"SN- 
 
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 Tvv
 
 UCSB LIBRARY 
 
 PICTURE LOGIC
 
 PRINTED BY 
 
 SI'OTTISVVOODE AND CO., NEW-STREET SQUARE 
 LONDON
 
 Frontispiece. 
 
 
 Destrawney, after carefully perusing the following pages, masters the Man-eater 
 Logic, and scares its foul offspring to flight from the bones of countless unhappy 
 victims upon which they were wont to gloat and feed.
 
 PICTUEE LOGIC 
 
 AN ATTEMPT TO POPULARISE THE SCIENCE OF 
 
 REASONING BK THE COMBINATION OF HUMOROUS PICTURES WITH 
 
 EXAMPLES OF Hl'ASONlNG TAKEN FROM DAILY LIFE 
 
 ALFRED JAMES SWINBURNE, B.A. 
 
 QUEEN'S COLLEGE, OXFOUD 
 
 The Lion of Human Understanding in the tangle of Logical 
 Knots assisted bv the Mouse of Illustration 
 
 WITH ORIGINAL ILLUSTRATIONS FROM DRAWINGS BY THE 
 AUTHOR ENRRAVED ON WOOD BY G. PEARSON 
 
 FIFTH EDITION 
 
 LONDON 
 LONGMANS, GREEN, AND CO. 
 
 AND NEW YORK : 15 EAST 16* STREET 
 
 1887 
 
 All riuht* ret'reed
 
 INTEODUCTION. 
 
 ii was at the beginning of a certain Long Vacation when 
 my father sent for me and delivered himself of the follow- 
 ing remarks : ' My son, your scores at cricket, your racquets, 
 your prowess in the hunting-field and in your college 
 steeple-chases, your numberless invitations and popularity, 
 to you doubtless appear all that can be desired ; to me, Sir, 
 they are nothing nay more they are even positively 
 harmful, seeing that by their fascinating brightness men 
 are blinded to all sense of their true interests and aim 
 viz., to secure their degree as soon as possible with a view 
 to a start in life.' Upon my replying to my father to the 
 effect that every allowance was to be made for him as 
 having left college five-and-twenty years if, as in the pre- 
 sent instance, he manifested lamentable ignorance of the 
 whole state of the University at the present day, and that 
 his milk-and-water reading man would certainly be regarded 
 with loathing and abhorrence by all ' our fellows ' and all 
 the best men at Oxford, and consequently, sinking into ob- 
 scurity, would be ruined for life, and upon my making 
 many other similar assertions, my father, with much 
 warmth, commanded me to be silent, and then asked me if 
 I expected I was to live a life of slothful ease, because I 
 was a rich man's son ; with several other questions which 
 were not meant to be answered ; finally becoming so excited
 
 VI INTRODUCTION. 
 
 as to refer me to his own university career, a subject which 
 he quickly dropped, remembering how often he had told me 
 stories of his undergraduate days before I was sent to col- 
 lege. The result was that I was ordered to select a tutor 
 for two months in the Long Vacation and pass my modera- 
 tions in the following term, or for ever be condemned to 
 the backless slippery heights of office stools. The awful 
 thought of ' wasting my sweetness ' and withering in such 
 a dry and uncongenial soil nerved me for a desperate effort. 
 Of a restless and excitable disposition I was for some time 
 after haunted by dreams of men with pens in their ears, 
 and ledgers with columns of figures to add, so lofty that 
 their bases were on the earth while their summits were lost 
 in the clouds. I never could do mathematics not that 1 
 was quick at any work even my mother allowed this, for 
 she wrote to my tutor for matriculation to the effect that 
 'our dear Douglas had manifested symptoms of future 
 greatness, when a child, and still possessed remarkable 
 ability, if it could only be drawn out ; but alas ! there was 
 a want of application, especially in his mathematics.' I 
 therefore determined to take up Logic as a substitute for 
 Mathematics, and wrote to inform my tutor that I should 
 only want help in this subject. He selected a charming 
 spot on the north coast of Devon and we met there. He 
 had one other pupil a very quiet youth and, as it seemed 
 to me, very clever, my fear of whom was heightened con- 
 siderably when I learnt that he had intended to try for a 
 class, but, finding his books in a very imperfect state, was 
 content with passing, though determined not to miss that. 
 The awe with which this piece of information filled me I 
 never succeeded in quite shaking off, though I liked him 
 very much afterwards. He always seemed to me a sort of 
 half-way house between Mr. Practical and myself the idea 
 of any one knowing more than Mr. Practical was an idea
 
 INTRODUCTION, Tli 
 
 that never for a moment entered iny heau Old Prac ' 
 (as we called him afterwards) had such a smooth, comfort- 
 able way of settling any difficulties I proposed so reassur- 
 ing that I verily believe if he had told me that the best way 
 to learn the art of diving and remaining under for a long 
 time was to tie a heavy stone round your neck and get some 
 one to push you in, I should have tried it. His last words 
 the first night were ' Logic to-morrow.' 
 
 It is needless to say my sleep was much disturbed that 
 night with anticipations and forebodings. What was this 
 new and strange study ? Had I not always heard men 
 speak of its difficulty ? How if the momentous question, 
 ' Was I possessed of a " turn " for Logic ? ' should be an- 
 swered in the negative ; and I fell asleep to dream of 
 mysterious figures, numbers, and symbols on the one hand 
 pitted against the mocking forms of clerks, managers, and 
 office boys on the other.
 
 CONTENTS. 
 
 CHAPTKK PAGE 
 
 INTRODUCTION ......... v 
 
 I. WHAT is SCIENCE? 1 
 
 II. WHAT is ART? 14 
 
 III. LOGIC is A SCIENCE AND AN ART 21 
 
 IV. FORM AND MATTER OF THOUGHT 29 
 
 V. THE KECONCILIATION, AND AXSO HOW LOGIC is MORE OF 
 
 A SCIENCE THAN AN ART 38 
 
 VI. LOGIC THE SCIENCE OF SCIENCES AND ART OF ARTS . 43 
 
 VII. THE BELATION OF LOGIC TO LANGUAGE . . . . 48 
 
 VIII. Aii THOUGHT is COMPARISON 53 
 
 IX. THE TERM 57 
 
 X. CONNOTATION AND DENOTATION 61 
 
 XI. PROPOSITIONS 70 
 
 XII. DISTRIBUTION OF TERMS IN A PROPOSITION . . .75 
 
 XIII HEADS OF PREDICABLF.S . 75 
 
 a
 
 X CONTENTS. 
 
 CHAPTER PAGE 
 
 XIV. DEFINITION 88 
 
 XV. DIVISION 96 
 
 XVI. INFERENCE 103 
 
 XVII. SYLLOGISM 113 
 
 XVIII. SYLLOGISM 123 
 
 XIX. SYLLOGISM CANON OF FIRST FIGURE REDUCTION . 128 
 
 XX. TRAINS OF REASONING SORITES 134 
 
 XXI. HYPOTHETICAL SYLLOGISMS 136 
 
 XXII. PROBABLE REASONING 142 
 
 XXIII. THE FALLACIES 146 
 
 APPENDIX A loo 
 
 APPENDIX B 162 
 
 APPENDIX C 163 
 
 A LIST OF USEFUL FACTS IN LOGIC 177
 
 LIST OF ILLUSTRATIONS. 
 
 DKSTRAWNEY OVERCOMES THE SPHINX ' LOGIC* . Frontispiece 
 
 NONPLUSSED 2 
 
 SCIENCE PRESERVED IN JARS > Tofacr 9 
 
 SUPERSTITION 11 
 
 THE BEGINNING OF SCIENCE 16 
 
 THE BEGINNING OF ART 17 
 
 ART 17 
 
 THE LOGICAL SAUSAGE MACHINE To face 35 
 
 TROJA FUIT 4.1 
 
 SlNDBAD AND THE SAILOR. . . ..... To face 4i) 
 
 LOGIC PATS A VISIT 49 
 
 LOGIC IN TROUBLE 50 
 
 THE LOGICAL HAND 60 
 
 DENOTATIVE AND CONNOTATIVE HAND ..... 63 
 
 THE GREAT LOGIC BRANCH 73 
 
 'A WORD TO THE WISH' 78 
 
 THE ESSENCE OF MAN To face 86
 
 xii LIST OF ILLUSTRATIONS. 
 
 PA OB 
 
 THE BIPED ANIMAL WHOSE SOLE METAL is MEMORY . . 9o 
 
 THE FIUHT OF PROPOSITIONS . . . . . . ..110 
 
 DEATH OF THE UNIVERSAL . . . . . . . .11" 
 
 THE SYLLOGISTIC ALP 114 
 
 THE FRONT OF A COLLAR 118 
 
 MOOD-HUNTING To face 126
 
 PICTURE LOGIC. 
 
 CHAPTEE 1. 
 
 WHAT IS SCIENCE? 
 
 NEXT morning Mr. Practical assumed a grave look and 
 began : ' There is no lack of treatises on Logic, but 
 there is a lack of people who understand them. It is 
 the custom of Passmen to attempt to learn by heart 
 a great deal of matter they do not in the least com- 
 prehend, without attempting to realise the meaning, 
 and so fixing it in the memory. A little understood 
 is better than a volume learnt by heart. I shall not 
 expect you to remember anything you do not under- 
 stand ; nor shall I ever make use of instances other 
 than those of everyday life ; and if my illustrations 
 be too familiar to appear scientific, my excuse will be 
 that I wish to bring home to you what I say, that 
 you may realise and appreciate and so remember its 
 meaning, as a man who has swum two miles, or been 
 ill eight hours on a boat, has no difficulty in remem- 
 bering the force of the expressions " long swim " or 
 
 B
 
 2 PICTURE LOGIC. 
 
 " unpleasant cruise." The neat and concise phrases 
 you meet with in your treatises on Logic are decep- 
 tive like the ease of a good skater or runner, they 
 are the results of hard work, and you might as well 
 expect to get that ease at once without practice, as 
 imagine that by learning off those phrases you have 
 mastered Logic. Therefore, pass over all words and 
 
 Nonplussed. 
 
 instances that you do not understand as you read 
 your treatises side by side with my attempts at ex- 
 planation.' 
 
 It would be difficult to express my sensation of 
 relief at these words ; for already I had opened my 
 new ' Elements of Logic,' and, flushed with hope, 
 peeped at Chapter I. ; but, confronted by the very 
 first word, * Psychology,' I felt as staggered and faint
 
 WHAT IS SCIENCE? 8 
 
 as when, burning to learn the noble art of self- 
 defence, I put on the gloves with the noted Punisher, 
 and he knocked me down the very first blow of the 
 first lesson. * Courage,' I muttered, and pushing on, 
 saw something about * analysing phenomena ' and 
 their ' mutual relations ' and ' the mode of their 
 generation ; ' and after this, I became unconscious, 
 until I was aroused by a shout of breakfast, and 
 found myself sitting staring blankly at my book with 
 ideas of chemists, newspaper accounts of * a strange 
 phenomenon,' aunts and cousins hopelessly com- 
 plicated, and letters in the ' Field ' about the breed- 
 ing of fowls, crowding in wild confusion across my 
 mind. 
 
 ' Tell me,' resumed my tutor, < what you mean 
 by Logic, Dyver.' * Logic,' replied he, ' is the 
 science and art of reasoning, or the science of the 
 conditions upon which correct thinking depends, 
 and the art of attaining to correct thinking, or the 
 science of the formal laws of thought and other 
 definitions might be given.' 
 
 Observing my look of despair, Mr. Practical went 
 on : ' Logic seems to be a science and an art, but if I 
 asked you what is a serpent, and you replied "a 
 reptile," this would be no answer if I did not know 
 what " reptile " meant. " This is no answer, thou 
 unfeeling man ! " the beginner might well exclaim, 
 were I to rest content with defining Logic as the 
 science and art of reasoning. If Logic is a science 
 
 B 2
 
 <t PICTURE LOGIC. 
 
 and art let us leave Logic alone for the present, and 
 when we have grappled with these two mysterious 
 shadows Science and Art, return to our definitions to 
 find that the apparently different accounts of Logic 
 are only various ways of expressing the same thing. 
 Science is knowledge but this is no explanation 
 until we know what knowledge is. First, then, let 
 us try and explain, what knowledge is. 
 
 Imagine the whole world (i.e. everything that 
 exists including of course the stars and the heavens 
 and yourself) to be divided into two parts ; on the one 
 hand yourself, a being with faculties of observation ; 
 and, on the other hand, everything but yourself, ob- 
 jects which fall under that observation. And you must 
 remember that the observing powers can be turned 
 back upon yourself, so that in this sense you yourself 
 may be said at the same time to belong to both parts, 
 as being the person observing and the object observed. 
 You don't follow, Destrawney? It will be clearer 
 presently. Now all that vast number of things which 
 form the part which is not yourself have, so to speak, 
 peculiar features and differences, qualities, or attri- 
 butes, or whatever you choose to call them. What I 
 mean is that they affect you differently as you hear, 
 see, smell, touch, or taste them. Take one or two 
 instances, a star a tree a pond. Each of these 
 objects has its peculiarities or attributes. The star 
 shines, the tree blooms, the pond is stagnant. You 
 are differently affected as you glance from the one
 
 WHAT IS SCIENCE? 5 
 
 to the other. And this employment of the senses 
 given you by nature is knowledge. The world around 
 you is teeming with attributes, qualities, or pecu- 
 liarities ; particular facts you may call them or 
 phenomena (from the Greek fyaivopai, I appear or 
 show myself), and the noting or acceptation of these 
 particular facts by the senses is knowledge. The 
 iion roars, the rain falls, the flame rises, &c., and when 
 I say so I prove the existence of knowledge in me.' 
 
 ' I think I have some vague idea of your meaning,' 
 said I, ' but I always thought knowledge was some- 
 thing grander more difficult somehow.' 
 
 ' Of course,' he went on, < I only take the simplest 
 instances of the employment of our senses on the 
 world around us. It must be borne in mind that 
 each thing included under that term has an infinite 
 number of such attributes or phenomena. Take the 
 moon. That it is round and mountainous, &c., we 
 know, but there are a countless number of pecu 
 liarities of the moon that we do not know anything 
 about, and the advance of knowledge only means the 
 observation of, or direction of our senses to, attri- 
 butes or phenomena not yet discovered or known to 
 exist. The man who first applied steam to loco- 
 motion had noticed an attribute in steam hitherto 
 unobserved, viz. its elasticity. Knowledge, then, is 
 the application of our senses to the phenomena or 
 attributes of things around us. But it is something 
 more than the mere five senses that man employs.
 
