it was stated1 at p4 #cc1 to be equivalent to the ,double ,proposition ,some x are y and no x are y' 7i4e4 ,some xy exist and no xy' exist74 ,the explanation is that the ,proposition ,some xy exist contains superfluous information4 ,some x exist is enough for our purpose4 ,this expression may be written in a shorter form1 viz4 x#ay'#j1 since each ,subscript takes effect back to the beginning of the expression4 ,similarly we may represent the seven similar ,propositions ,all x are y'1 ,all x' are y1 ,all x' are y'1 ,all y are x1 ,all y are x'1 ,all y' are x1 and ,all y' are x'4 ,the ,reader should make out all these for himself4 ,it will be convenient to remember that1 in translating a ,proposition1 beginning with ,all1 from abstract form into subscript form1 or vice vers1 the ,predicate changes sign 7that is1 changes from positive to negative1 or else from negative to positive74 ,thus1 the ,proposition ,all y are x' becomes y#ax#j1 where the ,predicate changes from x' to x4 ,again1 the expression x'#ay'#j becomes ,all x' are y1 where the ,predicate changes for y' to y4 pg#jgc ,,chapter ,,iii4 ,,syllogisms4 #a4 ,representation of ,syllogisms4 ,we already know how to represent each of the three ,propositions of a ,syllogism in subscript form4 ,when that is done1 all we need1 besides1 is to write the three expressions in a row1 with between the ,premisses1 and before the ,conclusion4 ,thus the ,syllogism ,no x are m'2 ,all m are y4 4'4 ,no x are y'4 may be represented thus3-- xm'#j m#ay'#j xy'#j ,when a ,proposition has to be translated from concrete form into subscript form1 the ,reader will find it convenient1 just at first1 to translate it into abstract form1 and thence into subscript form4 ,but1 after a little practice1 he will find it quite easy to go straight from concrete form to subscript form4 pg#jgd #b4 ,formul for solving ,problems in ,syllogisms4 ,when once we have found1 by ,diagrams1 the ,conclusion to a given ,pair of ,premisses1 and have represented the ,syllogism in subscript form1 we have a ,formula1 by which we can at once find1 without having to use ,diagrams again1 the ,conclusion to any other ,pair of ,premisses having the same subscript forms4 ,thus1 the expression xm#j ym'#j xy#j is a ,formula1 by which we can find the ,conclusion to any ,pair of ,premisses whose subscript forms are xm#j ym'#j ,for example1 suppose we had the ,pair of ,propositions ,no gluttons are healthy2 ,no unhealthy men are strong4 proposed as ,premisses4 ,taking men as our ',universe'1 and making m healthy2 x gluttons2 y strong2 we might translate the ,pair into abstract form1 thus3-- ,no x are m2 ,no m' are y4 ,these1 in subscript form1 would be xm#j m'y#j which are identical with those in our ,formula4 ,hence we at once know the ,conclusion to be xy#j that is1 in abstract form1 ,no x are y2 that is1 in concrete form1 ,no gluttons are strong4 ,i shall now take three different forms of ,pairs of ,premisses1 and work out their ,conclusions1 once for all1 by ,diagrams2 and thus obtain some useful ,formul4 ,i shall call them ,fig4 ,i1 ,fig4 ,,ii1 and ,fig4 ,,iii4 pg#jge ,fig4 ,i4 ,this includes any ,pair of ,premisses which are both of them ,nullities1 and which contain ,unlike ,eliminands4 ,the simplest case is --------------- ------- xm#j ym'#j 7,o7 7,o7 ------ ------ 7,o77,o7 ------------ ------- ------ 4'4 xy#j 7,o7 --------------- ,in this case we see that the ,conclusion is a ,nullity1 and that the ,retinends have kept their ,signs4 ,and we should find this ,rule to hold good with any ,pair of ,premisses which fulfil the given conditions4 ,the ,reader had better satisfy himself of this1 by working out1 on ,diagrams1 several varieties1 such as m#ax#j ym'#j 7which xy#j7 xm'#j m#ay#j 7which xy#j7 x'm#j ym'#j 7which x'y#j7 m'#ax'#j m#ay'#j 7which x'y'#j74 ,if either ,retinend is asserted in the ,premisses to exist1 of course it may be so asserted in the ,conclusion4 ,hence we get two ,variants of ,fig4 ,i1 viz4 7a7 where one ,retinend is so asserted2 7b7 where both are so asserted4 ,the ,reader had better work out1 on ,diagrams1 examples of these two ,variants1 such as m#ax#j y#am'#j 7which proves y#ax#j7 x#am'#j m#ay#j 7which proves x#ay#j7 x'#am#j y#am'#j 7which proves x'#ay#j y#ax'#j74 ,the ,formula1 to be remembered1 is xm#j ym'#j xy#j with the following two ,rules3-- 7#a7 ,two ,nullities1 with ,unlike ,eliminands1 yield a ,nullity1 in which both ,retinends keep their ,signs4 pg#jgf 7#b7 ,a ,retinend1 asserted in the ,premisses to exist1 may be so asserted in the ,conclusion4 ,note that ,rule 7#a7 is merely the ,formula expressed in words4 ,fig4 ,,ii4 ,this includes any ,pair of ,premisses1 of which one is a ,nullity and the other an ,entity1 and which contain ,like ,eliminands4 ,the simplest case is xm#j ym#a --------------- ------- ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 x'y#a --------------- ,in this case we see that the ,conclusion is an ,entity1 and that the ,nullity-,retinend has changed its ,sign4 ,and we should find this ,rule to hold good with any ,pair of ,premisses which fulfil the given conditions4 ,the ,reader had better satisfy himself of this1 by working out1 on ,diagrams1 several varieties1 such as x'm#j ym#a 7which xy#a7 x#am'#j y'm'#a 7which x'y'#a7 m#ax#j y'm#a 7which x'y'#a74 ,the ,formula1 to be remembered1 is1 xm#j ym#a x'y#a with the following ,rule3-- ,a ,nullity and an ,entity1 with ,like ,eliminands1 yield an ,entity1 in which the ,nullity-,retinend changes its ,sign4 ,note that this ,rule is merely the ,formula expressed in words4 pg#jgg ,fig4 ,,iii4 ,this includes any ,pair of ,premisses which are both of them ,nullities1 and which contain ,like ,eliminands asserted to exist4 ,the simplest case is xm#j ym#j m#a ,note that m#a is here stated separately1 because it does not matter in which of the two ,premisses it occurs3 so that this includes the three forms m#ax#j ym#j1 xm#j m#ay#j1 and m#ax#j m#ay#j4 --------------- ------- ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,o77,i7 ------ 4'4 x'y'#a --------------- ,in this case we see that the ,conclusion is an ,entity1 and that both ,retinends have changed their ,signs4 ,and we should find this ,rule to hold good with any ,pair of ,premisses which fulfil the given conditions4 ,the ,reader had better satisfy himself of this1 by working out1 on ,diagrams1 several varieties1 such as x'm#j m#ay#j 7which xy'#a7 m'#ax#j m'y'#j 7which x'y#a7 m#ax'#j m#ay'#j 7which xy#a74 ,the ,formula1 to be remembered1 is xm#j ym#j m#a x'y'#a with the following ,rule 7which is merely the ,formula expressed in words73-- ,two ,nullities1 with ,like ,eliminands asserted to exist1 yield an ,entity1 in which both ,retinends change their ,signs4 99 99 99 99 99 ,in order to help the ,reader to remember the peculiarities and ,formul of these three ,figures1 ,i will put them all together in one ,table4 pg#jgh ,,table ,,ix4 ,fig4 ,i4 xm#j ym'#j xy#j ,two ,nullities1 with ,unlike ,eliminands1 yield a ,nullity1 in which both ,retinends keep their ,signs4 ,a ,retinend1 asserted in the ,premisses to exist1 may be so asserted in the ,conclusion4 ,fig4 ,,ii4 xm#j ym#a x'y#a ,a ,nullity and an ,entity1 with ,like ,eliminands1 yield an ,entity1 in which the ,nullity-,retinend changes its ,sign4 ,fig4 ,,iii4 xm#j ym#j m#a x'y'#a ,two ,nullities1 with ,like ,eliminands asserted to exist1 yield an ,entity1 in which both ,retinends change their ,signs4 ,i will now work out1 by these ,formul1 as models for the ,reader to imitate1 some ,problems in ,syllogisms which have been already worked1 by ,diagrams1 in ,book ,v41 ,chap4 ,,ii4 7#a7 see p4 #fd ,no son of mine is dishonest2 ,people always treat an honest man with respect4 ,univ4 men2 m honest2 x my sons2 y treated with respect4 xm'#j m#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no son of mine ever fails to be treated with respect4 pg#jgi 7#b7 see p4 #fd ,all cats understand ,french2 ,some chickens are cats4 ,univ4 creatures2 m cats2 x understanding ,french2 y chickens4 m#ax'#j ym#a xy#a ,fig4 ,,ii4 i4e4 ,some chickens understand ,french4 7#c7 see p4 #fd ,all diligent students are successful2 ,all ignorant students are unsuccessful4 ,univ4 students2 m successful2 x diligent2 y ignorant4 x#am'#j y#am#j x#ay#j y#ax#j ,fig4 ,i 7b74 i4e4 ,all diligent students are learned2 and all ignorant students are idle4 7#d7 see p4 #ff ,all soldiers are strong2 ,all soldiers are brave4 ,some strong men are brave4 ,univ4 men2 m soldiers2 x strong2 y brave4 m#ax'#j m#ay'#j xy#a ,fig4 ,,iii4 ,hence proposed ,conclusion is right4 7#e7 see p4 #fg ,i admire these pictures2 ,when ,i admire anything1 ,i wish to examine it thoroughly4 ,i wish to examine some of these pictures thoroughly4 ,univ4 things2 m admired by me2 x these2 y things which ,i wish to examine thoroughly4 x#am'#j m#ay'#j x#ay'#j ,fig4 ,i 7a74 ,hence proposed ,conclusion1 xy#a1 is incomplete1 the complete one being ,i wish to examine all these pictures thoroughly4 pg#jhj 7#f7 see p4 #fg ,none but the brave deserve the fair2 ,some braggarts are cowards4 ,some braggarts do not deserve the fair4 ,univ4 persons2 m brave2 x deserving of the fair2 y braggarts4 m'x#j ym'#a x'y#a ,fig4 ,,ii4 ,hence proposed ,conclusion is right4 7#g7 see p4 #fi ,no one1 who means to go by the train and cannot get a conveyance1 and has not enough time to walk to the station1 can do without running2 ,this party of tourists mean to go by the train and cannot get a conveyance1 but they have plenty of time to walk to the station4 ,this party of tourists need not run4 ,univ4 persons meaning to go by the train1 and unable to get a conveyance2 m having enough time to walk to the station2 x needing to run2 y these tourists4 m'x'#j y#am'#j do not come under any of the three ,figures4 ,hence it is necessary to return to the ,method of ,diagrams1 as shown at p4 #fi4 ,hence there is no ,conclusion4 ,work ,examples #d1 #ab-bj 7p4 #ajj72 #e1 #ac-bd 7pp4 #aja1 #ajb72 #f1 #a-f 7p4 #ajf72 #g1 #a-c 7pp4 #ajg1 #ajh74 ,also read ,note 7,a71 at p4 #afd4 pg#jha #c4 ,fallacies4 ,any argument which deceives us1 by seeming to prove what it does not really prove1 may be called a ',fallacy' 7derived from the ,latin verb fallo ,i deceive73 but the particular kind1 to be now discussed1 consists of a ,pair of ,propositions1 which are proposed as the ,premisses of a ,syllogism1 but yield no ,conclusion4 ,when each of the proposed ,premisses is a ,proposition in ,i1 or ,e1 or ,a1 7the only kinds with which we are now concerned17 the ,fallacy may be detected by the ',method of ,diagrams1' by simply setting them out on a ,triliteral ,diagram1 and observing that they yield no information which can be transferred to the ,biliteral ,diagram4 ,but suppose we were working by the ',method of ,subscripts1' and had to deal with a ,pair of proposed ,premisses1 which happened to be a ',fallacy1' how could we be certain that they would not yield any ,conclusion8 ,our best plan is1 ,i think1 to deal with ,fallacies in the same was as we have already dealt with ,syllogisms3 that is1 to take certain forms of ,pairs of ,propositions1 and to work them out1 once for all1 on the ,triliteral ,diagram1 and ascertain that they yield no ,conclusion2 and then to record them1 for future use1 as ,formul for ,fallacies1 just as we have already recorded our three ,formul for ,syllogisms4 pg#jhb ,now1 if we were to record the two ,sets of ,formul in the same shape1 viz4 by the ,method of ,subscripts1 there would be considerable risk of confusing the two kinds4 ,hence1 in order to keep them distinct1 ,i propose to record the ,formul for ,fallacies in words1 and to call them ,forms instead of ,formul4 ,let us now proceed to find1 by the ,method of ,diagrams1 three ,forms of ,fallacies1 which we will then put on record for future use4 ,they are as follows3-- 7#a7 ,fallacy of ,like ,eliminands not asserted to exist4 7#b7 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 7#c7 ,fallacy of two ,entity-,premisses4 ,these shall be discussed separately1 and it will be seen that each fails to yield a ,conclusion4 7#a7 ,fallacy of ,like ,eliminands not asserted to exist4 ,it is evident that neither of the given ,propositions can be an ,entity1 since that kind asserts the existence of both of its ,terms 7see p4 #bj74 ,hence they must both be ,nullities4 ,hence the given ,pair may be represented by 7xm#j ym#j71 with or without x#a1 y#a4 ,these1 set out on ,triliteral ,diagrams1 are xm#j ym#j x#am#j ym#j --------------- --------------- 7,i7 ------ ------ 7,o77,o7 7,o77,o7 ------------ ------------ 7,o7 7,o7 ------ ------ --------------- --------------- xm#j y#am#j x#am#j y#am#j --------------- --------------- 7,i7 ------ ------ 7,o77,o7 7,o77,o7 7,i7--------- 7,i7--------- 7,o7 7,o7 ------ ------ --------------- --------------- pg#jhc 7#b7 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 ,here the given ,pair may be represented by 7xm#j ym'#a7 with or without x#a or m#a4 ,these1 set out on ,triliteral ,diagrams1 are xm#j ym'#a x#am#j ym'#a m#ax#j ym'#a --------------- --------------- --------------- 7,i7 ------ ------ ------ 7,o77,o7 7,o77,o7 7,o77,o7 7,i7--------- 7,i7--------- 7,i7--------- 7,i7 ------ ------ ------ --------------- --------------- --------------- 7#c7 ,fallacy of two ,entity-,premisses4 ,here the given ,pair may be represented by either 7xm#a ym#a7 or 7xm#a ym'#a74 ,these1 set out on ,triliteral ,diagrams1 are xm#a ym#a xm#a ym'#a --------------- --------------- ------ ------ 7,i7 7,i7 ---7,i7------ 7,i7--------- ------ ------ --------------- --------------- pg#jhd #d4 ,method of proceeding with a given ,pair of ,propositions4 ,let us suppose that we have before us a ,pair of ,propositions of ,relation1 which contain between them a ,pair of codivisional ,classes1 and that we wish to ascertain what ,conclusion1 if any1 is consequent from them4 ,we translate them1 if necessary1 into subscript-form1 and then proceed as follows3-- 7#a7 ,we examine their ,subscripts1 in order to see whether they are 7a7 a ,pair of ,nullities2 or 7b7 a ,nullity and an ,entity2 or 7c7 a ,pair of ,entities4 7#b7 ,if they are a ,pair of ,nullities1 we examine their ,eliminands1 in order to see whether they are ,unlike or ,like4 ,if their ,eliminands are ,unlike1 it is a case of ,fig4 ,i4 ,we then examine their ,retinends1 to see whether one or both of them are asserted to exist4 ,if one ,retinend is so asserted1 it is a case of ,fig4 ,i 7a72 if both1 it is a case of ,fig4 ,i 7b74 ,if their ,eliminands are ,like1 we examine them1 in order to see whether either of them is asserted to exist4 ,if so1 it is a case of ,fig4 ,,iii42 if not1 it is a case of ,fallacy of ,like ,eliminands not asserted to exist4 7#c7 ,if they are a ,nullity and an ,entity1 we examine their ,eliminands1 in order to see whether they are ,like or ,unlike4 ,if their ,eliminands are ,like1 it is a case of ,fig4 ,,ii42 if ,unlike1 it is a case of ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 7#d7 ,if they are a ,pair of ,entities1 it is a case of ,fallacy of two ,entity-,premisses4 ,work ,examples #d1 #a-aa 7p4 #ajj72 #e1 #a-ab 7p4 #aja72 #f1 #g-ab 7p4 #ajf72 #g1 #g-ab 7p4 #ajh74 pg#jhe ,,book ,,vii4 ,,soriteses4 ,,chapter ,i4 ,,introductory4 ,when a ,set of three or more ,biliteral ,propositions are such that all their ,terms are ,species of the same ,genus1 and are also so related that two of them1 taken together1 yield a ,conclusion1 which1 taken with another of them1 yields another ,conclusion1 and so on1 until all have been taken1 it is evident that1 if the original ,set were true1 the last ,conclusion would also be true4 ,such a ,set1 with the last ,conclusion tacked on1 is called a ',sorites'2 the original ,set of ,propositions is called its ',premisses'2 each of the intermediate ,conclusions is called a ',partial ,conclusion' of the ,sorites2 the last ,conclusion is called its ',complete ,conclusion1' or1 more briefly1 its ',conclusion'2 the ,genus1 of which all the ,terms are ,species1 is called its ',universe of ,discourse'1 or1 more briefly1 its ',univ4'2 the ,terms1 used as ,eliminands in the ,syllogisms1 are called its ',eliminands'2 and the two ,terms1 which are retained1 and therefore appear in the ,conclusion1 are called its ',retinends'4 ,note that each ,partial ,conclusion contains one or two ,eliminands2 but that the ,complete ,conclusion contains ,retinends only4 ,the ,conclusion is said to be 'consequent' from the ,premisses2 for which reason it is usual to prefix to it the word ,therefore 7or the symbol 4'474 ,note that the question1 whether the ,conclusion is or is not consequent from the ,premisses1 is not affected by the actual truth or falsity of any one of the ,propositions which make up the ,sorites1 by depends entirely on their relationship to one another4 pg#jhf ,as a specimen-,sorites1 let us take the following ,set of #e ,propositions3-- 7#a7 ,no a are b'2 7#b7 ,all b are c2 7#c7 ,all c are d2 7#d7 ,no e' are a'2 7#e7 ,all h are e'4 ,here the first and second1 taken together1 yield ,no a are c'4 ,this1 taken along with the third1 yields ,no a are d'4 ,this1 taken along with the fourth1 yields ,no d' are e'4 ,and this1 taken along with the fifth1 yields ,all h are d4 ,hence1 if the original ,set were true1 this would also be true4 ,hence the original ,set1 with this tacked on1 is a ,sorites2 the original ,set is its ,premisses2 the ,proposition ,all h are d is its ,conclusion2 the ,terms a1 b1 c1 e are its ,eliminands2 and the ,terms d and h are its ,retinends4 ,hence we may write the whole ,sorites thus3-- ,no a are b'2 ,all b are c2 ,all c are d2 ,no e' are a'2 ,all h are e'4 4'4 ,all h are d4 ,in the above ,sorites1 the #c ,partial ,conclusions are the ,positions ,no a are e'1 ,no a are d'1 ,no d' are e'2 but1 if the ,premisses were arranged in other ways1 other ,partial ,conclusions might be obtained4 ,thus1 the order #daebc yields the ,partial ,conclusions ,no c' are b'1 ,all h are b1 ,all h are c4 ,there are altogether nine ,partial ,conclusions to this ,sorites1 which the ,reader will find it an interesting task to make out for himself4 pg#jhg ,,chapter ,,ii4 ,,problems ,,in ,,soriteses4 #a4 ,introductory4 ,the ,problems we shall have to solve are of the following form3-- ,given three or more ,propositions of ,relation1 which are proposed as ,premisses3 to ascertain what ,conclusion1 if any1 is consequent from them4 ,we will limit ourselves1 at present1 to ,problems which can be worked by the ,formul of ,fig4 ,i4 7,see p4 #ge47 ,those1 that require other ,formul1 are rather too hard for beginners4 ,such ,problems may be solved by either of two ,methods1 viz4 7#a7 ,the ,method of ,separate ,syllogisms2 7#b7 ,the ,method of ,underscoring4 ,these shall be discussed separately4 pg#jhh #b4 ,solution by ,method of ,separate ,syllogisms4 ,the ,rules1 for doing this1 are as follows3-- 7#a7 ,name the ',universe of ,discourse'4 7#b7 ,construct a ,dictionary1 making a1 b1 c1 c4 represent the ,terms4 7#c7 ,put the ,proposed ,premisses into subscript form4 7#d7 ,select two which1 containing between them a pair of codivisional ,classes1 can be used as the ,premisses of a ,syllogism4 7#e7 ,find their ,conclusion by ,formula4 7#f7 ,find a third ,premiss which1 along with this ,conclusion1 can be used as the ,premisses of a second ,syllogism4 7#g7 ,find a second ,conclusion by ,formula4 7#h7 ,proceed thus1 until all the proposed ,premisses have been used4 7#i7 ,put the last ,conclusion1 which is the ,complete ,conclusion of the ,sorites1 into concrete form4 ,as an example of this process1 let us take1 as the proposed ,set of ,premisses1 7#a7 ,all the policemen on this beat sup with our cook2 7#b7 ,no man with long hair can fail to be a poet2 7#c7 ,amos ,judd has never been in prison2 7#d7 ,our cook's 'cousins' all love cold mutton2 7#e7 ,none but policemen on this beat are poets2 7#f7 ,none but her 'cousins' ever sup with our cook2 7#g7 ,men with short hair have all been in prison4 ,univ4 men2 a ,amos ,judd2 b cousins of our cook2 c having been in prison2 d long-haired2 e loving cold mutton2 h poets2 k policemen on this beat2 l supping with our cook pg#jhi ,we now have to put the proposed ,premisses into subscript form4 ,let us begin by putting them into abstract form4 ,the result is 7#a7 ,all k are l2 7#b7 ,no d are h'2 7#c7 ,all a are c'2 7#d7 ,all b are e2 7#e7 ,no k' are h2 7#f7 ,no b' are l2 7#g7 ,all d' are c4 ,and it is now easy to put them into subscript form1 as follows3-- 7#a7 k#al'#j 7#b7 dh'#j 7#c7 a#a;c#j 7#d7 b#a;e'#j 7#e7 k'h#j 7#f7 b'l#j 7#g7 d'#a;c'#j ,we now have to find a pair of ,premisses which will yield a ,conclusion4 ,let us begin with ,no4 7#a71 and look down the list1 till we come to one which we can take along with it1 so as to form ,premisses belonging to ,fig4 ,i4 ,we find that ,no4 7#e7 will do1 since we can take k as our ,eliminand4 ,so our first syllogism is 7#a7 k#al'#j 7#e7 k'h#j 4'4 l'h#j 444 7#h7 ,we must now begin again with l'h#j and find a ,premiss to go along with it4 ,we find that ,no4 7#b7 will do1 h being our ,eliminand4 ,so our next ,syllogism is 7#h7 l'h#j 7#b7 dh'#j 4'4 l'd#j 444 7#i7 ,we have now used up ,nos4 7#a71 7#e71 and 7#b71 and must search among the others for a partner for l'd#j4 ,we find that ,no4 7#f7 will do4 ,so we write 7#i7 l'd#j 7#f7 b'l#j 4'4 db'#j 444 7#aj7 ,now what can we take along with db'#j8 ,no4 7#d7 will do4 7#aj7 db'#j 7#d7 b#a;e'#j 4'4 de'#j 444 7#aa7 pg#jij ,along with this we may take ,no4 7#g74 7#aa7 de'#j 7#g7 d'#a;c'#j 4'4 c'e'#j 444 7#ab7 ,and along with this we may take ,no4 7#c74 7#ab7 c'e'#j 7#c7 a#a;c#j 4'4 a#a;e'#j ,this ,complete ,conclusion1 translated into abstract form1 is ,all a are e2 and this1 translated into concrete form1 is ,amos ,judd loves cold mutton4 ,in actually working this ,problem1 the above explanations would1 of course1 be omitted1 and all1 that would appear on paper1 would be as follows3-- 7#a7 k#al'#j 7#b7 dh'#j 7#c7 a#a;c#j 7#d7 b#a;e'#j 7#e7 k'h#j 7#f7 b'l#j 7#g7 d'#a;c'#j 7#a7 k#al'#j 7#e7 k'h#j 4'4 l'h#j 444 7#h7 7#h7 l'h#j 7#b7 dh'#j 4'4 l'd#j 444 7#i7 7#i7 l'd#j 7#f7 b'l#j 4'4 db'#j 444 7#aj7 7#aj7 db'#j 7#d7 b#a;e'#j 4'4 de'#j 444 7#aa7 7#aa7 de'#j 7#g7 d'#a;c'#j 4'4 c'e'#j 444 7#ab7 7#ab7 c'e'#j 7#c7 a#a;c#j 4'4 a#a;e'#j ,note that1 in working a ,sorites by this ,process1 we may begin with any ,premiss we choose4 pg#jia #c4 ,solution by ,method of ,underscoring4 ,consider the ,pair of ,premisses xm#j ym'#j which yield the ,conclusion xy#j ,we see that1 in order to get this ,conclusion1 we must eliminate m and m'1 and write x and y together in one expression4 ,now1 if we agree to mark m and m' as eliminated1 and to read the two expressions together1 as if they were written in one1 the two ,premisses will then exactly represent the ,conclusion1 and we need not write it out separately4 ,let us agree to mark the eliminated letters by underscoring them1 putting a single score under the first1 and a double one under the second4 ,the two ,premisses now become xm#j ym'#j - which we read as xy#j4 ,in copying out the ,premisses for underscoring1 it will be convenient to omit all subscripts4 ,as to the #j's we may always suppose them written1 and1 as to the #a's1 we are not concerned to know which ,terms are asserted to exist1 except those which appear in the ,complete ,conclusion2 and for them it will be easy enough to refer to the original list4 pg#jib ,i will now go through the process of solving1 by this method1 the example worked in #b4 ,the ,data are #a #b #c #d k#al'#j dh'#j a#a;c#j b#a;e'#j #e #f #g k'h#j b'l#j d'#a;c'#j ,the ,reader should take a piece of paper1 and write out this solution for himself4 ,the first line will consist of the above ,data2 the second must be composed1 bit by bit1 according to the following directions4 ,we begin by writing down the first ,premiss1 with its numeral over it1 but omitting the subscripts4 ,we have now to find a ,premiss which can be combined with this1 i4e41 a ,premiss containing either k' or l4 ,the first we find is ,no4 #e2 and this we tack on1 with a 4 ,to get the ,conclusion from these1 k and k' must be eliminated1 and what remains must be taken as one expression4 ,so we underscore them1 putting a single score under k1 and a double one under k'4 ,the result we read as l'h4 ,we must now find a ,premiss containing either l or h'4 ,looking along the row1 we fix on ,no4 #b1 and tack it on4 ,now these #c ,nullities are really equivalent to 7l'h dh'71 in which h and h' must be eliminated1 and what remains taken as one expression4 ,so we underscore them4 ,the result reads as l'd4 ,we now want a ,premiss containing l or d'4 ,no4 #f will do4 ,these #d ,nullities are really equivalent to 7l'd b'l74 ,so we underscore l' and l4 ,the result reads as db'4 ,we now want a ,premiss containing d' or b4 ,no4 #d will do4 ,here we underscore b' and b4 ,the result reads as de'4 ,we now want a ,premiss containing d' or e4 ,no4 #g will do4 ,here we underscore d and d'4 ,the result reads as c'e'4 ,we now want a ,premiss containing c or e4 ,no4 #c will do--in fact must do1 as it is the only one left4 ,here we underscore c' and c2 and1 as the whole thing now reads as e'a1 we tack on e'a#j as the ,conclusion1 with a 4 ,we now look along the row of ,data1 to see whether e' or a has been given as existent4 ,we find that a has been so given in ,no4 #c4 ,so we add this fact to the ,conclusion1 which now stands as e'a#j a#a1 i4e4 a#a;e'#j2 i4e4 ,all a are e4 ,if the ,reader has faithfully obeyed the above directions1 his written solution will now stand as follows3-- #a #b #c #d k#al'#j dh'#j a#a;c#j b#a;e'#j #e #f #g k'h#j b'l#j d'#a;c'#j #a #e #b #f #d #g #c kl' k'h dh' b'l be' d'c' ac -- - - - - e'a#j a#a i4e4 a#a;e'#j2 i4e4 ,all a are e4 pg#jic ,the ,reader should now take a second piece of paper1 and copy the ,data only1 and try to work out the solution for himself1 beginning with some other ,premiss4 ,if he fails to bring out the ,conclusion a#a;e'#j1 ,i would advise him to take a third piece of paper1 and begin again6 ,i will now work out1 in its briefest form1 a ,sorites of #e ,premisses1 to serve as a model for the ,reader to imitate in working examples4 7#a7 ,i greatly value everything that ,john gives me2 7#b7 ,nothing but this bone will satisfy my dog2 7#c7 ,i take particular care of everything that ,i greatly value2 7#d7 ,this bone was a present from ,john2 7#e7 ,the things1 of which ,i take particular care1 are things ,i do not give to my dog4 ,univ4 things2 a given by ,john to me2 b given by me to my dog2 c greatly valued by me2 d satisfactory to my dog2 e taken particular care of by me2 h this bone4 #a #b #c #d #e a#a;c'#j h'd#j c#a;e'#j h#a;a'#j e#a;b#j #a #c #d #b #e ac' ce' ha' h'd eb db#j -- - - i4e4 ,nothing1 that ,i give my dog1 satisfies him1 or1 ,my dog is not satisfied with anything that ,i give him6 ,note that1 in working a ,sorites by this process1 we may begin with any ,premiss we choose4 ,for instance1 we might begin with ,no4 #e1 and the result would then be #e #c #a #d #b eb ce' ac' ha' h'd bd#j - - - - ,work ,examples #d1 #be-cj 7p4 #ajj72 #e1 #be-cj 7p4 #ajb72 #f1 #ac-ae 7p4 #ajf72 #g1 #ac-ae 7p4 #ajh72 #h1 #a-d1 #ac1 #ad1 #ai1 #bd 7pp4 #aaj1 #aaa72 #i1 #a-d1 #bf1 #bg1 #dj1 #dh 7pp4 #aab1 #aaf1 #aai1 #aba74 pg#jid ,the ,reader1 who has successfully grappled with all the ,examples hitherto set1 and who thirsts1 like ,alexander the ,great1 for more worlds to conquer1 may employ his spare energies on the following #ag ,examination-,papers4 ,he is recommended not to attempt more than one ,paper on any one day4 ,the answers to the questions about words and phrases may be found by referring to the ,index at p4 #aig4 ,i4 #d1 #ca 7p4 #ajj72 #e1 #ca-cd 7p4 #ajb72 #f1 #af1 #ag 7p4 #ajf72 #g1 #af 7p4 #ajh72 #h1 #e1 #f 7p4 #aaj72 #i1 #e1 #bb1 #db 7pp4 #aab1 #aae1 #aai74 ,what is ',classification'8 ,and what is a ',class'8 ,,ii4 #d1 #cb 7p4 #ajj72 #e1 #ce-ch 7pp4 #ajb1 #ajc72 #f1 #ah 7p4 #ajg72 #g1 #ag1 #ah 7p4 #ajh72 #h1 #g1 #h 7p4 #aaj72 #i1 #f1 #bc1 #dc 7pp4 #aab1 #aae1 #aai74 ,what are ',genus'1 ',species'1 and ',differentia'8 ,,iii4 #d1 #cc 7p4 #ajj72 #e1 #ci-db 7p4 #ajc72 #f1 #ai1 #bj 7p4 #ajg72 #g1 #ai 7p4 #aji72 #h1 #i1 #aj 7p4 #aaa72 #i1 #g1 #bd1 #dd 7pp4 #aac1 #aaf1 #abj74 ,what are ',real' and ',imaginary' ,classes8 ,,iv4 #d1 #cd 7p4 #ajj72 #e1 #dc-df 7p4 #ajc72 #f1 #ba 7p4 #ajg72 #g1 #bj1 #ba 7p4 #aji72 #h1 #aa1 #ab 7p4 #aaa72 #i1 #h1 #be1 #de 7pp4 #aac1 #aaf1 #abj74 ,what is ',division'8 ,when are ,classes said to be ',codivisional'8 ,v4 #d1 #ce 7p4 #ajj72 #e1 #dg-ej 7p4 #ajc72 #f1 #bb1 #bc 7p4 #ajg72 #g1 #bb 7p4 #aji72 #h1 #ae1 #af 7p4 #aaa72 #i1 #i1 #bh1 #df 7pp4 #aac1 #aaf1 #abj74 ,what is ',dichotomy'8 ,what arbitrary rule does it sometimes require8 pg#jie ,,vi4 #d1 #cf 7p4 #ajj72 #e1 #ea-ed 7p4 #ajc72 #f1 #bd 7p4 #ajg72 #g1 #bc1 #bd 7p4 #aji72 #h1 #ag 7p4 #aaa72 #i1 #aj1 #bi1 #dg 7pp4 #aac1 #aag1 #abj74 ,what is a ',definition'8 ,,vii4 #d1 #cg 7p4 #ajj72 #e1 #ee-eh 7pp4 #ajc1 #ajd72 #f1 #be1 #bf 7p4 #ajg72 #g1 #be 7p4 #aji72 #h1 #ah 7p4 #aaa72 #i1 #aa1 #cj1 #di 7pp4 #aac1 #aag1 #aba74 ,what are the ',subject' and the ',predicate' of a ,proposition8 ,what is its ',normal' form8 ,,viii4 #d1 #ch 7p4 #ajj72 #e1 #ei-fb 7p4 #ajd72 #f1 #bg 7p4 #ajg72 #g1 #bf1 #bg 7p4 #aji72 #h1 #bj 7p4 #aaa72 #i1 #ab1 #ca1 #ej 7pp4 #aac1 #aag1 #aba74 ,what is a ,proposition 'in ,i'8 ',in ,e'8 ,and 'in ,a'8 ,,ix4 #d1 #ci 7p4 #ajj72 #e1 #fc-ff 7p4 #ajd72 #f1 #bh1 #bi 7p4 #ajg72 #g1 #bh 7p4 #aji72 #h1 #ba 7p4 #aaa72 #i1 #ac1 #cb1 #ea 7pp4 #aad1 #aag1 #aba74 ,what is the ',normal' form of a ,proposition of ,existence8 ,x4 #d1 #dj 7p4 #ajj72 #e1 #fg-gj 7p4 #ajd72 #f1 #cj 7p4 #ajg72 #g1 #bi1 #cj 7p4 #aji72 #h1 #bb 7p4 #aaa72 #i1 #ad1 #cc1 #eb 7pp4 #aad1 #aag1 #abb74 ,what is the ',universe of ,discourse'8 ,,xi4 #d1 #da 7p4 #ajj72 #e1 #ga-gd 7p4 #ajd72 #f1 #ca1 #cb 7p4 #ajg72 #g1 #ca 7p4 #aji72 #h1 #bc 7p4 #aaa72 #i1 #ae1 #cd1 #ec 7pp4 #aad1 #aah1 #abb74 ,what is implied1 in a ,proposition of ,relation1 as to the ,reality of its ,terms8 ,,xii4 #d1 #db 7p4 #ajj72 #e1 #ge-gh 7p4 #aje72 #f1 #cc 7p4 #ajg72 #g1 #cb1 #cc 7pp4 #aji1 #aaj72 #h1 #be 7p4 #aaa72 #i1 #af1 #ce1 #ed 7pp4 #aad1 #aah1 #abb74 ,explain the phrase sitting on the fence4 ,,xiii4 #e1 #gi-hc 7p4 #aje72 #f1 #cd1 #ce 7p4 #ajg72 #g1 #cd 7p4 #aaj72 #h1 #bf 7p4 #aaa72 #i1 #ag1 #cf1 #ee 7pp4 #aad1 #aah1 #abb74 ,what are ',converse' ,propositions8 ,,xiv4 #e1 #hd-hh 7p4 #aje72 #f1 #cf 7p4 #ajg72 #g1 #ce1 #cf 7p4 #aaj72 #h1 #bg 7p4 #aaa72 #i1 #ah1 #cg1 #ef 7pp4 #aad1 #aah1 #abc74 ,what are ',concrete' and ',abstract' ,propositions8 pg#jif ,,xv4 #e1 #hi-ic 7p4 #aje72 #f1 #cg1 #ch 7p4 #ajg72 #g1 #cg 7p4 #aaj72 #h1 #bh 7p4 #aaa72 #i1 #ai1 #ch1 #eg 7pp4 #aae1 #aah1 #abc74 ,what is a ',syllogism'8 ,and what are its ',premisses' and its ',conclusion'8 ,,xvi4 #e1 #id-ig 7p4 #ajf72 #f1 #ci 7p4 #ajg72 #g1 #ch1 #ci 7p4 #aaj72 #h1 #bi 7p4 #aaa72 #i1 #bj1 #ci1 #eh 7pp4 #aae1 #aai1 #abc74 ,what is a ',sorites'8 ,and what are its ',premisses'1 its ',partial ,conclusions'1 and its ',complete ,conclusion'8 ,,xvii4 #e1 #ih-aja 7p4 #ajf72 #f1 #dj 7p4 #ajg72 #g1 #dj 7p4 #aaj72 #h1 #cj 7p4 #aaa72 #i1 #ba1 #da1 #ei1 #fj 7pp4 #aae1 #aai1 #abd74 ,what are the ',universe of ,discourse'1 the ',eliminands'1 and the ',retinends'1 of a ,syllogism8 ,and of a ,sorites8 pg#jig ,,book ,,viii4 ,,examples1 ,,answers1 ,,and ,,solutions4 ,n4,b4 ,reference tags for ,examples1 ,answers ,solutions will be found in the right margin4 ,,chapter ,i4 ,,examples4 #a4 ,,ex#a ,propositions of ,relation1 to be reduced to normal form4 #a4 ,i have been out for a walk4 #b4 ,i am feeling better4 #c4 ,no one has read the letter but ,john4 #d4 ,neither you nor ,i are old4 #e4 ,no fat creatures run well4 #f4 ,none but the brave deserve the fair4 #g4 ,no one looks poetical unless he is pale4 #h4 ,some judges lose their tempers4 #i4 ,i never neglect important business4 #aj4 ,what is difficult needs attention4 #aa4 ,what is unwholesome should be avoided4 #ab4 ,all the laws passed last week relate to excise4 #ac4 ,logic puzzles me4 #ad4 ,there are no ,jews in the house4 #ae4 ,some dishes are unwholesome if not well-cooked4 #af4 ,unexciting books make one drowsy4 #ag4 ,when a man knows what he's about1 he can detect a sharper4 #ah4 ,you and ,i know what we're about4 #ai4 ,some bald people wear wigs4 #bj4 ,those who are fully occupied never talk about their grievances4 #ba4 ,no riddles interest me if they can be solved4 pg#jih #b4 ,,ex#b ,pairs of ,abstract ,propositions1 one in terms of x and m1 and the other in terms of y and m1 to be represented on the same ,triliteral ,diagram4 #a4 ,no x are m2 ,no m' are y4 #b4 ,no x' are m'2 ,all m' are y4 #c4 ,some x' are m2 ,no m are y4 #d4 ,all m are x2 ,all m' are y'4 #e4 ,all m' are x2 ,all m' are y'4 #f4 ,all x' are m'2 ,no y' are m4 #g4 ,all x are m2 ,all y' are m'4 #h4 ,some m' are x'2 ,no m are y4 #i4 ,all m are x'2 ,no m are y4 #aj4 ,no m are x'2 ,no y are m'4 #aa4 ,no x' are m'2 ,no m are y4 #ab4 ,some x are m2 ,all y' are m4 #ac4 ,all x' are m2 ,no m are y4 #ad4 ,some x are m'2 ,all m are y4 #ae4 ,no m' are x'2 ,all y are m4 #af4 ,all x are m'2 ,no y are m4 #ag4 ,some m' are x2 ,no m' are y'4 #ah4 ,all x are m'2 ,some m' are y'4 #ai4 ,all m are x2 ,some m are y'4 #bj4 ,no x' are m2 ,some y are m4 #ba4 ,some x' are m'2 ,all y' are m4 #bb4 ,no m are x2 ,some m are y4 #bc4 ,no m' are x2 ,all y are m'4 #bd4 ,all m are x2 ,no y' are m'4 #be4 ,some m are x2 ,no y' are m4 #bf4 ,all m' are x'2 ,some y are m'4 #bg4 ,some m are x'2 ,no y' are m'4 #bh4 ,no x are m'2 ,all m are y'4 #bi4 ,no x' are m2 ,no m are y'4 #cj4 ,no x are m2 ,some y' are m'4 #ca4 ,some m' are x2 ,all y' are m2 #cb4 ,all x are m'2 ,all y are m4 pg#jii #c4 ,,ex#c ,marked ,triliteral ,diagrams1 to be interpreted in terms of x and y4 #a --------------- 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ 7,o7 --------------- #b --------------- 7,o7 ------ 7,o7 ---------7,i7 7,o7 ------ 7,o7 --------------- #c --------------- 7,o7 ------ 7,o77,o7 ------------ 7,i7 ------ 7,o7 --------------- #d --------------- 7,o7 7,o7 ------ 7,o7 ------7,i7--- 7,o7 ------ --------------- #e --------------- 7,i7 ------ 7,o7 ------------ 7,o7 ------ 7,o7 7,o7 --------------- #f --------------- 7,o7 7,o7 ------ ------------ 7,o7 ------ 7,i7 7,o7 --------------- #g --------------- 7,o7 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ --------------- #h --------------- 7,i7 ------ 7,o7 ------------ 7,o77,i7 ------ 7,o7 --------------- #i --------------- ------ 7,o7 ------------ 7,o77,i7 ------ 7,o7 7,o7 --------------- #aj --------------- 7,o7 7,o7 ------ 7,o77,i7 ------------ 7,o7 ------ --------------- #aa --------------- 7,o7 7,o7 ------ 7,i7 ------------ 7,o7 ------ 7,o7 --------------- #ab --------------- 7,o7 ------ ---7,i7------ ------ 7,o7 7,i7 --------------- #ac --------------- 7,o7 7,i7 ------ 7,o7 ------------ 7,o7 ------ 7,o7 --------------- #ad --------------- 7,o7 7,o7 ------ 7,o7 ------------ 7,o7 ------ 7,i7 --------------- #ae --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- #af --------------- 7,i7 ------ ------------ 7,o7 ------ 7,o7 7,o7 --------------- #ag --------------- 7,o7 ------ 7,i7 ------------ 7,o77,o7 ------ 7,i7 7,o7 --------------- #ah --------------- 7,o7 7,o7 ------ 7,o77,i7 ------------ 7,o7 ------ 7,i7 --------------- #ai --------------- 7,o7 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ 7,i7 --------------- #bj --------------- 7,o7 ------ 7,o77,o7 ------------ 7,i7 ------ 7,o7 --------------- pg#ajj #d4 ,,ex#d ,pairs of ,abstract ,propositions1 proposed as ,premisses3 ,conclusions to be found4 #a4 ,no m are x'2 ,all m' are y4 #b4 ,no m' are x2 ,some m' are y'4 #c4 ,all m' are x2 ,all m' are y'4 #d4 ,no x' are m'2 ,all y' are m4 #e4 ,some m are x'2 ,no y are m4 #f4 ,no x' are m2 ,no m are y4 #g4 ,no m are x'2 ,some y' are m4 #h4 ,all m' are x'2 ,no m' are y4 #i4 ,some x' are m'2 ,no m are y'4 #aj4 ,all x are m2 ,all y' are m'4 #aa4 ,no m are x2 ,all y' are m'4 #ab4 ,no x are m2 ,all y are m4 #ac4 ,all m' are x2 ,no y are m4 #ad4 ,all m are x2 ,all m' are y4 #ae4 ,no x are m2 ,no m' are y4 #af4 ,all x are m'2 ,all y are m4 #ag4 ,no x are m2 ,all m' are y4 #ah4 ,no x are m'2 ,no m are y4 #ai4 ,all m are x2 ,all m are y'4 #bj4 ,no m are x2 ,all m' are y4 #ba4 ,all x are m2 ,some m' are y4 #bb4 ,some x are m2 ,all y are m4 #bc4 ,all m are x2 ,some y are m4 #bd4 ,no x are m2 ,all y are m4 #be4 ,some m are x'2 ,all y' are m'4 #bf4 ,no m are x'2 ,all y are m4 #bg4 ,all x are m'2 ,all y' are m4 #bh4 ,all m are x'2 ,some m are y4 #bi4 ,no m are x2 ,all y are m'4 #cj4 ,all x are m'2 ,some y are m4 #ca4 ,all x are m2 ,all y are m4 #cb4 ,no x are m'2 ,all m are y4 #cc4 ,no m are x2 ,no m are y4 #cd4 ,no m are x'2 ,some y are m4 #ce4 ,no m are x2 ,all y are m4 #cf4 ,all m are x'2 ,some y are m4 #cg4 ,all m are x2 ,no y are m4 #ch4 ,no m are x2 ,no m' are y4 #ci4 ,some m are x'2 ,no m are y4 #dj4 ,no x' are m2 ,all y' are m4 #da4 ,all x are m'2 ,no y are m'4 #db4 ,no m' are x2 ,no y are m4 pg#aja #e4 ,,ex#e ,pairs of ,concrete ,propositions1 proposed as ,premisses3 ,conclusions to be found4 #a4 ,i have been out for a walk2 ,i am feeling better4 #b4 ,no one has read the letter but ,john2 ,no one1 who has not read it1 knows what it is about4 #c4 ,those who are not old like walking2 ,you and ,i are young4 #d4 ,your course is always honest2 ,your course is always the best policy4 #e4 ,no fat creatures run well2 ,some greyhounds run well4 #f4 ,some1 who deserve the fair1 get their deserts2 ,none but the brave deserve the fair4 #g4 ,some ,jews are rich2 ,all ,esquimaux are ,gentiles4 #h4 ,sugar-plums are sweet2 ,some sweet things are liked by children4 #i4 ,john is in the house2 ,everybody in the house is ill4 #aj4 ,umbrellas are useful on a journey2 ,what is useless on a journey should be left behind4 #aa4 ,audible music causes vibration in the air2 ,inaudible music is not worth paying for4 #ab4 ,some holidays are rainy2 ,rainy days are tiresome4 #ac4 ,no ,frenchmen like plumpudding2 ,all ,englishmen like plumpudding4 #ad4 ,no portrait of a lady1 that makes her simper or scowl1 is satisfactory2 ,no photograph of a lady ever fails to make her simper or scowl4 #ae4 ,all pale people are phlegmatic2 ,no one looks poetical unless he is pale4 #af4 ,no old misers are cheerful2 ,some old misers are thin4 #ag4 ,no one1 who exercises self-control1 fails to keep his temper2 ,some judges lose their tempers4 pg#ajb #ah4 ,all pigs are fat2 ,nothing that is fed on barley-water is fat4 #ai4 ,all rabbits1 that are not greedy1 are black2 ,no old rabbits are free from greediness4 #bj4 ,some pictures are not first attempts2 ,no first attempts are really good4 #ba4 ,i never neglect important business2 ,your business is unimportant4 #bb4 ,some lessons are difficult2 ,what is difficult needs attention4 #bc4 ,all clever people are popular2 ,all obliging people are popular4 #bd4 ,thoughtless people do mischief2 ,no thoughtful person forgets a promise4 #be4 ,pigs cannot fly2 ,pigs are greedy4 #bf4 ,all soldiers march well2 ,some babies are not soldiers4 #bg4 ,no bride-cakes are wholesome2 ,what is unwholesome should be avoided4 #bh4 ,john is industrious2 ,no industrious people are unhappy4 #bi4 ,no philosophers are conceited2 ,some conceited persons are not gamblers4 #cj4 ,some excise laws are unjust2 ,all the laws passed last week relate to excise4 #ca4 ,no military men write poetry2 ,none of my lodgers are civilians4 #cb4 ,no medicine is nice2 ,senna is a medicine4 #cc4 ,some circulars are not read with pleasure2 ,no begging-letters are read with pleasure4 #cd4 ,all ,britons are brave2 ,no sailors are cowards4 #ce4 ,nothing intelligible ever puzzles me2 ,logic puzzles me4 #cf4 ,some pigs are wild2 ,all pigs are fat4 pg#ajc #cg4 ,all wasps are unfriendly2 ,all unfriendly creatures are unwelcome4 #ch4 ,no old rabbits are greedy2 ,all black rabbits are greedy4 #ci4 ,some eggs are hard-boiled2 ,no eggs are uncrackable4 #dj4 ,no antelope is ungraceful2 ,graceful creatures delight the eye4 #da4 ,all well-fed canaries sing loud2 ,no canary is melancholy if it sings loud4 #db4 ,some poetry is original2 ,no original work is producible at will4 #dc4 ,no country1 that has been explored1 is infested by dragons2 ,unexplored countries are fascinating4 #dd4 ,no coals are white2 ,no niggers are white4 #de4 ,no bridges are made of sugar2 ,some bridges are picturesque4 #df4 ,no children are patient2 ,no impatient person can sit still4 #dg4 ,no quadrupeds can whistle2 ,some cats are quadrupeds4 #dh4 ,bores are terrible2 ,you are a bore4 #di4 ,some oysters are silent2 ,no silent creatures are amusing4 #ej4 ,there are no ,jews in the house2 ,no ,gentiles have beards a yard long4 #ea4 ,canaries1 that do not sing loud1 are unhappy2 ,no well-fed canaries fail to sing loud4 #eb4 ,all my sisters have colds2 ,no one can sing who has a cold4 #ec4 ,all that is made of gold is precious2 ,some caskets are precious4 #ed4 ,some buns are rich2 ,all buns are nice4 #ee4 ,all my cousins are unjust2 ,all judges are just4 pg#ajd #ef4 ,pain is wearisome2 ,no pain is eagerly wished for4 #eg4 ,all medicine is nasty2 ,senna is a medicine4 #eh4 ,some unkind remarks are annoying2 ,no critical remarks are kind4 #ei4 ,no tall men have woolly hair2 ,niggers have woolly hair4 #fj4 ,all philosophers are logical2 ,an illogical man is always obstinate4 #fa4 ,john is industrious2 ,all industrious people are happy4 #fb4 ,these dishes are all well-cooked2 ,some dishes are unwholesome if not well-cooked4 #fc4 ,no exciting books suit feverish patients2 ,unexciting books make one drowsy4 #fd4 ,no pigs can fly2 ,all pigs are greedy4 #fe4 ,when a man knows what he's about1 he can detect a sharper2 ,you and ,i know what we're about4 #ff4 ,some dreams are terrible2 ,no lambs are terrible4 #fg4 ,no bald creature needs a hairbrush2 ,no lizards have hair4 #fh4 ,all battles are noisy2 ,what makes no noise may escape notice4 #fi4 ,all my cousins are unjust2 ,no judges are unjust4 #gj4 ,all eggs can be cracked2 ,some eggs are hard-boiled4 #ga4 ,prejudiced persons are untrustworthy2 ,some unprejudiced persons are disliked4 #gb4 ,no dictatorial person is popular2 ,she is dictatorial4 #gc4 ,some bald people wear wigs2 ,all your children have hair4 #gd4 ,no lobsters are unreasonable2 ,no reasonable creatures expect impossibilities4 pg#aje #ge4 ,no nightmare is pleasant2 ,unpleasant experiences are not eagerly desired4 #gf4 ,no plumcakes are wholesome2 ,some wholesome things are nice4 #gg4 ,nothing that is nice need be shunned2 ,some kinds of jam are nice4 #gh4 ,all ducks waddle2 ,nothing that waddles is graceful4 #gi4 ,sandwiches are satisfying2 ,nothing in this dish is unsatisfying4 #hj4 ,no rich man begs in the street2 ,those who are not rich should keep accounts4 #ha4 ,spiders spin webs2 ,some creatures1 that do not spin webs1 are savage4 #hb4 ,some of these shops are not crowded2 ,no crowded shops are comfortable4 #hc4 ,prudent travelers carry plenty of small change2 ,imprudent travelers lose their luggage4 #hd4 ,some geraniums are red2 ,all these flowers are red4 #he4 ,none of my cousins are just2 ,all judges are just4 #hf4 ,no ,jews are mad2 ,all my lodgers are ,jews4 #hg4 ,busy folk are not always talking about their grievances2 ,discontented folk are always talking about their grievances4 #hh4 ,none of my cousins are just2 ,no judges are unjust4 #hi4 ,all teetotalers like sugar2 ,no nightingale drinks wine4 #ij4 ,no riddles interest me if they can be solved2 ,all these riddles are insoluble4 #ia4 ,all clear explanations are satisfactory2 ,some excuses are unsatisfactory4 #ib4 ,all elderly ladies are talkative2 ,all good-tempered ladies are talkative4 #ic4 ,no kind deed is unlawful2 ,what is lawful may be done without scruple4 pg#ajf #id4 ,no babies are studious2 ,no babies are good violinists4 #ie4 ,all shillings are round2 ,all these coins are round4 #if4 ,no honest men cheat2 ,no dishonest men are trustworthy4 #ig4 ,none of my boys are clever2 ,none of my girls are greedy4 #ih4 ,all jokes are meant to amuse2 ,no ,act of ,parliament is a joke4 #ii4 ,no eventful tour is ever forgotten2 ,uneventful tours are not worth writing a book about4 #ajj4 ,all my boys are disobedient2 ,all my girls are discontented4 #aja4 ,no unexpected pleasure annoys me2 ,your visit is an unexpected pleasure4 #f4 ,,ex#f ,trios of ,abstract ,propositions1 proposed as ,syllogisms3 to be examined4 #a4 ,some x are m2 ,no m are y'4 ,some x are y4 #b4 ,all x are m2 ,no y are m'4 ,no y are x'4 #c4 ,some x are m'2 ,all y' are m4 ,some x are y4 #d4 ,all x are m2 ,no y are m4 ,all x are y'4 #e4 ,some m' are x'2 ,no m' are y4 ,some x' are y'4 #f4 ,no x' are m2 ,all y are m'4 ,all y are x'4 #g4 ,some m' are x'2 ,all y' are m'4 ,some x' are y'4 #h4 ,no m' are x'2 ,all y' are m'4 ,all y' are x4 #i4 ,some m are x'2 ,no m are y4 ,some x' are y'4 #aj4 ,all m' are x'2 ,all m' are y4 ,some y are x'4 #aa4 ,all x are m'2 ,some y are m4 ,some y are x'4 #ab4 ,no x are m2 ,no m' are y'4 ,no x are y'4 #ac4 ,no x are m2 ,all y' are m4 ,all y' are x'4 #ad4 ,all m' are x'2 ,all m' are y4 ,some y are x'4 #ae4 ,some m are x'2 ,all y are m'4 ,some x' are y'4 #af4 ,no x' are m2 ,all y' are m'4 ,some y' are x4 #ag4 ,no m' are x2 ,all m' are y'4 ,some x' are y'4 pg#ajg #ah4 ,no x' are m2 ,some m are y4 ,some x are y4 #ai4 ,some m are x2 ,all m are y4 ,some y are x'4 #bj4 ,no x' are m'2 ,some m' are y'4 ,some x are y'4 #ba4 ,no m are x2 ,all m are y'4 ,some x' are y'4 #bb4 ,all x' are m2 ,some y are m'4 ,all x' are y'4 #bc4 ,all m are x2 ,no m' are y'4 ,no x' are y'4 #bd4 ,all x are m'2 ,all m' are y4 ,all x are y4 #be4 ,no x are m'2 ,all m are y4 ,no x are y'4 #bf4 ,all m are x'2 ,all y are m4 ,all y are x'4 #bg4 ,all x are m2 ,no m are y'4 ,all x are y4 #bh4 ,all x are m2 ,no y' are m'4 ,all x are y4 #bi4 ,no x' are m2 ,no m' are y'4 ,no x' are y'4 #cj4 ,all x are m2 ,all m are y'4 ,all x are y'4 #ca4 ,all x' are m'2 ,no y' are m'4 ,all x' are y4 #cb4 ,no x are m2 ,no y' are m'4 ,no x are y'4 #cc4 ,all m are x'2 ,all y' are m4 ,all y' are x'4 #cd4 ,all x are m'2 ,some y are m'4 ,some y are x4 #ce4 ,some x are m2 ,all m are y4 ,some x are y4 #cf4 ,all m are x'2 ,all y are m4 ,all y are x'4 #cg4 ,no m are x'2 ,all m are y'4 ,some x are y'4 #ch4 ,no x are m2 ,no m are y'4 ,no x are y'4 #ci4 ,no m are x2 ,some m are y'4 ,some x' are y'4 #dj4 ,no m are x'2 ,some y are m4 ,some x are y4 #g4 ,,ex#g ,trios of ,concrete ,propositions1 proposed as ,syllogisms3 to be examined4 #a4 ,no doctors are enthusiastic2 ,you are enthusiastic4 ,you are not a doctor4 #b4 ,dictionaries are useful2 ,useful books are valuable4 ,dictionaries are valuable4 #c4 ,no misers are unselfish2 ,none but misers save egg-shells4 ,no unselfish people save egg-shells4 #d4 ,some epicures are ungenerous2 ,all my uncles are generous4 ,my uncles are not epicures4 pg#ajh #e4 ,gold is heavy2 ,nothing but gold will silence him4 ,nothing light will silence him4 #f4 ,some healthy people are fat2 ,no unhealthy people are strong4 ,some fat people are not strong4 #g4 ,i saw it in a newspaper4 ,all newspapers tell lies4 ,it was a lie4 #h4 ,some cravats are not artistic2 ,i admire anything artistic4 ,there are some cravats that ,i do not admire4 #i4 ,his songs never last an hour2 ,a song1 that lasts an hour1 is tedious4 ,his songs are never tedious4 #aj4 ,some candles give very little light2 ,candles are meant to give light4 ,some things1 that are meant to give light1 give very little4 #aa4 ,all1 who are anxious to learn1 work hard2 ,some of these boys work hard4 ,some of these boys are anxious to learn4 #ab4 ,all lions are fierce2 ,some lions do not drink coffee4 ,some creatures that drink coffee are not fierce4 #ac4 ,no misers are generous2 ,some old men are ungenerous4 ,some old men are misers4 #ad4 ,no fossil can be crossed in love2 ,an oyster may be crossed in love4 ,oysters are not fossils4 #ae4 ,all uneducated people are shallow2 ,students are all educated4 ,no students are shallow4 #af4 ,all young lambs jump2 ,no young animals are healthy1 unless they jump4 ,all young lambs are healthy4 #ag4 ,ill-managed business is unprofitable2 ,railways are never ill-managed4 ,all railways are profitable4 #ah4 ,no ,professors are ignorant2 ,all ignorant people are vain4 ,no professors are vain4 pg#aji #ai4 ,a prudent man shuns hynas2 ,no banker is imprudent4 ,no banker fails to shun hynas4 #bj4 ,all wasps are unfriendly2 ,no puppies are unfriendly4 ,puppies are not wasps4 #ba4 ,no ,jews are honest2 ,some ,gentiles are rich4 ,some rich people are dishonest4 #bb4 ,no idlers win fame2 ,some painters are not idle4 ,some painters win fame4 #bc4 ,no monkeys are soldiers2 ,all monkeys are mischievous4 ,some mischievous creatures are not soldiers4 #bd4 ,all these bonbons are chocolate-creams2 ,all these bonbons are delicious4 ,chocolate-creams are delicious4 #be4 ,no muffins are wholesome2 ,all buns are unwholesome4 ,buns are not muffins4 #bf4 ,some unauthorised reports are false2 ,all authorised reports are trustworthy4 ,some false reports are not trustworthy4 #bg4 ,some pillows are soft2 ,no pokers are soft4 ,some pokers are not pillows4 #bh4 ,improbable stories are not easily believed2 ,none of his stories are probable4 ,none of his stories are easily believed4 #bi4 ,no thieves are honest2 ,some dishonest people are found out4 ,some thieves are found out4 #cj4 ,no muffins are wholesome2 ,all puffy food is unwholesome4 ,all muffins are puffy4 #ca4 ,no birds1 except peacocks1 are proud of their tails2 ,some birds1 that are proud of their tails1 cannot sing4 ,some peacocks cannot sing4 #cb4 ,warmth relieves pain2 ,nothing1 that does not relieve pain1 is useful in toothache4 ,warmth is useful in toothache4 pg#aaj #cc4 ,no bankrupts are rich2 ,some merchants are not bankrupts4 ,some merchants are rich4 #cd4 ,bores are dreaded2 ,no bore is ever begged to prolong his visit4 ,no one1 who is dreaded1 is ever begged to prolong his visit4 #ce4 ,all wise men walk on their feet2 ,all unwise men walk on their hands4 ,no man walks on both4 #cf4 ,no wheelbarrows are comfortable2 ,no uncomfortable vehicles are popular4 ,no wheelbarrows are popular4 #cg4 ,no frogs are poetical2 ,some ducks are unpoetical4 ,some ducks are not frogs4 #ch4 ,no emperors are dentists2 ,all dentists are dreaded by children4 ,no emperors are dreaded by children4 #ci4 ,sugar is sweet2 ,salt is not sweet4 ,salt is not sugar4 #dj4 ,every eagle can fly2 ,some pigs cannot fly4 ,some pigs are not eagles4 #h4 ,,ex#h ,sets of ,abstract ,propositions1 proposed as ,premisses for ,soriteses3 ,conclusions to be found4 ,n4,b4 ,at the end of this ,section instructions are given for varying these ,examples4 #a4 #a4 ,no c are d2 #b4 ,all a are d2 #c4 ,all b are c4 #b4 #a4 ,all d are b2 #b4 ,no a are c'2 #c4 ,no b are c4 #c4 #a4 ,no b are a2 #b4 ,no c are d'2 #c4 ,all d are b4 #d4 #a4 ,no b are c2 #b4 ,all a are b2 #c4 ,no c' are d4 #e4 #a4 ,all b' are a'2 #b4 ,no b are c2 #c4 ,no a' are d4 #f4 #a4 ,all a are b'2 #b4 ,no b' are c2 #c4 ,all d are a4 #g4 #a4 ,no d are b'2 #b4 ,all b are a2 #c4 ,no c are d'4 #h4 #a4 ,no b' are d2 #b4 ,no a' are b2 #c4 ,all c are d4 pg#aaa #i4 #a4 ,all b' are a2 #b4 ,no a are d2 #c4 ,all b are c4 #aj4 #a4 ,no c are d2 #b4 ,all b are c2 #c4 ,no a are d'4 #aa4 #a4 ,no b are c2 #b4 ,all d are a2 #c4 ,all c' are a'4 #ab4 #a4 ,no c are b'2 #b4 ,all c' are d'2 #c4 ,all b are a4 #ac4 #a4 ,all d are e2 #b4 ,all c are a2 #c4 ,no b are d'2 #d4 ,all e are a'4 #ad4 #a4 ,all e are b2 #b4 ,all a are e2 #c4 ,all d are b'2 #d4 ,all a' are c2 #ae4 #a4 ,no b' are d2 #b4 ,all e are c2 #c4 ,all b are a2 #d4 ,all d' are c'4 #af4 #a4 ,no a' are e2 #b4 ,all d are c'2 #c4 ,all a are b2 #d4 ,all e' are d4 #ag4 #a4 ,all d are c2 #b4 ,all a are e2 #c4 ,no b are d'2 #d4 ,all c are e'4 #ah4 #a4 ,all a are b2 #b4 ,all d are e2 #c4 ,all a' are c'2 #d4 ,no b are e4 #ai4 #a4 ,no b are c2 #b4 ,all e are h2 #c4 ,all a are b2 #d4 ,no d are h2 #e4 ,all e' are c4 #bj4 #a4 ,no d are h'2 #b4 ,no c are e2 #c4 ,all h are b2 #d4 ,no a are d'2 #e4 ,no b are e'4 #ba4 #a4 ,all b are a2 #b4 ,no d are h2 #c4 ,no c are e2 #d4 ,no a are h'2 #e4 ,all c' are b4 #bb4 #a4 ,all e are d'2 #b4 ,no b' are h'2 #c4 ,all c' are d2 #d4 ,all a are e2 #e4 ,no c are h4 #bc4 #a4 ,all b' are