 6 PICTUEE LOGIC. 
 
 The brute creation can hear, see, smell, touch, and 
 taste ; but man has a higher power as well that we 
 may call reason ; a faculty by which he can gather 
 and group together particular facts and form uni- 
 versal ideas and propositions. Not only are we 
 aware of the presence of " this horse," " that draper," 
 " yonder mountain ; " but we can close our eyes and 
 picture to ourselves the image of a horse generally 
 that is not any horse in particular ; and so with the 
 draper and the mountain. And not only can we 
 say " this horse is four-legged," " that draper is 
 weak," " yonder mountain attracts the clouds ; " 
 but we can also say, " all horses are four-legged," 
 " all drapers are weak," " all mountains attract the 
 clouds," supposing our observations to have been 
 sufficient to ground these universal propositions 
 upon. And notice the signs of the two different 
 propositions. The sign of a particular proposition is 
 generally "this " or "that "or " some "; l of a uni- 
 versal, "all" or "no."' 
 
 I could not help thinking how learned 1 was 
 becoming, and how easily I could now refute my 
 father if he ever again dared to argue with me. 
 
 ' Now, this second kind of knowledge we call 
 universal knowledge as opposed to particular know- 
 ledge, and the results attained to are called generali- 
 
 1 ' This ' or ' that ' may in another sense be regarded as the signs of 
 universal propositions, when they mean the ' whole of this ' or the 
 ' whole of that.' See p. 7*.
 
 WHAT IS SCIENCE? 7 
 
 sations, uniformities, universal propositions, or laws, 
 or principles, as opposed to the particular facts from 
 which they are derived.' 
 
 ' Need we remember all those names? ' I gasped. 
 
 * Never mind them for the present,' he continued. 
 ' Kemember that these universal propositions derived 
 from particular facts are called science, and thus 
 science is universal knowledge (where knowledge is 
 used for the results attained as well as the process of 
 attaining them) . And science is divided into branches 
 according to the nature of the objects with which it 
 is concerned, and each branch is spoken of as a 
 separate science. Thus, if I gather universal truths 
 from particular facts observed about the stars, the 
 science is astronomy ; and if about the earth, 
 geology ; and if about trees, botany. For instance, 
 I observe this tree buds in the spring, and that and 
 that, and so on until at last I lay aside my particulars, 
 and assert once for all that " all trees bud in the 
 spring," and this proposition forms a part of the 
 science of botany. Now, gather your universal 
 truths from particular facts observed about thought 
 and the science is Logic.' 
 
 At this triumphant flourish Dyver, who had for 
 some time exhibited signs of restlessness, could 
 restrain himself no longer, but burst in with his 
 difficulties. ' Firstly,' cried he, * what do you mean 
 by thought ? and secondly, why should men care to 
 draw these generalisations that you speak of?' 
 
 ' Of thought more anon,' replied our tutor ; ' as
 
 8 PICTUEE LOGIC. 
 
 to the generalisations, you must recall to your memory 
 the division above mentioned, yourself or mind, on 
 the one hand, and all external phenomena or matter 
 on the other ; and on the side of mind or yourself. 
 You will find implanted by nature an inclination to 
 gather together the like, to classify, and arrange, 
 and group similar phenomena together a yearning 
 after generalisation more conspicuous in women 
 than in men, because in women the natural impulses 
 are less restrained by reason. But of this hereafter ; 
 for the present recollect what we have said, that 
 knowledge was an employment of the senses upon 
 external phenomena ; that knowledge was of two 
 kinds, universal and particular ; and that universal 
 knowledge is called science, and that the branches 
 of science are named from the objects with which 
 they have to do ; and the science of thought is Logic. 
 Of art we must speak to-morrow.' 
 
 That day we went for a lovely walk, Dyver seem- 
 ing buried in meditations of future knots for logical 
 solution, and whether it was that I over-tired myself, 
 or whether it was through working a brain usually 
 idle, I don't know, but I had a remarkable dream 
 that night. I saw an old gentleman who had been 
 my house-master at Eton, standing at the foot of a 
 range of hills, and busily engaged in picking up 
 things, and putting something now and then into 
 a huge preserving jar that was at his side. On 
 approaching nearer I heard him muttering some-
 
 WHAT IS SCIENCE? 9 
 
 thing over and over again about knowledge and 
 triumphs; ' Bather tiring work, isn't it? ' I ventured 
 to ask. ( What triumphs do you refer to ? ' ' Why, 
 the triumphs of science, young man,' he sharply 
 retorted. * Don't you call it a triumph to arrange, 
 group, and classify yonder untidy wilderness of par- 
 ticulars ? to detect similarities and form universal 
 propositions, or uniformities, or laws, and lay by 
 these laws in jars for future use ? to introduce neat- 
 ness and order in that tangled medley before you, 
 that bewildering chaos of confusion ? ' * Most cer- 
 tainly I do, but I don't quite see how you mean. I 
 don't pretend to be clever, though,' 
 
 ' Keep silence, and observe the process. I'll take 
 a very simple uniformity to make it plain to you.' 
 He then picked up a stone and let go of it, and 
 it fell to the ground. ' This body tends to fall to 
 the earth,' said he; and repeated the operation 
 with a book, a chair, a bottle, a purse, and several 
 other things, each time repeating the formula, 
 ' This body tends to fall to the earth,' much in 
 the same way as a man repeats the responses in 
 church. Then he wrote something on a slip of 
 paper, and handed it to me. It was 'All bodies 
 tend to fall to the earth (uniformity or law of 
 gravity).' ' There,' said he, 'that's the process; of 
 course simple uniformities like these were observed 
 long ago. I'm engaged in much more abstruse and 
 complicated work now, but the process is precisely
 
 10 PICTURE LOGIC. 
 
 the same.' He slipped the paper into one of the 
 jars already filled, corked the jar carefully down, and 
 patting it affectionately, continued, 'You see the 
 advantage. What a saving of time and trouble, for 
 we need not look every time at our stone, book, 
 purse, &c., i.e. the particulars, but we have our com- 
 prehensive law once for all, and we can dispense 
 with all further experiments with the particular 
 facts. All knowledge, indeed, is power, and this is 
 as true in complicated instances but less obvious 
 than here. You hold in your hand a brittle orna- 
 ment ; without any physical effort your knowledge 
 gives you the power to break it, for you know that 
 if you let it go it will fall to the earth and break, 
 because you have drawn the law of gravity from the 
 observation of particular facts.' 
 
 ' Quite so,' said I, growing a little weary ; ( but 
 excuse me, what is that bump on your forehead ? ' 
 
 ' That,' said he, ' is the bump of generalisation, 
 and it indicates an innate desire in man to observe 
 similarities, and group and gather particulars, and in 
 virtue of the possession of similar qualities, and so 
 make laws. I've great trouble in preventing people, 
 especially women, from giving way to this impulse 
 too much. Men have what they call " hobbies," and 
 women "jump at conclusions." As 1 was musing 
 upon this, and thinking how I would enlighten their 
 dark minds at home, I was recalled to myself by 
 an angry shout from Mr. Science (for that he told
 
 WHAT IS SCIENCE? 11 
 
 me was his name). Turning my eyes in the direction 
 of his shout, I saw an old woman flying through the 
 air with a large comet under her right arm. She 
 clung tightly to it as if for support. 'Ho, there, 
 where are you going to with that comet ? ' cried he. 
 * please, Mr. Science,' said she, ' I've got a law at 
 home that "all comets are signs of war," and as mother 
 
 Superstition. 
 
 made the law without seein' no pertiklers, we thought 
 we'd collect pertiklers arterwards.' ' Be off,' yelled 
 the old man in a perfect frenzy of rage, ' how dare 
 you make laws without a sufficient number of par- 
 ticulars to warrant your conduct. Be off, I say, you 
 old baggage, and drop that comet this moment ! ' I 
 covered my face lest he should see my amusement at 
 his ferocious gesticulations, when the old woman fled, 
 still clasping the comet in her arms.
 
 12 PICTURE LOGIC. 
 
 * You see those two hills beyond,' he said, turn- 
 ing to me again ; ' we find it hard work there. We've 
 made most progress in mathematics and astronomy. 
 We can get our particulars separately there ; but 
 those hills are composed of the particulars of che- 
 mistry and human conduct, and they're very difficult 
 to get at. And as one of the chief advantages 01 
 science is its prediction (for when we know that all 
 steam is elastic, we can predict that any particular 
 steam will be elastic), we lose much by not having 
 its aid in the arrangement of these particulars.' 
 
 1 One might almost compare your work to mining,' 
 said I, ' you seek for the gold of truth in things, and 
 when you have found it you can throw away the 
 earth or particular facts.' This seemed to me a 
 splendid simile, and I only wish Dyver could have 
 heard it, but the old man took no notice of it at all. 
 
 * It's very hard to find uniformities in things,' he 
 continued, ' when you can't get them separately. 
 Supposing gunpowder was always found with some 
 other substance, and you couldn't separate them, 
 how would you know whether it was the gunpowder 
 or the other substance which possessed the quality of 
 exploding when a spark was applied ? So you can't 
 get your uniformities or laws, and science is back- 
 ward there.' 
 
 ' Or supposing,' said I, l two men always visited 
 your house together, and at the sight of them the 
 dog always exploded into barking, unless you could
 
 WHAT IS SCIENCE? 13 
 
 separate or isolate the men, you couldn't make any 
 law as to which of the men the dog was barking at.' 
 ' Yes,' said he, smiling contemptuously, * that 
 would do, but a better instance is' .... and he went 
 on talking about crystals and double refractory 
 powers till the whole scene changed, and I found 
 myself climbing up, as of yore, to get a nearer view 
 of the beautiful glass lustres of the chandelier at 
 home, and upsetting the ink, and being called by my 
 mother a refractory child, for that's all I knew about 
 * crystals ' and ' refractory powers.'
 
 14 PICTUEE LOGIC, 
 
 CHAPTER II. 
 
 WHAT IS ART? 
 
 NEXT morning I arose, wondering at my dream, in 
 which I had seen much more than I had heard from 
 Mr. Practical, and accounting for the prodigy by 
 supposing that all the scraps I had read at odd times 
 in our domestic British Encyclopaedia had been 
 aroused from their sleep in my memory by my late 
 efforts to think. 
 
 ' If science,' resumed Mr. Practical, * may be 
 called universal knowledge derived from particular 
 facts, art is the application of that universal 
 knowledge to particular facts, and we may speak 
 of the arts as we do of the sciences, meaning 
 thereby branches of one great art and branches 
 of one great science. By science I establish the 
 law, for instance, that "all trees bud in the 
 spring." Now supposing I were able to produce 
 a tree, I should say to myself, " Let me see, a tree is 
 to be produced ; first of all it must bud in the spring, 
 for unless it did so it would not be a perfect tree, 
 and then it must be something else, and so on ; and 
 as a sculptor complies with orders in a contract,
 
 WHAT IS ART? 15 
 
 so must I obey laws in the production of this tree, 
 and this is what we call the application of universal 
 knowledge to particular facts. And this is why the 
 laws of a science are also called conditions, because 
 without complying with them we cannot produce a 
 correct instance of a particular : e.g., from observa- 
 tion we enunciate the law, " all water has drowning 
 properties." Now this is a condition upon which 
 water's being water depends, for if a man pointed to 
 some water and said, " This water has no drowning 
 properties," we should say, " My good sir, this cannot 
 be water, then, for it does not comply with the con- 
 ditions required to constitute water." Now art is 
 the application of universal laws in this way to 
 particular facts, strictly speaking, in production, but 
 also in criticism.' 
 
 ' I don't quite understand,' said I. 
 
 * By production, I mean the process of making 
 something, as a picture, statue, or house ; by criticism 
 the process of testing the genuineness, or right to its 
 name, of something, as a star, tree, or man. In 
 either case we apply universal knowledge to particu- 
 lar facts, and the process is called art.' 
 
 Dyver, looking very subtle, here enquired whether 
 science was the process of attaining to universal 
 knowledge, or the knowledge so attained, for art 
 seemed to be the process only, and Mr. Practical 
 replied that it was difficult to say ; he believed science 
 was used for both, perhaps on the whole it was more
 
 16 PICTURE LOGIC. 
 
 often used for the knowledge attained, but it made 
 very little difference to the broad distinction between 
 science and art, and that was all he wanted to 
 show. 
 
 * To give you an illustration of what I mean by 
 science and art, I shall make a rough sketch with 
 my pencil,' he continued, scarcely a bit discomposed 
 by the penetrating subtlety of his senior pupil. 
 
 
 The Beginning of Science. 
 
 'Here we have an aged admirer of scenery. 
 Night after night he gazes on the sunset from his 
 rocky seat. He observes certain points possessed in 
 common by each sunset (to speak of sunsets as dis- 
 tinct particulars). The clouds may vary, but there 
 are certain particular rays of light he sees every 
 time he sees the sun set. He thinks to himself, " I 
 observe these sunsets agree in certain features they 
 all have certain rays of light, &c. These common
 
 WHAT IS ART? 17 
 
 elements, or uniformities, I will gather together and 
 
 make laws of them for the guidance of my boy, who 
 has shown a taste for painting." 
 
 5 Hw5 I *V4p3i& 
 
 The Beginning 01 Art. 
 
 So he draws up these common elements in the 
 form of laws, and teaches them to his boy. * All 
 
 c
 
 18 PICTURE LOGIC. 
 
 correct sunsets have such and such rays/ &c. And 
 the hoy grows up, and carries out in a particular 
 instance the laws his father drew from particular 
 instances, hy painting a picture of a particular sun- 
 set which obeys the laws his father drew ; and if it 
 obeys all of them, it is said to be a very good paint- 
 ing and a perfect work of art, and it hangs in some 
 national gallery. The first two illustrations here 
 would come under science ; the last, art.' While I 
 was laughing at the family likeness between the 
 father and son, * Could you give us an instance of 
 criticism as well ? ' asked Dyver ; f the above is 
 obviously production.' 
 
 ' I suppose it might fairly be called art to apply 
 universal laws to particulars in the way of testing 
 their truth or genuineness, and this would be criti- 
 cism. A judge of pictures looks at the sunset above 
 depicted, and tests its truth by calling up one after 
 another the laws gathered from the observation of 
 particular sunsets, and seeing whether the picture 
 before him complies with these laws. And this is 
 what is meant by saying that a picture presents to us 
 the essential, as well as any accidental, features of 
 its original.' 
 