a'2 #b4 ,no d are e'2 #c4 ,all h are b'2 #d4 ,no c are e2 #e4 ,all d' are a4 #bd4 #a4 ,all h' are k'2 #b4 ,no b' are a2 #c4 ,all c are d2 #d4 ,all e are h'2 #e4 ,no d are k'2 #f4 ,no b are c'4 #be4 #a4 ,all a are d2 #b4 ,all k are b2 #c4 ,all e are h2 #d4 ,no a' are b2 #e4 ,all d are c2 #f4 ,all h are k4 #bf4 #a4 ,all a' are h2 #b4 ,no d' are k'2 #c4 ,all e are b'2 #d4 ,no h are k2 #e4 ,all a are e2 #f4 ,no b' are d4 #bg4 #a4 ,all c are d'2 #b4 ,no h are b2 #c4 ,all a' are k2 #d4 ,no c are e'2 #e4 ,all b' are d2 #f4 ,no a are c'4 #bh4 #a4 ,no a' are k2 #b4 ,all e are b2 #c4 ,no h are k'2 #d4 ,no d' are c2 #e4 ,no a are b2 #f4 ,all c' are h4 #bi4 #a4 ,no e are k2 #b4 ,no b' are m2 #c4 ,no a are c'2 #d4 ,all h' are e2 #e4 ,all d are k2 #f4 ,no c are b2 #g4 ,all d' are l2 #h4 ,no h are m'4 #cj4 #a4 ,all n are m2 #b4 ,all a' are e2 #c4 ,no c' are l2 #d4 ,all k are r'2 #e4 ,no a are h'2 #f4 ,no d are l'2 #g4 ,no c are n'2 #h4 ,all e are b2 #i4 ,all m are r2 #aj4 ,all h are d4 ,n4,b4 ,in each ,example1 in ,sections #h and #i1 it is possible to begin with any ,premiss1 at pleasure1 and thus to get as many different ,solutions 7all of course yielding the same ,complete ,conclusion7 as there are ,premisses in the ,example4 ,hence #h really contains #abi different ,examples1 and #i contains #bgc4 pg#aab #i4 ,,ex#i ,sets of ,concrete ,propositions1 proposed as ,premisses for ,soriteses3 ,conclusions to be found4 #a4 7#a7 ,babies are illogical2 7#b7 ,nobody is despised who can manage a crocodile2 7#c7 ,illogical persons are despised4 ,univ4 persons2 a able to manage a crocodile2 b babies2 c despised2 d logical4 #b4 7#a7 ,my saucepans are the only things ,i have that are made of tin2 7#b7 ,i find all your presents very useful2 7#c7 ,none of my saucepans are of the slightest use4 ,univ4 things of mine2 a made of tin2 b my saucepans2 c useful2 d your presents4 #c4 7#a7 ,no potatoes of mine1 that are new1 have been boiled2 7#b7 ,all my potatoes in this dish are fit to eat2 7#c7 ,no unboiled potatoes of mine are fit to eat4 ,univ4 my potatoes2 a boiled2 b eatable2 c in this dish2 d new4 #d4 7#a7 ,there are no ,jews in the kitchen2 7#b7 ,no ,gentiles say shpoonj2 7#c7 ,my servants are all in the kitchen4 ,univ4 persons2 a in the kitchen2 b ,jews2 c my servants2 d saying shpoonj4 #e4 7#a7 ,no ducks waltz2 7#b7 ,no officers ever decline to waltz2 7#c7 ,all my poultry are ducks4 ,univ4 creatures2 a ducks2 b my poultry2 c officers2 d willing to waltz4 #f4 7#a7 ,every one who is sane can do ,logic2 7#b7 ,no lunatics are fit to serve on a jury2 7#c7 ,none of your sons can do ,logic4 ,univ4 persons2 a able to do ,logic2 b fit to serve on a jury2 c sane2 d your sons4 pg#aac #g4 7#a7 ,there are no pencils of mine in this box2 7#b7 ,no sugar-plums of mine are cigars2 7#c7 ,the whole of my property1 that is not in this box1 consists of cigars4 ,univ4 things of mine2 a cigars2 b in this box2 c pencils2 d sugar-plums4 #h4 7#a7 ,no experienced person is incompetent2 7#b7 ,jenkins is always blundering2 7#c7 ,no competent person is always blundering4 ,univ4 persons2 a always blundering2 b competent2 c experienced2 d ,jenkins4 #i4 7#a7 ,no terriers wander among the signs of the zodiac2 7#b7 ,nothing1 that does not wander among the signs of the zodiac1 is a comet2 7#c7 ,nothing but a terrier has a curly tail4 ,univ4 things2 a comets2 b curly-tailed2 c terriers2 d wandering among the signs of the zodiac4 #aj4 7#a7 ,no one takes in the ,times1 unless he is well-educated2 7#b7 ,no hedge-hogs can read2 7#c7 ,those who cannot read are not well-educated4 ,univ4 creatures2 a able to read2 b hedge-hogs2 c taking in the ,times2 d well-educated4 #aa4 7#a7 ,all puddings are nice2 7#b7 ,this dish is a pudding2 7#c7 ,no nice things are wholesome4 ,univ4 things2 a nice2 b puddings2 c this dish2 d wholesome4 #ab4 7#a7 ,my gardener is well worth listening to on military subjects2 7#b7 ,no one can remember the battle of ,waterloo1 unless he is very old2 7#c7 ,nobody is really worth listening to on military subjects1 unless he can remember the battle of ,waterloo4 ,univ4 persons2 a able to remember the battle of ,waterloo2 b my gardener2 c well worth listening to on military subjects2 d very old4 pg#aad #ac4 7#a7 ,all humming-birds are richly coloured2 7#b7 ,no large birds live on honey2 7#c7 ,birds that do not live on honey are dull in colour4 ,univ4 birds2 a humming-birds2 b large2 c living on honey2 d richly coloured4 #ad4 7#a7 ,no ,gentiles have hooked noses2 7#b7 ,a man who is a good hand at a bargain always makes money2 7#c7 ,no ,jew is ever a bad hand at a bargain4 ,univ4 persons2 a good hands at a bargain2 b hook-nosed2 c ,jews2 d making money4 #ae4 7#a7 ,all ducks in this village1 that are branded ',b1' belong to ,mrs4 ,bond2 7#b7 ,ducks in this village never wear lace collars1 unless they are branded ',b'2 7#c7 ,mrs4 ,bond has no gray ducks in this village4 ,univ4 ducks in this village2 a belonging to ,mrs4 ,bond2 b branded ',b'2 c gray2 d wearing lace-collars4 #af4 7#a7 ,all the old articles in this cupboard are cracked2 7#b7 ,no jug in this cupboard is new2 7#c7 ,nothing in this cupboard1 that is cracked1 will hold water4 ,univ4 things in this cupboard2 a able to hold water2 b cracked2 c jugs2 d old4 #ag4 7#a7 ,all unripe fruit is unwholesome2 7#b7 ,all these apples are wholesome2 7#c7 ,no fruit1 grown in the shade1 is ripe4 ,univ4 fruit2 a grown in the shade2 b ripe2 c these apples2 d wholesome4 #ah4 7#a7 ,puppies1 that will not lie still1 are always grateful for the loan of a skipping-rope2 7#b7 ,a lame puppy would not say thank you if you offered to lend it a skipping-rope4 7#c7 ,none but lame puppies ever care to do worsted-work4 ,univ4 puppies2 a caring to do worsted-work2 b grateful for the loan of a skipping-rope2 c lame2 d willing to lie still4 pg#aae #ai4 7#a7 ,no name in this list is unsuitable for the hero of a romance2 7#b7 ,names beginning with a vowel are always melodious2 7#c7 ,no name is suitable for the hero of a romance1 if it begins with a consonant4 ,univ4 names2 a beginning with a vowel2 b in this list2 c melodious2 d suitable for the hero of a romance4 #bj4 7#a7 ,all members of the ,house of ,commons have perfect self-command2 7#b7 ,no ,m4,p41 who wears a coronet1 should ride in a donkey-race2 7#c7 ,all members of the ,house of ,lords wear coronets4 ,univ4 ,m4,p4's2 a belonging to the ,house of ,commons2 b having perfect self-command2 c one who may ride in a donkey-race2 d wearing a coronet4 #ba4 7#a7 ,no goods in this shop1 that have been bought and paid for1 are still on sale2 7#b7 ,none of the goods may be carried away1 unless labeled sold2 7#c7 ,none of the goods are labeled sold1 unless they have been bought and paid for4 ,univ4 goods in this shop2 a allowed to be carried away2 b bought and paid for2 c labeled sold2 d on sale4 #bb4 7#a7 ,no acrobatic feats1 that are not announced in the bills of a circus1 are ever attempted there2 7#b7 ,no acrobatic feat is possible1 if it involves turning a quadruple somersault2 7#c7 ,no impossible acrobatic feat is ever announced in a circus bill4 ,univ4 acrobatic feats2 a announced in the bills of a circus2 b attempted in a circus2 c involving the turning of a quadruple somersault2 d possible4 #bc4 7#a7 ,nobody1 who really appreciates ,beethoven1 fails to keep silence while the ,moonlight-,sonata is being played2 7#b7 ,guinea-pigs are hopelessly ignorant of music2 7#c7 ,no one1 who is hopelessly ignorant of music1 ever keeps silence while the ,moonlight-,sonata is being played4 ,univ4 creatures2 a guinea-pigs2 b hopelessly ignorant of music2 c keeping silence while the ,moonlight-,sonata is being played2 d really appreciating ,beethoven4 pg#aaf #bd4 7#a7 ,coloured flowers are always scented2 7#b7 ,i dislike flowers that are not grown in the open air2 7#c7 ,no flowers grown in the open air are colourless4 ,univ4 flowers2 a coloured2 b grown in the open air2 c liked by me2 d scented4 #be4 7#a7 ,showy talkers think too much of themselves2 7#b7 ,no really well-informed people are bad company2 7#c7 ,people who think too much of themselves are not good company4 ,univ4 persons2 a good company2 b really well-informed2 c showy talkers2 d thinking too much of one's self4 #bf4 7#a7 ,no boys under #ab are admitted to this school as boarders2 7#b7 ,all the industrious boys have red hair2 7#c7 ,none of the day-boys learn ,greek2 7#d7 ,none but those under #ab are idle4 ,univ4 boys in this school2 a boarders2 b industrious2 c learning ,greek2 d red-haired2 e under #ab4 #bg4 7#a7 ,the only articles of food1 that my doctor allows me1 are such as are not very rich2 7#b7 ,nothing that agrees with me is unsuitable for supper2 7#c7 ,wedding-cake is always very rich2 7#d7 ,my doctor allows me all articles of food that are suitable for supper4 ,univ4 articles of food2 a agreeing with me2 b allowed by my doctor2 c suitable for supper2 d very rich2 e wedding-cake4 #bh4 7#a7 ,no discussions in our ,debating-,club are likely to rouse the ,british ,lion1 so long as they are checked when they become too noisy2 7#b7 ,discussions1 unwisely conducted1 endanger the peacefulness of our ,debating-,club2 7#c7 ,discussions1 that go on while ,tomkins is in the ,chair1 are likely to rouse the ,british ,lion2 7#d7 ,discussions in our ,debating-,club1 when wisely conducted1 are always checked when they become too noisy4 ,univ4 discussions in our ,debating-,club2 a checked when too noisy2 b dangerous to the peacefulness of our ,debating-,club2 c going on while ,tomkins is in the chair2 d likely to rouse the ,british ,lion2 e wisely conducted4 pg#aag #bi4 7#a7 ,all my sons are slim2 7#b7 ,no child of mine is healthy who takes no exercise2 7#c7 ,all gluttons1 who are children of mine1 are fat2 7#d7 ,no daughter of mine takes any exercise4 ,univ4 my children2 a fat2 b gluttons2 c healthy2 d sons2 e taking exercise4 #cj4 7#a7 ,things sold in the street are of no great value2 7#b7 ,nothing but rubbish can be had for a song2 7#c7 ,eggs of the ,great ,auk are very valuable2 7#d7 ,it is only what is sold in the street that is really rubbish4 ,univ4 things2 a able to be had for a song2 b eggs of the ,great ,auk2 c rubbish2 d sold in the street2 e very valuable4 #ca4 7#a7 ,no books sold here have gilt edges1 except what are in the front shop2 7#b7 ,all the authorised editions have red labels2 7#c7 ,all the books with red labels are priced at #es4 and upwards2 7#d7 ,none but authorised editions are ever placed in the front shop4 ,univ4 books sold here2 a authorised editions2 b gilt-edged2 c having red labels2 d in the front shop2 e priced at #es4 and upwards4 #cb4 7#a7 ,remedies for bleeding1 which fail to check it1 are a mockery2 7#b7 ,tincture of ,calendula is not to be despised2 7#c7 ,remedies1 which will check the bleeding when you cut your finger1 are useful2 7#d7 ,all mock remedies for bleeding are despicable4 ,univ4 remedies for bleeding2 a able to check bleeding2 b despicable2 c mockeries2 d ,tincture of ,calendula2 e useful when you cut your finger4 #cc4 7#a7 ,none of the unnoticed things1 met with at sea1 are mermaids2 7#b7 ,things entered in the log1 as met with at sea1 are sure to be worth remembering2 7#c7 ,i have never met with anything worth remembering1 when on a voyage2 7#d7 ,things met with at sea1 that are noticed1 are sure to be recorded in the log2 ,univ4 things met with at sea2 a entered in log2 b mermaids2 c met with by me2 d noticed2 e worth remembering4 pg#aah #cd4 7#a7 ,the only books in this library1 that ,i do not recommend for reading1 are unhealthy in tone2 7#b7 ,the bound books are all well-written2 7#c7 ,all the romances are healthy in tone2 7#d7 ,i do not recommend you to read any of the unbound books4 ,univ4 books in this library2 a bound2 b healthy in tone2 c recommended by me2 d romances2 e well-written4 #ce4 7#a7 ,no birds1 except ostriches1 are #i feet high2 7#b7 ,there are no birds in this aviary that belong to any one but me2 7#c7 ,no ostrich lives on mince-pies2 7#d7 ,i have no birds less than #i feet high4 ,univ4 birds2 a in this aviary2 b living on mince-pies2 c my2 d #i feet high2 e ostriches4 #cf4 7#a7 ,a plum-pudding1 that is not really solid1 is mere porridge2 7#b7 ,every plum-pudding1 served at my table1 has been boiled in a cloth2 7#c7 ,a plum-pudding that is mere porridge is indistinguishable from soup2 7#d7 ,no plum-puddings are really solid1 except what are served at my table4 ,univ4 plum-puddings2 a boiled in a cloth2 b distinguishable from soup2 c mere porridge2 d really solid2 e served at my table4 #cg4 7#a7 ,no interesting poems are unpopular among people of real taste2 7#b7 ,no modern poetry is free from affectation2 7#c7 ,all your poems are on the subject of soap-bubbles2 7#d7 ,no affected poetry is popular among people of real taste2 7#e7 ,no ancient poem is on the subject of soap-bubbles4 ,univ4 poems2 a affected2 b ancient2 c interesting2 d on the subject of soap-bubbles2 e popular among people of real taste2 h written by you4 #ch4 7#a7 ,all the fruit at this ,show1 that fails to get a prize1 is the property of the ,committee2 7#b7 ,none of my peaches have got prizes2 7#c7 ,none of the fruit1 sold off in the evening1 is unripe2 7#d7 ,none of the ripe fruit has been grown in a hot-house2 7#e7 ,all fruit1 that belongs to the ,committee1 is sold off in the evening4 ,univ4 fruit at this ,show2 a belonging to the ,committee2 b getting prizes2 c grown in a hot-house2 d my peaches2 e ripe2 h sold off in the evening4 pg#aai #ci4 7#a7 ,promise-breakers are untrustworthy2 7#b7 ,wine-drinkers are very communicative2 7#c7 ,a man who keeps his promises is honest2 7#d7 ,no teetotalers are pawnbrokers2 7#e7 ,one can always trust a very communicative person4 ,univ4 persons2 a honest2 b pawnbrokers2 c promise-breakers2 d trustworthy2 e very communicative2 h wine-drinkers4 #dj4 7#a7 ,no kitten1 that loves fish1 is unteachable2 7#b7 ,no kitten without a tail will play with a gorilla2 7#c7 ,kittens with whiskers always love fish2 7#d7 ,no teachable kitten has green eyes2 7#e7 ,no kittens have tails unless they have whiskers4 ,univ4 kittens2 a green-eyed2 b loving fish2 c tailed2 d teachable2 e whiskered2 h willing to play with a gorilla4 #da4 7#a7 ,all the ,eton men in this ,college play cricket2 7#b7 ,none but the ,scholars dine at the higher table2 7#c7 ,none of the cricketers row2 7#d7 ,my friends in this ,college all come from ,eton2 7#e7 ,all the ,scholars are rowing-men4 ,univ4 men in this ,college2 a cricketers2 b dining at the higher table2 c ,etonians2 d my friends2 e rowing-men2 h ,scholars4 #db4 7#a7 ,there is no box of mine here that ,i dare open2 7#b7 ,my writing-desk is made of rose-wood2 7#c7 ,all my boxes are painted1 except what are here2 7#d7 ,there is no box of mine that ,i dare not open1 unless it is full of live scorpions2 7#e7 ,all my rose-wood boxes are unpainted4 ,univ4 my boxes2 a boxes that ,i dare open2 b full of live scorpions2 c here2 d made of rose-wood2 e painted2 h writing-desks4 #dc4 7#a7 ,gentiles have no objection to pork2 7#b7 ,nobody who admires pigsties ever reads ,hogg's poems2 7#c7 ,no ,mandarin knows ,hebrew2 7#d7 ,every one1 who does not object to pork1 admires pigsties2 7#e7 ,no ,jew is ignorant of ,hebrew4 ,univ4 persons2 a admiring pigsties2 b ,jews2 c knowing ,hebrew2 d ,mandarins2 e objecting to pork2 h reading ,hogg's poems4 pg#abj #dd4 7#a7 ,all writers1 who understand human nature1 are clever2 7#b7 ,no one is a true poet unless he can stir the hearts of men2 7#c7 ,shakespeare wrote ,hamlet2 7#d7 ,no writer1 who does not understand human nature1 can stir the hearts of men2 7#e7 ,none but a true poet could have written ,hamlet42 ,univ4 writers2 a able to stir the hearts of men2 b clever2 c ,shakespeare2 d true poets2 e understanding human nature2 h writer of ',hamlet4' #de4 7#a7 ,i despise anything that cannot be used as a bridge2 7#b7 ,everything1 that is worth writing an ode to1 would be a welcome gift to me2 7#c7 ,a rainbow will not bear the weight of a wheel-barrow2 7#d7 ,whatever can be used as a bridge will bear the weight of a wheel-barrow2 7#e7 ,i would not take1 as a gift1 a thing that ,i despise4 ,univ4 things2 a able to bear the weight of a wheel-barrow2 b acceptable to me2 c despised by me2 d rainbows2 e useful as a bridge2 h worth writing an ode to4 #df4 7#a7 ,when ,i work a ,logic-example without grumbling1 you may be sure it is one that ,i can understand2 7#b7 ,these ,soriteses are not arranged in regular order1 like the examples ,i am used to2 7#c7 ,no easy example ever make my head ache2 7#d7 ,i ca'n't understand examples that are not arranged in regular order1 like those ,i am used to2 7#e7 ,i never grumble at an example1 unless it gives me a headache4 ,univ4 ,logic-examples worked by me2 a arranged in regular order1 like the examples ,i am used to2 b easy2 c grumbled at by me2 d making my head ache2 e these ,soriteses2 h understood by me4 #dg4 7#a7 ,every idea of mine1 that cannot be expressed as a ,syllogism1 is really ridiculous2 7#b7 ,none of my ideas about ,bath-buns are worth writing down2 7#c7 ,no idea of mine1 that fails to come true1 can be expressed as a ,syllogism2 7#d7 ,i never have any really ridiculous idea1 that ,i do not at once refer to my solicitor2 7#e7 ,my dreams are all about ,bath-buns2 7#f7 ,i never refer any idea of mine to my solicitor1 unless it is worth writing down4 ,univ4 my ideas2 a able to be expressed as a ,syllogism2 b about ,bath-buns2 c coming true2 d dreams2 e really ridiculous h referred to my solicitor2 k worth writing down4 pg#aba #dh4 7#a7 ,none of the pictures here1 except the battle-pieces1 are valuable2 7#b7 ,none of the unframed ones are varnished2 7#c7 ,all the battle-pieces are painted in oils2 7#d7 ,all those that have been sold are valuable2 7#e7 ,all the ,english ones are varnished2 7#f7 ,all those in frames have been sold4 ,univ4 the pictures here2 a battle-pieces2 b ,english2 c framed2 d oil-paintings2 e sold2 h valuable2 k varnished4 #di4 7#a7 ,animals1 that do not kick1 are always unexcitable2 7#b7 ,donkeys have no horns2 7#c7 ,a buffalo can always toss one over a gate2 7#d7 ,no animals that kick are easy to swallow2 7#e7 ,no hornless animal can toss one over a gate2 7#f7 ,all animals are excitable1 except buffaloes4 ,univ4 animals2 a able to toss one over a gate2 b buffaloes2 c donkeys2 d easy to swallow2 e excitable2 h horned2 k kicking4 #ej4 7#a7 ,no one1 who is going to a party1 ever fails to brush his hair2 7#b7 ,no one looks fascinating1 if he is untidy2 7#c7 ,opium-eaters have no self-command2 7#d7 ,every one1 who has brushed his hair1 looks fascinating2 7#e7 ,no one wears white kid gloves1 unless he is going to a party2 7#f7 ,a man is always untidy1 if he has no self-command4 ,univ4 persons2 a going to a party2 b having brushed one's hair2 c having self-command2 d looking fascinating2 e opium-eaters2 h tidy2 k wearing white kid gloves4 #ea4 7#a7 ,no husband1 who is always giving his wife new dresses1 can be a cross-grained man2 7#b7 ,a methodical husband always comes home for his tea2 7#c7 ,no one1 who hangs up his hat on the gas-jet1 can be a man that is kept in proper order by his wife2 7#d7 ,a good husband is always giving his wife new dresses2 7#e7 ,no husband can fail to be cross-grained1 if his wife does not keep him in proper order2 7#f7 ,an unmethodical husband always hangs up his hat on the gas-jet4 ,univ4 husbands2 a always coming home for his tea2 b always giving his wife new dresses2 c cross-grained2 d good2 e hanging up his hat on the gas-jet2 h kept in proper order2 k methodical4 pg#abb #eb4 7#a7 ,everything1 not absolutely ugly1 may be kept in a drawing-room2 7#b7 ,nothing1 that is encrusted with salt1 is ever quite dry2 7#c7 ,nothing should be kept in a drawing-room1 unless it is free from damp2 7#d7 ,bathing-machines are always kept near the sea2 7#e7 ,nothing1 that is made of mother-of-pearl1 can be absolutely ugly2 7#f7 ,whatever is kept near the sea gets encrusted with salt4 ,univ4 things2 a absolutely ugly2 b bathing-machines2 c encrusted with salt2 d kept near the sea2 e made of mother-of-pearl2 h quite dry2 k things that may be kept in a drawing-room4 #ec4 7#a7 ,i call no day unlucky1 when ,robinson is civil to me2 7#b7 ,wednesdays are always cloudy2 7#c7 ,when people take umbrellas1 the day never turns out fine2 7#d7 ,the only days when ,robinson is uncivil to me are ,wednesdays2 7#e7 ,everybody takes his umbrella with him when it is raining2 7#f7 ,my lucky days always turn out fine4 ,univ4 days2 a called by me 'lucky'2 b cloudy2 c days when people take umbrellas2 d days when ,robinson is civil to me2 e rainy2 h turning out fine2 k ,wednesdays4 #ed4 7#a7 ,no shark ever doubts that it is well fitted out2 7#b7 ,a fish1 that cannot dance a minuet1 is contemptible2 7#c7 ,no fish is quite certain that it is well fitted out1 unless it has three rows of teeth2 7#d7 ,all fishes1 except sharks1 are kind to children2 7#e7 ,no heavy fish can dance a minuet2 7#f7 ,a fish with three rows of teeth is not to be despised4 ,univ4 fishes2 a able to dance a minuet2 b certain that he is well fitted out2 c contemptible2 d having #c rows of teeth2 e heavy2 h kind to children2 k sharks4 #ee4 7#a7 ,all the human race1 except my footmen1 have a certain amount of common-sense2 7#b7 ,no one1 who lives on barley-sugar1 can be anything but a mere baby2 7#c7 ,none but a hop-scotch player knows what real happiness is2 7#d7 ,no mere baby has a grain of common sense2 7#e7 ,no engine-driver ever plays hop-scotch2 7#f7 ,no footman of mine is ignorant of what true happiness is4 ,univ4 human beings2 a engine-drivers2 b having common sense2 c hop-scotch players2 d knowing what real happiness is2 e living on barley-sugar2 h mere babies2 k my footmen4 pg#abc #ef4 7#a7 ,i trust every animal that belongs to me2 7#b7 ,dogs gnaw bones2 7#c7 ,i admit no animals into my study1 unless they will beg when told to do so2 7#d7 ,all the animals in the yard are mine2 7#e7 ,i admit every animal1 that ,i trust1 into my study2 7#f7 ,the only animals1 that are really willing to beg when told to do so1 are dogs4 ,univ4 animals2 a admitted to my study2 b animals that ,i trust2 c dogs2 d gnawing bones2 e in the yard2 h my2 k willing to beg when told4 #eg4 7#a7 ,animals are always mortally offended if ,i fail to notice them2 7#b7 ,the only animals that belong to me are in that field2 7#c7 ,no animal can guess a conundrum1 unless it has been properly trained in a ,board-,school2 7#d7 ,none of the animals in that field are badgers2 7#e7 ,when an animal is mortally offended1 it always rushes about wildly and howls2 7#f7 ,i never notice any animal1 unless it belongs to me2 7#g7 ,no animal1 that has been properly trained in a ,board-,school1 ever rushes about wildly and howls4 ,univ4 animals2 a able to guess a conundrum2 b badgers2 c in that field2 d mortally offended2 e my2 h noticed by me2 k properly trained in a ,board-,school2 l rushing about wildly and howling4 #eh4 7#a7 ,i never put a cheque1 received by me1 on that file1 unless ,i am anxious about it2 7#b7 ,all the cheques received by me1 that are not marked with a cross1 are payable to bearer2 7#c7 ,none of them are ever brought back to me1 unless they have been dishonoured at the ,bank2 7#d7 ,all of them1 that are marked with a cross1 are for amounts of over #ajj2 7#e7 ,all of them1 that are not on that file1 are marked not negotiable2 7#f7 ,no cheque of yours1 received by me1 has ever been dishonoured2 7#g7 ,i am never anxious about a cheque1 received by me1 unless it should happen to be brought back to me2 7#h7 ,none of the cheques received by me1 that are marked not negotiable1 are for amounts of over #ajj4 ,univ4 cheques received by me2 a brought back to me2 b cheques that ,i am anxious about2 c honoured2 d marked with a cross2 e marked 'not negotiable'2 h on that file2 k over #ajj2 l payable to bearer2 m your4 pg#abd #ei4 7#a7 ,all the dated letters in this room are written on blue paper2 7#b7 ,none of them are in black ink1 except those that are written in the third person2 7#c7 ,i have not filed any of them that ,i can read2 7#d7 ,none of them1 that are written on one sheet1 are undated2 7#e7 ,all of them1 that are not crossed1 are in black ink2 7#f7 ,all of them1 written by ,brown1 begin with ,dear ,sir2 7#g7 ,all of them1 written on blue paper1 are filed2 7#h7 ,none of them1 written on more than one sheet1 are crossed2 7#i7 ,none of them1 that begin with ,dear ,sir1 are written in the third person4 ,univ4 letters in this room2 a beginning with ,dear ,sir2 b crossed2 c dated2 d filed2 e in black ink2 h in third person2 k letters that ,i can read2 l on blue paper2 m on one sheet2 n written by ,brown4 #fj4 7#a7 ,the only animals in this house are cats2 7#b7 ,every animal is suitable for a pet1 that loves to gaze at the moon2 7#c7 ,when ,i detest an animal1 ,i avoid it2 7#d7 ,no animals are carnivorous1 unless they prowl at night2 7#e7 ,no cats fails to kill mice2 7#f7 ,no animals ever take to me1 except what are in this house2 7#g7 ,kangaroos are not suitable for pets2 7#h7 ,none but carnivora kill mice2 7#i7 ,i detest animals that do not take to me2 7#aj7 ,animals1 that prowl at night1 always love to gaze at the moon4 ,univ4 animals2 a avoided by me2 b carnivora2 c cats2 d detested by me2 e in this house2 h kangaroos2 k killing mice2 l loving to gaze at the moon2 m prowling at night2 n suitable for pets2 r taking to me4 pg#abe ,,chapter ,,ii4 ,,answers4 ,answers to #a4 ,,an#a #a4 ,all ,sign of ,quantity4 persons represented by the ,name ',i' 7or ,i's7 ,subject4 are ,copula4 persons who have been out for a walk ,predicate4 or1 more briefly1 ,all ',i's are persons who have been out for a walk4 #b4 ,all ',i's are persons who feel better4 #c4 ,no persons who are not ',john' are persons who have read the letter4 #d4 ,no ,members of the ,class 'you and ,i' are old persons4 #e4 ,no fat creatures are creatures that run well4 #f4 ,no not-brave persons are persons deserving of the fair4 #g4 ,no not-pale persons are persons who look poetical4 #h4 ,some judges are persons who lose their tempers4 #i4 ,all ',i's are persons who do not neglect important