 ' But is it the same,' said I, ' with the science 
 and art of riding, or swimming, or skating those 
 sixpenny sciences, I mean, that you buy in yellow 
 covers with pictures on ? ' ' Precisely,' replied he, 
 smiling at my earnestness; 'the particulars of swim-
 
 WHAT IS ART? 19 
 
 ining are the particular movements of the limbs by 
 this or that swimmer. These are observed by the 
 man of science their uniformities or common ele- 
 ments constituting laws or conditions and he 
 enunciates them : " All correct swimmers spread 
 their limbs in such a way," and several other laws. 
 Should he feel disposed to learn swimming himself, 
 and enter the water, attempting to spread his limbs 
 according to these laws, he would be employing art. 
 And the case is similar with shooting, or riding, or 
 skating. Wherever you draw universal knowledge 
 from particular facts you have science (the name 
 varying with the subject matter), and wherever you 
 apply your universal laws to particulars, again you 
 have art (the name varying in the same way), and 
 science and art applied to thought share the name of 
 Logic. Thus the beginning of science and art taken 
 together is the same as their end, viz. particular 
 facts, as you see in the case of the painter, the par- 
 ticular sunsets you see in fig. i. and fig. iii. are the 
 beginning and the end.' 
 
 All of a sudden Dyver clutched his pencil con- 
 vulsively, and became so engrossed in his note- book 
 that I very nearly burst out laughing ; it reminded me 
 so of the way we used to clasp our lexicons at school, 
 when the master returned unexpectedly, after leav- 
 ing us alone for a few moments. * Might not this 
 figure,' he presently asked, ' represent science and 
 art? it has just occurred to me it might/ This was 
 
 c 2
 
 20 
 
 PICTURE LOGIC. 
 
 the figure, and Mr. Practical was highly pleased 
 with it; and the more so because he told us uni- 
 versal knowledge is always regarded as something 
 
 Universals 
 
 Particulars 
 
 higher than particular we f ascend ' to it and deduce 
 from it and we talk of particulars depending upon 
 or hanging from laws or conditions.
 
 21 
 
 CHAPTER ITT. 
 
 LOGIC IS A SCIENCE AND AN ART. 
 
 ' YESTERDAY,' continued Mr. Practical, ' we saw 
 what science and art were. If Logic claims to be 
 considered a branch of science and art, we must 
 not be content until we have heard proof that Logic 
 gathers laws from particular facts, and applies laws 
 to particular facts. 
 
 ' We have already observed that the eye of the soul, 
 so to speak, can be turned back upon itself and we 
 can contemplate our very thoughts. And in this 
 field or sphere of thought we find particulars to work 
 upon, and Logic grounds upon these particular 
 thoughts uniformities, conditions, or laws in its 
 capacity of science, and applies these uniformities, 
 conditions, or laws to practice, in its capacity of art.' 
 
 * But thought,' said I, ' is so vague and difficult, 
 please make the whole thing clearer. I think I begin 
 to understand about some of it.' 
 
 'In a subsequent lecture I shall endeavour to 
 discuss thought more thoroughly showing how all 
 thought is comparison. To take, for the present, a 
 common-sense view of the matter, thought may be
 
 22 PICTUEE LOGIC. 
 
 either unexpressed or expressed. You may be sitting 
 next to a lady at dinner and you may think " This 
 lady is very ugly," this, we trust, would be an unex- 
 pressed thought. Or you may think " The weather 
 is lovely" and turning to the lady you may express 
 this thought, and it becomes a remark. Again, you 
 may in your mind form a more complicated kind of 
 thought. You may think, " All cucumber is indi- 
 gestible ; this is cucumber; therefore it is indi- 
 gestible," a thought unexpressed also. Or you may 
 think, " All young ladies are charming companions ; 
 my neighbour is a young lady ; therefore my neigh- 
 bour is a charming companion," a thought you may 
 express to her, and it becomes an inference. Now 
 it is obvious that there is an infinite number of re- 
 marks and inferences that one might make, and we 
 shall regard these remarks and inferences as thought 
 for the present for they are thought viewed from 
 the outside of the lips, so to speak, or Homer's spxos 
 686vro)v. Now, given a number of these various 
 remarks and inferences, you will find some correct, 
 some incorrect. Here, then, is work for science to 
 collect a number of correct remarks or inferences 
 (as they are called), find out their uniformities, their 
 common elements (for something in common they 
 must have, or why were they called by the same 
 name ?}, erect these into laws arid call these laws the 
 principles or conditions upon which correct remarks 
 or inferences depend precisely as the botanist did
 
 LOGIC IS A SCIENCE AND AN ART. 23 
 
 with his trees, the astronomer with his stars, and the 
 old man with the sunsets. Here, too, is work for 
 art, for the principles or conditions can be employed 
 either in the production of particular correct remarks 
 and inferences or in the criticism of the particular 
 remarks and inferences of others. And Logic is the 
 name given to the science and art, for these remarks 
 and inferences represent thoughts.' 
 
 ' How do you know when a remark or inference 
 is correct ?' asked Dyver. 
 
 I This is just what Logic would tell us, by giving 
 us the laws required to be complied with by any 
 remark or inference that is entitled to the name of 
 " correct." As a matter of fact, we generally know 
 by instinct and without any extraneous aid whether 
 any remark or inference is correct or not. Particular 
 correct thoughts were distinguished from particular 
 incorrect thoughts before Logic was thought of, but 
 Logic gives us the why and wherefore, and enables 
 us consciously to detect errors they unconsciously 
 detected before.' 
 
 I 1 am afraid I don't understand these last words,' 
 I remarked. 
 
 ' Never mind. All you need recollect is this 
 certain thoughts are called correct among men 
 and certain thoughts incorrect. You step into a 
 third class carriage. It is full of costermongers and 
 illiterate persons. The man next to the window 
 makes a remark, " Deep rivers is allers shallow." A
 
 24 PICTUEE LOGIC. 
 
 look of wonder steals slowly over every face. The 
 man proceeds to an inference. "Balloons is the 
 most riskiest travelling and I'm a goin' by the Under- 
 ground Railway ; so I think its pretty sartain I'm 
 a goin' by the most riskiest travellin'." There is a 
 hoarse laugh from all, and they tell the guard to look 
 after that man as a lunatic, one with reason or 
 thoughts perverted, for it wants no logic or clever- 
 ness to detect an incorrect thought. You return to 
 your first class carriage, and a friend tells you there 
 that what those men unconsciously did Logic enables 
 us consciously to do, for Logic gathers the common 
 elements of correct thoughts and making laws of 
 them gives us principles for guidance in the 
 production of thoughts ourselves and the criticism 
 of thoughts in the case of others.' 
 
 * Coiild you tell us any of these laws ? ' asked 
 Dyver. 
 
 ' There are three primary laws to which all the 
 laws of thought may be reduced ; and you only need 
 know their names for the present. They are 
 
 I. The Law of Identity (whatever is, is). 
 
 II. The Law of Contradiction (a thing cannot 
 
 both be and not be). 
 
 III. The Law of Excluded Middle (a thing must 
 
 either be or not be). 
 
 Simple and even absurd they appear at first sight, 
 but still they are laws obeyed, though unconsciously,
 
 LOGIC IS A SCIENCE AND AN ART. 25 
 
 by millions of men every day ; and until you realise 
 their meaning, respect them for their universality : I 
 shall devote more time to them afterwards.' 
 
 'Do you mean to say/ indignantly demanded 
 Dyver, ' that by learning these mere truisms for 
 that's what they seem to me to be that we are 
 helped at all in the attainment of correct thoughts, 
 and the avoidance of error? Suppose I want to 
 invest some money in the Peruvian Stocks. The 
 only question that frightens me is, " Is the guano 
 adulterated?" I consult a logician as the wisest 
 of men. His oracular response is, " In reference to 
 this matter, I can tell you one thing. If it is adul- 
 terated, it is adulterated ; and furthermore, since 
 you seem much excited about it, I will proceed to 
 the disclosure, 'that it can't be both adulterated 
 and not adulterated ' (at least, in the same place 
 and time) ; while, on the other hand, error might be 
 incurred, were you not to keep well in mind the fact 
 that guano must either be adulterated or not adul- 
 terated. ' What should I gain by such information ? 
 Should I not, in a fit of anger at his cold, dull cer- 
 tainties, probably invest, and lose my money? and 
 would not this be an error of judgment ? Ought he 
 not to have deterred me ? ' 
 
 I was highly delighted with this explosion, and 
 was half afraid that it would prove too much for our 
 dear old tutor ; but as the sounds of Dyver's voice 
 died way, like the smoke after a volley, I saw him
 
 26 PICTURE LOGIC. 
 
 sitting calmly and quite unhurt by what seemed to 
 me the murderous fire of his pupil. 
 
 ' You mistake,' said he, * the function of Logic. 
 You can't blame Logic for not accomplishing what it 
 never pretended or professed to accomplish. Logic 
 is only responsible for the form, and not the matter 
 of our thoughts. I shall explain form and matter in 
 due time. Here it will be enough to say that it is 
 when thoughts are self-contradictory or inconsistent 
 that Logic interferes. If a man says, " The deep is 
 shallow," Logic can correct him. If a man says, 
 " All deep water drowns ; this is shallow water ; 
 therefore it drowns," Logic can correct him, for the 
 remark was self-contradictory, and the inference in- 
 consistent. But if a man says, " This water is deep," 
 Logic cannot interfere ; and if a man says, "All shallow 
 water is safe for bathing ; this is shallow water ; 
 therefore it is safe for bathing ; " and then, with 
 Logic's consent, proceeds to bathe, and is drowned 
 (for the water turned out to be deep), you couldn't 
 blame Logic ; for, as far as Logic was concerned, his 
 thought was correct, his inference was logical ; the 
 only thing was that his data, his facts were not 
 correct; and for these facts (which we call matter) 
 Logic is not responsible. Given the facts, Logic can 
 tell you whether the remark is self-contradictory or 
 the inference inconsistent (i.e. can criticise the 
 form). Every science must have its data or facts to 
 start with, its materials to work upon. It's hard
 
 LOGIC IS A SCIENCE AND AN ART. 27 
 
 upon the oarsman if we blame his rowing, when we 
 gave him a rotten oar to start with, and be loses the 
 race ; and upon the weaver, if we blame his weaving, 
 when we gave him. bad wool to begin with, and the 
 cloth is useless. And it is hard upon the logician, 
 when we give him faulty remarks to pass judgment 
 upon, or faulty facts or data (or premisses) to draw 
 inferences or conclusions from, and then blame him 
 for any mistakes that may occur from acting upon 
 his decision. You bring this inference to the logi- 
 cian, "All speculation is profitable; this Peruvian 
 affair is a speculation; therefore it is profitable." " A 
 perfectly sound and correct inference ! " exclaims the 
 logician, and so you invest and lose your money ; 
 but it is you alone who are to blame, for you bring 
 him bad material to work upon. Tour remark, 
 " Ail speculation is profitable " is as faulty as the 
 most rotten of oars and the very worst of wool.' 
 
 The warmth of this reply quite restored my con- 
 fidence in our good tutor, and it was entertaining 
 too, as we knew he himself had lately lost some of 
 his money in the Peruvian Stocks ; and this is why 
 Dyver's illustration came home to him so well. 
 
 * After all, it cannot be denied that errors of form 
 in thought are more heinous than errors in matter. 
 We can make allowances for the latter, but not for 
 the former; and the science which remedies the 
 greater evil ought surely to be more highly valued. 
 
 ' But to sum up briefly. We have seen that
 
 28 PICTURE LOGIC. 
 
 knowledge is of two kinds, particular and universal. 
 Universal knowledge derived from particular is 
 called science, and applied to particular, is called 
 art. The name of the science or art depends upon 
 the objects with which it is concerned. We have 
 also seen that there are such things as particular 
 correct thoughts, and that science and art can be 
 introduced here, enunciating and applying the con- 
 ditions or laws upon which those correct thoughts 
 depend. And this is called Logic, and has only to 
 do with the form, as opposed to the matter of 
 thought, expressions which we have reserved with 
 the laws of thought for further explanation.'
 
 CHAPTER IV. 
 
 FORM AND MATTER OP THOUGHT. 
 
 ' BEFORE commencing our explanation of the form 
 and matter of thought, I should like to answer any 
 questions that may have occurred to either of you.' 
 
 * I am troubled about one thing,' said Dyver. 
 * What do we mean by saying a thing is " true " or 
 " correct " how would you express the meaning of 
 these words ? ' 
 
 ' There is no need whatever to resolve these words 
 or further explain them. In Logic we start with 
 particulars as in most, if not all, of the sciences (for 
 some maintain that there are sciences which start 
 from the universal and work downwards, as we shall 
 find in course of time), and we must accept without 
 question, or take for granted, these particulars, for 
 whether we start from universals or particulars we 
 must begin with assuming some thing, and believing 
 it by instinct or intuition. For if we did not do so 
 we could never start at all, nor have any basis for 
 the construction of science, so to speak. In Euclid 
 we start with certain postulates, and in botany we
 
 30 PICTURE LOGIC. 
 
 start with certain plants and trees, and in Logic we 
 start with " correct and incorrect thoughts." If any- 
 one asks us how we know a correct from an incorrect 
 thought, we should reply by instinct or intuition, and 
 that would be a sufficient answer. 
 
 ' Still, to gratify your thirst for knowledge, 1 
 should say that a thing is true when it agrees with 
 the impression of our own senses, and correct when 
 it agrees with the decision of our own reason. For 
 instance, if I heard a man say, " The comet is 
 visible," and then saw it myself, I should declare 
 the thing to be true ; or if I heard a man say, 
 " Comets are flying worlds," I should declare the 
 thing to be correct enough, but I could not answei 
 for its truth, whereas if he said " Comets are not 
 comets," I should declare the thought to be incor- 
 rect. Of course the impression upon the senses and 
 the decision of the reason of our fellow-men is con- 
 sidered almost as secure a pledge for the truth or 
 correctness of a thing as that of our own. But this 
 distinction I should not venture to insist upon.' 
 
 He then told us that to grasp the idea of form 
 and matter we must do as we did with science, that 
 is to say, we must first understand the idea generally, 
 and then apply it to thought. 
 