business4 #aj4 ,all difficult things are things that need attention4 #aa4 ,all unwholesome things are things that should be avoided4 #ab4 ,all laws passed last week are laws relating to excise4 #ac4 ,all logical studies are things that puzzle me4 #ad4 ,no persons in the house are ,jews4 #ae4 ,some not well-cooked dishes are unwholesome dishes4 #af4 ,all unexciting books are books that make one drowsy4 #ag4 ,all men who know what they're about are men who can detect a sharper4 #ah4 ,all ,members of the ,class 'you and ,i' are persons who know what they're about4 #ai4 ,some bald persons are persons accustomed to wear wigs4 #bj4 ,all fully occupied persons are persons who do not talk about their grievances4 #ba4 ,no riddles that can be solved are riddles that interest me4 pg#abf ,answers to #b4 ,,an#b #a --------------- 7,o7 ------ 7,o77,o7 ------------ ------ 7,o7 --------------- #b --------------- 7,i7 7,o7 ------ ------------ ------ 7,o7 7,o7 --------------- #c --------------- ------ 7,o7 ------------ 7,o77,i7 ------ --------------- #d --------------- 7,o7 ------ 7,i7 ---------7,i7 7,o77,o7 ------ 7,o7 --------------- #e --------------- 7,o7 7,i7 ------ ------------ ------ 7,o7 7,o7 --------------- #f --------------- ------ 7,o7 ------------ 7,o77,o7 ------ 7,i7 --------------- #g --------------- 7,o7 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ 7,i7 --------------- #h --------------- ------ 7,o7 ------------ 7,o7 ------ 7,i7 --------------- #i --------------- ------ 7,o77,o7 ------------ 7,o77,i7 ------ --------------- #aj --------------- 7,o7 ------ ------------ 7,o77,o7 ------ 7,o7 --------------- #aa --------------- ------ 7,o7 ------------ 7,o7 ------ 7,o7 7,o7 --------------- #ab --------------- 7,o7 ------ 7,i7 ------7,i7--- ------ 7,o7 --------------- #ac --------------- ------ 7,o7 ------------ 7,i77,o7 ------ 7,o7 7,o7 --------------- #ad --------------- 7,i7 ------ 7,o7 ---7,i7------ 7,o7 ------ --------------- #ae --------------- 7,o7 ------ ---7,i7------ ------ 7,o7 7,o7 --------------- #af --------------- 7,i7 ------ 7,o77,o7 ------------ 7,o7 ------ --------------- #ag --------------- 7,i7 7,o7 ------ ------------ ------ 7,o7 --------------- #ah --------------- 7,i7 ------ 7,o77,o7 ---------7,i7 ------ --------------- #ai --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- #bj --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- #ba --------------- 7,o7 ------ ------7,i7--- ------ 7,i7 7,o7 --------------- #bb --------------- ------ 7,o77,o7 ------------ 7,i7 ------ --------------- #bc --------------- 7,o7 7,o7 ------ 7,o7 ------------ 7,o7 ------ 7,i7 --------------- #bd --------------- 7,o7 ------ 7,i7 ------------ 7,o77,o7 ------ 7,o7 --------------- pg#abg #be --------------- ------ 7,i77,o7 ------------ 7,o7 ------ --------------- #bf --------------- 7,o7 7,o7 ------ ------------ ------ 7,i7 --------------- #bg --------------- 7,o7 ------ ------------ 7,i7 ------ 7,o7 --------------- #bh --------------- 7,o7 7,o7 ------ 7,o7 ------7,i7--- 7,o7 ------ --------------- #bi --------------- ------ 7,o7 ------------ 7,o77,o7 ------ --------------- #cj --------------- ------ 7,o77,o7 ---------7,i7 ------ --------------- #ca --------------- 7,i7 7,o7 ------ ------7,i7--- ------ 7,o7 --------------- #cb --------------- 7,o7 7,i7 ------ 7,o77,o7 ------------ 7,i7 ------ 7,o7 --------------- ,answers to #c4 ,,an#c #a4 ,some xy exist1 or some x are y1 or some y are x4 #b4 ,no information4 #c4 ,all y' are x'4 #d4 ,no xy exist1 c4 #e4 ,all y' are x4 #f4 ,all x' are y4 #g4 ,all x are y4 #h4 ,all x' are y'1 and all y are x4 #i4 ,all x' are y'4 #aj4 ,all x are y'4 #aa4 ,no information4 #ab4 ,some x'y' exist1 c4 #ac4 ,some xy' exist1 c4 #ad4 ,no xy' exist1 c4 #ae4 ,some xy exist1 c4 #af4 ,all y are x4 #ag4 ,all x' are y1 and all y' are x4 #ah4 ,all x are y'1 and all y are x'4 #ai4 ,all x are y1 and all y' are x'4 #bj4 ,all y are x'4 ,answers to #d4 ,,an#d #a4 ,no x' are y'4 #b4 ,some x' are y'4 #c4 ,some x are y'4 #d4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #e4 ,some x' are y'4 #f4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #g4 ,some x are y'4 #h4 ,some x' are y'4 #i4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #aj4 ,all x are y1 and all y' are x'4 #aa4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ab4 ,all y are x'4 #ac4 ,no x' are y4 #ad4 ,no x' are y'4 #ae4 ,no x are y4 #af4 ,all x are y'1 and all y are x'4 pg#abh #ag4 ,no x are y'4 #ah4 ,no x are y4 #ai4 ,some x are y'4 #bj4 ,no x are y'4 #ba4 ,some y are x'4 #bb4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #bc4 ,some x are y4 #bd4 ,all y are x'4 #be4 ,some y are x'4 #bf4 ,all y are x4 #bg4 ,all x are y1 and all y' are x'4 #bh4 ,some y are x'4 #bi4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #cj4 ,some y are x'4 #ca4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #cb4 ,no x are y'4 #cc4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #cd4 ,some x are y4 #ce4 ,all y are x'4 #cf4 ,some y are x'4 #cg4 ,some x are y'4 #ch4 ,no x are y4 #ci4 ,some x' are y'4 #dj4 ,all y' are x4 #da4 ,all x are y'4 #db4 ,no x are y4 ,answers to #e4 ,,an#e #a4 ,somebody who has been out for a walk is feeling better4 #b4 ,no one but ,john knows what the letter is about4 #c4 ,you and ,i like walking4 #d4 ,honesty is sometimes the best policy4 #e4 ,some greyhounds are not fat4 #f4 ,some brave persons get their deserts4 #g4 ,some rich persons are not ,esquimaux4 #h4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #i4 ,john is ill4 #aj4 ,some things1 that are not umbrellas1 should be left behind on a journey4 #aa4 ,no music is worth paying for1 unless it causes vibration in the air4 #ab4 ,some holidays are tiresome4 #ac4 ,englishmen are not ,frenchmen4 #ad4 ,no photograph of a lady is satisfactory4 #ae4 ,no one looks poetical unless he is phlegmatic4 #af4 ,some thin persons are not cheerful4 #ag4 ,some judges do not exercise self-control4 #ah4 ,pigs are not fed on barley-water4 #ai4 ,some black rabbits are not old4 pg#abi #bj4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ba4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #bb4 ,some lessons need attention4 #bc4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #bd4 ,no one1 who forgets a promise1 fails to do mischief4 #be4 ,some greedy creatures cannot fly4 #bf4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #bg4 ,no bride-cakes are things that need not be avoided4 #bh4 ,john is happy4 #bi4 ,some people1 who are not gamblers1 are not philosophers4 #cj4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ca4 ,none of my lodgers write poetry4 #cb4 ,senna is not nice4 #cc4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #cd4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ce4 ,logic is unintelligible4 #cf4 ,some wild creatures are fat4 #cg4 ,all wasps are unwelcome4 #ch4 ,all black rabbits are young4 #ci4 ,some hard-boiled things can be cracked4 #dj4 ,no antelopes fail to delight the eye4 #da4 ,all well-fed canaries are cheerful4 #db4 ,some poetry is not producible at will4 #dc4 ,no country infested by dragons fails to be fascinating4 #dd4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #de4 ,some picturesque things are not made of sugar4 #df4 ,no children can sit still4 #dg4 ,some cats cannot whistle4 #dh4 ,you are terrible4 #di4 ,some oysters are not amusing4 #ej4 ,nobody in the house has a beard a yard long4 #ea4 ,some ill-fed canaries are unhappy4 #eb4 ,my sisters cannot sing4 #ec4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ed4 ,some rich things are nice4 #ee4 ,my cousins are none of them judges1 and judges are none of them cousins of mine4 #ef4 ,something wearisome is not eagerly wished for4 #eg4 ,senna is nasty4 #eh4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ei4 ,niggers are not any of them tall4 #fj4 ,some obstinate persons are not philosophers4 #fa4 ,john is happy4 #fb4 ,some unwholesome dishes are not present here 7i4e4 cannot be spoken of as these74 #fc4 ,no books suit feverish patients unless they make one drowsy4 #fd4 ,some greedy creatures cannot fly4 #fe4 ,you and ,i can detect a sharper4 #ff4 ,some dreams are not lambs4 pg#acj #fg4 ,no lizard needs a hairbrush4 #fh4 ,some things1 that may escape notice1 are not battles4 #fi4 ,my cousins are not any of them judges4 #gj4 ,some hard-boiled things can be cracked4 #ga4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #gb4 ,she is unpopular4 #gc4 ,some people1 who wear wigs1 are not children of yours4 #gd4 ,no lobsters expect impossibilities4 #ge4 ,no nightmare is eagerly desired4 #gf4 ,some nice things are not plumcakes4 #gg4 ,some kinds of jam need not be shunned4 #gh4 ,all ducks are ungraceful4 #gi4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #hj4 ,no man1 who begs in the street1 should fail to keep accounts4 #ha4 ,some savage creatures are not spiders4 #hb4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #hc4 ,no travelers1 who do not carry plenty of small change1 fail to lose their luggage4 #hd4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #he4 ,judges are none of them cousins of mine4 #hf4 ,all my lodgers are sane4 #hg4 ,those who are busy are contented1 and discontented people are not busy4 #hh4 ,none of my cousins are judges4 #hi4 ,no nightingale dislikes sugar4 #ij4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ia4 ,some excuses are not clear explanations4 #ib4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ic4 ,no kind deed need cause scruple4 #id4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ie4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #if4 ,no cheats are trustworthy4 #ig4 ,no clever child of mine is greedy4 #ih4 ,some things1 that are meant to amuse1 are not ,acts of ,parliament4 #ii4 ,no tour1 that is ever forgotten1 is worth writing a book about4 #ajj4 ,no obedient child of mine is contented4 #aja4 ,your visit does not annoy me4 ,answers to #f4 ,,an#f #a4 ,conclusion right4 #b4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #c4 ,concl4 right4 #d4 ,concl4 right4 #e4 ,concl4 right4 #f4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #g4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #h4 ,concl4 right4 #i4 ,concl4 right4 #aj4 ,concl4 right4 #aa4 ,concl4 right4 #ab4 ,concl4 right4 #ac4 ,concl4 right4 #ad4 ,concl4 right4 #ae4 ,concl4 right4 pg#aca #af4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ag4 ,concl4 right4 #ah4 ,concl4 right4 #ai4 ,concl4 right4 #bj4 ,concl4 right4 #ba4 ,concl4 right4 #bb4 ,concl4 wrong3 the right one is ,some x are y4 #bc4 ,concl4 right4 #bd4 ,concl4 right4 #be4 ,concl4 right4 #bf4 ,concl4 right4 #bg4 ,concl4 right4 #bh4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #bi4 ,concl4 right4 #cj4 ,concl4 right4 #ca4 ,concl4 right4 #cb4 ,concl4 right4 #cc4 ,concl4 right4 #cd4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ce4 ,concl4 right4 #cf4 ,concl4 right4 #cg4 ,concl4 right4 #ch4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ci4 ,concl4 right4 #dj4 ,concl4 right4 ,answers to #g4 ,,an#g #a4 ,concl4 right4 #b4 ,concl4 right4 #c4 ,concl4 right4 #d4 ,concl4 wrong3 right one is ,some epicures are not uncles of mine4 #e4 ,concl4 right4 #f4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #g4 ,concl4 wrong3 right one is ,the publication1 in which ,i saw it1 tells lies4 #h4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #i4 ,concl4 wrong3 right one is ,some tedious songs are not his4 #aj4 ,concl4 right4 #aa4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ab4 ,concl4 wrong3 right one is ,some fierce creatures do not drink coffee4 #ac4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ad4 ,concl4 right4 #ae4 ,concl4 wrong3 right one is ,some shallow persons are not students4 #af4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ag4 ,concl4 wrong3 right one is ,some business1 other than railways1 is unprofitable4 #ah4 ,concl4 wrong3 right one is ,some vain persons are not ,professors4 #ai4 ,concl4 right4 #bj4 ,concl4 wrong3 right one is ,wasps are not puppies4 #ba4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #bb4 ,no ,concl4 ,same ,fallacy4 #bc4 ,concl4 right4 #bd4 ,concl4 wrong3 right one is ,some chocolate-creams are delicious4 #be4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #bf4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #bg4 ,concl4 wrong3 right one is ,some pillows are not pokers4 #bh4 ,concl4 right4 #bi4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #cj4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #ca4 ,concl4 right4 #cb4 ,no ,concl4 ,fallacy of ,like ,eliminands not asserted to exist4 #cc4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 pg#acb #cd4 ,concl4 wrong3 right one is ,some dreaded persons are not begged to prolong their visits4 #ce4 ,concl4 wrong3 right one is ,no man walks on neither4 #cf4 ,concl4 right4 #cg4 ,no ,concl4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ch4 ,concl4 wrong3 right one is ,some persons1 dreaded by children1 are not emperors4 #ci4 ,concl4 incomplete3 the omitted portion is ,sugar is not salt4 #dj4 ,concl4 right4 ,answers to #h4 ,,an#h #a4 a#a;b#j b#a;a#j4 #b4 d#a;a#j4 #c4 ac#j4 #d4 a#a;d#j4 #e4 cd#j4 #f4 d#a;c#j4 #g4 a'c#j4 #h4 c#a;a'#j4 #i4 c'd#j4 #aj4 b#a;a#j4 #aa4 d#a;b#j4 #ab4 a'd#j4 #ac4 e#a;b#j4 #ad4 d#a;e'#j4 #ae4 e#a;a'#j4 #af4 b'c#j4 #ag4 a#a;b#j4 #ah4 d#a;c#j4 #ai4 a#a;d#j4 #bj4 ac#j4 #ba4 de#j4 #bb4 a#a;b'#j4 #bc4 h#a;c#j4 #bd4 e#a;a#j4 #be4 e#a;c'#j4 #bf4 e#a;c'#j4 #bg4 hk'#j4 #bh4 e#a;d'#j4 #bi4 l'a#j4 #cj4 k#a;b'#j4 ,answers to #i4 ,,an#i #a4 ,babies cannot manage crocodiles4 #b4 ,your presents to me are not made of tin4 #c4 ,all my potatoes in this dish are old ones4 #d4 ,my servants never say shpoonj4 #e4 ,my poultry are not officers4 #f4 ,none of your sons are fit to serve on a jury4 #g4 ,no pencils of mine are sugar-plums4 #h4 ,jenkins is inexperienced4 #i4 ,no comet has a curly tail4 #aj4 ,no hedge-hog takes in the ,times4 #aa4 ,this dish is unwholesome4 #ab4 ,my gardener is very old4 #ac4 ,all humming-birds are small4 #ad4 ,no one with a hooked nose ever fails to make money4 #ae4 ,no gray ducks in this village wear lace collars4 #af4 ,no jug in this cupboard will hold water4 #ag4 ,these apples were grown in the sun4 #ah4 ,puppies1 that will not lie still1 never care to do worsted work4 #ai4 ,no name in this list is unmelodious4 #bj4 ,no ,m4,p4 should ride in a donkey-race1 unless he has perfect self-command4 #ba4 ,no goods in this shop1 that are still on sale1 may be carried away4 pg#acc #bb4 ,no acrobatic feat1 which involves turning a quadruple somersault1 is ever attempted in a circus4 #bc4 ,guinea-pigs never really appreciate ,beethoven4 #bd4 ,no scentless flowers please me4 #be4 ,showy talkers are not really well-informed4 #bf4 ,none but red-haired boys learn ,greek in this school4 #bg4 ,wedding-cake always disagrees with me4 #bh4 ,discussions1 that go on while ,tomkins is in the chair1 endanger the peacefulness of our ,debating-,club4 #bi4 ,all gluttons1 who are children of mine1 are unhealthy4 #cj4 ,an egg of the ,great ,auk is not to be had for a song4 #ca4 ,no books sold here have gilt edges1 unless they are priced at #es4 and upwards4 #cb4 ,when you cut your finger1 you will find ,tincture of ,calendula useful4 #cc4 ,i have never come across a mermaid at sea4 #cd4 ,all the romances in this library are well-written4 #ce4 ,no bird in this aviary lives on mince-pies4 #cf4 ,no plum-pudding1 that has not been boiled in a cloth1 can be distinguished from soup4 #cg4 ,all your poems are uninteresting4 #ch4 ,none of my peaches have been grown in a hot-house4 #ci4 ,no pawnbroker is dishonest4 #dj4 ,no kitten with green eyes will play with a gorilla4 #da4 ,all my friends dine at the lower table4 #db4 ,my writing-desk is full of live scorpions4 #dc4 ,no ,mandarin ever reads ,hogg's poems4 #dd4 ,shakespeare was clever4 #de4 ,rainbows are not worth writing odes to4 #df4 ,these ,sorites-examples are difficult4 #dg4 ,all my dreams come true4 #dh4 ,all the ,english pictures here are painted in oils4 #di4 ,donkeys are not easy to swallow4 #ej4 ,opium-eaters never wear white kid gloves4 #ea4 ,a good husband always comes home for his tea4 #eb4 ,bathing-machines are never made of mother-of-pearl4 #ec4 ,rainy days are always cloudy4 #ed4 ,no heavy fish is unkind to children4 #ee4 ,no engine-driver lives on barley-sugar4 #ef4 ,all the animals in the yard gnaw bones4 #eg4 ,no badger can guess a conundrum4 #eh4 ,no cheque of yours1 received by me1 is payable to order4 #ei4 ,i cannot read any of ,brown's letters4 #fj4 ,i always avoid a kangaroo4 pg#acd ,,chapter ,,iii4 ,,solutions4 #a4 ,propositions of ,relation reduced to normal form4 ,solutions for #a4 ,,sl#a #a4 ,the ,univ4 is persons4 ,the ,individual ,i may be regarded as a ,class1 of persons1 whose peculiar ,attribute is represented by the ,name ',i'1 and may be called the ,class of ,i's4 ,it is evident that this ,class cannot possibly contain more than one ,member3 hence the ,sign of ,quantity is all4 ,the verb have been may be replaced by the phrase are persons who have been4 ,the ,proposition may be written thus3-- ,all ,sign of ,quantity4 ,i's ,subject4 are ,copula4 persons who have been out for a walk ,predicate4 or1 more briefly1 ,all ,i's are persons who have been out for a walk4 #b4 ,the ,univ4 and the ,subject are the same as in ,ex4 #a4 ,the ,proposition may be written ,all ,i's are persons who feel better4 #c4 ,univ4 is persons4 ,the ,subject is evidently the ,class of persons from which ,john is excluded2 i4e4 it is the ,class containing all persons who are not ,john4 ,the ,sign of ,quantity is no4 ,the verb has read may be replaced by the phrase are persons who have read4 ,the ,proposition may be written ,no persons who are not ',john' are persons who have read the letter4 #d4 ,univ4 is persons4 ,the ,subject is evidently the ,class of persons whose only two ,members are you and ,i4 ,hence the ,sign of ,quantity is no4 ,the ,proposition may be written ,no ,members of the ,class 'you and ,i' are old persons4 pg#ace #e4 ,univ4 is creatures4 ,the verb run well may be replaced by the phrase are creatures that run well4 ,the ,proposition may be written ,no fat creatures are creatures that run well4 #f4 ,univ4 is persons4 ,the ,subject is evidently the ,class of persons who are not brave4 ,the verb deserve may be replaced by the phrase are deserving of4 ,the ,proposition may be written ,no not-brave persons are persons deserving of the fair4 #g4 ,univ4 is persons4 ,the phrase looks poetical evidently belongs to the ,predicate2 and the ,subject is the ,class1 of persons1 whose peculiar ,attribute is not-pale4 ,the ,proposition may be written ,no not-pale persons are persons who look poetical4 #h4 ,univ4 is persons4 ,the ,proposition may be written ,some judges are persons who lose their tempers4 #i4 ,univ4 is persons4 ,the phrase never neglect is merely a stronger form of the phrase am a person who does not neglect4 ,the ,proposition may be written ,all ',i's' are persons who do not neglect important business4 #aj4 ,univ4 is things4 ,the phrase what is difficult 7i4e4 that which is difficult7 is equivalent to the phrase all difficult things4 ,the ,proposition may be written ,all difficult things are things that need attention4 #aa4 ,univ4 is things4 ,the phrase what is unwholesome may be interpreted as in ,ex4 #aj4 ,the ,proposition may be written ,all unwholesome things are things that should be avoided4 #ab4 ,univ4 is laws4 ,the ,predicate is evidently a ,class whose peculiar ,attribute is relating to excise4 ,the ,proposition may be written ,all laws passed last week are laws relating to excise4 #ac4 ,univ4 is things4 ,the ,subject is evidently the ,class1 of studies1 whose peculiar ,attribute is logical2 hence the ,sign of ,quantity is all4 ,the ,proposition may be written ,all logical studies are things that puzzle me4 #ad4 ,univ4 is persons4 ,the ,subject is evidently persons in the house4 ,the ,proposition may be written ,no persons in the house are ,jews4 #ae4 ,univ4 is dishes4 ,the phrase if not well-cooked is equivalent to the ,attribute not well-cooked4 ,the ,proposition may be written ,some not well-cooked dishes are unwholesome dishes4 pg#acf #af4 ,univ4 is books4 ,the phrase make one drowsy may be replaced by the phrase are books that make one drowsy4 ,the ,sign of ,quantity is evidently all4 ,the ,proposition may be written ,all unexciting books are books that make one drowsy4 #ag4 ,univ4 is men4 ,the ,subject is evidently a man who knows what he's about2 and the word when shows that the ,proposition is asserted of every such man1 i4e4 of all such men4 ,the verb can may be replaced by are men who can4 ,the ,proposition may be written ,all men who know what they're about are men who can detect a sharper4 #ah4 ,the ,univ4 and the ,subject are the same as in ,ex4 #d4 ,the ,proposition may be written ,all ,members of the ,class 'you and ,i' are persons who know what they're about4 #ai4 ,univ4 is persons4 ,the verb wear may be replaced by the phrase are accustomed to wear4 ,the ,proposition may be written ,some bald persons are persons accustomed to wear wigs4 #bj4 ,univ4 is persons4 ,the phrase never talk is merely a stronger form of are persons who do not talk4 ,the ,proposition may be written ,all fully occupied persons are persons who do not talk about their grievances4 #ba4 ,univ4 is riddles4 ,the phrase if they can be solved is equivalent to the ,attribute that can be solved4 ,the ,proposition may be written ,no riddles that can be solved are riddles that interest me4 #b4 ,method of ,diagrams4 ,solutions for #d1 ,nos4 #a-ab4 ,,sl#d-;,a --------------- ------- #a4 ,no m are x'2 7,o7 ,all m' are y4 ------ ------ 7,o7 7,i7--------- ------- 7,o77,o7 ------ 4'4 ,no x' are y'4 7,o7 --------------- pg#acg --------------- ------- #b4 ,no m' are x2 7,o7 7,o7 ,some m' are y'4 ------ ------ 7,i7 ------------ ------- ------ 4'4 ,some x are y'4 7,i7 --------------- --------------- ------- #c4 ,all m' are x2 7,o7 7,i7 7,i7 ,all m' are y'4 ------ ------ ------------ ------- ------ 4'4 ,some x are y'4 7,o7 7,o7 --------------- --------------- #d4 ,no x' are m'2 7,o7 ,all y' are m4 ------ ------7,i7--- ,there is no ,conclusion4 ------ 7,o7 7,o7 --------------- --------------- ------- #e4 ,some m are x'2 ,no y are m4 ------ ------ 7,o7 7,i7 ------------ ------- 7,o77,i7 ------ 4'4 ,some x' are y'4 --------------- --------------- #f4 ,no x' are m2 ,no m are y4 ------ 7,o7 ------------ ,there is no ,conclusion4 7,o77,o7 ------ --------------- --------------- ------- #g4 ,no m are x'2 7,i7 ,some y' are m4 ------ ------ 7,i7 ------------ ------- 7,o77,o7 ------ 4'4 ,some x are y'4 --------------- --------------- ------- #h4 ,all m' are x'2 7,o7 7,o7 ,no m' are y4 ------ ------ 7,i7 ------------ ------- ------ 4'4 ,some x' are y'4 7,o7 7,i7 --------------- pg#ach --------------- #i4 ,some x' are m'2 ,no m are y'4 ------ 7,o7 ------------ ,there is no ,conclusion4 7,o7 ------ 7,i7 --------------- --------------- ------- #aj4 ,all x are m2 7,o7 7,o7 7,i77,o7 ,all y' are m'4 ------ ------ 7,i77,o7 7,i7 ------------ ------- 7,o7 ------ 4'4 ,all x are y2 7,i7 ,all y' are x'4 --------------- --------------- #aa4 ,no m are x2 ,all y' are m'4 ------ 7,o77,o7 ---------7,i7 ,there is no ,conclusion4 7,o7 ------ --------------- --------------- ------- #ab4 ,no x are m2 7,o7 7,o7 ,all y are m4 ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 ,all y are x'4 7,o7 --------------- ,solutions for #e1 ,nos4 #a-ab4 ,,sl#e-;,a #a4 ,i have been out for a walk2 ,i am feeling better4 ,univ4 is persons2 m the ,class of ,i's2 x persons who have been out for a walk2 y persons who are feeling better4 --------------- ------- ,all m are x2 7,i7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,some x are y4 --------------- i4e4 ,somebody1 who has been out for a walk1 is feeling better4 pg#aci #b4 ,no one has read the letter but ,john2 ,no one1 who has not read it1 knows what it is about4 ,univ4 is persons2 m persons who have read the letter2 x the ,class of ,johns2 y persons who know what the letter is about4 --------------- ------- ,no x' are m2 7,o7 ,no m' are y4 ------ ------ 7,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- i4e4 ,no one1 but ,john1 knows what the letter is about4 #c4 ,those who are not old like walking2 ,you and ,i are young4 ,univ4 is persons2 m old2 x persons who like walking2 y you and ,i4 --------------- ------- ,all m' are x2 7,i7 7,i7 ,all y are m'4 ------ ------ 7,o7 7,o7 ------------ ------- 7,o7 ------ 4'4 ,all y are x4 7,o7 7,o7 --------------- i4e4 ,you and ,i like walking4 #d4 ,your course is always honest2 ,your course is always the best policy4 ,univ4 is courses2 m your2 x honest2 y courses which are the best policy4 --------------- ------- ,all m are x2 7,i7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,some x are y4 --------------- i4e4 ,honesty is sometimes the best policy4 #e4 ,no fat creatures run well2 ,some greyhounds run well4 ,univ4 is creatures2 m creatures that run well2 x fat2 y greyhounds4 --------------- ------- ,no x are m2 ,some y are m4 ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 ,some y are x'4 --------------- i4e4 ,some greyhounds are not fat4 pg#adj #f4 ,some1 who deserve the fair1 get their deserts2 ,none but the brave deserve the fair4 ,univ4 is persons2 m persons who deserve the fair2 x persons who get their deserts2 y brave4 --------------- ------- ,some m are x2 7,i7 ,no y' are m4 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,some y are x4 --------------- i4e4 ,some brave persons get their deserts4 #g4 ,some ,jews are rich2 ,all ,esquimaux are ,gentiles4 ,univ4 is persons2 m ,jews2 x rich2 y ,esquimaux4 --------------- ------- ,some m are x2 7,i7 ,all y are m'4 ------ ------ 7,o77,i7 7,i7--------- ------- 7,o7 ------ 4'4 ,some x are y'4 --------------- i4e4 ,some rich persons are not ,esquimaux4 #h4 ,sugar-plums are sweet2 ,some sweet things are liked by children4 ,univ4 is things2 m sweet2 x sugar-plums2 y things that are liked by children4 --------------- ,all x are m2 7,o7 7,o7 ,some