 * Take any three statues; they may be of Mars, 
 Apollo, and Venus, and all of gold, when they would 
 differ in form and be the same in matter ; or they
 
 FOEM AND MATTER OF THOUGHT. 31 
 
 may be of gold, copper, and brass, and all of Apollo, 
 when they would differ in matter but be the same 
 in form. And so with houses. You may have a 
 villa, a mansion, or a public-house all built of brick, 
 or a villa of wood, brick, or stone. The more homely 
 instance is still better. A jelly, a cream, and a 
 blanc- mange may be all turned out of one shape or 
 mould, and then they would be different in matter 
 but of the same form ; and three jellies may be turned 
 out of three different shapes or moulds, and then 
 they would be the same in matter but different in 
 form. 
 
 * Apply this distinction to thought. Any thoughts 
 may differ in matter and be the same in form, or 
 vice versa, as the statues, houses, or jellies. The 
 matter of a thought is that about which one is 
 thinking, and the form is the shape or mould into 
 which we cast the thought. There are an infinite 
 number of things which go to make up the matter 
 of thought. But the forms of thought are three (as 
 recognised by Logic) : 
 
 (1.) The Term or Concept. 
 
 (2.) The Proposition or Judgment. 
 
 (3.) The Syllogism or Inference.' 
 
 I shuddered as I heard that word syllogism, so 
 often had I heard of it before, as one of those tilings 
 that nobody could understand, and had we really
 
 32 PICTUEE LOGIC. 
 
 penetrated so far into the domains of Logic as to 
 stir this giant from his lair? I was full of awe. 
 
 ' Into one or other of these three forms or moulds 
 Logic casts all the matter of thought ; in other words, 
 everything we know of or can conceive. Of the pro- 
 position or judgment, and the syllogism or inference, 
 we have already spoken under the names by which 
 they are known outside the pale of Logic, viz. 
 remarks and inferences. To consider these three 
 forms separately. 
 
 ' (1.) The Term or Concept is, roughly speaking, 
 the name of anything we can see or imagine. Horse, 
 star, James, white, black, fire, philosopher, hippo- 
 potamus, priest, are all very different things to an 
 observer who regards their matter, but to the Logician, 
 who pays exclusive attention to the form, they are 
 all terms or concepts. Fierce or tame, small or 
 great, they are all equally terms to him. Were a 
 Logician to be told first that a bedstead, and then 
 that a rabid tiger were in the next room, separated 
 by a thin partition, in so far as he was a Logician 
 he would evince no emotion at the second piece of 
 intelligence, but would simply reply, " Two terms," 
 for the Logician is only concerned with the form.' 
 
 ' In so far as he was a human being though,' 
 said I, ' he would not stay long enough to say even 
 that.' 
 
 * Quite so ; because the matter of thought makes
 
 FORM AND MATTP:R OF THOUGHT. 38 
 
 a great difference in the regulation of conduct, but 
 is not recognised at all in Logic. 
 
 * (2.) The Proposition or Judgment is a combination 
 of two terms, and is the mould into which Logic 
 casts ah 1 those " remarks " we spoke of above as the 
 beginning of thought. " Horses are swift," " stars 
 twinkle," " James is a haughty footman," " white is 
 dazzling," "fire is comforting," "philosophers stoop," 
 " hippopotami are large," and " priests are good," are 
 all very different things to an observer who regards 
 the matter of thought, but to the logician who pa} s 
 exclusive attention to the form, they are all proposi- 
 tions or judgments. False or true, dogmatic or 
 liberal, interesting or dry, they are all equally 
 propositions or judgments to him. Tell him three 
 facts " The mixture of chloride of mercury with 
 iodide of potassium produces a colourless liquid over 
 a brilliant red precipitate," " beautiful women are 
 fatal to the peace of man," and " rabid tigers infest 
 the adjoining room," and in so far as he is a logi- 
 cian he will simply articulate " propositions," for 
 it is the form and not the matter with which he is 
 concerned.' 
 
 ' But surely those long instances are more than 
 the mere combination of a couple of terms,' said 
 Dyver. 
 
 * It makes no difference how many words there 
 are; there are only two ideas, though there are 
 
 D
 
 34 PICTURE LOGIC. 
 
 several words; and this we shall explain when we 
 discuss propositions more fully. To proceed : 
 
 ' (3.) The Syllogism or Inference couples together 
 two propositions and produces a conclusion. Here, 
 as in the case of propositions, it makes no difference 
 whatever to the logician what the matter of thought 
 may be. You may say to the logician " The mixture 
 of chloride of mercury and iodide of potassium pro- 
 duces certain results ; 
 
 This is such a mixture, 
 
 Therefore this produces certain results ; " 
 
 or you may say, " Beautiful women are fatal to the 
 peace of men ; 
 
 My cousin is a beautiful woman, 
 
 Therefore she is fatal to the peace of men," 
 
 and he will, in so far as he is a logician, say nothing 
 more than "syllogisms," for such is the form or 
 mould into which both these thoughts must fall. 
 Thus is Logic said to be a formal science, and in this 
 way is it concerned with the forms, ways, or modes 
 in which people think/ 
 
 1 1 sincerely trust,' said I, laughing, ' that in so far 
 as I become more of a logician my peace of mind 
 will be less molested by what you call the " matter " 
 of thought, for it would save much worry.' 
 
 That night, my nerves being, I suppose, in an
 
 FOKM AND MATTER OF THOUGHT. 35 
 
 excited state from my attempts to follow my tutor's 
 arguments for application to study was quite novel 
 to me I dreamed a strange dream about the form 
 and matter of thought. In the midst of a plain I 
 beheld a huge machine. At first sight it resembled a 
 coffee grinder, but on closer inspection it proved to 
 be more like a monster sausage-machine. A college 
 friend of mind was working it by a small handle, the 
 perspiration pouring from his forehead. 
 
 On the left of the machine sat an old Professor, 
 and on the right of the machine there was an indes- 
 cribable confusion of all kinds of things ; there were 
 birds, balloons, pyramids, and I could not tell how 
 many more things there a lion was just entering 
 the machine, followed by a lady, a frog, a tortoise, 
 and a clergyman. I should never have had my 
 curiosity satisfied, had not the lion roared terribly in 
 his reluctance to enter, thereby eliciting the follow- 
 ing remarks from my friend at the wheel. * Now 
 then, in with you, you needn't make all that fuss ; 
 you're not in the least degree formidable to us ; why 
 we had a whole menagerie through the other day, 
 and trains, elephants, whales, worlds all have to 
 pass through this machine and become terms for the 
 inspection of the great Professor Logic.* 
 
 For the first time I then noticed some things 
 that looked like sausages issuing from the left side 
 of the machine, only from having such big things 
 
 P 2
 
 36 PICTURE LOGIC. 
 
 inside them they were swollen to the shape of eggs. 
 In one I observed a fish, in another a house, in a 
 third a bird, and in a fourth a man all were pain- 
 fully cramped for want of room. 
 
 e Ah ! yes,' he went on, ' it's with our machine 
 here as it is with the common ordinary sausage 
 machine, never mind what the material is so long 
 as the shape is right. Large or small, young or old, 
 flesh or stone, you must all pass through, for 
 Professor Logic isn't particular about the matter, all 
 he concerns himself with is the form/ and he laughed 
 as well as he could with his hard work, the thought 
 of the common ordinary sausage amused him so 
 much. 
 
 ' Hard work, Frank,' said I. 
 
 ' Indeed it is,' said he, without the smallest sign 
 ol surprise at seeing me. * Do you know the old boy 
 sitting there says, " One of the advantages, or prac- 
 tical utilities of being a student under me is that it 
 affords hard exercise to, and is therefore invigorating 
 to, your faculties," and I agree with him.' 
 
 ' But what does he do with these terms when he's 
 made them ? ' 
 
 ' I'll show you. I've done my share of turning 
 for to-day. The Professor likes us to work the terms 
 out ourselves; he says it makes us understand the 
 process, and I must get it up, you know, for my 
 exam. Still, I've done my share to-day.' 
 
 So, leaving the handle to another student, he
 
 FORM AND MATTER OF THOUGHT. 87 
 
 conducted me to the Professor's workshop, where 1 
 saw a vast number of terms from the machine linked 
 together in couples, and they were called propositions. 
 I afterwards learnt the meaning of the words written 
 over them. There were also syllogisms or inferences 
 composed of these same terms, and wondering at 
 them, I awoke.
 
 88 PICTURE LOGIC. 
 
 CHAPTER V. 
 
 THE RECONCILIATION, AND ALSO HOW LOGIC IS MOEE 
 OF A SCIENCE THAN AN AET. 
 
 ' WE can now proceed to reconcile the various defi- 
 nitions of Logic,' resumed Mr. Practical. e According 
 to some, Logic is the science of reasoning. Science 
 is now no longer a difficult word to us, and reasoning 
 is the process employed in the syllogism (to speak 
 technically), or in the inference as opposed to the 
 remark (to speak roughly). As the syllogism implies 
 the existence of the proposition, reasoning is equi- 
 valent in this sense to thought ; and, if we suppose 
 that science also implies art, the definition becomes 
 Logic is the science and art of thought. It has also 
 been defined as " the science of the necessary forms 
 of thought," and so it has been called a " formal 
 science ; " for, as we have seen, Logic is only con- 
 cerned with the forms or modes in which people 
 think as opposed to the matter. It has also been 
 called "the art of thinking," i.e. the application of 
 universal laws to particular thoughts; and the 
 universal laws imply the existence of science. Lastly, 
 it has been well defined as "the science of the
 
 THE RECONCILIATION. 39 
 
 conditions on which correct thoughts depend, and 
 the art of attaining to correct and avoiding incorrect 
 thoughts." ' 
 
 But which should we give as our definition P ' I 
 asked. 
 
 ' Provided you were ready with an explanation, 
 and thoroughly understood what you meant by the 
 words, you might be content with this Logic is 
 the science and art of thought. 5 
 
 f I begin now to realise the meaning of the ex- 
 pressions. " Science is knowing " or " a knowledge 
 of what is," and " art gives rules for practice " and 
 acts, and science is theoretical and art practical.' 
 
 ' The next thing to be shown is that Logic is 
 more of a science than an art ; that is to say, more 
 employed as a science than an art. Let us consider 
 the results of the employment of Logic as a science 
 and as an art, and then, if we find that we already 
 have the one and not the other, we shall perceive 
 that Logic is more useful as supplying us with what 
 we have not, than with what we have. Eoughly 
 speaking, the results of Logic as a science are laws, 
 and the results of Logic as an art are particular 
 thoughts in accordance with those laws. Now we 
 already have the particular correct thoughts. We 
 do not want Logic to tell us when a thought is 
 correct or not. The costermonger detects a contra- 
 diction or inconsistency in almost all cases as quickly 
 as the Logician, though he may not be able to say
 
 40 PICTURE LOGIC. 
 
 why the thought is wrong. Whereas, we have not 
 already the laws. Therefore Logic is more useful to 
 us as a science than an art.' 
 
 Dyver looked a little puzzled, and then asked, 
 ' If art were only manifested in production, or 
 whether it were not also manifested in criticism?' 
 
 ' I was about to add that in the case of criticism 
 the art of Logic would be of great use ; but, insomuch 
 as production is the chief part of art, Logic is not 
 held in good repute as an art. It is for this reason 
 that the practical utility of Logic has so often been 
 called into question. Of this we shall speak again. 
 The case would be the same with the science and 
 art of healthy breathing. It would be interesting 
 and profitable to know the laws upon which healthy 
 breathing depended, but few would have any idea of 
 changing their manner of breathing by an applica- 
 tion of those laws. It is thus that Logic is more of 
 a science than an art.' 
 
 It so happened that we had our Logic lecture 
 after supper this time, to enable us to make a sailing 
 expedition in the daytime ; and, partly from fatigue, 
 partly from the effects of supper and work, I actually 
 dreamt about Logic again. I thought I was wan- 
 dering in the parks at Oxford, and I came across an 
 old woman of so pitiable an aspect and such miserable 
 attire that I could not forbear stopping to inquire 
 what she did there and whence she came. She sat, 
 with a ba.sket on her lap, swaying slowly from side
 
 THE RECONCILIATION. 
 
 41 
 
 to side, and took no notice of ine. At last she 
 heaved a sigh and began, * Ah, me ! poor Dr. Logic 
 (he ain't what once he was !). Good sir, I'm his 
 errand girl. I takes round what he makes up. 
 Deary me ! day after day, door after door, the same 
 
 old answer. Fust of all I says, " D' ye please to 
 require any of my master's beautiful works? I've 
 two sorts here, I says ; beautiful * results of art ' on 
 this right side o' my basket." " What d'ye mean? " 
 says they. " Why," says I, " pertikler kerrect 
 thoughts just made and ready for use please to 
 give 'em a look ! " And they says, " 0, then ! we
 
 42 PICTURE LOGIC. 
 
 won't trouble you we ain't out of them we've got 
 as many as we want of our own ; " and 'ow can I ask 
 'em to buy what they've got aready? Ah, deary 
 me ! poor Dr. Logic ; he ain't o' much account now- 
 a-days. I catches 'em up, 'owever, and says, " Well, 
 you ain't got these others in this left side these 
 splendid * results of the science,' the laws upon which 
 them pertikler kerrect thoughts as you've got a'ready 
 dippends ; and they says, " no, we ain't," and maybe 
 they'll take some o' them that left side 's all poor 
 Doctor ever sells ! But, bless yer 'art alive, sir ; 
 there's many of 'em as won't take even them. " We 
 ain't got 'em ? no ! and we don't want 'em. None of 
 yer humbuggy, cranky, theoretical stuff 'ere prac- 
 tical results that's what we want. Come be off! " ' 
 I woke, thoroughly moved to pity, and vowing I 
 would never treat poor Dr. Logic so badly.
 
 43 
 
 CHAPTER VI. 
 
 LOGIC THE SCIENCE OP SCIENCES AND AET OF AETS. 
 
 ' TELL us, Destrawney, what you mean by science of 
 sciences.' 
 
 ' It seems to me to mean " best of all sciences ; " 
 science science I forget the word par exemple? 
 no, no ! something like that dear me ' 
 
 'Par excellence,' suggested Dyver. 
 
 ' That's it,' said I ; * science par excellence.' 
 