m are y4 ------ 7,i7 ---7,i7------ ------ --------------- ,there is no ,conclusion4 #i4 ,john is in the house2 ,everybody in the house is ill4 ,univ4 is persons2 m persons in the house2 x the ,class of ,johns2 y ill4 --------------- ------- ,all x are m2 7,o7 7,o7 7,i77,o7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,all x are y4 --------------- i4e4 ,john is ill4 pg#ada #aj4 ,umbrellas are useful on a journey2 ,what is useless on a journey should be left behind4 ,univ4 is things2 m useful on a journey2 x umbrellas2 y things that should be left behind4 --------------- ------- ,all x are m2 7,o7 7,o7 ,all m' are y4 ------ ------ 7,i7 7,i7 ------------ ------- ------ 4'4 ,some x' are y4 7,i7 7,o7 --------------- i4e4 ,some things1 that are not umbrellas1 should be left behind on a journey4 #aa4 ,audible music causes vibration in the air2 ,inaudible music is not worth paying for4 ,univ4 is music2 m audible2 x music that causes vibration in the air2 y worth paying for4 --------------- ------- ,all m are x2 7,o7 ,all m' are y'4 ------ ------ 7,i7 7,o7 ---------7,i7 ------- 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- i4e4 ,no music is worth paying for1 unless it causes vibration in the air4 #ab4 ,some holidays are rainy2 ,rainy days are tiresome4 ,univ4 is days2 m rainy2 x holidays2 y tiresome4 --------------- ------- ,some x are m2 7,i7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,some x are y4 --------------- i4e4 ,some holidays are tiresome4 ,solutions for #f1 ,nos4 #a-aj4 ,,sl#f-;,a #a4 ,some x are m2 ,no m are y'4 ,some x are y4 --------------- ------- 7,i7 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ ,hence proposed ,conclusion is right4 --------------- pg#adb #b4 ,all x are m2 ,no y are m'4 ,no y are x'4 --------------- 7,o7 7,o7 ------ 7,i7 ------------ ,there is no ,conclusion4 ------ 7,o7 --------------- #c4 ,some x are m'2 ,all y' are m4 ,some x are y4 --------------- ------- 7,i7 7,o7 7,i7 ------ ------ ------7,i7--- ------- ------ ,hence proposed ,conclusion is right4 7,o7 --------------- #d4 ,all x are m2 ,no y are m4 ,all x are y'4 --------------- ------- 7,o7 7,o7 7,o77,i7 ------ ------ 7,o77,i7 ------------ ------- 7,o7 ------ ,hence proposed ,conclusion is right4 --------------- #e4 ,some m' are x'2 ,no m' are y4 ,some x' are y'4 --------------- ------- 7,o7 ------ ------ 7,i7 ------------ ------- ------ ,hence proposed ,conclusion is right4 7,o7 7,i7 --------------- #f4 ,no x' are m2 ,all y are m'4 ,all y are x4 --------------- ------ 7,o7 7,i7--------- ,there is no ,conclusion4 7,o77,o7 ------ --------------- pg#adc #g4 ,some m' are x'2 ,all y' are m'4 ,some x' are y'4 --------------- ------ 7,o7 ---------7,i7 ,there is no ,conclusion4 7,o7 ------ 7,i7 --------------- #h4 ,no m' are x'2 ,all y' are m'4 ,all y' are x4 --------------- ------- 7,i7 7,i7 ------ ------ 7,o7 7,o7 ------------ ------- 7,o7 ------ ,hence proposed ,conclusion is right4 7,o7 7,o7 --------------- #i4 ,some m are x'2 ,no m are y4 ,some x' are y'4 --------------- ------- ------ ------ 7,o7 7,i7 ------------ ------- 7,o77,i7 ------ ,hence proposed ,conclusion is right4 --------------- #aj4 ,all m' are x'2 ,all m are y4 ,some y are x'4 --------------- ------- 7,o7 7,o7 ------ ------ 7,i7 ------------ ------- ------ ,hence proposed ,conclusion is right4 7,i7 7,o7 --------------- pg#add ,solutions for #g1 ,nos4 #a-f4 ,,sl#g-;,a #a4 ,no doctors are enthusiastic2 ,you are enthusiastic4 ,you are not a doctor4 ,univ4 persons2 m enthusiastic2 x doctors2 y you4 --------------- ------- 7,o7 7,o7 ------ ------ ,no x are m2 7,o77,o7 7,i7 ,all y are m4 ------------ ------- ,all y are x'4 7,i7 ------ 4'4 ,all y are x'4 7,o7 --------------- ,hence proposed ,conclusion is right4 #b4 ,all dictionaries are useful2 ,useful books are valuable4 ,dictionaries are valuable4 ,univ4 books2 m useful2 x dictionaries2 y valuable4 --------------- ------- 7,o7 7,o7 7,i77,o7 ------ ------ ,all x are m2 7,i77,o7 ,all m are y4 ------------ ------- ,all x are y4 7,o7 ------ 4'4 ,all x are y4 --------------- ,hence proposed ,conclusion is right4 #c4 ,no misers are unselfish2 ,none but misers save egg-shells4 ,no unselfish people save egg-shells4 ,univ4 people2 m misers2 x selfish2 y people who save egg-shells4 --------------- ------- 7,o7 ------ ------ ,no m are x'2 7,o7 ,no m' are y4 ------------ ------- ,no x' are y4 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- ,hence proposed ,conclusion is right4 pg#ade #d4 ,some epicures are ungenerous2 ,all my uncles are generous4 ,my uncles are not epicures4 ,univ4 persons2 m generous2 x epicures2 y my uncles4 --------------- ------- 7,o7 7,i7 7,i7 ------ ------ ,some x are m'4 ,all y are m4 ---7,i7------ ------- ,all y are x'4 ------ 4'4 ,some x are y'4 7,o7 --------------- ,hence proposed ,conclusion is wrong1 the right one being ,some epicures are not uncles of mine4 #e4 ,gold is heavy2 ,nothing but gold will silence him4 ,nothing light will silence him4 ,univ4 things2 m gold2 x heavy2 y able to silence him4 --------------- ------- 7,o7 ------ ------ ,all m are x2 7,i7 7,o7 ,no m' are y4 ------------ ------- ,no x' are y4 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- ,hence proposed ,conclusion is right4 #f4 ,some healthy people are fat2 ,no unhealthy people are strong4 ,some fat people are not strong4 ,univ4 persons2 m healthy2 x fat2 y strong4 --------------- 7,o7 ------ ,some m are x2 7,i7 ,no m' are y4 ------------ ,there is no ,conclusion4 ,some x are y'4 ------ 7,o7 --------------- pg#adf #c4 ,method of ,subscripts4 ,solutions for #d4 ,,sl#d-;,b #a4 mx'#j m'#ay'#j x'y'#j ,fig4 ,i4 i4e4 ,no x' are y'4 #b4 m'x#j m'y'#a x'y'#a ,fig4 ,,ii4 i4e4 ,some x' are y'4 #c4 m'#ax'#j m'#ay#j xy'#a ,fig4 ,,iii4 i4e4 ,some x are y'4 #d4 x'm'#j y'#am'#j nothing4 ,fallacy of ,like ,eliminands not asserted to exist4 #e4 mx'#a ym#j x'y'#a ,fig4 ,,ii4 i4e4 ,some x' are y'4 #f4 x'm#j my#j nothing4 ,fallacy of ,like ,eliminands not asserted to exist4 #g4 mx'#j y'm#a xy'#a ,fig4 ,,ii4 i4e4 ,some x are y'4 #h4 m'#ax#j m'y#j x'y'#a ,fig4 ,,iii4 i4e4 ,some x' are y'4 #i4 x'm'#a my#j nothing4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #aj4 x#am'#j y'#am#j x#ay'#j y'#ax#j ,fig4 ,i 7b74 i4e4 ,all x are y1 and all y' are x'4 #aa4 mx#j y'#am#j nothing4#a ,fallacy of ,like ,eliminands not asserted to exist4 #ab4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,all y are x'4 #ac4 m'#ax'#j ym#j x'y#j ,fig4 ,i4 i4e4 ,no x' are y4 #ad4 m#ax'#j m'#ay'#j x'y'#j ,fig4 ,i4 i4e4 ,no x' are y'4 #ae4 xm#j m'y#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 #af4 x#am#j y#am'#j 7x#ay#j y#ax#j7 ,fig4 ,i 7b74 i4e4 ,all x are y' and all y are x'4 #ag4 xm#j m'#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no x are y'4 #ah4 xm'#j my#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 #ai4 m#ax'#j m#ay#j xy'#a ,fig4 ,,iii4 i4e4 ,some x are y'4 #bj4 mx#j m'#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no x are y'4 #ba4 x#am'#j m'y#a x'y#a ,fig4 ,,ii4 i4e4 ,some x' are y4 #bb4 xm#a y#am'#j nothing4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #bc4 m#ax'#j ym#a xy#a ,fig4 ,,ii4 i4e4 ,some x are y4 #bd4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,all y are x'4 #be4 mx'#a my'#j x'y#a ,fig4 ,,ii4 i4e4 ,some x' are y4 #bf4 mx'#j y#am'#j y#ax'#j ,fig4 ,i 7a74 i4e4 ,all y are x4 #bg4 x#am#j y'#am'#j 7x#ay'#j y'#ax#j7 ,fig4 ,i 7b74 i4e4 ,all x are y1 and all y' are x'4 #bh4 m#ax#j my#a x'y#a ,fig4 ,,ii4 i4e4 ,some x' are y4 #bi4 mx#j y#am#j nothing4 ,fallacy of ,like ,eliminands not asserted to exist4 #cj4 x#am#j ym#a x'y#a ,fig4 ,,ii4 i4e4 ,some y are x'4 #ca4 x#am'#j y#am'#j nothing4 ,fallacy of ,like ,eliminands not asserted to exist4 pg#adg #cb4 xm'#j m#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no x are y'4 #cc4 mx#j my#j nothing4 ,fallacy of ,like ,eliminands not asserted to exist4 #cd4 mx'#j ym#a xy#a ,fig4 ,,ii4 i4e4 ,some x are y4 #ce4 mx#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,all y are x'4 #cf4 m#ax#j ym#a x'y#a ,fig4 ,,ii4 i4e4 ,some x' are y4 #cg4 m#ax'#j ym#j xy'#a ,fig4 ,,iii4 i4e4 ,some x are y'4 #ch4 mx#j m'y#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 #ci4 mx'#a my#j x'y'#a ,fig4 ,,ii4 i4e4 ,some x' are y'4 #dj4 x'm#j y'#am'#j y'#ax'#j ,fig4 ,i 7a74 i4e4 ,all y' are x4 #da4 x#am#j ym'#j x#ay#j ,fig4 ,i 7a74 i4e4 ,all x are y'4 #db4 m'x#j ym#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 ,solutions for #e1 ,nos4 #ac-bd4 ,,sl#e-;,b #ac4 ,no ,frenchmen like plumpudding2 ,all ,englishmen like plumpudding4 ,univ4 men2 m liking plumpudding2 x ,french2 y ,english4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,englishmen are not ,frenchmen4 #ad4 ,no portrait of a lady1 that makes her simper or scowl1 is satisfactory2 ,no photograph of a lady ever fails to make her simper or scowl4 ,univ4 portraits of ladies2 m making the subject simper or scowl2 x satisfactory2 y photographic4 mx#j ym'#j xy#j ,fig4 ,i4 i4e4 ,no photograph of a lady is satisfactory4 #ae4 ,all pale people are phlegmatic2 ,no one looks poetical unless he is pale4 ,univ4 people2 m pale2 x phlegmatic2 y looking poetical4 m#ax'#j m'y#j x'y#j ,fig4 ,i4 i4e4 ,no one looks poetical unless he is phlegmatic4 #af4 ,no old misers are cheerful2 ,some old misers are thin4 ,univ4 persons2 m old misers2 x cheerful2 y thin4 mx#j my#a x'y#a ,fig4 ,,ii4 i4e4 ,some thin persons are not cheerful4 #ag4 ,no one1 who exercises self-control1 fails to keep his temper2 ,some judges lose their tempers4 ,univ4 persons2 m keeping their tempers2 x exercising self-control2 y judges4 xm'#j ym'#a x'y#a ,fig4 ,,ii4 i4e4 ,some judges do not exercise self-control4 pg#adh #ah4 ,all pigs are fat2 ,nothing that is fed on barley-water is fat4 ,univ4 is things2 m fat2 x pigs2 y fed on barley-water4 x#am'#j ym#j x#ay#j ,fig4 ,i 7a74 i4e4 ,pigs are not fed on barley-water4 #ai4 ,all rabbits1 that are not greedy1 are black2 ,no old rabbits are free from greediness4 ,univ4 is rabbits2 m greedy2 x black2 y old4 m'#ax'#j ym'#j xy'#a ,fig4 ,,iii4 i4e4 ,some black rabbits are not old4 #bj4 ,some pictures are not first attempts2 ,no first attempts are really good4 ,univ4 is things2 m first attempts2 x pictures2 y really good4 xm'#a my#j nothing4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ba4 ,i never neglect important business2 ,your business is unimportant4 ,univ4 is business2 m important2 x neglected by me2 y your4 mx#j y#am#j nothing4 ,fallacy of ,like ,eliminands not asserted to exist4 #bb4 ,some lessons are difficult2 ,what is difficult needs attention4 ,univ4 is things2 m difficult2 x lessons2 y needing attention4 xm#a m#ay'#j xy#a ,fig4 ,,ii4 i4e4 ,some lessons need attention4 #bc4 ,all clever people are popular2 ,all obliging people are popular4 ,univ4 is people2 m popular2 x clever2 y obliging4 x#am'#j y#am'#j nothing4 ,fallacy of ,like ,eliminands not asserted to exist4 #bd4 ,thoughtless people do mischief2 ,no thoughtful person forgets a promise4 ,univ4 is persons2 m thoughtful2 x mischievous2 y forgetful of promises4 m'#ax'#j my#j x'y#j i4e4 ,no one1 who forgets a promise1 fails to do mischief4 ,solutions for #f4 ,,sl#f-;,b #a4 xm#a my'#j xy#a ,fig4 ,,ii4 ,concl4 right4 #b4 x#am'#j ym'#j ,fallacy of ,like ,eliminands not asserted to exist4 #c4 xm'#a y'#am'#j xy#a ,fig4 ,,ii4 ,concl4 right4 pg#adi #d4 x#am'#j ym#j x#ay#j ,fig4 ,i 7a74 ,concl4 right4 #e4 m'x'#a m'y#j x'y'#a ,fig4 ,,ii4 #f4 x'm#j y#am#j ,fallacy of ,like ,eliminands not asserted to exist4 #g4 m'x'#a y'#am#j ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #h4 m'x'#j y'#am#j y'#ax'#j ,fig4 ,i 7a74 ,concl4 right4 #i4 mx'#a my#j x'y'#a ,fig4 ,,ii4 #aj4 m'#ax#j m'#ay'#j x'y#a ,fig4 ,,iii4 #aa4 x#am#j ym#a x'y#a ,fig4 ,,ii4 #ab4 xm#j m'y'#j xy'#j ,fig4 ,i4 #ac4 xm#j y'#am'#j y'#ax#j ,fig4 ,i 7a74 #ad4 m'#ax#j m'#ay'#j x'y#a ,fig4 ,,iii4 #ae4 mx'#a y#am#j x'y'#a ,fig4 ,,ii4 #af4 x'm#j y'#am#j ,fallacy of ,like ,eliminands not asserted to exist4 #ag4 m'x#j m'#ay#j x'y'#a ,fig4 ,,iii4 ,concl4 right4 #ah4 x'm#j my#a xy#a ,fig4 ,,ii4 #ai4 mx'#a m#ay'#j x'y#a #bj4 x'm'#j m'y'#a xy'#a #ba4 mx#j m#ay#j x'y'#a ,fig4 ,,iii4 #bb4 x'#am'#j ym'#a xy#a ,fig4 ,,ii4 ,concl4 wrong3 the right one is ,some x are y4 #bc4 m#ax'#j m'y'#j x'y'#j ,fig4 ,i4 ,concl4 right4 #bd4 x#am#j m'#ay'#j x#ay'#j ,fig4 ,i 7a74 #be4 xm'#j m#ay'#j xy'#j ,fig4 ,i4 #bf4 m#ax#j y#am'#j y#ax#j ,fig4 ,i 7a74 #bg4 x#am'#j my'#j x#ay'#j #bh4 x#am'#j y'm'#j ,fallacy of ,like ,eliminands not asserted to exist4 #bi4 x'm#j m'y'#j x'y'#j ,fig4 ,i4 ,concl4 right4 #cj4 x#am'#j m#ay#j x#ay#j ,fig4 ,i 7a74 #ca4 x'#am#j y'm'#j x'#ay'#j #cb4 xm#j y'm'#j xy'#j ,fig4 ,i4 #cc4 m#ax#j y'#am'#j y'#ax#j ,fig4 ,i 7a74 #cd4 x#am#j ym'#a ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ce4 xm#a m#ay'#j xy#a ,fig4 ,,ii4 ,concl4 right4 #cf4 m#ax#j y#am'#j y#ax#j ,fig4 ,i 7a74 #cg4 mx'#j m#ay#j xy'#a ,fig4 ,,iii4 #ch4 xm#j my'#j ,fallacy of ,like ,eliminands not asserted to exist4 #ci4 mx#j my'#a x'y'#a ,fig4 ,,ii4 ,concl4 right4 #dj4 mx'#j ym#a xy#a ,fig4 ,,ii4 pg#aej ,solutions for #g4 ,,sl#g-;,b #a4 ,no doctors are enthusiastic2 ,you are enthusiastic4 ,you are not a doctor4 ,univ4 persons2 m enthusiastic2 x doctors2 y you4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 ,conclusion right4 #b4 ,dictionaries are useful2 ,useful books are valuable4 ,dictionaries are valuable4 ,univ4 books2 m useful2 x dictionaries2 y valuable4 x#am'#j m#ay'#j x#ay'#j ,fig4 ,i 7a74 ,conclusion right4 #c4 ,no misers are unselfish2 ,none but misers save egg-shells4 ,no unselfish people save egg-shells4 ,univ4 people2 m misers2 x selfish2 y people who save egg-shells4 mx'#j m'y#j x'y#j ,fig4 ,i4 ,conclusion right4 #d4 ,some epicures are ungenerous2 ,all my uncles are generous4 ,my uncles are not epicures4 ,univ4 persons2 m generous2 x epicures2 y my uncles4 xm'#a y#am'#j xy'#a ,fig4 ,,ii4 ,conclusion wrong3 right one is ,some epicures are not uncles of mine4 #e4 ,gold is heavy2 ,nothing but gold will silence him4 ,nothing light will silence him4 ,univ4 things2 m gold2 x heavy2 y able to silence him4 m#ax'#j m'y#j x'y#j ,fig4 ,i4 ,conclusion right4 #f4 ,some healthy people are fat2 ,no unhealthy people are strong4 ,some fat people are not strong4 ,univ4 people2 m healthy2 x fat2 y strong4 mx#a m'y#j ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #g4 ,i saw it in a newspaper2 ,all newspapers tell lies4 ,it was a lie4 ,univ4 publications2 m newspapers2 x publications in which ,i saw it2 y telling lies4 x#am'#j m#ay'#j x#ay'#j ,fig4 ,i 7a74 ,conclusion wrong3 right one is ,the publication1 in which ,i saw it1 tells lies4 pg#aea #h4 ,some cravats are not artistic2 ,i admire anything artistic4 ,there are some cravats that ,i do not admire4 ,univ4 things2 m artistic2 x cravats2 y things that ,i admire4 xm#a m#ay#j ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #i4 ,his songs never last an hour4 ,a song1 that lasts an hour1 is tedious4 ,his songs are never tedious4 ,univ4 songs2 m lasting an hour2 x his2 y tedious4 x#am#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion wrong3 right one is ,some tedious songs are not his4 #aj4 ,some candles give very little light2 ,candles are meant to give light4 ,some things1 that are meant to give light1 give very little4 ,univ4 things2 m candles2 x giving c42 y meant c4 mx#a m#ay'#j xy#a ,fig4 ,,ii4 ,conclusion right4 #aa4 ,all1 who are anxious to learn1 work hard4 ,some of these boys work hard4 ,some of these boys are anxious to learn4 ,univ4 persons2 m hard-working2 x anxious to learn2 y these boys4 x#am'#j ym#a ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ab4 ,all lions are fierce2 ,some lions do not drink coffee4 ,some creatures that drink coffee are not fierce4 ,univ4 creatures2 m lions2 x fierce2 y creatures that drink coffee4 m#ax'#j my'#a xy'#a ,fig4 ,,ii4 ,conclusion wrong3 right one is ,some fierce creatures do not drink coffee4 #ac4 ,no misers are generous2 ,some old men are ungenerous4 ,some old men are misers4 ,univ4 persons2 m generous2 x misers2 y old men4 xm#j ym'#a ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ad4 ,no fossil can be crossed in love2 ,an oyster may be crossed in love4 ,oysters are not fossils4 ,univ4 things2 m things that can be crossed in love2 x fossils2 y oysters4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 ,conclusion right4 pg#aeb #ae4 ,all uneducated people are shallow2 ,students are all educated4 ,no students are shallow4 ,univ4 people2 m educated2 x shallow2 y students4 m'#ax'#j y#am'#j xy'#a ,fig4 ,,iii4 ,conclusion wrong3 right one is ,some shallow people are not students4 #af4 ,all young lambs jump2 ,no young animals are healthy1 unless they jump4 ,all young lambs are healthy4 ,univ4 young animals2 m young animals that jump2 x lambs2 y healthy4 x#am'#j m'y#j ,no ,conclusion4 ,fallacy of ,like ,eliminands not asserted to exist4 #ag4 ,ill-managed business is unprofitable2 ,railways are never ill-managed4 ,all railways are profitable4 ,univ4 business2 m ill-managed2 x profitable2 y railways4 m#ax#j y#am#j x'y'#a ,fig4 ,,iii4 ,conclusion wrong3 right one is ,some business1 other than railways1 is profitable4 #ah4 ,no ,professors are ignorant2 ,all ignorant people are vain4 ,no ,professors are vain4 ,univ4 people2 m ignorant2 x ,professors2 y vain4 xm#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion wrong3 right one is ,some vain persons are not ,professors4 #ai4 ,a prudent man shuns hynas4 ,no banker is imprudent4 ,no banker fails to shun hynas4 ,univ4 men2 m prudent2 x shunning hynas2 y bankers4 m#ax'#j ym'#j x'y#j ,fig4 ,i4 ,conclusion right4 #bj4 ,all wasps are unfriendly2 ,no puppies are unfriendly4 ,no puppies are wasps4 ,univ4 creatures2 m friendly2 x wasps2 y puppies4 x#am#j ym'#j x#ay#j ,fig4 ,i 7a74 ,conclusion incomplete3 complete one is ,wasps are not puppies4 #ba4 ,no ,jews are honest2 ,some ,gentiles are rich4 ,some rich people are dishonest4 ,univ4 persons2 m ,jews2 x honest2 y rich4 mx#j m'y#a ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 pg#aec #bb4 ,no idlers win fame2 ,some painters are not idle4 ,some painters win fame4 ,univ4 persons2 m idlers2 x persons who win fame2 y painters4 mx#j ym'#a ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #bc4 ,no monkeys are soldiers2 ,all monkeys are mischievous4 ,some mischievous creatures are not soldiers4 ,univ4 creatures2 m monkeys2 x soldiers2 y mischievous4 mx#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion right4 #bd4 ,all these bonbons are chocolate-creams2 ,all these bonbons are delicious4 ,chocolate-creams are delicious4 ,univ4 food2 m these bonbons2 x chocolate-creams2 y delicious4 m#ax'#j m#ay'#j xy#a ,fig4 ,,iii4 ,conclusion wrong1 being in excess of the right one1 which is ,some chocolate-creams are delicious4 #be4 ,no muffins are wholesome2 ,all buns are unwholesome4 ,buns are not muffins4 ,univ4 food2 m wholesome2 x muffins2 y buns4 xm#j y#am#j ,no ,conclusion4 ,fallacy of ,like ,eliminands not asserted to exist4 #bf4 ,some unauthorised reports are false2 ,all authorised reports are trustworthy4 ,some false reports are not trustworthy4 ,univ4 reports2 m authorised2 x true2 y trustworthy4 m'x'#a m#ay'#j ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #bg4 ,some pillows are soft2 ,no pokers are soft4 ,some pokers are not pillows4 ,univ4 things2 m soft2 x pillows2 y pokers4 xm#a ym#j xy'#a ,fig4 ,,ii4 ,conclusion wrong3 right one is ,some pillows are not pokers4 #bh4 ,improbable stories are not easily believed2 ,none of his stories are probable4 ,none of his stories are easily believed4 ,univ4 stories2 m probable2 x easily believed2 y his4 m'#ax#j ym#j xy#j ,fig4 ,i4 ,conclusion right4 pg#aed #bi4 ,no thieves are honest2 ,some dishonest people are found out4 ,some thieves are found out4 ,univ4 people2 m honest2 x thieves2 y found out4 xm#j m'y#a ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #cj4 ,no muffins are wholesome2 ,all puffy food is unwholesome4 ,all muffins are puffy4 ,univ4 is food2 m wholesome2 x muffins2 y puffy4 xm#j y#am#j ,no ,conclusion4 ,fallacy of ,like ,eliminands not asserted to exist4 #ca4 ,no birds1 except peacocks1 are proud of their tails2 ,some birds1 that are proud of their tails1 cannot sing4 ,some peacocks cannot sing4 ,univ4 birds2 m proud of their tails2 x peacocks2 y birds that cannot sing4 x'm#j my'#a xy'#a ,fig4 ,,ii4 ,conclusion right4 #cb4 ,warmth relieves pain2 ,nothing1 that does not relieve pain1 is useful in toothache4 ,warmth is useful in toothache4 ,univ4 applications2 m relieving pain2 x warmth2 y useful in toothache4 x#am'#j m'y#j ,no ,conclusion4 ,fallacy of ,like ,eliminands not asserted to exist4 #cc4 ,no bankrupts are rich2 ,some merchants are not bankrupts4 ,some merchants are rich4 ,univ4 persons2 m bankrupts2 x rich2 y merchants4 mx#j ym'#a ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #cd4 ,bores are dreaded2 ,no bore is ever begged to prolong his visit4 ,no one1 who is dreaded1 is ever begged to prolong his visit4 ,univ4 persons2 m bores2 x dreaded2 y begged to prolong their visits4 m#ax'#j my#j xy'#a ,fig4 ,,iii4 ,conclusion wrong3 the right one is ,some dreaded persons are not begged to prolong their visits4 #ce4 ,all wise men walk on their feet2 ,all unwise men walk on their hands4 ,no man walks on both4 ,univ4 men2 m wise2 x walking on their feet2 y walking on their hands4 m#ax'#j m'#ay'#j x'y'#j ,fig4 ,i4 ,conclusion wrong3 right one is ,no man walks on neither4 pg#aee #cf4 ,no wheelbarrows are comfortable2 ,no uncomfortable vehicles are popular4 ,no wheelbarrows are popular4 ,univ4 vehicles2 m comfortable2 x wheelbarrows2 y popular4 xm#j m'x#j xy#j ,fig4 ,i4 ,conclusion right4 #cg4 ,no frogs are poetical2 ,some ducks are unpoetical4 ,some ducks are not frogs4 ,univ4 creatures2 m poetical2 x frogs2 y ducks4 xm#j ym'#a ,no ,conclusion4 ,fallacy of ,unlike ,eliminands with an ,entity-,premiss4 #ch4 ,no emperors are dentists2 ,all dentists are dreaded by children4 ,no emperors are dreaded by children4 ,univ4 persons2 m dentists2 x emperors2 y dreaded by children4 xm#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion wrong3 right one is ,some persons1 dreaded by children1 are not emperors4 #ci4 ,sugar is sweet2 ,salt is not sweet4 ,salt is not sugar4 ,univ4 things2 m sweet2 x sugar2 y salt4 x#am'#j y#am#j 7x#ay#j y#ax#j7 ,fig4 ,i 7b74 ,conclusion incomplete3 omitted portion is ,sugar is not salt4 #dj4 ,every eagle can fly2 ,some pigs cannot fly4 ,some pigs are not eagles4 ,univ4 creatures2 m creatures that can fly2 x eagles2 y pigs4 x#am'#j ym'#a x'y#a ,fig4 ,,ii4 ,conclusion right4 ,solutions for #h4 ,,sl#h #a #b #c #a4 cd#j a#a;d'#j b#a;c'#j2 #a #b #c cd ad' bc' ab#j a#a b#a -- i4e4 a#a;b#j b#a;a#j #a #b #c #b4 d#a;b'#j ac'#j bc#j2 #a #c #b db' bc ac' da#j d#a i4e4 d#a;a#j - - #a #b #c #c4 ba#j cd'#j d#a;b'#j2 #a #c #b ba db' cd' ac#j - - #a #b #c #d4 bc#j a#a;b'#j c'd#j2 #a #b #c bc ab' c'd ad#j a#a i4e4 a#a;d#j -- pg#aef #a #b #c #a #b #c #e4 b'#a;a#j bc#j a'd#j2 b'a bc a'd cd#j - - #a #b #c #f4 a#a;b#j b'c#j d#a;a'#j2 #a #b #c ab b'c da' cd#j d#a i4e4 d#a;c#j -- #a #b #c #a #b #c #g4 db'#j b#a;a'#j cd'#j2 db' ba' cd' a'c#j -- #a #b #c #h4 b'd#j a'b#j c#a;d'#j2 #a #b #c b'd a'b cd' a'c#j c#a i4e4 c#a;a'#j - - #a #b #c #i4 b'#a;a'#j ad#j b#a;c'#j2 #a #b #c b'a' ad bc' dc'#j - - #a #b #c #aj4 cd#j b#a;c'#j ad'#j2 #a #b #c cd bc' ad' ba#j b#a i4e4 b#a;a#j -- #a #b #c #aa4 bc#j d#a;a'#j c'#a;a#j2 #a #c #b bc c'a da' bd#j d#a i4e4 d#a;b#j - - #a #b #c #ab4 cb'#j c'#a;d#j b#a;a'#j2 #a #b #c cb' c'd ba' da'#j -- #a #b #c #d #ac4 d#a;e'#j c#a;a'#j bd'#j e#a;a#j2 #a #c #d #b de' bd' ea ca' bc#j c#a i4e4 c#a;b#j -- - #a #b #c #d #ad4 c#a;b'#j a#a;e'#j d#a;b#j a'#a;c'#j2 #a #c #d #b cb' db a'c' ae' de'#j d#a i4e4 d#a;e'#j -- - #a #b #c #d #ae4 b'd#j e#a;c'#j b#a;a'#j d'#a;c#j2 #a #c #d #b b'd ba' d'c ec' a'e#j e#a i4e4 e#a;a'#j - - - #a #b #c #d #af4 a'e#j d#a;c#j a#a;b'#j e'#a;d'#j2 #a #c #d #b a'e ab' e'd' dc b'c#j - - - #a #b #c #d #ag4 d#a;c'#j a#a;e'#j bd'#j c#a;e#j2 #a #c #d #b dc' bd' ce ae' ba#j a#a i4e4 a#a;b#j -- - #a #b #c #d #ah4 a#a;b'#j d#a;e'#j a'#a;c#j be#j2 #a #c #d #b ab' a'c be de' cd#j d#a i4e4 d#a;c#j -- - #a #b #c #d #e #ai4 bc#j e#a;h'#j a#a;b'#j dh#j e'#a;c'#j2 #a #c #e #b #d bc ab' e'c' eh' dh ad#j a#a -- - - i4e4 a#a;d#j #a #b #c #d #e #bj4 dh'#j ce#j h#a;b'#j ad'#j be'#j2 #a #c #d #e #b dh' hb' ad' be' ce ac#j -- - - #a #b #c #d #e #ba4 b#a;a'#j dh#j ce#j ah'#j c'#a;b'#j2 #a #d #b #e #c ba' ah' dh c'b' ce de#j -- - - #a #b #c #d #e #bb4 e#a;d#j b'h'#j c'#a;d'#j a#a;e'#j ch#j2 #a #c #d #e #b ed c'd' ae' ch b'h' ab'#j a#a -- - - i4e4 a#a;b#j pg#aeg #a #b #c #d #e #bc4 b'#a;a#j de'#j h#a;b#j ce#j d'#a;a'#j2 #a #c #e #b #d b'a hb d'a' de' ce - - - - hc#j h#a i4e4 h#a;c#j #a #b #c #d #e #f #bd4 h'#ak#j b'a#j c#a;d'#j e#a;h#j dk'#j bc'#j2 #a #d #e #c #f #b h'k eh dk' cd' bc' b'a ea#j e#a - - - - - i4e4 e#a;a#j #a #b #c #d #be4 a#a;d'#j k#a;b'#j e#a;h'#j a'b#j #e #f d#a;c'#j h#ak'#j2 #a #d #b #e #f #c ad' a'b kb' dc' hk' eh' c'e#j e#a -- - - - i4e4 e#a;c'#j #a #b #c #d #e #bf4 a'#a;h'#j d'k'#j e#a;b#j hk#j a#a;c'#j #f b'd#j2 #a #d #b #e #f #c a'h' hk d'k' ac' b'd eb c'e#j e#a - - - - - i4e4 e#a;c'#j #a #b #c #d #e #bg4 e#a;d#j hb#j a'#ak'#j ce'#j b'#a;d'#j #f ac'#j2 #a #d #e #b #f #c ed ce' b'd' hb ac' a'k' hk'#j -- - - - #a #b #c #d #e #bh4 a'k#j e#a;b'#j hk'#j d'c#j ab#j #f c'#a;h'#j2 #a #c #e #b #f #d a'k hk' ab eb' c'h' d'c ed'#j e#a - - - - - i4e4 e#a;d'#j #a #b #c #d #e #bi4 ek#j b'm#j ac'#j h'#a;e'#j d#ak'#j #f #g #h cb#j d'#al'#j hm'#j2 #a #d #e #g #h #b #f #c ek h'e' dk' d'l' hm' b'm cb ac' -- - - - - - l'a#j #a #b #c #d #e #cj4 n#am'#j a'#a;e'#j c'l#j k#ar#j ah'#j #f #g #h #i #aj dl'#j cn'#j e#a;b'#j m#ar'#j h#a;d'#j2 #a #g #c #f #i #d #aj #e #b #h nm' cn' c'l dl' mr' kr hd' ah' a'e' eb' -- - - - - - - - kb'#j k#a i4e4 k#a;b'#j ,solutions for #i4 ,,sl#i #a4 #a #b #c b#a;d#j ac#j d'#a;c'#j2 #a #c #b bd d'c' ac ba#j b#a1 i4e4 b#a;a#j - - i4e4 ,babies cannot manage crocodiles4 #b4 #a #b #c a#a;b'#j d#a;c'#j bc#j2 #a #c #b ab' bc dc' ad#j d#a1 i4e4 d#a;a#j - - i4e4 ,your presents to me are not made of tin4 pg#aeh #c4 #a #b #c da#j c#a;b'#j a'b#j2 #a #c #b da a'b cb' dc#j c#a1 i4e4 c#a;d#j - - i4e4 ,all my potatoes in this dish are old ones4 #d4 #a #b #c ba#j b'd#j c#a;a'#j2 #a #b #c ba b'd ca' dc#j c#a1 i4e4 c#a;d#j -- i4e4 ,my servants never say shpoonj4 #e4 #a #b #c ad#j cd'#j b#a;a'#j2 #a #b #c ad cd' ba' cb#j b#a1 i4e4 b#a;c#j -- i4e4 ,my poultry are not officers4 #f4 #a #b #c #a #b #c c#a;a'#j c'b#j da#j2 ca' c'b da bd#j -- i4e4 ,none of your sons are fit to serve on a jury4 #g4 #a #b #c #a #c #b cb#j da#j b'#a;a'#j2 cb b'a' da cd#j - - i4e4 ,no pencils of mine are sugarplums4 #h4 #a #b #c cb'#j d#a;a'#j ba#j2 #a #c #b cb' ba da' cd#j d#a1 i4e4 d#a;c#j - - i4e4 ,jenkins is inexperienced4 #i4 #a #b #c #a #b #c cd#j d'a#j c'b#j2 cd d'a c'b ab#j -- i4e4 ,no comet has a curly tail4 #aj4 #a #b #c #a #c #b d'c#j ba#j a'#a;d#j2 d'c a'd ba cb#j - - i4e4 ,no hedgehog takes in the ,times4 #aa4 #a #b #c b#a;a'#j c#a;b'#j ad#j2 #a #b #c ba' cb' ad cd#j c#a1 i4e4 c#a;d#j -- i4e4 ,this dish is unwholesome4 #ab4 #a #b #c b#a;c'#j d'a#j a'c#j2 #a #c #b bc' a'c d'a bd'#j b#a1 i4e4 b#a;d'#j - - i4e4 ,my gardener is very old4 #ac4 #a #b #c a#a;d'#j bc#j c'#a;d#j2 #a #c #b ad' c'd bc ab#j a#a1 i4e4 a#a;b#j - - i4e4 ,all humming-birds are small4 pg#aei #ad4 #a #b #c #a #c #b c'b#j a#a;d'#j ca'#j2 c'b ca' ad' bd'#j - - i4e4 ,no one with a hooked nose ever fails to make money4 #ae4 #a #b #c #a #b #c b#a;a'#j b'#a;d#j ca#j2 ba' b'd ca dc#j -- i4e4 ,no gray ducks in this village wear lace collars4 #af4 #a #b #c #a #b #c d#a;b'#j cd'#j ba#j2 db' cd' ba ca#j -- i4e4 ,no jug in this cupboard will hold water4 #ag4 #a #b #c b'#a;d#j c#a;d'#j ab#j2 #a #b #c b'd cd' ab ca#j c#a1 i4e4 c#a;a#j - - i4e4 ,these apples were grown in the sun4 #ah4 #a #b #c d'#a;b'#j c#a;b#j c'a#j2 #a #b #c d'b' cb c'a d'a#j d'#a1 i4e4 d'#a;a#j - - i4e4 ,puppies1 that will not lie still1 never care to do worsted-work4 #ai4 #a #b #c #a #c #b bd'#j a#a;c'#j a'd#j2 bd' a'd ac' bc'#j - - i4e4 ,no name in this list is unmelodious4 #bj4 #a #b #c #a #c #b a#a;b'#j dc#j a'#a;d'#j2 ab' a'd' dc b'c#j - - i4e4 ,no ,m4,p4 should ride in a donkey-race1 unless he has perfect self-command4 #ba4 #a #b #c #a #c #b bd#j c'a#j b'c#j2 bd b'c c'a da#j - - i4e4 ,no goods in this shop1 that are still on sale1 may be carried away4 #bb4 #a #b #c #a #c #b a'b#j cd#j d'a#j2 a'b d'a cd bc#j - - i4e4 ,no acrobatic feat1 which involves turning a quadruple somersault1 is ever attempted in a circus4 #bc4 #a #b #c dc'#j a#a;b'#j bc#j2 #a #c #b dc' bc ab' da#j a#a1 i4e4 a#a;d#j - - i4e4 ,guinea-pigs never really appreciate ,beethoven4 pg#afj #bd4 #a #b #c #a #c #b a#a;d'#j b'#a;c#j ba'#j2 ad' ba' b'c d'c#j - - i4e4 ,no scentless flowers please me4 #be4 #a #b #c c#a;d'#j ba'#j d#a;a#j2 #a #c #b cd' da ba' cb#j c#a1 i4e4 c#a;b#j - - i4e4 ,showy talkers are not really well-informed4 #bf4 #a #b #c #d ea#j b#a;d'#j a'#a;c#j e'b'#j2 #a #c #d #b ea a'c e'b' bd' cd'#j -- - i4e4 ,none but red-haired boys learn ,greek in this school4 #bg4 #a #b #c #d b#a;d#j ac'#j e#a;d'#j c#a;b'#j2 #a #c #d #b bd ed' cb' ac' ea#j e#a1 i4e4 e#a;a#j -- - i4e4 ,wedding-cake always disagrees with me4 #bh4 #a #b #c #d ad#j e'#a;b'#j c#a;d'#j e#a;a'#j2 #a #c #d #b ad cd' ea' e'b' cb'#j c#a1 i4e4 c#a;b'#j -- - i4e4 ,discussions1 that go on while ,tomkins is in the chair1 endanger the peacefulness of our ,debating-,club4 #bi4 #a #b #c #d d#a;a#j e'c#j b#a;a'#j d'e#j2 #a #c #d #b da ba' d'e e'c bc#j b#a1 i4e4 b#a;c#j -- - i4e4 ,all gluttons in my family are unhealthy4 #cj4 #a #b #c #d d#a;e#j c'a#j b#a;e'#j c#a;d'#j2 #a #c #d #b de be' cd' c'a ba#j b#a1 i4e4 b#a;a#j -- - i4e4 ,an egg of the ,great ,auk is not to be had for a song4 #ca4 #a #b #c #d d'b#j a#a;c'#j c#a;e'#j a'd#j2 #a #d #b #c d'b a'd ac' ce' be'#j - - - i4e4 ,no books sold here have gilt edges unless they are priced at #es4 and upwards4 #cb4 #a #b #c #d a'#a;c'#j d#a;b#j a#a;e'#j c#a;b'#j2 #a #c #d #b a'c' ae' cb' db e'd#j d#a1 i4e4 d#a;e'#j - - - i4e4 ,when you cut your finger1 you will find ,tincture of ,calendula useful4 #cc4 #a #b #c #d d'b#j a#a;e'#j ec#j d#a;a'#j2 #a #d #b #c d'b da' ae' ec bc#j - - - i4e4 ,i have never come across a mermaid at sea4 pg#afa #cd4 #a #b #c #d c'#a;b#j a#a;e'#j d#a;b'#j a'#a;c#j2 #a #c #d #b c'b db' a'c ae' de'#j d#a1 i4e4 d#a;e'#j - - - i4e4 ,all the romances in this library are well-written4 #ce4 #a #b #c #d e'd#j c'a#j eb#j d'c#j2 #a #c #d #b e'd eb d'c c'a ba#j - - - i4e4 ,no bird in this aviary lives on mince-pies4 #cf4 #a #b #c #d d'#a;c'#j e#a;a'#j c#a;b#j e'd#j2 #a #c #d #b d'c' cb e'd ea' ba'#j - - - i4e4 ,no plum-pudding1 that has not been boiled in a cloth1 can be distinguished from soup4 #cg4 #a #b #c #d #e ce'#j b'a'#j h#a;d'#j ae#j bd#j2 #a #d #b #e #c ce' ae b'a' bd hd' ch#j h#a1 i4e4 h#a;c#j - - - - i4e4 ,all your poems are uninteresting4 #ch4 #a #b #c #d #e b'#a;a'#j db#j he'#j ec#j a#a;h'#j2 #a #b #e #c #d b'a' db ah' he' ec dc#j - - - - i4e4 ,none of my peaches have been grown in a hothouse4 #ci4 #a #b #c #d #e c#a;d#j h#a;e'#j c'#a;a'#j h'b#j e#a;d'#j2 #a #c #e #b #d cd c'a' ed' he' h'b a'b#j -- - - i4e4 ,no pawnbroker is dishonest4 #dj4 #a #b #c #d #e bd'#j c'h#j e#a;b'#j da#j e'c#j2 #a #c #d #e #b bd' eb' da e'c c'h ah#j -- - - i4e4 ,no kitten with green eyes will play with a gorilla4 #da4 #a #b #c #d #e c#a;a'#j h'b#j ae#j d#a;c'#j h#a;e'#j2 #a #c #d #e #b ca' ae dc' he' h'b db#j d#a1 i4e4 d#a;b#j -- - - i4e4 ,all my friends in this ,college dine at the lower table4 #db4 #a #b #c #d #e ca#j h#a;d'#j c'#a;e'#j b'a'#j d#a;e#j2 #a #c #d #e #b ca c'e' b'a' de hd' b'h#j h#a1 -- - - i4e4 h#a;b'#j i4e4 ,my writing-desk is full of live scorpions4 #dc4 #a #b #c #d #e b'#a;e#j ah#j dc#j e'#a;a'#j bc'#j #a #d #b #e #c b'e e'a' ah bc' dc hd#j - - - - i4e4 ,no ,mandarin ever reads ,hogg's poems4 pg#afb #dd4 #a #b #c #d #e e#a;b'#j a'd#j c#a;h'#j e'a#j d'h#j2 #a #d #b #e #c eb' e'a a'd d'h ch' b'c#j c#a1 - - - - i4e4 c#a;b'#j i4e4 ,shakespeare was clever4 #de4 #a #b #c #d #e e'#a;c'#j hb'#j d#a;a#j e#a;a'#j c#a;b#j2 #a #d #c #e #b e'c' ea' da cb hb' dh#j d#a1 i4e4 d#a;h#j - - - - i4e4 ,rainbows are not worth writing odes to4 #df4 #a #b #c #d #e c'#a;h'#j e#a;a#j bd#j a'#a;h#j d'c#j2 #a #d #b #e #c c'h' a'h ea d'c bd eb#j e#a1 i4e4 e#a;b#j - - - - i4e4 ,these ,sorites-examples are difficult4 #dg4 #a #b #c #d #e #f a'#a;e'#j bk#j c'a#j eh'#j d#a;b'#j k'h#j2 #a #c #d #f #b #e a'e' c'a eh' k'h bk db' c'd#j d#a1 - - - - - i4e4 d#a;c'#j i4e4 ,all my dreams come true4 #dh4 #a #b #c #d #e #f a'h#j c'k#j a#a;d'#j e#a;h'#j b#ak'#j c#a;e'#j2 #a #c #d #f #b #e a'h ad' eh' ce' c'k bk' d'b#j b#a1 - - - - - i4e4 b#a;d'#j i4e4 ,all the ,english pictures here are painted in oils4 #di4 #a #b #c #d #e #f k'#a;e#j c#a;h#j b#a;a'#j kd#j h'a#j b'#a;e'#j2 #a #d #f #c #e #b k'e kd b'e' ba' h'a ch dc#j c#a1 - - - - - i4e4 c#a;d#j i4e4 ,donkeys are not easy to swallow4 #ej4 #a #b #c #d #e #f ab'#j h'd#j e#a;c#j b#a;d'#j a'k#j c'#a;h#j2 #a #d #b #e #f #c ab' bd' h'd a'k c'h ec ke#j e#a1 -- - - - i4e4 e#ak#j i4e4 ,opium-eaters never wear white kid gloves4 #ea4 #a #b #c #d #e #f bc#j k#a;a'#j eh#j d#a;b'#j h'c'#j k'#a;e'#j2 #a #d #e #c #f #b bc db' h'c' eh k'e' ka' da'#j d#a1 -- - - - i4e4 d#a;a'#j i4e4 ,a good husband always comes home for his tea4 #eb4 #a #b #c #d #e #f a'#ak'#j ch#j h'k#j b#a;d'#j ea#j d#a;c'#j #a #c #b #f #d #e a'k' h'k ch dc' bd' ea be#j b#a1 - - - - - i4e4 b#a;e#j i4e4 ,bathing-machines are never made of mother-of-pearl4 pg#afc #ec4 #a #b #c #d #e da'#j k#a;b'#j c#a;h#j d'#ak'#j e#a;c'#j #f a#a;h'#j2 #a #d #b #f #c #e da' d'k' kb' ah' ch ec' -- - - - b'e#j e#a1 i4e4 e#a;b'#j i4e4 ,rainy days are always cloudy4 #ed4 #a #b #c #d #e #f kb'#j a'#a;c'#j d'b#j k'#a;h'#j ea#j d#a;c#j2 #a #c #d #f #b #e kb' d'b k'h' dc a'c' ea -- - - - h'e#j i4e4 ,no heavy fish is unkind to children4 #ee4 #a #b #c #d #e #f k'#a;b'#j eh'#j c'd#j hb#j ac#j kd'#j2 #a #d #b #f #c #e k'b' hb eh' kd' c'd ac ea#j - - - - - i4e4 ,no engine-driver lives on barley-sugar4 #ef4 #a #b #c #d #e h#a;b'#j c#a;d'#j k'a#j e#a;h'#j b#a;a'#j #f k#a;c'#j2 #a #d #e #c #f #b hb' eh' ba' k'a kc' cd' -- - - - ed'#j e#a1 i4e4 e#a;d'#j i4e4 ,all the animals in the yard gnaw bones4 #eg4 #a #b #c #d #e #f h'#a;d'#j e#a;c'#j k'a#j cb#j d#al'#j e'h#j #g kl#j2 #a #e #g #c #f #b #d h'd' dl' kl k'a e'h ec' cb ab#j - - - - - - i4e4 ,no badger can guess a conundrum4 #eh4 #a #b #c #d #e #f b'h#j d'#al'#j ca#j d#ak'#j h'#a;e'#j mc'#j #g #h a'b#j ek#j2 #a #e #g #c #f #h #d #b b'h h'e' a'b ca mc' ek dk' d'l' ml'#j - - - - - - - i4e4 ,no cheque of yours1 received by me1 is payable to order4 #ei4 #a #b #c #d #e #f c#al'#j h'e#j kd#j mc'#j b'#a;e'#j n#a;a'#j #g #h #i l#a;d'#j m'b#j ah#j2 #a #d #g #c #h #e #b #i #f cl' mc' ld' kd m'b b'e' h'e ah na' -- - - - - - - kn#j i4e4 ,i cannot read any of ,brown's letters4 #fj4 #a #b #c #d #e #f e#a;c'#j l#an'#j d#a;a'#j m'b#j ck'#j e'r#j #g #h #i #aj h#an#j b'k#j r'#a;d'#j m#al'#j2 #a #e #f #h #d #i #c #aj #b #g ec' ck' e'r b'k m'b r'd' da' ml' ln' hn -- - - - - - - - a'h#j h#a1 i4e4 h#a;a'#j i4e4 ,i always avoid a kangaroo4 pg#afd ,,notes4 7,a7 ,see p4 #hj4 ,one of the favourite objections1 brought against the ,science of ,logic by its detractors1 is that a ,syllogism has no real validity as an argument1 since it involves the ,fallacy of ,petitio ,principii 7i4e4 ,begging the ,question1 the essence of which is that the whole ,conclusion is involved in one of the ,premisses74 ,this formidable objection is refuted1 with beautiful clearness and simplicity1 by these three ,diagrams1 which show us that1 in each of the three ,figures1 the ,conclusion is really involved in the two ,premisses taken together1 each contributing its share4 ,thus1 in ,fig4 ,i41 the ,premiss xm#j empties the ,inner ,cell of the ,n4,w4 ,quarter1 while the ,premiss ym#j empties its ,outer ,cell4 ,hence it needs the two ,premisses to empty the whole of the ,n4,w4 ,quarter1 and thus to prove the ,conclusion xy#j4 ,again1 in ,fig4 ,,ii41 the ,premiss xm#j empties the ,inner ,cell of the ,n4,w4 ,quarter4 ,the ,premiss ym#a merely tells us that the ,inner ,portion of the ,w4 ,half is occupied1 so that we may place a ',i' in it1 somewhere2 but1 if this were the whole of our information1 we should not know in which ,cell to place it1 so that it would have to 'sit on the fence'3 it is only when we learn1 from the other ,premiss1 that the upper of these two ,cells is empty1 that we feel authorised to place the ',i' in the lower ,cell1 and thus to prove the ,conclusion x'y#a4 ,lastly1 in ,fig4 ,,iii41 the information1 that m exists1 merely authorises us to place a ',i' somewhere in the ,inner ,square----but it has large choice of fences to sit upon6 ,it needs the ,premiss xm#j to drive it out of the ,n4 ,half of that ,square2 and it needs the ,premiss ym#j to drive it out of the ,w4 ,half4 ,hence it needs the two ,premisses to drive it into the ,inner ,portion of the ,s4,e4 ,quarter1 and thus to prove the ,conclusion x'y'#a4 pg#afe ,,appendix1 ,,addressed ,,to ,,teachers4 #a4 ,introductory4 ,there are several matters1 too hard to discuss with ,learners1 which nevertheless need to be explained to any ,teachers1 into whose hands this book may fall1 in order that they may thoroughly understand what my ,symbolic ,method is1 and in what respects it differs from the many other ,methods already published4 ,these matters are as follows3-- ,the ,existential ,import of ,propositions4 ,the use of is-not 7or are-not7 as a ,copula4 ,the theory two ,negative ,premisses prove nothing4 ,euler's ,method of ,diagrams4 ,venn's ,method of ,diagrams4 ,my ,method of ,diagrams4 ,the ,solution of a ,syllogism by various ,methods4 ,my ,method of treating ,syllogisms and ,sorites4 ,some account of ,parts ,,ii1 ,,iii4 #b4 ,the ,existential ,import of ,propositions4 ,the writers1 and editors1 of the ,logical text-books which run in the ordinary grooves----to whom ,i shall hereafter refer by the 7,i hope inoffensive7 title ,the ,logicians----take1 on this subject1 what seems to me to be a more humble position than is at all necessary4 ,they speak of the ,copula of a ,proposition with bated breath1 almost as if it were a living1 conscious ,entity1 capable of declaring for itself what it chose to mean1 and that we1 poor human creatures1 had nothing to do but to ascertain what was its sovereign will and pleasure1 and submit to it4 pg#aff ,in opposition to this view1 ,i maintain that any writer of a book is fully authorised in attaching any meaning he likes to any word or phrase he intends to use4 ,if ,i find an author saying1 at the beginning of his book1 ,let it be understood that by the word 'black' ,i shall always mean 'white'1 and that by the word 'white' ,i shall always mean 'black'1 ,i meekly accept his ruling1 however injudicious ,i may think it4 ,and so1 with regard to the question whether a ,proposition is or is not to be understood as asserting the existence of its ,subject1 ,i maintain that every writer may adopt his own rule1 provided of course that it is consistent with itself and with the accepted facts of ,logic4 ,let us consider certain views that may logically be held1 and thus settle which of them may conveniently be held2 after which ,i shall hold myself free to declare which of them ,i intend to hold4 ,the kinds of ,propositions1 to be considered1 are those that begin with some1 with no1 and with all4 ,these are usually called ,propositions in ,i1 in ,e1 and in ,a4 ,first1 then1 a ,proposition in ,i may be understood as asserting1 or else as not asserting1 the existence of its ,subject4 7,by existence ,i mean of course whatever kind of existence suits its nature4 ,the two ,propositions1 dreams exist and drums exist1 denote two totally different kinds of existence4 ,a dream is an aggregate of ideas1 and exists only in the mind of a dreamer3 whereas a drum is an aggregate of wood and parchment1 and exists in the hands of a drummer47 ,first1 let us suppose that ,i asserts 7i4e4 asserts the existence of its ,subject74 ,here1 of course1 we must regard a ,proposition in ,a as making the same assertion1 since it necessarily contains a ,proposition in ,i4 ,we now have ,i and ,a asserting4 ,does this leave us free to make what supposition we choose as to ,e8 ,my answer is ,no4 ,we are tied down to the supposition that ,e does not assert4 ,this can be proved as follows3-- ,if possible1 let ,e assert4 ,then 7taking x1 y1 and z to represent ,attributes7 we see that1 if the ,proposition ,no xy are z be true1 some things exist with the ,attributes x and y3 i4e4 ,some x are y4 pg#afg ,also we know that1 if the ,proposition ,some xy are z be true1 the same result follows4 ,but these two ,propositions are ,contradictories1 so that one or other of them must be true4 ,hence this result is always true3 i4e4 the ,proposition ,some x are y is always true6 ,quod est absurdum4 7,see ,note 7,a71 p4 #aie74 ,we see1 then1 that the supposition ,i asserts necessarily leads to ,a asserts1 but ,e does not4 ,and this is the first of the various views that may conceivably be held4 ,next1 let us suppose that ,i does not assert4 ,and1 along with this1 let us take the supposition that ,e does assert4 ,hence the ,proposition ,no x are y means ,some x exist1 and none of them are y3 i4e4 all of them are not-y1 which is a ,proposition in ,a4 ,we also know1 of course1 that the ,proposition ,all x are not-y proves ,no x are y4 ,now two ,propositions1 each of which proves the other1 are equivalent4 ,hence every ,proposition in ,a is equivalent to one in ,e1 and therefore asserts4 ,hence our second conceivable view is ,e and ,a assert1 but ,i does not4 ,this view does not seen to involve any necessary contradiction with itself or with the accepted facts of ,logic4 ,but1 when we come to test it1 as applied to the actual facts of life1 we shall find ,i think1 that it fits in with them so badly that its adoption would be1 to say the least of it1 singularly inconvenient for ordinary folk4 ,let me record a little dialogue ,i have just held with my friend ,jones1 who is trying to form a new ,club1 to be regulated on strictly ,logical principles4 ,author4 ,well1 ,jones6 ,have you got your new ,club started yet8 ,jones 7rubbing his hands74 ,you'll be glad to hear that some of the ,members 7mind1 ,i only say 'some'7 are millionaires6 ,rolling in gold1 my boy6 ,author4 ,that sounds well4 ,and how many ,members have entered8 ,jones 7staring74 ,none at all4 ,we haven't got it started yet4 ,what makes you think we have8 ,author4 ,why1 ,i thought you said that some of the ,members---- pg#afh ,jones 7contemptuously74 ,you don't seem to be aware that we're working on strictly ,logical principles4 ,a ,particular ,proposition does not assert the existence of its ,subject4 ,i merely meant to say that we've made a ,rule not to admit any ,members till we have at least three ,candidates whose incomes are over ten thousand a year6 ,author4 ,oh1 that's what you meant1 is it8 ,let's hear some more of your ,rules4 ,jones4 ,another is1 that no one1 who has been convicted seven times of forgery1 is admissible4 ,author4 ,and here1 again1 ,i suppose you don't mean to assert there are any such convicts in existence8 ,jones4 ,why1 that's exactly what ,i do mean to assert6 ,don't you know that a ,universal ,negative asserts the existence of its ,subject8 ,of course we didn't make that ,rule till we had satisfied ourselves that there are several such convicts now living4 ,the ,reader can now decide for himself how far this second conceivable view would fit in with the facts of life4 ,he will1 ,i think1 agree with me that ,jones' view1 of the ',existential ,import' of ,propositions1 would lead to some inconvenience4 ,thirdly1 let us suppose that neither ,i nor ,e asserts4 ,now the supposition that the two ,propositions1 ,some x are y and ,no x are not-y1 do not assert1 necessarily involves the supposition that ,all x are y does not assert1 since it would be absurd to suppose that they assert1 when combined1 more than they do when taken separately4 ,hence the third 7and last7 of the conceivable views is that neither ,i1 nor ,e1 nor ,a1 asserts4 ,the advocates of this third view would interpret the ,proposition ,some x are y to mean ,if there were any x in existence1 some of them would be y2 and so with ,e and ,a4 ,it admits of proof that this view1 as regards ,a1 conflicts with the accepted facts of ,logic4 ,let us take the ,syllogism ,darapti1 which is universally accepted as valid4 ,its form is ,all m are x2 ,all m are y4 4'4 ,some y are x4 pg#afi ,this they would interpret as follows3-- ,if there were any m in existence1 all of them would be x2 ,if there were any m in existence1 all of them would be y4 4'4 ,if there were any y in existence1 some of them would be x4 ,that this ,conclusion does not follow has been so briefly and clearly explained by ,mr4 ,keynes 7in his ,formal ,logic1 dated #ahid1 pp4 #cef1 #ceg71 that ,i prefer to quote his words3-- ,let no proposition imply the existence either of its subject or of its predicate4 ,take1 as an example1 a syllogism in ,darapti3-- ',all ,m is ,p1 ,all ,m is ,s1 4'4 ,some ,s is ,p4' ,taking ,s1 ,m1 ,p1 as the minor1 middle1 and major terms respectively1 the conclusion will imply that1 if there is an ,s1 there is some ,p4 ,will the premisses also imply this8 ,if so1 then the syllogism is valid2 but not otherwise4 ,the conclusion implies that if ,s exists ,p exists2 but1 consistently with the premisses1 ,s may be existent while ,m and ,p are both non-existent4 ,an implication is1 therefore1 contained in the conclusion1 which is not justified by the premisses4 ,this seems to me entirely clear and convincing4 ,still1 to make sicker1 ,i may as well throw the above 7soi-disant7 ,syllogism into a concrete form1 which will be within the grasp of even a non-logical ,reader4 ,let us suppose that a ,boys' ,school has been set up1 with the following system of ,rules3-- ,all boys in the ,first 7the highest7 ,class are to do ,french1 ,greek1 and ,latin4 ,all in the ,second ,class are to do ,greek only4 ,all in the ,third ,class are to do ,latin only4 ,suppose also that there are boys in the ,third ,class1 and in the ,second2 but that no boy has yet risen into the ,first4 ,it is evident that there are no boys in the ,school doing ,french3 still we know1 by the ,rules1 what would happen if there were any4 pg#agj ,we are authorised1 then1 by the ,data1 to assert the following two ,propositions3-- ,if there were any boys doing ,french1 all of them would be doing ,greek2 ,if there were any boys doing ,french1 all of them would be doing ,latin4 ,and the ,conclusion1 according to ,the ,logicians would be ,if there were any boys doing ,latin1 some of them would be doing ,greek4 ,here1 then1 we have two true ,premisses and a false ,conclusion 7since we know that there are boys doing ,latin1 and that none of them are doing ,greek74 ,hence the argument is invalid4 ,similarly it may be shown that this non-existential interpretation destroys the validity of ,disamis1 ,datisi1 ,felapton1 and ,fresison4 ,some of ,the ,logicians will1 no doubt1 be ready to reply ,but we are not ,aldrichians6 ,why should we be responsible for the validity of the ,syllogisms of so antiquated an author as ,aldrich8 ,very good4 ,then1 for the special benefit of these friends of mine 7with what ominous emphasis that name is sometimes used6 ,i must have a private interview with you1 my young friend1 says the bland ,dr4 ,birch1 in my library1 at #i a4m4 tomorrow4 ,and you will please to be punctual671 for their special benefit1 ,i say1 ,i will produce another charge against this non-existential interpretation4 ,it actually invalidates the ordinary ,process of ,conversion1 as applied to ,proposition in ',i'4 ,every logician1 ,aldrichian or otherwise1 accepts it as an established fact that ,some x are y may be legitimately converted into ,some y are x4 ,but is it equally clear that the ,proposition ,if there were any x1 some of them would be y may be legitimately converted into ,if there were any y1 some of them would be x8 ,i trow not4 ,the example ,i have already used----of a ,boys' ,school with a non-existent ,first ,class----will serve admirably to illustrate this new flaw in the theory of ,the ,logicians4 pg#aga ,let us suppose that there is yet another ,rule in this ,school1 viz4 ,in each ,class1 at the end of the ,term1 the head boy and the second boy shall receive prizes4 ,this ,rule entirely authorises us to assert 7in the sense in which ,the ,logicians would use the words7 ,some boys in the ,first ,class will receive prizes1 for this simply means 7according to them7 ,if there were any boys in the ,first ,class1 some of them would receive prizes4 ,now the ,converse of this ,proposition is1 of course1 ,some boys1 who will receive prizes1 are in the ,first ,class1 which means 7according to ,the ,logicians7 ,if there were any boys about to receive prizes1 some of them would be in the ,first ,class 7which ,class we know to be empty74 ,of this ,pair of ,converse ,propositions1 the first is undoubtedly true3 the second1 as undoubtedly1 false4 ,it is always sad to see a batsman knock down his own wicket3 one pities him1 as a man and a brother1 but1 as a cricketer1 one can but pronounce him ,out6 ,we see1 then1 that1 among all the conceivable views we have here considered1 there are only two which can logically be held1 viz4 ,i and ,a assert1 but ,e does not4 ,e and ,a assert1 but ,i does not4 ,the second of these ,i have shown to involve great practical inconvenience4 ,the first is the one adopted in this book4 7,see p4 #ai47 ,some further remarks on this subject will be found in ,note 7,b71 at p4 #aif4 #c4 ,the use of is-not 7or are-not7 as a ,copula4 ,is it better to say ,john is-not in-the-house or ,john is not-in-the-house8 ,some of my acquaintances are-not men-,i-should-like-to-be-seen-with or ,some of my acquaintances are men-,i-should-not-like-to-be-seen-with8 ,that is the sort of question we have now to discuss4 pg#agb ,this is no question of ,logical ,right and ,wrong3 it is merely a matter of taste1 since the two forms mean exactly the same thing4 ,and here1 again1 ,the ,logicians seem to me to take much too humble a position4 ,when they are putting the final touches to the grouping of their ,proposition1 just before the curtain goes up1 and when the ,copula----always a rather fussy 'heavy father'1 asks them ,am ,i to have the 'not'1 or will you tack it on to the ,predicate8 they are much too ready to answer1 like the subtle cab-driver1 ,leave it to you1 ,sir6 ,the result seems to be1 that the grasping ,copula constantly gets a not that had better have been merged in the ,predicate1 and that ,propositions are differentiated which had better have been recognised as precisely similar4 ,surely it is simpler to treat ,some men are ,jews and ,some men are ,gentiles as being both of them1 affirmative ,propositions1 instead of translating the latter into ,some men are-not ,jews1 and regarding it as a negative ,propositions8 ,the fact is1 ,the ,logicians have somehow acquired a perfectly morbid dread of negative ,attributes1 which makes them shut their eyes1 like frightened children1 when they come across such terrible ,propositions as ,all not-x are y2 and thus they exclude from their system many very useful forms of ,syllogisms4 ,under the influence of this unreasoning terror1 they plead that1 in ,dichotomy by ,contradiction1 the negative part is too large to deal with1 so that it is better to regard each ,thing as either included in1 or excluded from1 the positive part4 ,i see no force in this plea3 and the facts often go the other way4 ,as a personal question1 dear ,reader1 if you were to group your acquaintances into the two ,classes1 men that you would like to be seen with1 and men that you would not like to be seen with1 do you think the latter group would be so very much the larger of the two8 ,for the purposes of ,symbolic ,logic1 it is so much the most convenient plan to regard the two sub-divisions1 produced by ,dichotomy1 on the same footing1 and to say1 of any ,thing1 either that it is in the one1 or that it is in the other1 that ,i do not think any ,reader of this book is likely to demur to my adopting that course4 pg#agc #d4 ,the theory that two ,negative ,premisses prove nothing4 ,this ,i consider to be another craze of ,the ,logicians1 fully as morbid as their dread of a negative ,attribute4 ,it is1 perhaps1 best refuted by the method of ,instantia ,contraria4 ,take the following ,pairs of ,premisses3-- ,none of my boys are conceited2 ,none of my girls are greedy4 ,none of my boys are clever2 ,none but a clever boy could solve this problem4 ,none of my boys are learned2 ,some of my boys are not choristers4 7,this last ,proposition is1 in my system1 an affirmative one1 since ,i should read it are not-choristers2 but1 in dealing with ,the ,logicians1 ,i may fairly treat it as a negative one1 since they would read it are-not choristers47 ,if you1 dear ,reader1 declare1 after full consideration of these ,pairs of ,premisses1 that you cannot deduce a ,conclusion from any of them----why1 all ,i can say is that1 like the ,duke in ,patience1 you will have to be contented with our heart-felt sympathy6 ,see ,note 7,c71 p4 #aif4 #e4 ,euler's ,method of ,diagrams4 ,diagrams seem to have been used1 at first1 to represent ,propositions only4 ,in ,euler's well-known ,circles1 each was supposed to contain a class1 and the ,diagram consisted of two circles1 which exhibited the relations1 as to inclusion and exclusion1 existing between the two ,classes4 _/ _/ _/ y _/ x _/ _/ ,thus1 the ,diagram1 here given1 exhibits the two ,classes1 whose respective ,attributes are x and y1 as so related to each other that the following ,propositions are all simultaneously true3--,all x are y1 ,no x are not-y1 ,some x are y1 ,some y are not-x1 ,some not-y are not-x1 and1 of course1 the ,converses of the last four4 pg#agd _/ _/ _/ y _/ x _/ _/ ,similarly1 with this ,diagram1 the following ,propositions are true3--,all y are x1 ,no y are not-x1 ,some y are x1 ,some x are not-y1 ,some not-x are not-y1 and1 of course1 the ,converses of the last four4 _/ _/ _/ _/ x y _/ _/ _/ _/ ,similarly1 with this ,diagram1 the following are true3--,all x are not-y1 ,all y are not-x1 ,no x are y1 ,some x are not-y1 ,some y are not-x1 ,some not-x are not-y1 and the ,converses of the last four4 _/ _/ _/ _/ x y _/ _/ _/ _/ ,similarly1 with this ,diagram1 the following are true3--,some x are y1 ,some x are not-y1 ,some not-x are y1 ,some not-x are not-y1 and of course1 their four ,converses4 ,note that all ,euler's ,diagrams assert ,some not-x are not-y4 ,apparently it never occured to him that it might sometimes fail to be true6 ,now1 to represent ,all x are y1 the first of these ,diagrams would suffice4 ,similarly1 to represent ,no x are y1 the third would suffice4 ,but to represent any ,particular ,proposition1 at least three ,diagrams would be needed 7in order to include all the possible cases71 and1 for ,some not-x are not-y1 all the four4 #f4 ,venn's ,method of ,diagrams4 ,let us represent not-x by x'4 ,mr4 ,venn's ,method of ,diagrams is a great advance on the above ,method4 ,he uses the last of the above ,diagrams to represent any desired relation between x and y1 by simply shading a ,compartment known to be empty1 and placing a in one known to be occupied4 ,thus1 he would represent the three ,propositions ,some x are y1 ,no x are y1 and ,all x are y1 as follows3-- _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/ _/_/ _/ _/ _/ _/ pg#age ,it will be seen that1 of the four ,classes1 whose peculiar ,sets of ,attributes are xy1 xy'1 x'y1 and x'y'1 only three are here provided with closed ,compartments1 while the fourth is allowed the rest of the ,infinite ,plane to range about in6 ,this arrangement would involve us in very serious trouble1 if we ever attempted to represent ,no x' are y'4 ,mr4 ,venn once 7at p4 #bha7 encounters this awful task2 but evades it1 in a quite masterly fashion1 by the simple foot-note ,we have not troubled to shade the outside of this diagram6 ,to represent two ,propositions 7containing a common ,term7 together1 a three-letter ,diagram is needed4 ,this is the one used by ,mr4 ,venn4 _/ _/ x _/ _/ _/ _/ _/ _/ m _/ y _/ _/ _/ ,here1 again1 we have only seven closed ,compartments1 to accommodate the eight ,classes whose peculiar ,sets of ,attributes are xym1 xym'1 c4 ,with four terms in request1 ,mr4 ,venn says1 the most simple and symmetrical diagram seems to me that produced by making four ellipses intersect one another in the desired manner4 ,this1 however1 provides only fifteen closed compartments4 b c _/ _/ a _/ _/ d _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/ _/ _/_/_/ _/ _/_/ ,for five letters1 the simplest diagram ,i can suggest1 ,mr4 ,venn says1 is one like this 7the small ellipse in the centre is to be regarded as a portion of the outside of c2 i4e4 its four component portions are inside b and d but are no part of c74 ,it must be admitted that such a diagram is not quite so simple to draw as one might wish it to be2 but then consider what the alternative is of one undertakes to deal with five terms and all their combinations--nothing short of the disagreeable task of writing out1 or in some way putting before us1 all the #cb combinations involved4 b c d _/ _/ _/ a _/ _/ _/ _/ _/ e _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/_/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/_/_/ _/ _/ _/ _/ _/ pg#agf ,this ,diagram gives us #ca closed compartments4 ,for six letters1 ,mr4 ,venn suggests that we might use two ,diagrams1 like the above1 one for the f-part1 and the other for the not-f-part1 of all the other combinations4 ,this1 he says1 would give the desired #fd subdivisions4 ,this1 however1 would only give #fb closed ,compartments1 and one infinite area1 which the two ,classes1 a'b'c'd'e'f and a'b'c'd'e'f'1 would have to share between them4 ,beyond six letters ,mr4 ,venn does not go4 #g4 ,my ,method of ,diagrams4 ,my ,method of ,diagrams resembles ,mr4 ,venn's1 in having separate ,compartments assigned to the various ,classes1 and in marking these ,compartments as occupied or as empty2 but it differs from his ,method1 in assigning a closed area to the ,universe of ,discourse1 so that the ,class which1 under ,mr4 ,venn's liberal sway1 has been ranging at will through ,infinite ,space1 is suddenly dismayed to find itself cabin'd1 cribb'd1 confined1 in a limited ,cell like any other ,class6 ,also ,i use rectilinear1 instead of curvilinear1 ,figures2 and ,i mark an occupied ,cell with a ',i' 7meaning that there is at least one ,thing in it71 and an empty ,cell with a ',o' 7meaning that there is no ,thing in it74 ,for two letters1 ,i use this ,diagram1 in which the ,north ,half is assigned to 'x'1 the ,south to 'not-x' 7or 'x''71 the ,west to y1 and the ,east to y'4 ,thus the ,n4,w4 ,cell contains the xy-,class1 the ,n4,e4 ,cell the xy'-,class1 and so on4 ------- ------ ------- ,for three letters1 ,i subdivide these four ,cells1 by drawing an ,inner ,square1 which ,i assign to m1 the ,outer ,border being assigned to m'4 ,i thus get eight ,cells that are needed to accommodate the eight ,classes1 whose peculiar ,sets of ,attributes are xym1 xym'1 c4 --------------- ------ ------------ ------ --------------- ,this last ,diagram is the most complex that ,i use in the ,elementary ,part of my ',symbolic ,logic4' ,but ,i may as well take this opportunity of describing the more complex ones which will appear in ,part ,,ii4 pg#agg ,for four letters 7which ,i call a1 b1 c1 d7 ,i use this ,diagram2 assigning the ,north ,half to a 7and of course the rest of the ,diagram to a'71 the ,west ,half to b1 the ,horizontal ,oblong to c1 and the ,upright ,oblong to d4 ,we have now got #af ,cells4 --------------------- ------ ------------ ---------------- ------------ ------ --------------------- ,for five letters 7adding e7 ,i subdivide the #af ,cells of the previous ,diagram by oblique partitions1 assigning all the upper portions to e1 and all the lower portions to e'4 ,here1 ,i admit1 we lose the advantage of having the e-,class all together1 in a ring-fence1 like the other #d ,classes4 ,still1 it is very easy to find2 and the operation1 of erasing it1 is nearly as easy as that of erasing any other ,class4 ,we have now got #cb ,cells4 --------------------- _/ _/ _/ ------ _/ _/ _/ _/ _/ ------------ _/ _/ _/ _/ ---------------- _/ _/ _/ _/ ------------ _/ _/ _/ _/ _/ ------ _/ _/ _/ --------------------- ,for six letters 7adding h1 as ,i avoid tailed letters7 ,i substitute upright crosses for the oblique partitions1 assigning the #d portions1 into which each of the #af ,cells is thus divided1 to the four ,classes eh1 eh'1 e'h1 e'h'4 ,we have now got #fd ,cells4 ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h-------,h----,h----,h-------,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----,h----,h----,h----,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h,h,h,h--,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----,h----,h----,h----,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h-------,h----,h----,h-------,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h pg#agh ,for seven letters 7adding k7 ,i add1 to each upright cross1 a little inner square4 ,all these #af little squares are assigned to the k-,class1 and all outside them to the k'-,class2 so that #h little ,cells 7into which each of the #af ,cells is divided7 are respectively assigned to the #h ,classes ehk1 ehk'1 c4 ,we have now got #abh ,cells4 ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h-----------,h--------,h--------,h----- ------,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h--------,h--------,h--------,h-------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h,h,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h--------,h--------,h--------,h-------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h-----------,h--------,h--------,h----- ------,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,for eight letters 7adding l7 ,i place1 in each of the #af ,cells1 a lattice1 which is a reduced copy of the whole ,diagram2 and1 just as the #af large ,cells of the whole ,diagram are assigned to the #af ,classes abcd1 abcd'1 c41 so the #af little ,cells of each lattice are assigned to the #af ,classes ehkl1 ehkl'1 c4 ,thus1 the lattice in the ,n4,w4 corner serves to accommodate the #af ,classes abc'd'ehkl1 abc'd'eh'kl'1 c4 ,this ,octoliteral ,diagram 7see next page7 contains #bef ,cells4 ,for nine letters1 ,i place #b ,octoliteral ,diagrams side by side1 assigning one of them to m1 and the other to m'4 ,we have now got #eab ,cells4 pg#agi ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h-------------,h----------,h----------, h-------------,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----------,h----------,h----------,h-- --------,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h,h,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----------,h----------,h----------,h-- --------,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h-------------,h----------,h----------, h-------------,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,finally1 for ten letters1 ,i arrange #d ,octoliteral ,diagrams1 like the above1 in a square1 assigning them to the #d ,classes mn1 mn'1 m'n1 m'n'4 ,we have now got #ajbd ,cells4 #h4 ,solution of a ,syllogism by various ,methods4 ,the best way1 ,i think1 to exhibit the differences between these various ,methods of solving ,syllogisms1 will be to take a concrete example1 and solve it by each ,method in turn4 ,let us take1 as our example1 ,no4 #bi 7see p4 #ajb74 ,no philosophers are conceited2 ,some conceited persons are not gamblers4 4'4 ,some persons1 who are not gamblers1 are not philosophers4 pg#ahj 7#a7 ,solution by ordinary ,method4 ,these ,premisses1 as they stand1 will give no ,conclusion1 as they are both negative4 ,if by ',permutation' or ',obversion'1 we write the ,minor ,premiss thus1 ',some conceited persons are not-gamblers1' we can get a ,conclusion in ,fresison1 viz4 ,no philosophers are conceited2 ,some conceited persons are not-gamblers4 4'4 ,some not-gamblers are not philosophers ,this can be proved by reduction to ,ferio1 thus3-- ,no conceited persons are philosophers2 ,some not-gamblers are conceited4 4'4 ,some not-gamblers are not philosophers4 ,the validity of ,ferio follows directly from the ,axiom ',de ,omni et ,nullo'4 7#b7 ,symbolic ,representation4 ,before proceeding to discuss other ,methods of ,solution1 it is necessary to translate our ,syllogism into an abstract form4 ,let us take persons as our ',universe of ,discourse'2 and let x philosophers1 m conceited1 and y gamblers4 ,then the ,syllogism may be written thus3-- ,no x are m2 ,some m are y'4 4'4 ,some y' are x'4 7#c7 ,solution by ,euler's ,method of ,diagrams4 ,the ,major ,premiss requires only one ,diagram1 viz4 #a _/ _/ _/ _/ x m _/ _/ _/ _/ pg#aha ,the ,minor requires three1 viz4 #b _/ _/ _/ _/ y m _/ _/ _/ _/ #c _/ _/ _/ _/ y m _/ _/ _/ _/ #d _/ _/ _/ y _/ m _/ _/ ,the combination of ,major and ,minor1 in every possible way requires nine1 viz4 ,figs4 #a and #b give #e _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #f _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #g _/ _/ _/ _/ xy m _/ _/ _/ _/ #h _/ _/ _/ _/ x _/ _/ m y _/ _/ _/ _/ #i _/ _/ _/ _/ y _/ _/ m x _/ _/ _/ _/ ,figs4 #a and #c give #aj _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #aa _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #ab _/ _/ _/ _/ x _/ _/ m y _/ _/ _/ _/ ,figs4 #a and #d give #ac _/ _/ _/ _/ _/ y x _/ _/ m _/ _/ _/ ,from this group 7,figs4 #e to #ac7 we have1 by disregarding m1 to find the relation of x and y4 ,on examination we find that ,figs4 #e1 #aj1 #ac express the relation of entire mutual exclusion2 that ,figs4 #f1 #aa express partial inclusion and partial exclusion2 that ,fig4 #g expresses coincidence2 that ,figs4 #h1 #ab express entire inclusion of x in y2 and that ,fig4 #i expresses entire inclusion of y in x4 pg#ahb ,we thus get five ,biliteral ,diagrams for x and y1 viz4 #ad _/ _/ _/ _/ x y _/ _/ _/ _/ #ae _/ _/ _/ _/ x y _/ _/ _/ _/ #af _/ _/ xy _/ _/ #ag _/ _/ _/ x _/ y _/ _/ #ah _/ _/ _/ y _/ x _/ _/ where the only ,proposition1 represented by them all1 is ,some not-y are not-x1 i4e4 ,some persons1 who are not gamblers1 are not philosophers----a result which ,euler would hardly have regarded as a valuable one1 since he seems to have assumed that a ,proposition of this form is always true6 7#d7 ,solution by ,venn's ,method of ,diagrams4 ,the following ,solution has been kindly supplied to me ,mr4 ,venn himself4 ,the ,minor ,premiss declares that some of the constituents in my' must be saved3 mark these constituents with a cross4 _/ _/ _/_/ _/ _/ _/ _/ m _/ y _/ _/ _/ ,the ,major declares that all xm must be destroyed2 erase it4 ,then1 as some my' is to be saved1 it must clearly be my'x'4 ,that is1 there must exist my'x'2 or eliminating m1 y'x'4 ,in common phraseology1 ',some y' are x'1' or1 ',some not-gamblers are not-philosophers4' pg#ahc 7#e7 ,solution by my ,method of ,diagrams4 ,the first ,premiss asserts that no xm exist3 so we mark the xm-,compartment as empty1 by placing a ',o' in each of its ,cells4 ,the second asserts that some my' exist3 so we mark the my'-,compartment as occupied1 by placing a ',i' in its only available ,cell4 --------------- ------ 7,o77,o7 ------------ 7,i7 ------ --------------- ,the only information1 that this gives us as to x and y1 is that the x'y'-,compartment is occupied1 i4e4 that some x'y' exist4 ,hence ,some x' are y'3 i4e4 ,some persons1 who are not philosophers1 are not gamblers4 7#f7 ,solution by my ,method of ,subscripts4 xm#j my'#a x'y'#a i4e4 ,some persons1 who are not philosophers1 are not gamblers4 #i4 ,my ,method of treating ,syllogisms and ,sorites4 ,of all the strange things1 that are to be met with in the ordinary text-books of ,formal ,logic1 perhaps the strangest is the violent contrast one finds to exist between their ways of dealing with these two subjects4 ,while they have elaborately discussed no less than nineteen different forms of ,syllogisms----each with its own special and exasperating ,rules1 while the whole constitute an almost useless machine1 for practical purposes1 many of the ,conclusions being incomplete1 and many quite legitimate forms being ignored----they have limited ,sorites to two forms only1 of childish simplicity2 and these they have dignified with special names1 apparently under the impression that no other possible forms existed6 ,as to ,syllogisms1 ,i find that their nineteen forms1 with about a score of others which they have ignored1 can all be arranged under three forms1 each with a very simple ,rule of its own2 and the only question the ,reader has to settle1 in working any one of the #aja ,examples given at p4 #aja of this book1 is ,does it belong to ,fig4 ,i41 ,,ii41 or ,,iii48 pg#ahd ,as to ,sorites1 the only two forms1 recognised by the text-books1 are the ,aristotelian1 whose ,premisses are a series of ,propositions in ,a1 so arranged that the ,predicate of each is the ,subject of the next1 and the ,goclenian1 whose ,premisses are the very same series1 written backwards4 ,goclenius1 it seems1 was the first who noticed the startling fact that it does not affect the force of a ,syllogism to invert the order of its ,premisses1 and who applied this discovery to a ,sorites4 ,if we assume 7as surely we may87 that he is the same man as that transcendent genius who first noticed that #d times #e is the same thing as #e times #d1 we may apply to him what somebody 7,edmund ,yates1 ,i think it was7 has said of ,tupper1 viz41 here is a man who1 beyond all others of his generation1 has been favoured with ,glimpses of the ,obvious6 ,these puerile----not to say infantine----forms of a ,sorites ,i have1 in this book1 ignored from the very first1 and have not only admitted freely ,propositions in ,e1 but have purposely stated the ,premisses in random order1 leaving to the ,reader the useful task of arranging them1 for himself1 in an order which can be worked as a series of regular ,syllogisms4 ,in doing this1 he can begin with any one of them he likes4 ,i have tabulated1 for curiosity1 the various orders in which the ,premisses of the ,aristotelian ,sorites #a4 ,all a are b2 #b4 ,all b are c2 #c4 ,all c are d2 #d4 ,all d are e2 #e4 ,all e are h4 4'4 ,all a are h4 may be syllogistically arranged1 and ,i find there are no less than sixteen such orders1 viz41 #abcde1 #bacde1 #bcade1 #bcdae1 #bcdea1 #cbade1 #cbdae1 #cbdea1 #cdbae1 #cdbea1 #cdeba1 #dcbae1 #dcbea1 #dceba1 #decba1 #edcba4 ,of these the first and the last have been dignified with names2 but the other fourteen----first enumerated by an obscure ,writer on ,logic1 towards the end of the ,nineteenth ,century----remain without a name6 pg#ahe #aj4 ,some account of ,parts ,,ii1 ,,iii4 ,in ,part ,,ii4 will be found some of the matters mentioned in this ,appendix1 viz41 the ,existential ,import of ,propositions1 the use of a negative ,copula1 and the theory that two negative ,premisses prove nothing4 ,i shall also extend the range of ,syllogisms1 by introducing ,propositions containing alternatives 7such as ,not-all x are y71 ,propositions containing #c or more ,terms 7such as ,all ab are c1 which1 taken along with ,some bc' are d1 would prove ,some d are a'71 c4 ,i shall also discuss ,sorites containing ,entities1 and the very puzzling subjects of ,hypotheticals and ,dilemmas4 ,i hope1 in the course of ,part ,,ii41 to go over all the ground usually traversed in the text-books used in our ,schools and ,universities1 and to enable my ,readers to solve ,problems of the same kind as1 and far harder than1 those that are at present set in their ,examinations4 ,in ,part ,,iii4 ,i hope to deal with many curious and out-of-the-way subjects1 some of which are not even alluded to in any of the treatises ,i have met with4 ,in this ,part will be found such matters as the ,analysis of ,propositions into their ,elements 7let the ,reader1 who has never gone into this branch of the subject1 try to make out for himself what additional ,proposition would be needed to convert ,some a are b into ,some a are bc71 the treatment of ,numerical and ,geometrical ,problems1 the construction of ,problems1 and the solution of ,syllogisms and ,sorites containing ,propositions more complex than any that ,i have used in ,part ,,ii4 ,i will conclude with eight ,problems1 as a taste of what is coming in ,part ,,ii4 ,i shall be very glad to receive1 from any ,reader1 who thinks he has solved any one of them 7more especially if he has done so without using any ,method of ,symbols71 what he conceives to be its complete ,conclusion4 ,it may be well to explain what ,i mean by the complete ,conclusion of a ,syllogism or a ,sorites4 ,i distinguish their ,terms as being of two kinds----those which can be eliminated 7e4g4 the ,middle ,term of a ,syllogism71 which ,i call the ,eliminands1 and those which cannot1 which ,i call the ,retinends2 and ,i do not call the ,conclusion complete1 unless it states all the relations among the ,retinends only1 which can be deduced from the ,premisses4 pg#ahf #a4 ,all the boys1 in a certain ,school1 sit together in one large room every evening4 ,they are of no less than five nationalities----,english1 ,scotch1 ,welsh1 ,irish1 and ,german4 ,one of the ,monitors 7who is a great reader of ,wilkie ,collins' novels7 is very observant1 and takes ,,ms4 notes of almost everything that happens1 with the view of being a good sensational witness1 in case any conspiracy to commit a murder should be on foot4 ,the following are some of his notes3-- 7#a7 ,whenever some of the ,english boys are singing ,rule ,britannia1 and some not1 some of the ,monitors are wide-awake2 7#b7 ,whenever some of the ,scotch are dancing reels1 and some of the ,irish fighting1 some of the ,welsh are eating toasted cheese2 7#c7 ,whenever all the ,germans are playing chess1 some of the ,eleven are not oiling their bats2 7#d7 ,whenever some of the ,monitors are asleep1 and some not1 some of the ,irish are fighting2 7#e7 ,whenever some of the ,germans are playing chess1 and none of the ,scotch are dancing reels1 some of the ,welsh are not eating toasted cheese2 7#f7 ,whenever some of the ,scotch are not dancing reels1 and some of the ,irish not fighting1 some of the ,germans are playing chess2 7#g7 ,whenever some of the ,monitors are awake1 and some of the ,welsh are eating toasted cheese1 none of the ,scotch are dancing reels2 7#h7 ,whenever some of the ,germans are not playing chess1 and some of the ,welsh are not eating toasted cheese1 none of the ,irish are fighting2 pg#ahg 7#i7 ,whenever all the ,english are singing ,rule ,britannia1 and some of the ,scotch are not dancing reels1 none of the ,germans are playing chess2 7#aj7 ,whenever some of the ,english are singing ,rule ,britannia1 and some of the ,monitors are asleep1 some of the ,irish are not fighting2 7#aa7 ,whenever some of the ,monitors are awake1 and some of the ,eleven are not oiling their bats1 some of the ,scotch are dancing reels2 7#ab7 ,whenever some of the ,english are singing ,rule ,britannia1 and some of the ,scotch are not dancing reels1 99 99 99 99 ,here the ,,ms4 breaks off suddenly4 ,the ,problem is to complete the sentence1 if possible4 ,n4,b4 ,in solving this ,problem1 it is necessary to remember that the ,proposition ,all x are y is a ,double ,proposition1 and is equivalent to ,some x are y1 and none are y'4 ,see p4 #ag4 #b4 7#a7 ,a logician1 who eats pork-chops for supper1 will probably lose money2 7#b7 ,a gambler1 whose appetite is not ravenous1 will probably lose money2 7#c7 ,a man who is depressed1 having lost money and being likely to lose more1 always rises at #e a4m42 7#d7 ,a man1 who neither gambles nor eats pork-chops for supper1 is sure to have a ravenous appetite2 7#e7 ,a lively man1 who goes to bed before #d a4m41 had better take to cab-driving2 7#f7 ,a man with a ravenous appetite1 who has not lost money and does not rise at #e a4m41 always eats pork-chops for supper2 7#g7 ,a logician1 who is in danger of losing money1 had better take to cab-driving2 7#h7 ,an earnest gambler1 who is depressed though he has not lost money1 is in no danger of losing any2 7#i7 ,a man1 who does not gamble1 and whose appetite is not ravenous1 is always lively2 pg#ahh 7#aj7 ,a lively logician1 who is really in earnest1 is in no danger of losing money2 7#aa7 ,a man with a ravenous appetite has no need to take to cab-driving1 if he is really in earnest2 7#ab7 ,a gambler1 who is depressed though in no danger of losing money1 sits up till #d a4m4 7#ac7 ,a man1 who has lost money and does not eat pork-chops for supper1 had better take to cab-driving1 unless he gets up at #e a4m4 7#ad7 ,a gambler1 who goes to bed before #d a4m41 need not take to cab-driving1 unless he has a ravenous appetite2 7#ae7 ,a man with a ravenous appetite1 who is depressed though in no danger of losing1 is a gambler4 ,univ4 men2 a earnest2 b eating pork-chops for supper2 c gamblers2 d getting up at #e2 e having lost money2 h having a ravenous appetite2 k likely to lose money2 l lively2 m logicians2 n men who had better take to cab-driving2 r sitting up till #d4 ,n4,b4 ,in this ,problem1 clauses1 beginning with though1 are intended to be treated as essential parts of the ,propositions in which they occur1 just as if they had begun with and4 #c4 7#a7 ,when the day is fine1 ,i tell ,froggy ,you're quite the dandy1 old chap62 7#b7 ,whenever ,i let ,froggy forget that #aj he owes me1 and he begins to strut about like a peacock1 his mother declares ,he shall not go out a-wooing62 7#c7 ,now that ,froggy's hair is out of curl1 he has put away his gorgeous waistcoat2 7#d7 ,whenever ,i go out on the roof to enjoy a quiet cigar1 ,i'm sure to discover that my purse is empty2 7#e7 ,when my tailor calls with his little bill1 and ,i remind ,froggy of that #aj he owes me1 he does not grin like a hyna2 pg#ahi 7#f7 ,when it is very hot1 the thermometer is high2 7#g7 ,when the day is fine1 and ,i'm not in the humour for a cigar1 and ,froggy is grinning like a hyna1 ,i never venture to hint that he's quite the dandy2 7#h7 ,when my tailor calls with his little