 ' I should rather say that science of sciences and 
 art of arts means the science which is concerned 
 with every other science, and the art with every 
 other art. And this may be put simply thus : 
 Thought is required for every science and art ; for 
 without thought we cannot ascend from particulars 
 to universals, or descend from universals to parti- 
 culars, and this is science and art. It is for this 
 reason that the animals are destitute of science and 
 art. They have sensation that is to say, they can 
 apprehend particulars, but general notions or uni- 
 versal propositions or inferences we have every reason 
 to suppose they cannot attain to. The dog knows* 
 "this fire" and "this fire burns." But it is very
 
 44 PICTURE LOGIC. 
 
 improbable that the dog can form the general 
 notion " fire," or the universal proposition " all 
 fire burns," or the deliberate inference " all fire 
 burns my nose ; master's cigar is fire ; there- 
 fore master's cigar burns my nose." Though the 
 bird and the beaver and the bee evince marvellous 
 sagacity, it is probably without any power to ascend 
 to the universal ; or, at all events, to ascend con- 
 sciously, as man does. Thought, then, is required 
 for every science and art ; but thought itself is, so to 
 speak, subject to its own science and art, Logic. 
 Thoup-ht has its laws, and must obey them wherever 
 it goes, if it would be called correct thought, as much 
 as men have their laws and must obey them wherever 
 they go if they would be called respectable men. 
 Consequently Logic is the science and art of every 
 science and art. 
 
 ' To put it briefly. Where thought goes there the 
 science and art of thought go also. 
 
 ' But the science and art of thought were proved 
 to be Logic. 
 
 ' Therefore where thought goes, there Logic goes 
 also. 
 
 * But thought goes into every science and art. 
 
 ' Therefore Logic goes into every science and art. 
 
 * Therefore Logic is the science of sciences and art 
 of arts.' 
 
 'Q.E.D.' muttered I mechanically and with an 
 involuntary shudder at the thought that Logic seemed
 
 SIXDBAD THE SAILOR.
 
 LOGIC THE SCIENCE OF SCIENCES. 45 
 
 turning into mathematics ; 'but still I don't under- 
 stand yet.' 
 
 * Here is an illustration. The man with the high- 
 forehead is Thought. Chained to his neck is Logic, 
 holding perpetually before his eyes the rules he must 
 obey, never mind what field he wanders through. 
 Thought has a staff, for he is a great traveller. It 
 would be impossible to enumerate the fields through 
 which he passes. Four of them are given as speci- 
 mens. Take botany. Thought lingers by a stream 
 and gathers rushes. "Bushes are light," he re- 
 marks, and Logic is to all appearance asleep. He 
 gathers more and murmurs, "Rushes are heavy." 
 A smart blow on the head from Logic and a cracked 
 voice crying, " Nonsense ; WILL you look at your laws. 
 How can they be both heavy and light ? You meant 
 when you had a big bundle they were heavy ? then 
 I wish you'd say what you mean and not give 
 me the trouble of showing you the law of contradic- 
 tion." Thought meekly raises his head to read the 
 laws once more, and catches sight of some stars in 
 the sky. Gazing in wonder he meditates aloud, 
 " Tender's a lovely star ; most assuredly that star 
 must be a planet, for I know some stars are planets." 
 A violent pinch from Logic and a heap of reproaches 
 for the unwarrantable inference, and Thought 
 wanders on patiently listening to the monitor that 
 accompanies him wherever he goes, for though his 
 voice is harsh, dry, and difficult to understand
 
 46 PICTURE LOGIC. 
 
 Thought knows that the restriction is good for him, 
 for he remembers that when, upon one occasion, he 
 silenced that squeaky voice by diving so deep into 
 metaphysics that the poor little monitor became in- 
 sensible, he was caught in a whirlpool of circular 
 arguments, dashed along wild torrents of fancy, and 
 hurled into fathomless depths of conjecture to such 
 an extent that it was with the greatest difficulty he 
 ever escaped to dry land to become the laughing- 
 stock of men. And many a time a Mrs. Cawdle has 
 made such havoc of the distinction between universal 
 and particular statements, by turning a deaf ear to 
 the voice of Logic, that Thought has been exposed to 
 sad ridicule and contempt. For upon Mr. Cawdle's 
 once bringing in a friend late at night we find her 
 indignantly demanding what he meant by day after 
 day making a habit of bringing in mobs of the 
 wildest of the wild to eat legs upon legs of cold pork 
 and send girls miles for pickled walnuts in the 
 middle of the night through depths of snow. Or, 
 again, we find her violating the laws of contradic- 
 tion by lecturing Mr. Cawdle for what he had not 
 done, on the assumption that a man could both 
 do a thing and not do it at the same place and 
 time, e.g., when she upbraids him at length for 
 flirting at Greenwich fair, and upon his denying the 
 charge retorts that if he didn't " it was no fault of 
 his" and continues the lecture precisely as if he had 
 pleaded guilty to the chaige. Or, again, when she
 
 LOGIC THE SCIENCE OF SCIENCES. 47 
 
 expresses herself as being very anxious to learn the 
 Masonic secret, and at the same time declares it to be 
 a matter of the utmost indifference to her ; or dwells 
 upon the pain caused her by some slight on the part 
 of Mr. Cawdle, and at the same time entreats him 
 not to allow himself for a moment to imagine that 
 any conduct of his can possibly produce the smallest 
 effect upon her ; or, lastly, when she bitterly reviles 
 him for the loan of 51. to a friend, casting in his 
 teeth at least 100. worth of damages in the house 
 that might have been repaired with that five pounds 
 thereby violating the law of contradiction to the 
 extent of 95Z. Consequently thought has no wish to 
 rebel against Logic, whose sway is (in one sex at all 
 events) undisputed.' 
 
 'I have read,' remarked Dyver, who seemed a 
 little impatient of anything like homely instances 
 though I always liked them better than scientific 
 ones * that the words biology, zoology, chronology, 
 &c., are equivalent to " Logic applied to life," " Logic 
 applied to animals," " Logic applied to time, &c." ; 
 
 * Quite so,' replied Mr. Practical, ' and it is always 
 >vell to aid the memory as much as possible by under- 
 standing the derivation and meaning of the names 
 you meet with.'
 
 48 PICTURE LOGIC. 
 
 CHAPTER VII. 
 
 THE EELATION OP LOGIC TO LANGUAGE. 
 
 NEXT day Mr. Practical was compelled to visit the 
 metropolis, and after a brief explanation of the 
 relation of Logic to language he took his departure, 
 expressing a wish that we should both endeavour 
 to illustrate his meaning during his absence. 
 
 He told us that Logic was really connected with 
 thought, but as it was impossible to get at thought 
 (or at least at other men's thoughts) without the aid 
 of language of some kind or other, Logic was so far 
 connected with thought. The relation of Logic to 
 thought he characterised as primary, while that of 
 Logic to language was secondary. He also showed 
 us how Logic had been held by some to be pri- 
 marily connected with language, and so through 
 errors arising from the inability of language to ex- 
 press exactly what we think, Logic had fallen into 
 disrepute. The remedy for such mistakes was the 
 'knowledge of more than one language. As an 
 instance of such errors he gave us the notion that 
 the copula implied existence, and promised to explain 
 this farther. Dyver retired to his corner and I to
 
 THE KELATION OF LOGIC TO LANGUAGE. 
 
 49 
 
 mine, and on the following day we produced a couple 
 of rough sketches. 
 
 This was Dyver's relation of logic to language. 
 
 Logic pays a Visit. 
 
 Scene, a man's mouth. Thought peeping from 
 the throat. Language telling Logic (who has come 
 to visit Thought) that his orders are that no. one can 
 see Thought, and that all communications must be 
 made through him (Language). 'So you'd better 
 by 'alf tell me what you want 'owever.' 
 
 And Logic mutters, * What a coarse medium !
 
 50 
 
 But there is no help for it. 
 and confusions will arise ! ' 
 And this was mine. 
 
 PICTUEE LOGIC. 
 
 Alas ! what mistakes 
 
 Logic in Trouble. 
 
 A friend of mine, named Jones, who lived in 
 lodgings, used to work with a tutor for Latin 
 prose. Jones was in the habit of leaving his pro- 
 ductions daily at his tutor's, and calling next morning 
 to see the mistakes ; but as Jones was not an early 
 riser his tutor would often step over to his lodgings, 
 and leave the corrected prose with the people of the
 
 THE EELATION OF LOGIC TO LANGUAGE. 51 
 
 house, pointing out the faults, and begging them to 
 point them out to Jones as soon as he appeared, for 
 he was not yet to be seen. It so happened that the 
 landlady's daughter was very attractive, and by some 
 accident she always chanced to be at hand when 
 Jones's tutor called. Scandal might have arisen from 
 the protracted interviews in the course of which 
 Jones's tutor pointed out to Jones's landlady's daugh- 
 ter the defects in Jones's Latin composition, had it 
 not been well known that the primary object for which 
 the tutor came was not to converse with the damsel, 
 but to instruct the pupil, and being unable to see the 
 pupil, he was compelled to employ the aid of a third 
 person as a medium. His relation to the pupil was, 
 so to speak, primary, his relation to the landlady's 
 daughter secondary. After a time, however, Jones 
 left, but the tutor still continued his visits, and 
 ended by marrying the landlady's daughter. So 
 Logic, led away by the allurements of language, has 
 sometimes neglected thought, the object with which 
 it is primarily concerned, and has thereby become 
 involved in troubles and mistakes, and has fallen into 
 bad repute. 
 
 Mr. Practical was highly pleased with both our 
 illustrations, and added something to mine which I 
 had not thought of. ' Had your unfortunate tutor,' 
 he said, * moved more in society, and known several 
 of the fair sex, and become more inured to their 
 attractions, he would not, in all probability, have 
 
 E 2
 
 52 PICTUEE LOGIC. 
 
 been led into a mesalliance, and in the same way 
 had Logic been conversant with several languages, 
 and become acquainted with their powers of mis- 
 leading and beguiling, instead of only knowing one, 
 Logic would not in all probability have been led into 
 entering upon a relationship with Language which 
 was likely to bring difficulties, error, and evil 
 repute.
 
 53 
 
 CHAPTER VIII. 
 
 ALL THOUGHT IS COMPAEISON. 
 
 ' WE have seen,' resumed Mr. Practical, that Logic 
 has for its subject-matter thought. What is thought? 
 To give a rough answer to this difficult question, we 
 must say that " all thought is comparison." We 
 have already spoken of thought as consisting of 
 remarks and inferences, for we may consider thought 
 as unexpressed in the mind, or expressed in lan- 
 guage. But these remarks are compounded of two 
 things, something about which we are speaking, and 
 something that we affirm or deny of it. If I say 
 " dogs are animals " I am speaking about " dogs," 
 * and I say something about them " that they are 
 animals." Thought may therefore be divided into 
 three parts The term or concept ; the proposition 
 or judgment ; and the inference or syllogism.' 
 
 ' Do you mean by thought here the process of 
 thinking or the results attained to ? ' asked Dyver. 
 
 * I should say the results attained to ; of the 
 faculties we shall speak hereafter, so that if we can 
 show that the term, the proposition, and the infer- 
 ence or syllogism are the results of comparison, we
 
 54 PICTURE LOGIC. 
 
 shall have proved that all thinking is comparison ; 
 nor need you be alarmed, Destrawney, at any nice 
 distinctions of the sort, for to pass your examination 
 it is not necessary to notice them at all. Remember 
 this : 
 
 ' 1. The term or concept is anything we can see 
 or imagine. Our minds are stocked with concepts 
 or terms formed in our earliest years. How came 
 they there ? Take an infant, hold a dog up to it, 
 and the infant will recoil with a start of horror ; it 
 has experienced a mere undefined sensation of the 
 presence of something strange, and therefore terrible. 
 .Repeat the operation daily, always taking care to 
 accompany it with the word u bow-wow," and the 
 child, from a comparison of the sensations, forms a 
 concept, and associates these familiar sensations 
 grouped into one idea with the name of " bow-wow," 
 and if, after a time, you merely say " bow-wow," 
 without introducing the dog, the child will manifest 
 joy or terror according as it likes or dislikes the dog, 
 proving that it has formed in its mind the concept or 
 term dog, and can shut its eyes, so to speak, and 
 see a dog though no dog is near. Thus, concepts 
 are the results of the comparison of simple sensa- 
 tions and concepts expressed are terms. We gradually 
 accumulate our concepts and distinguish one from 
 another. As infants we had only a few under which 
 to arrange all the objects that met our view. Papa, 
 moo-cow, gee-gee, and bow-bow formed our stock,
 
 ALL THOUGHT IS COMPARISON. 55 
 
 then, and under one or other of these heads caine 
 every man and every animal we saw. Nor can we 
 boast much now, for in botany, for instance, many of 
 us have one vague concept, " plant," under which 
 to arrange all the phenomena of that science, and in 
 geology it is generally considered a sufficient reply to 
 the question, " What is this ? " if we say " A kind of 
 rock." 
 
 * (2.) As the term or concept is a result of the 
 comparison of simple sensations, so the proposition 
 or judgment is a result of the comparison of terms or 
 concepts, and henceforth we shall speak only of 
 terms and propositions, having shown that they are 
 identical with concepts and judgments. With pro- 
 positions thought proper begins. It is true that 
 terms are necessary to form propositions, but they 
 do not by themselves constitute a thought. We 
 cannot have a brace of birds without single birds ; 
 but single birds do not by themselves constitute a 
 brace. Suppose our infant to have formed several 
 terms horse, book, house, sun, large, dry, tall, 
 bright, &c. and never to attempt to couple them 
 together, but simply to repeat them singly, we 
 should at once question its sanity, as being unable 
 to attain to a thought, for, as we have said, 
 man has an innate tendency to group together the 
 like, and this is the origin of thought. We should 
 exclaim impatiently, " Horse, horse, horse ! What 
 about it ? What is the use of going on repeating
 
 c5 PICTUEE LOGIC. 
 
 house, house, house sun, sun, sun ? If you repeat 
 them from your birth to your death you will not 
 have expressed a thought ! " Thought begins when 
 the child, having formed in one part, so to speak, of 
 his mind a term for instance, book, derived from 
 observations in his father's library, &c., and in 
 another part another term, for instance, " nasty," 
 derived from sensations of medicine, chastisement, 
 &c., couples the two together, and exclaims " Books 
 are nasty." Thus propositions are the results of a 
 comparison of terms. 
 
 * (3.) Lastly, the syllogism is a result of the 
 comparison of two propositions. When the child 
 upon being told to open its spelling book says 
 " nasty," and further, upon being asked why he 
 thinks the book nasty, replies " all books are nasty," 
 he has given utterance to a syllogism which in its 
 full form would read " All books are nasty ; this is a 
 book ; therefore it is nasty." 
 
 ' We have traced, then, the gradual formation of 
 the term from sensations, the proposition from 
 terms, and the syllogism from propositions ; and 
 shown that they are all results of comparison ; and 
 these are the three parts of thought ; they are also 
 called (as we have seen) the forms of thought.
 
 57 
 
 CHAPTER IX. 
 
 THE TERM. 
 
 ' As thought,' resumed Mr. Practical, ' is divided 
 into term, proposition, inference, so Logic, or the 
 science of thought, is divided into three parts, under 
 the heads of TERM, PROPOSITION, and INFERENCE ; and 
 you will find this analysis of the subject very useful. 
 
 I. The term. 
 
 1. Definition of term and various kinds of terms. 
 
 2. Connotation and denotation of terms. 
 II. The proposition. 
 
 1. Definition of proposition and various kinds of propositions. 
 
 2. The copula of a proposition. 
 
 3. Distribution of terms in a proposition. 
 
 4. Heads of predicables, or a list of the relations which the 
 
 predicate of a proposition can bear to the subject. 
 6. Definition, or propositions expressing the connotation of ;i 
 
 term. 
 6. Division, or propositions expressing the denotation of a 
 
 term. 
 ILL The inference or syllogism. 1 
 
 1 . Definition of inference and various kinds of inference. 
 
 2. Moods and figures. 
 
 3. Principles, laws, and canons of syllogism. 
 
 4. Reduction of syllogisms. 
 
 5. Trains of syllogisms. 
 
 6. Hypothetical syllogisms. 
 
 7. Probable reasoning. 
 
 8. The fallacies. 
 
 1 The third division, ' inference,' includes inductive inference as 
 well as deductive inference, or the syllogism. But we are only now 
 concerned with that part of inference called ' syllogism.'
 
 58 PICTUEE LOGIC. 
 
 If you learn this analysis and can give some account 
 of each of the heads, your knowledge will be 
 sufficient for the purpose in view. The analysis is 
 taken from Mr. Fowler's " Deductive Logic," and I 
 refer you to that work or to Mr. Jevons's " Logic " 
 for information upon points that do not seem to 
 require further explanation.' 
 
 ' I hope,' said I, * you will not leave us too much 
 to our own reading, for somehow or other things 
 seem to me to be put so difficultly in books.' 
 
 ' I will do my best,' he continued ; ' and first let 
 us discuss the term. It comes from " terminus," or 
 " boundary," because terms are the boundaries of pro- 
 positions ; for a term is defined as anything that may 
 stand as the subject or predicate of a proposition. 
 If a term is to express anything we can see or 
 imagine, it is clear that we must give an exhaustive 
 account of all things if we wish to enumerate terms. 
 Now everything that we can see or think of must be 
 a thing or a quality of thing ; in other words, an 
 individual or an attribute of an individual. Mention 
 a few things, Destrawney.' 
 
 ' A star, fair, whiteness, chair, Lexicon, beauty,' 
 said I ; ( fun, William, suicide.' 
 
 'Every one of these is either an individual or 
 thing, or an attribute or quality ; and you must con- 
 tent yourselves with these expressions, as the question 
 as to " What is the meaning of thing ? " is beyond 
 the sphere of Logic.'
 
 THE TERM. 59 
 
 Dyver here took occasion to observe that he 
 knew that individual meant something incapable of 
 further division, i.e. a simple whole ; and that attri- 
 butes meant the properties ascribed to such a whole, 
 e.g., tree and greenness, or man and reason, for you 
 couldn't saw the tree or the man asunder without 
 destroying them, and greenness and reason were said 
 to be attributes of tree and man, and ' thing ' and 
 1 quality ' meant the same as ' individual ' and 
 * attribute.' 
 
 ' Well, then, a term expresses either an indi- 
 vidual or group of individuals, or an attribute or 
 group of attributes ; and this is as much as to say 
 that terms are an exhaustive enumeration of all that 
 we can see or think of. Take your fingers and thumb, 
 and remember the five terms thus : (See diagram on 
 next page). 
 
 " If a term expresses an individual it is a singular 
 term, e.g., Socrates (thumb). If it expresses a group 
 of individuals, it may either express the group and 
 not each individual as well; or the group and each 
 individual as well. Thus, the " BLACK WATCH " ex- 
 presses a group of soldiers, but you can't call each 
 soldier a " Black Watch ; " whereas " horse " ex- 
 presses a group of animals, and you can call each of 
 those animals a "horse." The former are called 
 collective terms, e.g., " the Black Watch " (1st finger) ; 
 the latter, common terms, e.g., horse (2nd finger). 
 If a term expresses an attribute or group of attri-
 
 60 
 
 PICTURE LOGIC. 
 
 butes, it is called either abstract (3rd finger) or 
 attributive (4th finger), the abstract term being a 
 substantive, the attributive an adjective.' 
 
 / % ~* 
 p 3-X X* 
 
 1. Socrates. 
 
 
 %> ,-^ 
 
 2. The Black Watch. 
 
 r 
 
 ^.%\ * 
 
 3. A horse. 
 
 1 
 
 /] %O * 
 
 
 I 
 
 m \ 
 
 4. Whiteness. 
 
 J 
 
 fi H 
 I/// 
 
 5. White. 
 
 N.B. The second finger 
 the largest, and the 
 common term the most 
 important. 
 
 The Logical Hand. 
 
 ' Are there not several other kinds of terms ? ' 
 asked Dyver. 
 
 4 Yes ; but it is my intention to work through 
 our analysis first, and afterwards to explain briefly 
 any names that may seem to interfere with the sim- 
 plicity of our scheme of Logic.'
 
 61 
 
 CHAPTEE X. 
 
 CONNOTATION AND DENOTATION. 
 
 * OP the five terms, the common term is that with 
 which we shall have most to do. Let tis endeavour 
 to explain connotation and denotation by taking a 
 common term or class name as an instance. To the 
 question "What is a man?" two answers may be 
 given. Firstly, closing our eyes, we may give the 
 attributes, the possession of which entitles a man 
 to the name of a man saying, " by man is meant 
 the combination of the attributes of life, reason, 
 &c. ; " or secondly, walking to the window, we 
 may point out Smith, Jones, &c. in the street and 
 say, " Those are men." The first answer would give 
 the connotation of man, the second the denotation. 
 Do you follow ? ' 
 
 ' No!' said I. 
 
 ' Well, then, look at it thus: Every common term, 
 or class name, is a name given to certain individuals 
 upon their complying with certain conditions, so to 
 speak. You walk in the fields with a friend. Tou 
 speak of trees, men, stones, birds ; and your friend 
 understands you to mean by them four distinct
 
 62 PICTURE LOGIC. 
 
 things. They all have attributes, and if those attri- 
 butes were all the same, why should you not speak 
 of them all four as " trees ? " ' 
 
 ' But,' said I, ' their attributes are not the same ; 
 at least, I do not feel my senses affected in the same 
 way when I look at a stone and a tree.' 
 
 ' Exactly so ! and these very attributes are what 
 we mean by the connotation. With the origin of 
 common terms we have nothing to do. All we know 
 is that certain, class names or common terms exist, 
 and that as fresh individuals present themselves we 
 enroll them under one or other of these names 
 according as they possess certain attributes, e.g., class 
 man, attributes required for admittance rational and 
 animal qualities. Any individual possessing these 
 would be entitled to become a member of the class 
 "man," and so "rational and animal qualities" are 
 the connotation ; and Jones, Brown, Smith, Socrates, 
 &c., are the denotation of the common term " man." 
 Thus the connotation means the attributes in virtue 
 of the possession of which an individual belongs to 
 its class, and the denotation means the individuals 
 which, in virtue of the possession of certain attributes, 
 belong to a class. The connotation answers the 
 question " what ?" and the denotation answers the 
 question "which?" e.g., "What is a steam-ship?" a 
 combination of the attributes of vessel with those of 
 steam ; in other words, " a vessel propelled by steam." 
 "Which are steam-ships?" The Great Eastern,
 
 CONNOTATION AND DENOTATION. 63 
 
 the Husband's boat, &c. ; or, again : last week when 
 we went gull- shooting, I said, " Perhaps we shall 
 get a puffin ; " and you asked, " What is a puffin ? " 
 and I replied a bird with such and such attributes, 
 with form, colour, flight, &c. (connotation). Soon 
 after several flew over and I said, " Look ! there 
 those are puffins" (denotation). The connotation of 
 a term (under the name of intension] has been well de- 
 fined as the qualities necessarily possessed by objects 
 bearing the name, and the denotation (under the 
 name of extension) as the objects to which the term 
 may be applied. It has also been said that a term con- 
 notes attributes and denotes individuals, and the five 
 terms are thus said to be connotative or denotative. 
 
 BOTH 
 
 DENOTATIVE/ M l\ * CONNOTATIVE 
 
 Denotative and Connotative HanO. 
 
 'The singular and collective have only denota- 
 tion; the abstract and attributive only connotation; 
 and the common terms, both. For the singular term 
 is a mere mark arbitrarily imposed upon an indivi- 
 dual, not in virtue of the possession of certain attri-
 
 t>4 PICTURE LOGIC. 
 
 butes, but simply that we may be able to know it 
 from its fellows. When our clergyman christened 
 his boy " Harold " it was not because the boy mani- 
 fested any peculiar attributes or qualities, but simply 
 to distinguish him from his numerous brethren, so 
 that (for instance) when they said " It was Harold 
 who set fire to the barn," he might know which son 
 to chastise. And what the singular term is to an 
 individual, the collective is to a group of individuals 
 a mere mark affixed arbitrarily, for the sake of 
 convenience. 
 
 ' The abstract and attributive express only attri- 
 butes, and therefore cannot be denotative; though 
 both are capable of being regarded as common 
 terms ; for " redness " and " red " may be regarded 
 as " red things," a class name or common term.' 
 
 ' I can't quite understand the difference between 
 singular and common terms with regard to connota- 
 tion,' said I. 
 
 * Take an instance. In my stables I keep a mare 
 known as " Fanny," and a cow known as " Polly." 
 One day I say to my man, " John, we'll change these 
 names ; in future if men ask for their names, tell 
 them the mare is called * Polly,' and the cow 
 ' Fanny.' " Werry good, sir," says John. Next 
 day I add, " John, a further change is necessary ; 
 we will call the mare a cow and the cow a mare, 
 and when men ask what they are, say this (the 
 mare) is a cow and the other a mare." But
 
 CONNOTATION AND DENOTATION. 65 
 
 John stoutly refuses, and why 9 because the 
 names "mare" and "cow" are common terms 
 awarded to certain animals in virtue of their posses- 
 sion of certain attributes, whereas singular terms are 
 mere marks arbitrarily affixed. Thus common terms 
 are connotative, as implying the possession of certain 
 attributes, and denotative as pointing to certain in- 
 dividuals, while singular terms are only denotative. 
 
 'You will see how the connotation of a common 
 term increases as its denotation decreases, and vice 
 versa ; for the more attributes required as a qualifi- 
 cation for admission into a class, the fewer the 
 individuals admitted.' 
 
 ' Something like an examination which requires 
 wide knowledge, or a club which is very exclusive,' 
 I suggested, ' for the individuals who pass or are 
 admitted are very few.' 
 
 ' Quite so. Ask for a rose. The connotation is 
 small : " a flower with certain peculiarities ; " the de- 
 notation or individuals answering to that description 
 very numerous. The common rose is plentiful. 
 Then ask for a moss rose. The connotation is now 
 larger. Candidates successful in the previous de- 
 mand are now rejected as lacking the qualities im- 
 plied by the word " moss ; " and so the denotation is 
 smaller, and you may continue the process until you 
 get your connotation so large that there is only one 
 individual, perhaps, that can satisfy all requirements 
 a prize plant and the property of a nobleman. 
 
 F
 
 66 PICTURE LOGIC. 
 
 Take one more instance. You advertise in the 
 " Field," " Wanted, a servant ; salary enormous. 
 A. B., High. Street, Oxford." Next morning 
 the whole High, from Carfax to Magdalen, is a 
 seething mass of human beings. The Mayor is 
 furious, and compels you to withdraw your advertise- 
 ment. After a while you insert the advertisement 
 again, only this time you write the word " male " 
 before servant. Once more the High is in an 
 uproar, and the Mayor interferes ; but the numbers 
 are now reduced by about a half, though selection is 
 still hopeless. Angry with your own thoughtless- 
 ness, you determine to cut down still further the 
 number of applicants by adding more qualifications, 
 and eventually your advertisement reads, " Wanted, 
 a male servant, good looking, active, honest, with a 
 perfect knowledge of cooking and riding, who has 
 been in a training stable, and is able to translate 
 Livy and Virgil at sight, and to prepare all his 
 master's lecture- work." People now understand 
 why the salary is large, and upon looking from your 
 window you see two men, or one, or none, to answer 
 the advertisement. Thus the denotation dwindles 
 as the connotation grows.' 
 
 ' Are not these contrary processes to be seen in 
 the growth of language,' asked Dyver, ' under the 
 names of generalization and specialization ? ' 
 
 * Yes ; and to remember which is which bear 
 in mind the fact that it is from the denotation
 
 CONNOTATION AND DENOTATION. 67 
 
 the names are taken. The word " paper " (or papy- 
 rus) originally meant " writing materials made of 
 byblus ; " it gradually came to mean " writing mate- 
 rial made of rags, straw, or anything." The deno- 
 tation has thus grown by the admission of several 
 other kinds of writing material ; and the connota- 
 tion has diminished, for, at first, unless a candidate 
 for the class " paper " (so to speak) could show that 
 it possessed the attribute " made of byblus," it was 
 not admitted ; whereas now the class has been 
 thrown open, and anything that possesses the attri- 
 butes of "writing material" is admitted. On the 
 other hand, "physician" originally meant <f>v<TiKos, 
 " a man who studied nature." It gradually came to 
 mean " a man who studied nature in respect of heal- 
 ing man." The denotation has here diminished, for 
 the men who studied nature in other ways, e.g., 
 botanists, are excluded from the class ; and the con- 
 notation has grown; for whereas, at first, any one 
 who studied nature could have claimed admittance 
 into the class physician, now more attributes are 
 required to entitle individuals to admission into that 
 class.' 
 