bill and finds me with an empty purse1 ,i remind ,froggy of that #aj he owes me2 7#i7 ,my railway-shares are going up like anything6 7#aj7 ,when my purse is empty1 and when1 noticing that ,froggy has got his gorgeous waistcoat on1 ,i venture to remind him of that #aj he owes me1 things are apt to get rather warm2 7#aa7 ,now that it looks like rain1 and ,froggy is grinning like a hyna1 ,i can do without my cigar2 7#ab7 ,when the thermometer is high1 you need not trouble yourself to take an umbrella2 7#ac7 ,when ,froggy has his gorgeous waistcoat on1 but is not strutting about like a peacock1 ,i betake myself to a quiet cigar2 7#ad7 ,when ,i tell ,froggy that he's quite the dandy1 he grins like a hyna2 7#ae7 ,when my purse is tolerably full1 and ,froggy's hair is one mass of curls1 and when he is not strutting about like a peacock1 ,i go out on the roof2 7#af7 ,when my railway-shares are going up1 and when it is chilly and looks like rain1 ,i have a quiet cigar2 7#ag7 ,when ,froggy's mother lets him go a-wooing1 he seems nearly mad with joy1 and puts on a waistcoat that is gorgeous beyond words2 7#ah7 ,when it is going to rain1 and ,i am having a quiet cigar1 and ,froggy is not intending to go a-wooing1 you had better take an umbrella2 7#ai7 ,when my railway-shares are going up1 and ,froggy seems nearly mad with joy1 that is the time my tailor always chooses for calling with his little bill2 7#bj7 ,when the day is cool and the thermometer low1 and ,i say nothing to ,froggy about his being quite the dandy1 and there's not the ghost of a grin on his face1 ,i haven't the heart for my cigar6 pg#aij #d4 7#a7 ,any one1 fit to be an ,m4,p41 who is not always speaking1 is a public benefactor2 7#b7 ,clear-headed people1 who express themselves well1 have had a good education2 7#c7 ,a woman1 who deserves praise1 is one who can keep a secret2 7#d7 ,people1 who benefit the public1 but do not use their influence for good purpose1 are not fit to go into ,parliament2 7#e7 ,people1 who are worth their weight in gold and who deserve praise1 are always unassuming2 7#f7 ,public benefactors1 who use their influence for good objects1 deserve praise2 7#g7 ,people1 who are unpopular and not worth their weight in gold1 never can keep a secret2 7#h7 ,people1 who can talk for ever and are fit to be ,members of ,parliament1 deserve praise2 7#i7 ,any one1 who can keep a secret and who is unassuming1 is a never-to-be-forgotten public benefactor2 7#aj7 ,a woman1 who benefits the public1 is always popular2 7#aa7 ,people1 who are worth their weight in gold1 who never leave off talking1 and whom it is impossible to forget1 are just the people whose photographs are in all the shop-windows2 7#ab7 ,an ill-educated woman1 who is not clear-headed1 is not fit to go into ,parliament2 7#ac7 ,any one1 who can keep a secret and is not for ever talking1 is sure to be unpopular2 7#ad7 ,a clear-headed person1 who has influence and uses it for good objects1 is a public benefactor2 7#ae7 ,a public benefactor1 who is unassuming1 is not the sort of person whose photograph is in every shop-window2 7#af7 ,people1 who can keep a secret and who use their influence for good purposes1 are worth their weight in gold2 7#ag7 ,a person1 who has no power of expression and who cannot influence others1 is certainly not a woman2 pg#aia 7#ah7 ,people1 who are popular and worthy of praise1 either are public benefactors or else are unassuming4 ,univ4 persons2 a able to keep a secret2 b clear-headed2 c constantly talking2 d deserving praise2 e exhibited in shop-windows2 h expressing oneself well2 k fit to be an ,m4,p42 l influential2 m never-to-be-forgotten2 n popular2 r public benefactors2 s unassuming2 t using one's influence for good objects2 v well-educated2 w women2 z worth one's weight in gold4 #e4 ,six friends1 and their six wives1 are staying in the same hotel2 and they all walk out daily1 in parties of various size and composition4 ,to ensure variety in these daily walks1 they have agree to observe the following ,rules3-- 7#a7 ,if ,acres is with 7i4e4 is in the same party with7 his wife1 and ,barry with his1 and ,eden with ,mrs4 ,hall1 ,cole must be with ,mrs4 ,dix2 7#b7 ,if ,acres is with his wife1 and ,hall with his1 and ,barry with ,mrs4 ,cole1 ,dix must not be with ,mrs4 ,eden2 7#c7 ,if ,cole and ,dix and their wives are all in the same party1 and ,acres not with ,mrs4 ,barry1 ,eden must not be with ,mrs4 ,hall2 7#d7 ,if ,acres is with his wife1 and ,dix with his1 and ,barry not with ,mrs4 ,cole1 ,eden must be with ,mrs4 ,hall2 7#e7 ,if ,eden is with his wife1 and ,hall with his1 and ,cole with ,mrs4 ,dix1 ,acres must not be with ,mrs4 ,barry2 7#f7 ,if ,barry and ,cole and their wives are all in the same party1 and ,eden not with ,mrs4 ,hall1 ,dix must be with ,mrs4 ,eden4 ,the ,problem is to prove that there must be1 every day1 at least one married couple who are not in the same party4 pg#aib #f4 ,after the six friends1 named in ,problem #e1 had returned from their tour1 three of them1 ,barry1 ,cole1 and ,dix1 agreed1 with two other friends of theirs1 ,lang and ,mill1 that the five should meet1 every day1 at a certain table d'hte4 ,remembering how much amusement they had derived from their code of rules for walking-parties1 they devised the following rules to be observed whenever beef appeared on the table3-- 7#a7 ,if ,barry takes salt1 then either ,cole or ,lang takes one only of the two condiments1 salt and mustard3 if he takes mustard1 then either ,dix takes neither condiment1 or ,mill takes both4 7#b7 ,if ,cole takes salt1 then either ,barry takes only one condiment1 or ,mill takes neither3 if he takes mustard1 then either ,dix or ,lang takes both4 7#c7 ,if ,dix takes salt1 then either ,barry takes neither condiment or ,cole take both3 if he takes mustard1 then either ,lang or ,mill takes neither4 7#d7 ,if ,lang takes salt1 then ,barry or ,dix takes only one condiment3 if he takes mustard1 then either ,cole or ,mill takes neither4 7#e7 ,if ,mill takes salt1 then either ,barry or ,lang takes both condiments3 if he takes mustard1 then either ,cole or ,dix takes only one4 ,the ,problem is to discover whether these rules are compatible2 and1 if so1 what arrangements are possible4 ,n4,b4 ,in this ,problem1 it is assumed that the phrase if ,barry takes salt allows of two possible cases1 viz4 7#a7 he takes salt only2 7#b7 he takes both condiments4 ,and so with all similar phrases4 ,it is also assumed that the phrase either ,cole or ,lang takes one only of the two condiments allows three possible cases1 viz4 7#a7 ,cole takes one only1 ,lang takes both or neither2 7#b7 ,cole takes both or neither1 ,lang takes one only2 7#c7 ,cole takes one only1 ,lang takes one only4 ,and so with all similar phrases4 ,it is also assumed that every rule is to be understood as implying the words and vice vers4 ,thus the first rule would imply the addition and1 if either ,cole or ,lang takes only one condiment1 then ,barry takes salt4 pg#aic #g4 7#a7 ,brothers1 who are much admired1 are apt to be self-conscious2 7#b7 ,when two men of the same height are on opposite sides in ,politics1 if one of them has his admirers1 so also has the other2 7#c7 ,brothers1 who avoid general ,society1 look well when walking together2 7#d7 ,whenever you find two men1 who differ in ,politics and in their views of ,society1 and who are not both of them ugly1 you may be sure that they look well when walking together2 7#e7 ,ugly men1 who look well when walking together1 are not both of them free from self-consciousness2 7#f7 ,brothers1 who differs in ,politics1 and are not both of them handsome1 never give themselves airs2 7#g7 ,john declines to go into ,society1 but never gives himself airs2 7#h7 ,brothers1 who are apt to be self-conscious1 though not both of them handsome1 usually dislike ,society2 7#i7 ,men of the same height1 who do not give themselves airs1 are free from self-consciousness2 7#aj7 ,men1 who agree on questions of ,art1 though they differ in ,politics1 and who are not both of them ugly1 are always admired2 7#aa7 ,men1 who hold opposite views about ,art and are not admired1 always give themselves airs2 7#ab7 ,brothers of the same height always differ in ,politics2 7#ac7 ,two handsome men1 who are neither both of them admired nor both of them self-conscious1 are no doubt of different heights2 7#ad7 ,brothers1 who are self-conscious1 and do not both of them like ,society1 never look well when walking together4 ,n4,b4 ,see ,note at end of ,problem #b4 pg#aid #h4 7#a7 ,a man can always master his father2 7#b7 ,an inferior of a man's uncle owes that man money2 7#c7 ,the father of an enemy of a friend of a man owes that man nothing2 7#d7 ,a man is always persecuted by his son's creditors2 7#e7 ,an inferior of the master of a man's son is senior to that man2 7#f7 ,a grandson of a man's junior is not his nephew2 7#g7 ,a servant of an inferior of a friend of a man's enemy is never persecuted by that man2 7#h7 ,a friend of a superior of the master of a man's victim is that man's enemy2 7#i7 ,an enemy of a persecutor of a servant of a man's father is that man's friend4 ,the ,problem is to deduce some fact about great-grandsons4 ,n4,b4 ,in this ,problem1 it is assumed that all the men1 here referred to1 live in the same town1 and that every pair of them are either friends or enemies1 that every pair are related as senior and junior1 superior and inferior1 and that certain pairs are related as creditor and debtor1 father and son1 master and servant1 persecutor and victim1 uncle and nephew4 #i4 ,jack ,sprat could eat no fat3 ,his wife could eat no lean3 ,and so1 between them both1 ,they licked the platter clean4 ,solve this as a ,sorites-,problem1 taking lines #c and #d as the ,conclusion to be proved4 ,it is permitted to use1 as ,premisses1 not only all that is here asserted1 but also all that we may reasonably understand to be implied4 pg#aie ,,notes ,,to ,,appendix4 7,a7 ,see p4 #afg1 line #f4 ,it may1 perhaps1 occur to the ,reader1 who has studied ,formal ,logic that the argument1 here applied to the ,propositions ,i and ,e1 will apply equally well to the ,propositions ,i and ,a 7since1 in the ordinary text-books1 the ,propositions ,all xy are z and ,some xy are not z are regarded as ,contradictories74 ,hence it may appear to him that the argument might have been put as follows3-- ,we now have ,i and ,a 'asserting4' ,hence1 if the ,proposition ',all xy are z' be true1 some things exist with the ,attributes x and y3 i4e4 ',some x are y4' ,also we know that1 if the ,proposition ',some xy are not-z' be true the same result follows4 ,but these two ,propositions are ,contradictories1 so that one or other of them must be true4 ,hence this result is always true3 i4e4 the ,proposition ',some x are y' is always true6 ,quod est absurdum4 ,hence ,i cannot assert4 ,this matter will be discussed in ,part ,,ii2 but ,i may as well give here what seems to me to be an irresistable proof that this view 7that ,a and ,i are ,contradictories71 though adopted in the ordinary text-books1 is untenable4 ,the proof is as follows3-- ,with regard to the relationship existing between the ,class 'xy' and the two ,classes 'z' and 'not-z'1 there are four conceivable states of things1 viz4 7#a7 ,some xy are z1 and some are not-z2 7#b7 none 7#c7 ,no xy some 7#d7 none ,of these four1 ,no4 7#b7 is equivalent to ,all xy are z1 ,no4 7#c7 is equivalent to ,all xy are not-z1 and ,no4 7#d7 is equivalent to ,no xy exist4 ,now it is quite undeniable that1 of these four states of things1 each is1 a priori1 possible1 some one must be true1 and the other three must be false4 ,hence the ,contradictory to 7#b7 is ,either 7#a7 or 7#c7 or 7#d7 is true4 ,now the assertion ,either 7#a7 or 7#c7 is true is equivalent to ,some xy are not-z2 and the assertion 7#d7 is true is equivalent to ,no xy exist4 ,hence the ,contradictory to ,all xy are z may be expressed as the ,alternative ,proposition ,either some xy are not-z1 or no xy exist1 but not as the ,categorical ,proposition ,some y are not-z4 pg#aif 7,b7 ,see p4 #aga1 at end of ,section #b4 ,there are yet other views current among ,the ,logicians1 as to the ,existential ,import of ,propositions1 which have not been mentioned in this ,section4 ,one is1 that the ,proposition some x are y is to be interpreted1 neither as ,some x exist and are y1 nor yet as ,if there were any x in existence1 some of them would be y1 but merely as ,some x can be y2 i4e4 the ,attributes x and y are compatible4 ,on this theory1 there would be nothing offensive in my telling my friend ,jones ,some of your brothers are swindlers2 since1 if he indignantly retorted ,what do you mean by such insulting language1 you scoundrel81 ,i should calmly reply ,i merely mean that the thing is conceivable----that some of your brothers might possibly be swindlers4 ,but it may well be doubted whether such an explanation would entirely appease the wrath of ,jones6 ,another view is1 that the ,proposition ,all x are y sometimes implies the actual existence of x1 and sometimes does not imply it2 and that we cannot tell1 without having it in concrete form1 which interpretation we are to give to it4 ,this view is1 ,i think1 strongly supported by common usage2 and it will be fully discussed in ,part ,,ii3 but the difficulties1 which it introduces1 seem to me too formidable to be even alluded to in ,part ,i1 which ,i am trying to make1 as far as possible1 easily intelligible to mere beginners4 7,c7 ,see p4 #agc1 #d4 ,the three ,conclusions are ,no conceited child of mine is greedy2 ,none of my boys could solve this problem2 ,some unlearned boys are not choristers4 pg#aig ,,index4 #a4 ,tables4 ,i4 ,biliteral ,diagram4 ,attributes of ,classes1 and ,compartments1 or ,cells1 assigned to them #be ,,ii4 do4 ,representation of ,uniliteral ,propositions of ,existence #cd ,,iii4 do4 ,representation of ,biliteral ,propositions of ,existence and of ,relation #ce ,,iv4 ,triliteral ,diagram4 ,attributes of ,classes1 and ,compartments1 or ,cells1 assigned to them #db ,v4 do4 ,representation of ,particular and ,universal ,negative ,propositions1 of ,existence and of ,relation1 in terms of x and m #df ,,vi4 do4 do41 in terms of y and m #dg ,,vii4 do4 ,representation of ,universal ,affirmative ,propositions of ,relation1 in terms of x and m #dh ,,viii4 do4 do4 in terms of y and m #di ,,ix4 ,method of ,subscripts4 ,formul and ,rules for ,syllogisms #gh #b4 ,words c4 explained4 ',abstract' ,proposition #ei ',adjuncts' #a ',affirmative' ,proposition #aj ',attributes' #a ',biliteral' ,diagram #bb ,proposition #bg ',class' #a ,classes1 arbitrary limits of #c 1 subdivision of #d pg#aih ',classification' #a ',codivisional' ,classes #c ',complete' ,conclusion of a ,sorites #he ',conclusion' of a ,sorites ,syllogism #ef ',concrete' ,proposition #ei ',consequent' in a ,sorites #he ,syllogism #ef ',converse' ,propositions #ca ',conversion' of a ,proposition ',copula' of a ,proposition #i ',definition' #f ',dichotomy' #c ',differentia' #a ',division' #c ',eliminands' of a ,sorites #he ,syllogism #ef ',entity' #gj ',equivalent' ,propositions #ag ',fallacy' #ha ',genus' #a ',imaginary' ,class ,name #d ',individual' #b ',like'1 and ',unlike'1 ,signs of ,terms #gj ',name' #d ',negative' ,proposition #aj ',normal' form of a ,proposition #i of ,existence #aa of ,relation #ab ',nullity' #gj ',partial' ,conclusion of a ,sorites #he ',particular' ,proposition #i ',peculiar' ,attributes #a ',predicate' of a ,proposition #i of a ,proposition of ,existence #aa ,relation #ab ',premisses' of a ,sorites #he ,syllogism #ef pg#aii ',proposition' #h 'in ,i'1 'in ,e'1 and 'in ,a' #i 'in terms of' certain ,letters #bg of ,existence #aa of ,relation #ab ',real' ,class #a ',retinends' of a ,sorites #he ,syllogism #ef ',sign of ,quantity' in a ,proposition #i ',sitting on the ,fence' #bf ',some'1 technical meaning of #h ',sorites' #he ',species' #a ',subject' of a ,proposition #i of ,existence #aa of ,relation #ab ',subscripts' of ,terms #gj ',syllogism' #ef ,symbol 4'4 and #gj ',terms' of a ,proposition #i ',things' #a ,translation of ,proposition from 'concrete' to 'abstract' #ei 'abstract' to 'subscript' #gb ',triliteral' ,diagram #ci ',underscoring' of letters #ia ',uniliteral' ,proposition #bg ',universal' #aj ',universe of ,discourse' 7or ',univ4'7 #ab ',unreal' ,class #a ',unreal' ,name #d pg#bjj ,,the ,,end4 px-#a ,,works ,,by ,,lewis ,,carroll4 99 99 99 99 99 ,,published ,,by ,,macmillan ,,and ,,co41 ,,ltd41 ,,london4 99 99 99 99 99 ,,alice',s ,,adventures ,,in ,,wonderland4 ,with ,forty-two ,illustrations by ,,tenniel4 7,first published in #ahfe47 ,cr4 #hvo1 cloth1 gilt edges1 price #fs4 net4 ,eighty-sixth ,thousand4 ,,the ,,same2 ,,people',s ,,edition4 7,first published in #ahhg47 ,cr4 #hvo1 cloth1 price #bs4 #f;d4 net4 ,forty-eighth ,thousand4 ,,aventures ,d',,alice ,,au ,,pays ,,des ,,merveilles4 ,traduit de l',anglais par ,,henri ,,bu4 ,ouvrage illustr de #db ,vignettes par ,,john ,,tenniel4 7,first published in #ahfi47 ,cr4 #hvo1 cloth1 gilt edges1 price #fs4 net4 ,second ,thousand4 ,alice's ,abenteuer im ,wunderland4 ,aus dem ,englischen von ,antonie ,zimmermann4 ,mit #db ,illustrationen von ,,john ,,tenniel4 7,first published in #ahfi47 ,crown #hvo1 cloth1 gilt edges1 price #fs4 net4 ,,le ,,avventure ,d',,alice ,,nel ,,paese ,,delle ,,meraviglie4 ,tradotte dall' ,inglese da ,t4 ,,pietrocola-,,rossetti4 ,con #db ,vignette di ,,giovanni ,,tenniel4 7,first published in #ahgb47 ,crown #hvo1 cloth1 gilt edges1 price #fs4 net4 ,,alice',s ,,adventures ,,under ,,ground4 ,being a ,facsimile of the original ,,ms4 ,book1 which was afterwards developed into ,alice's ,adventures in ,wonderland4 ,with ,thirty-seven ,illustrations by the ,author4 7,begun1 ,july #ahfb2 finished1 ,feb4 #ahfc2 first published1 in facsimile1 in #ahhf47 ,crown #hvo1 cloth1 gilt edges1 price #ds4 net4 ,third ,thousand4 ,,the ,,nursery ,,alice4 ,containing ,twenty ,coloured ,enlargements from ,,tenniel',s ,illustrations to ,alice's ,adventures in ,wonderland4 ,with text adapted to ,nursery ,readers4 ,cover designed by ,e4 ,,gertrude ,,thomson4 7,first published in #ahij47 #dto1 boards1 price #as4 net4 ,eleventh ,thousand4 px-#b ,,through ,,the ,,looking-,,glass1 ,,and ,,what ,,alice ,,found ,,there4 ,with ,fifty ,illustration by ,,tenniel4 7,first published in #ahga47 ,cr4 #hvo1 cloth1 gilt edges1 price #fs4 net4 ,sixty-first ,thousand4 ,,through ,,the ,,looking-,,glass1 ,,and ,,what ,,alice ,,found ,,there2 ,,people',s ,,edition4 7,first published in #ahhg47 ,crown #hvo1 cloth1 gilt edges1 price #bs4 #f;d4 net4 ,thirtieth ,thousand4 ,,alice',s ,,adventures ,,in ,,wonderland2 ,,and ,,through ,,the ,,looking-,,glass2 ,,people',s ,,editions4 ,both ,books together in ,one ,volume4 7,first published in #ahhg47 ,crown #hvo1 cloth1 gilt edges1 price #ds4 #f;d4 net4 ,twelfth ,thousand4 ,,the ,,hunting ,,of ,,the ,,snark4 ,an ,agony in ,eight ,fits4 ,with ,nine ,illustrations1 and two large gilt designs on cover1 by ,,henry ,,holiday4 7,first published in #ahgf47 ,crown #hvo1 cloth1 gilt edges1 price #ds4 #f;d4 net4 ,twentieth ,thousand4 ,,rhyme8 ,,and ,,reason8 ,with ,sixty-five ,illustrations by ,,arthur ,b4 ,,frost1 and nine by ,,henry ,,holiday4 7,first published in #ahhc1 being a reprint1 with a few additions1 of the comic portion of ,phantasmagoria and other ,poems1 published in #ahfi1 and of ,the ,hunting of the ,snark1 published in #ahgf47 ,crown #hvo1 cloth1 gilt edges1 price #ds4 #f;d4 net4 ,sixth ,thousand4 ,,symbolic ,,logic4 ,in three ,parts1 which will be issued separately3-- ,,part ,i4 ,elementary4 7,first published in #ahif47 ,crown #hvo1 limp cloth1 price #bs4 net4 ,second ,thousand1 ,fourth ,edition4 ,,part ,,ii4 ,advanced4 ,,part ,,iii4 ,transcendental4 ,in preparation4 ,n4,b4--,an envelope1 containing two blank ,diagrams 7,biliteral and ,triliteral7 and #i ,counters 7#d ,red and #e ,grey7 can be had for #c;d41 by post #d;d4 px-#c ,a ,,tangled ,,tale4 ,reprinted from ,the ,monthly ,packet4 ,with ,six ,illustrations by ,,arthur ,b4 ,,frost4 7,first published in #ahhe47 ,crown #hvo1 cloth1 gilt edges1 price #ds4 #f;d4 net4 ,fourth ,thousand4 ,,sylvie ,,and ,,bruno4 ,with ,forty-six ,illustrations by ,,harry ,,furniss4 7,first published in #ahhi47 ,crown #hvo1 cloth1 gilt edges1 price #gs4 #f;d4 net4 ,twelfth ,thousand4 ,n4,b4--,this book contains #cie pages--nearly as much as the two ,alice' books put together4 ,,sylvie ,,and ,,bruno ,,concluded4 ,with ,forty-six ,illustrations by ,,harry ,,furniss4 7,first published in #ahic47 ,crown #hvo1 cloth1 gilt edges1 price #gs4 #f;d4 net4 ,third ,thousand4 ,n4,b4--,this book contains #daa pages4 ,,original ,,games ,,and ,,puzzles4 ,crown #hvo1 cloth1 gilt edges4 ,in preparation4 ,,three ,,sunsets1 and ,other ,poems4 ,with ,twelve ,illustrations by ,e4 ,,gertrude ,,thomson4 ,fcap4 #dto1 cloth1 gilt edges4 ,n4,b4--,this will be a reprint1 possibly with a few additions1 of the serious portion of ,phantasmagoria1 and other ,poems1 published in #ahfi4 99 99 99 99 99 ,,advice ,,to ,,writers4 ,buy ,,the ,,wonderland ,,case ,,for ,,postage-,,stamps1 invented by ,,lewis ,,carrol1 ,oct4 #bi1 #ahhh1 size #d inches by #c1 containing #ab separate pockets for stamps of different values1 #b ,coloured ,pictorial ,surprises taken from ,alice in ,wonderland1 and #h or #i ,wise ,words about ,letter-,writing4 ,it is published by ,messrs4 ,,emberlin ,,son1 #d ,magdalene ,street1 ,oxford4 ,price #as4 ,n4,b4--,if ordered by ,post1 an additional payment will be required1 to cover cost of postage1 as follows3-- ,one copy1 #a;d4 ,two or three do41 #b;d4 ,four do41 #b;d4 ,five to fourteen do41 #c;d4 ,each subsequent fourteen or fraction thereof1 #a;d4 99 99 99 99 99 99 99 99 99 99 ,transcriber's ,note ,this book makes extensive use of page references4 ,to assist the reader1 page markers in the forms pg-ix1 pg#aic px-#c have been included in the right margin at points corresponding closely to the tops of the original pages4 ,these may be searched for to locate the material referred to4 ,in the main section1 these page markers are always given with #c digits including1 if necessary1 leading zeroes4 ,this book contains a large number of line drawn illustrations which are un-credited4 ,as these cannot be rendered here in the original manner they have been reproduced as well as possible in the manner known as ,,ascii art4 ,a number of transcription errors were found in the original book4 ,as these were clearly not part of the ,author's intention they have1 as far as possible1 been identified and corrected in accordance with the methods given by the ,author4 ,these corrections are listed here below with their locations and original text4 ,in these notes the word 'natural' identifies a letter symbol occurring without a prime mark4 ,page viii3 #ahi corrected to #aid4 ,page viii3 #ahh corrected to #aib4 ,page xv1 ',real' and ',unreal'1 or ',imaginary'1 ,classes3 #a corrected to #b4 ,page xix1 ,propositions beginning with ,some3 #ah corrected to #ai4 ,page xix1 ,rules3 #ai corrected to #bj4 ,page xix1 ,the ,west and ,east ,halves 4443 #bd corrected to #bc4 ,page xxi1 ,the ,proposition ,all x are y 4443 was originally shown as occurring in page #cd4 ,page xxii1 ,and of three other similar arrangements3 #cg corrected to #cf4 ,page xxiii1 ,the ,proposition ',no xm exist'3 #dc corrected to #dd4 ,page #jfj3 contruct corrected to construct4 ,page #jid1 ,paper ,v3 missing word it supplied4 ,page #aaa1 #bh3 ,no h are k-natural corrected to ,no h are k-prime4 ,page #aaa1 #cj3 ,no a are h-natural corrected to ,no a are h-prime4 ,page #aaa1 #cj3 ,no c are n-natural corrected to ,no c are n-prime4 ,page #abc1 #eg 7d73 mortally offended if ,i fail to notice them corrected to mortally offended4 ,page #abh1 #cd3 ,some x-prime are y corrected to ,some x-natural are y4 ,page #adf1 #cj3 x#am-prime#j corrected to x#am-natural#j4 ,page #adg1 #cb3 xm-natural#j corrected to xm-prime#j4 ,page #aef1 #ah 7#d_/a73 be corrected to be-sub3zero4 ,page #aef1 #bb 7#e_/a73 ch corrected to ch-sub3zero4 ,page #aeg1 #bc 7#e_/b73 second underline corrected from single to double4 ,page #aeg1 #bc 7#b_/b73 first underline corrected from single to double4 ,page #aeg1 #bc 7#b73 h#a;c corrected to h#a;c-sub3zero4 ,page #aeg1 #bf 7#e_/a73 a#a;c-natural#j corrected to a#a;c-prime#j4 ,page #aeg1 #bf 7#b73 e#a;c-natural#j corrected to e#a;c-prime#j4 ,page #aeg1 #bi 7#h_/b73 first underline corrected from single to double4 ,page #afa1 #cf 7#d_/b73 e'd-prime corrected to e'd-natural4 ,page #afa1 #ci 7#a_/b73 c-primed corrected to c-naturald4 ,page #afa1 #dj3 a and b interchanged4 ,page #afa1 #dc 7#a_/a73 b-natural#a;e#j corrected to b-prime#a;e#j4 ,page #afb1 #eb 7#c_/a73 h'k-prime#j corrected to h'k-natural#j4 ,page #afc1 #ee 7#c_/b73 c'd-prime corrected to c'd-natural4 ,page #afc1 #eg 7#a_/b73 h-naturald' corrected to h-primed'4 ,in the original book at the top of page #ig1 the following text occurred3 ,n4,b4 ,the numbers at the foot of each page indicate the pages where the corresponding matter may be found4 ,in accordance with the un-paged medium here this has been changed to3 ,n4,b4 ,reference tags for ,examples1 ,answers ,solutions will be found in the right margin4 ,the part of the book to which this relates contains1 by sections1 ,examples 7,exercises for the student71 ,answers 7to the ,examples7 ,solutions 7,worked ,answers74 ,all ,example sections have corresponding ,answer sections4 ,for ,sections #b #c1 worked ,solutions are not supplied2 for ,sections #d-g1 ,solutions are given by #b different methods4 ,in association with this1 the original text contained editorial notes at the foot of each page giving the page numbers for the related ,sections4 ,in this version1 these notes are replaced with marginal tags such as ,,ex#c1 ,,an#d1 ,,sl#e1 ,,sl#f-;,a and ,,sl#g-;,b which are placed at the top of each ,section to identify the current location4 ,as with page tags1 these may be searched for to locate the material refered to4 7,a search for ,,sl#d should find successively both ,,sl#d-;,a ,,sl#d-;,b47 ,these tags are unique regardless of case4