 That night I dreamed I was sitting in my rooms 
 working, past midnight, when the door slowly 
 opened, and a most strange figure entered. He 
 seemed very unhappy. I asked his name and what 
 he was ? ' Ah, sir,' he sobbed, ' long years have made 
 
 v 2
 
 68 PICTURE LOGIC. 
 
 havoc of memory. Every one I meet I ask, What 
 am I ? and where is the class to which I belong ? 
 No one knows. A student like you I thought might 
 give me help. My name? I've a faint recollection 
 of being called " Scaly." ' * Ah ! that,' said I, ' was 
 a mere mark, a singular term.' ' A what ? ' he 
 gasped. ( The thing to do is to find your connota- 
 tion and denotation ; for you have attributes, and 
 you're a connotative term.' 'Alas ! what mean these 
 rile names ? ' ' Come with me,' said I, laughing, 
 
 * and we will find your class. 5 We went to a kind of 
 Zoological Garden on a gigantic scale. The first 
 cage we came to had a notice-board over the door. 
 
 * Class, Man Connotation, Rational and Animal 
 Qualities : none admitted unless they possess these 
 qualities.' Innumerable swarms of individuals formed 
 the denotation in that cage. * Can you satisfy the 
 requirement on that board ? ' said I. He said he 
 could not, and we passed to the metal cage, and the 
 plant cage, &c., but we could not find his class. At 
 last a thought struck me. ' You are painfully thin,' 
 said I ; ' did you ever hear the name " Euclid ? " * 
 He started, and seemed violently agitated, muttering, 
 'That name, that name!' 'Come,' said I, as we 
 hurried to that part of the gardens where the figures 
 were. ' Do you feel very empty, as though you had 
 nothing in you, and were only " lines enclosing a 
 space ? " ' 'I do.' ' Then,' said I, ' you're a figure ; 
 we shall soon find your class now, only " figure "is
 
 CONNOTATION AND DENOTATION. 69 
 
 so vague and general ; one might as well direct a 
 letter " Smith, America," as expect you to find 
 your class when you're only told you're a figure. 
 There are countless millions of them.' * True,' said 
 he. We came to a sign-post just then, on which was 
 printed : * To the Curvilineal Figures ; To the Recti- 
 lineal Figures,' with the hands pointing different 
 ways. ' Are you rectilineal ? ' I asked. ' Don't look 
 so scared ; it only means are your lines straight or 
 curved ? ' ' Straight,' said he, feeling his sides. We 
 hadn't gone far before we came to a place where the 
 road branched off into three directions, with a sign- 
 post marked, 'To the Rectilineal Figures of three 
 sides (Triangles) ; To the Rectilineal Figures of four 
 sides (Quadrilateral) ; and, To the Rectilineal Figures 
 of more than four sides (Polygon).' ' How many 
 sides have you ? ' I asked. * Three.' ( Then you're 
 a triangle ! This is our way.' In spite of his over 
 flowing gratitude, we hurried on and found a large 
 building with the name ' Triangles ' over the en- 
 trance. The interior was divided into three com- 
 partments. For triangles with all sides equal 
 (equilateral) ; for triangles with two sides equal 
 (isosceles) ; and for triangles with no sides equal 
 (scalene). I had not time to answer to his cry of 
 delight, ' Oh, joy ! my scalene brethren ! ' before he 
 was in their midst, and I slipped away, and awoke 
 muttering, ' A scalene triangle, of course ! '
 
 70 PICTURE LOGIC. 
 
 CHAPTER XI. 
 
 PEOPOSITIONS. 
 
 * WE now pass to our second head, Propositions. A 
 proposition compares two terms, asserting or denying 
 one of the other. One of these terms is called the 
 subject, the other the predicate ; and the verb which 
 intervenes is called the copula. To find the subject 
 ask yourself, "What am I talking about what is 
 the subject of my remark ? " To find the predicate 
 ask yourself, "What do I say about this subject?" 
 for prsedico means " to assert." 
 
 * Oughtn't the (i) to be long ? ' asked Dyver, * and 
 doesn't it come from prce and dico, to foretell.' 
 
 * No ! there are two words ; prsedico, " to say be- 
 fore " (in the sense of time), and prsedico, " to say 
 before " (in the sense of place, i.e. publicly) ; and 
 prsedico is equivalent to KaTrjyopsw, and means " to 
 assert, or declare ; " hence predicate. 
 
 * Take an instance. " The sun is bright." Sun, 
 subject is, copula bright, predicate.' 
 
 ' Then in " Pair was her form," said I ; ' fair, sub- 
 ject was, copula her form, predicate ? ' 
 
 'No! remember the questions you are to ask
 
 PROPOSITIONS. 71 
 
 yourself, and pay no regard to the position of the 
 words. You are talking of " her form," and you say 
 of it that it was " fair." " Her form " is subject, and 
 " fair " predicate. 
 
 ' The copula is some part of the present tense of 
 the verb " to be." It is the sign of comparison, or 
 of that innate tendency all men have to gather to- 
 gether similar things and separate dissimilar things. 
 To state propositions logically, remember, they are 
 ideas and not words, with which you have to do. A 
 term often covers a multitude of words, e.g., 
 
 Subject. 
 The sun . 
 Fires 
 The ' Faraday ' 
 
 on-the-shore 
 
 Copula. 
 
 arc . 
 is not 
 
 the-telegraph-cable. 
 The-sound-of-the-waves- 
 
 Predicate. 
 
 bright. 
 
 burning. 
 
 a-ship-that-will-convey 
 
 beautiful. 
 
 There are three important remarks to make upon the 
 copula. 
 
 1. It conveys no notion of time. If you want to 
 express logically the fact " that Elizabeth was a good 
 queen" say "Elizabeth is a-person-who-was-a- 
 good-queen," and so with the future. 
 
 * 2. It conveys no notion of existence. The an- 
 cients said, " The unicorn is a non-existent animal." 
 Ergo, " The unicorn exists a non-existent animal." 
 Ergo, " The unicorn exists and does not exist," which 
 is absurd. The confusion arose from the idea that 
 " is " always means " exists," and is one of the mis-
 
 72 PICTURE LOGIC. 
 
 takes we hinted at as due to the influence of language. 
 The copula only means " is equivalent to," or " not 
 equivalent to." 
 
 ' (3.) It conveys no notion of probability, &c. 
 The question of the modality of the copula is the 
 question whether we are allowed to assert or deny the 
 predicate of the subject in a certain manner (cum 
 modo), i.e. conditionally, or with some qualifying 
 word joined to the copula, or whether we are only 
 allowed to assert or deny the predicate of the subject 
 simply. The proposition, " Oysters are plentiful " is 
 called a pure proposition ; " Oysters are possibly (or 
 probably, or certainly) plentiful " is a modal proposi- 
 tion. Now, may the words " possibly, &c.," be 
 joined to the copula? No. All words of this de- 
 scription must be pressed into the subject or the 
 predicate, i.e. modal propositions must be reduced to 
 pure ones ; e.g., "Prawns are possibly fierce" becomes 
 either " That-prawns-are-fierce is possible," or 
 " Prawns are possibly-fierce." 
 
 * To impress upon your minds these three facts look 
 at this rough sketch. The copula is the coupling 
 chain between two railway carriages, the subject 
 and the predicate, which form a train, and if Time, 
 Existence, or Probability wish to travel on the Logic 
 line they must get into one or other of these carri- 
 ages. It is unreasonable to suppose that they are to
 
 PBOPOSITIONS. 
 
 73 
 
 be allowed to travel on the coupling chain however 
 full the carriages may be they must squeeze in some- 
 where, or not go at all. 
 
 
 GREAT LOGIC BRANCH 
 
 Jmporfct/nSNuTICE-ta WORDS 
 
 7b ^.ce/nqati wwyina 
 
 EXISTENCE -TIME -or 
 r , . PROBABILITY 
 ms 
 
 The Great Logic Branch. 
 
 4 Lastly, propositions are divided into universal 
 and particular according as their subjects are used 
 in their full extent or not, and into affirmative 
 and negative according as their copulse affirm or 
 deny the predicate of the subject. We may say, 
 
 [ Cretans are liars," or " Some Cretans 
 or no) or are not j 
 
 liars," and the first of these are universal propositions, 
 the second particulars, and they are said to differ in 
 quantity because they differ in the amount of Cretans 
 to whom the term " liar " may be applied. Again, 
 we may say, " Cretans are liars," or " Cretans are 
 not liars," and these two are said to differ in quality.
 
 74 PICTURE LOGIC. 
 
 We have thus four forms into one or other of which 
 all propositions must fall before Logic can pass 
 judgment upon them 
 
 Universal affirmative . " All Cretans are liars " . .A 
 
 Universal negative . " No Cretans are liars " . . E 
 
 Particular affirmative . " Some Cretans are liars" . I 
 
 Particular negative . " Some Cretans are not liars " . 
 
 A and I from Affirm o, and E and O from nEgO. 
 There are many other kinds of propositions which 
 we shall explain afterwards, but these are the only 
 forms with which Logic is generally concerned.' 
 
 * Under which of these four would you put, 
 " Harold is brave," " The ' Black Watch' is a heroic 
 band," " Virtue is rare ? " ' asked Dyver. 
 
 * Singular and collective terms rank as universals. 
 When you say, " Socrates is bilious," you mean all of 
 Socrates ; and as for abstract terms like virtue, it is 
 best to reduce them to common terms by saying, 
 " Virtuous men are rare " ; and as for common terms, 
 remember Logic has no power to pass judgment upon 
 propositions unless they are brought to one or other 
 of the logical forms. The proposition, " Cretans are 
 liars " is called indefinite, and with such Logic is not 
 concerned. You must specify the quantity or you 
 can get no help from Logic.'
 
 75 
 
 CHAPTER Xli. 
 
 DISTRIBUTION OP TERMS IN A PROPOSITION. 
 
 MR. PRACTICAL began this lecture by shaking several 
 blots from his pen on to a sheet of note-paper. 
 * This paper is wet with ink/ said he, ' and yet I can 
 put my finger upon it without soiling my finger with 
 ink.* " 
 
 ' Of course ;' said I, ' you touch the paper between 
 the blots ; if the paper were wet all over with ink 
 you could not do it.' 
 
 ' It seems, then,' said he, ' that I used the words 
 " this paper " in a partial sense, as meaning " part of 
 this paper." Now terms thus used in Logic are said 
 to be " undistributed," whereas terms used in their 
 fall extent are said to be "distributed." In the 
 proposition, " All foxes are sly " the subject is dis- 
 tributed, i.e. we use " foxes " in its full extent ; but 
 the predicate is undistributed, i.e. the word " sly " or 
 " sly thing " is not used so, for there are many other 
 " sly things " besides foxes. 
 
 c To apply this distinction to our five terms, we 
 find singular and collective terms are always distri- 
 buted (e.g., " Socrates is ill," where "All of Socrates "
 
 76 PICTURE LOGIC. 
 
 is meant) and abstract and attributives may be treated 
 as common terms, and for common terms in proposi- 
 tions we have these two rules. 
 
 (1.) All universal propositions distribute their 
 
 subject. 
 (2.) All negative propositions distribute their 
 
 predicate. 
 
 ' (1) Is obvious, for the sign of every universal pro- 
 position is "all" or " no," and " all " or "no " attached 
 to the subject of a proposition prove that we are using 
 that subject in its full extent. If we say " All men 
 are animals," or " No men are stars," we use the word 
 " men " in both propositions in its full extent. 
 
 1 (2) All negatives distribute their predicate ; for 
 in every negative proposition we may suppose our- 
 selves to be excluding the things implied by the 
 subject from the class implied by the predicate. In 
 " No men are stars," " Some men are not poets," we 
 exclude the things " men " from the class " stars," and 
 the things " some men " from the class "poets." Now, 
 before we are justified in excluding anything from a 
 class we must look all through the class to be sure 
 that the thing does not belong to it. Suppose I say 
 " There are no blank pages in this book," which be- 
 comes " No blank-pages are pages-in-this-book ;" 
 without thoroughly looking through the " pages-in- 
 this-book " the result is an error, for one of you will 
 quickly turn to the fly-leaves to prove I am wrong.
 
 DISTRIBUTION OF TERMS IN A PROPOSITION. 77 
 
 Again, if I say, " There are no violets in this park," 
 which becomes, " No violets are flowers-in-this- 
 park," I must look carefully through the class 
 " flowers-in-this-park ' before I am sure of this pro- 
 position ; in other words, I use the predicate in its 
 full extent; i.e. the predicate must be distributed. 
 And so with the particular negative ; e.g., " Some men 
 are not poets/' we must look all through the class 
 " poets " before we can say that the " some men " re- 
 ferred to do not belong to that class.' 
 
 * I can't quite see how the particular negative dis- 
 tributes its predicate,' said I. 
 
 * Suppose I say " Some pheasants are not in the 
 stubble field," which becomes " Some-pheasants are 
 not things-in-the- stubble-field," I must look all 
 through " things-in-the-stubble-field " before I can 
 be sure of this remark, and even more carefully than 
 if I had said " No pheasants are in the stubble 
 field ; " for by " some pheasants " I might have 
 meant " white pheasants ; " and though I found a 
 thousand ordinary pheasants, it would not overthrow 
 my remark, " Some pheasants are not in the stubble 
 field ;" but in both cases I must look through the 
 predicate. Hence it is far easier to affirm than to 
 deny to say " Some Irish girls are pretty," than 
 " Some Irish girls are not pretty ; " for in the one 
 case, if you met three instances, it would be enough ; 
 in the other you would have to go through the whole
 
 78 
 
 PICTURE LOGIC. 
 
 class " pretty things " to be sure that your " some 
 Irish girls " were not among them. 
 
 'Apply these two rules to A E I O, the four 
 forms of propositions. A (universal affirmative) must 
 obey rule (1) and distribute its subject ; E (universal 
 negative) must obey both rules (1) and (2) and distri- 
 bute both its subject and predicate; I (particular 
 affirmative) obeys neither and distributes neither ; O 
 (particular negative) must obey (2) and distribute its 
 predicate. 
 
 ' Eemember this by the word AsEblnOp 
 (A subject, E both, I neither, predicate).' 
 
 A Word to the Wise.'
 
 79 
 
 CHAPTER XIII. 
 
 HEADS OF PREDICABLES. 
 
 4 TnE heads of predicables is the name given to 
 an exhaustive enumeration of the relations which 
 the predicate of a proposition can bear to the subject. 
 We are discussing propositions. In every one we 
 find a subject and a predicate, but not always in the 
 same relation to one another. Our aim is to find 
 out all the different relations in which the predicate 
 can stand to the subject. In " all men are animals " 
 the predicate is a larger class including smaller 
 classes. In " some men are yellow " the predicate is 
 an attribute belonging to the subject. A deeper 
 investigation than is necessary for us now has proved 
 that these heads are five genus, species, differentia, 
 property, accident. The definitions of these may be 
 thus expressed : 
 
 A genus is a larger class, including smaller classes. 
 A species is one of the classes included in the 
 
 genus. 
 A differentia is an attribute which is part of the 
 
 connotation of a term, and marks off the species 
 
 from the genus.
 
 80 PICTURE LOGIC. 
 
 A property is an attribute which is not part of, 
 but follows from the connotation of a term. 
 
 An accident is any attribute that is not a differ- 
 entia or a property. 
 
 Don't look so scared, Douglas ; remember we are 
 only stating the ways in which a predicate can be 
 related to its subject, and we are only concerned 
 with common terms or class names. " What pudding 
 was that we had yesterday ? " " Dumplings." 
 " What kind of dumplings ? " "Apple dumplings."- 
 " Are there any other kinds of dumplings ? " " Yes, 
 currant dumplings, suet dumplings, &c." "Very well; 
 here dumpling is the genus, and apple dumpling, 
 currant dumpling, &c., the species, and the attri- 
 butes " made of apple, made of suet, &c.," are the 
 differentiae ; for they are that which makes one class 
 of dumpling differ from another, and part of the con- 
 notation of the terms (the connotation being the 
 meaning of the word).' 
 
 'What would be the property and accident?' 
 asked Dyver. 
 
 ' A property of " apple dumplings " would be that 
 they are " good for the health," for though it is not 
 a. part of it, it follows from the meaning of the name 
 " apple dumpling," for apples are good for the health.' 
 
 ' But,' said I, laughing, * you complained of in- 
 digestion after them.' 
 
 * True ; but if " apple dumplings " are so made 
 that they cease to be entitled to the name, you can't
 
 HEADS OF PKEDICABLES. 81 
 
 expect the properties which follow from the meaning 
 of a term to remain when the meaning itself is gone. 
 I refer of course to " apple dumplings " rightly so 
 called. It was an " accident " of our candidates for 
 that name that they were heavy ; for it is no part of, 
 nor does it follow from the meaning of, apple dump- 
 lings that they should be " heavy." We have now 
 all five heads, but be careful not to forget that they 
 express relationship between the two terms of a proposi- 
 tion. If asked for the above heads, you would not 
 say " dumpling," " apple dumpling," " made of 
 apple," &c. ; but you first give the connotation or 
 meaning of the subject, and then give the various 
 relations of the predicate thus : 
 
 Given the term " This pudding" (which we will call T. P.). 
 (Connotation, or meaning " apple dumpling.") 
 T. P. is a dumpling (genus) 
 
 T. P. is an apple, dumpling (species) 
 T. P. is made-of-apple (differentia) 
 T. P. is good-for-health (property) 
 T. P. is heavy (accident) 
 
 Of course the above example is for explanation 
 only, and not for use. The instances you would use 
 are the following pair, which are to be worked out in 
 precisely the same way as the above : 
 
 Given the term " Man." 
 
 (Connotation " rational animal.") 
 Man is an animal (genus) 
 
 Man is a rational animal (species) 
 Man is rational (differentia) 
 
 Man is able-to-do-Euclid (property) 
 Man is unwell or well (accident) 
 
 8
 
 82 PICTURE LOGIC. 
 
 Given the term " triangle." 
 
 (Connotation " three-sided, rectilineal figure.") 
 Triangles are rectilineal figures (genus) 
 
 Triangles are three-sided, rectilineal figures (species) 
 Triangles are three-sided (differentia) 
 
 Triangles have two sides greater than the third (property) 
 Triangles are large or small (accident) 
 
 Notice the arbitrary character of these heads in 
 two respects. 1. The heads themselves are not fixed, 
 but vary according to your wish. 2. The connota- 
 tion varies according to the point of view you choose 
 to take. 
 
 * 1. The genus answers the question "What?" 
 (TI ; quid ?). The species, the question " What kind? " 
 (TTOIOV rt ; quale quid ?). " What is a dog ? " Answer, 
 " An animal." Of course it is ; every one knows 
 that ; that's only the genus. We want to know 
 " what kind of animal ? " We want the differentia, 
 or attributes which distinguish " dog " from all the 
 other classes in the same genus. We want the 
 species, for the differentia plus the genus gives the 
 species. The differentia (certain attributes, irra- 
 tional, domestic, &c.) is added to the genus, and we 
 get " animal with certain attributes, irrational, 
 domestic, &c. " for the species. But what is species 
 one moment may be genus the next. Man is a 
 species of the genus animal, but a genus of the 
 species European. There is, however, one genus 
 which never stands as a species, and one species 
 whi.h never stands as a genus (the summum genus 
 and the infima species). Man is a species of animal,
 
 HEADS OF PKEDICABLES. 
 
 88 
 
 animal is a species of living being, living being of 
 thing and we can get no farther. So thing is the 
 summum genus. So man may be subdivided till we 
 come to a class which contains no classes, but only 
 individuals, which is called " infima species." Even 
 these are arbitrary, in so far as we may fix our own 
 highest and lowest classes, provided we are consistent, 
 as in the following tree of Porphyry. Man is re 
 garded as an infima species. 
 
 SUBSTANCE (or thing) 
 
 Corporeal Incorporeal substance 
 
 substance = BODY (as air) 
 
 Animate Inanimate body 
 
 body = LIVING BEING (stones) 
 
 Sensible 
 living being = 
 
 Eational 
 animal 
 
 Socrates 
 
 Insensible living being 
 
 Irrational animal 
 (brute creation) 
 
 Plato 
 
 ' Suppose you are being cross-examined thus : 
 You speak of Plato. What is Plato ? " "A man." 
 
 G 2
 
 34 PICTUEE LOGIC. 
 
 " What is a man ? " "A rational animal " (genus 
 -'animal;" differentia, "rational"). "What thei 
 do you mean by ' animal ? ' ' " Living being with 
 powers of feeling (i.e. sensible), for plants are 'living 
 beings,' but they cannot feel ; so ' sensible ' is the 
 differentia here, and ' living being ' the genus." 
 " But pray what do you mean by living being ? " 
 " A kind of body ; the genus ' body ' is divided into 
 two species, ' body with life and body without life ' 
 (e.g., stones and stocks). Body with life is 'living 
 being.' " " Please tell us what body is ? " Body 
 is a kind or species of thing things being divided 
 into corporeal (as stones, &c.) or incorporeal (as air, 
 spirit). Body is a solid, tangible thing." "What 
 then is a thing or substance ? " "A thing is a thing 
 there is no higher class ; consequently no expla- 
 nation or unfolding into simpler elements. It's a 
 ' summuin genus,' and I can'l answer any more." 
 
 ' 2. The connotation varies according to the point 
 of view taken. We have already shown how conno- 
 tation (or meaning) is the attributes implied by a 
 name. I see certain individuals ; I group them into 
 a class and select certain attributes as characteristic 
 of these similar individuals, so that if I see any more 
 individuals I may be able to admit them into my 
 class or exclude them according as they possess or 
 do not possess these attributes. Obviously the attri- 
 butes thus selected are not all the attributes possessed 
 by the individuals (for it would be a hopeless task tc
 
 HEADS OF PRZDICABLES. 85 
 
 enumerate them all), but only a few of them. Never- 
 theless, these few are called the connotation or 
 meaning or essence of the name ; and thus, the 
 connotation of a word, which strictly should be all 
 its attributes, is in reality only a few. The question 
 is : " If all the attributes can't be taken, which shall 
 be the privileged few to stand as connotation and to 
 be applied as a test to all candidates for admittance 
 into the class ? " The answer is, " The attributes 
 which are most prominent ; " and prominence of 
 course depends upon the side you stand on, or the 
 point of view you take, and so there are as many 
 connotations or meanings of a word as there are 
 points of view from which to regard it.' 
 
 * Please give us an instance to make it clearer,' I 
 gasped. 
 
 ' Take the term " man." Here we have a group 
 of individuals a class. They resemble one another 
 in countless attributes ; which of those attributes are 
 we to select as connotation ? It's impossible to take 
 them all. We must have some to apply as a test, 
 and to exclude such animals as gorillas that clamour 
 for admittance. Take the most prominent. " Rational 
 and animal qualities " generally seem the most pro- 
 minent. But change our point of view and our 
 differentia (half-the-connotation) will change. Man 
 and his attributes are like the round table we sit at ; 
 the part that is prominent to you is not prominent 
 to me. Here is an illustration.
 
 86 PICTUEE LOG10. 
 
 ' According to all these " Ms " connotation differs. 
 The popular point of view seems the best. It is 
 represented by ascending steps. First things, the 
 stocks and stones ; then plants (life without feeling) ; 
 then animals (life with feeling) ; and at the top men 
 (life with feeling and reason) ; and here " animal and 
 rational qualities" are the connotation, intension, 
 meaning, or essence (for these all mean the same) of 
 man. To make this still clearer, take the expression 
 " a good country." This to the hunting man means 
 " with good fields and fences," to the painter " with 
 fine landscapes," to the botanist " with rare flowers," 
 to the thirsty man " with frequent public-houses," and 
 to the missionary, " with pious views." Here the 
 connotation or essential attributes vary with the 
 position of the spectator. Thus we hear people 
 rebuke those who take mistaken views of life, " You 
 seem to think life means nothing but * eating and 
 drinking/ " say they, where Logic would say, " You 
 seem to think the connotation of life is eating and 
 drinking qualities, and that * man is an eating and 
 drinking (instead of a rational) bea.st.' ' : 
 
 * Lastly, remember verbal (or explicative, or 
 essential) propositions are those where the predicate 
 unfolds the meaning or essence of the subject, and 
 so tells you what you already knew, if you knew 
 what the subject meant. Eeal (ampliative or acci- 
 dental) propositions tell you something more than you 
 necessarily knew, if you knew the meaning of the
 
 Jrom tlv'u (xjtTvt of TjUiiJ, .Alau 
 
 coohinq aiiimtLl ^ t 
 a-nlu aiiMaal that coolw itJ 
 food. 
 
 5rom taij |>oint of mfu, 
 
 THE ESSENCE OF MAN.
 
 HEADS OF PKEDICABLES. 87 
 
 subject. Man is an animal, is verbal. Man is white 
 or black, real. Of the five heads of predicables, the 
 first three form verbal propositions, the other two real 
 propositions. 
 
 * With regard to accidents, notice that they are of 
 two kinds, separable and inseparable. " Some men 
 are Europeans," is an inseparable accident. It is not 
 a part of, nor does it follow from, the meaning of 
 man (" rational animal") that he is a European, and 
 so it is an accident ; at the same time it is an abid- 
 ing attribute, so to speak, as compared with such an 
 attribute as " Some men are ill, or eating, &c.," 
 which is called a separable accident. So we talk of 
 men as " inseparables " when they are always found 
 together, though they are not obliged to be together, 
 and man and wife might be called " separables " 
 because to-day they live together and to-morrow they 
 inav be divorced. 5
 
 88 PICTUEE LOGIC. 
 
 CHAPTER XIV. 
 
 DEFINITION. 
 
 ' You have now some idea of the signification of 
 connotation, otherwise called intension, essence, or 
 meaning. The proposition which expresses this 
 connotation is called definition, as the proposition 
 which expresses the denotation or extension is called 
 division. It will be easy to follow now, if the idea of 
 connotation is once grasped. Remember 
 
 1. What can't be defined. 
 
 2. All definition is incomplete in three ways. 
 
 3. All definition is relative. 
 
 4. All definition is " per genus et difFerentiam." 
 
 5. Rules of definition. 
 
 ' 1. Singular and collective terms can't be defined. 
 Why ? Definition gives connotation, and these two 
 have none. You give your gardener wasps and ask 
 him for the honey. He says they haven't any. So 
 definition can't give you the connotation of singular 
 and collective terms. Again, simple ideas can't be 
 defined, for all definition is an unfolding, and you 
 can't unfold what is already unfolded. So " thing
 
 DEFINITION. 89 
 
 or substance," the suinmum genus, can't be defined ; 
 and so sweet, bitter, harsh, &c. " What is love ? " 
 asks your iinsusceptible friend. " Oh, it's very nice, 
 but I can't explain it," you reply. " You must feel 
 it to understand it ; you'll know some day ; it's one 
 of those things that nobody can define. To under- 
 stand what ' sweet ' means, you must taste sugar." 
 
 * 2. All definition is incomplete because (a) the 
 connotation it gives is only a part of the attributes 
 As we have seen, " man " has an infinite number of 
 attributes, but those implied by " rational animal " 
 are considered enough to represent the class. 
 (6) Even the attributes thus given are not in their 
 simplest form " rational " and " animal " are both 
 capable of analysis (or breaking up into simpler 
 elements). A being of another world may ask you, 
 " What is man ? " and upon your replying " A 
 rational animal," may go on "Yes, but what is 
 * rational,' and what is ' animal ' ? Are not these 
 also open to further explanation ? " and you would 
 have to give a long explanation of both by help of 
 Porphyry's tree. Thus a beggar at your door might 
 receive a crust of bread, and depart grumbling at 
 your charity as doubly incomplete First, because 
 of all your luxuries you only gave him a crust ; and, 
 secondly, because upon inspection even that crust 
 turned out to be mouldy. So definition only gives us 
 a few out of many attributes, and even those few are 
 not in their simplest form, (c) All definition de-
 
 90 PICTURE LOGIC. 
 
 pends upon the existing state of our knowledge. 
 Fresh discoveries upset old definitions. We talk of 
 plants and animals as two distinct kingdoms, but 
 the jelly fish looks very like a vegetable and certain 
 flowers strongly resemble animals. How if they were 
 discovered to be all one great kingdom instead of 
 two ? All the definitions existing in the two king- 
 doms would be bundled away and vanish as the 
 coaches upon the invention of the rail. 
 
 '3. All definition is relative. Relative (re-fero) 
 means " has reference to something," and we have 
 seen how the connotation depends upon the point of 
 view you take. The prominent attributes, the " iin- 
 portant-for-the-time-being " attributes are the con- 
 notation, and the prominence depends upon the posi- 
 tion of the spectator. So definition is relative 
 has reference to the point of view, and there are as 
 many definitions of a term as there are points of 
 view from which it can be regarded, e.g., " good 
 country." 
 
 * 4. All definition is per genus et dijferentiam. If 
 you are asked to define words in examination re- 
 member this. Always make your genus, find your 
 differentia, add the two, and you get genus + differ- 
 entia = species = whole essence, connotation, inten- 
 sion, or meaning : and this is what definition gives, 
 for these four words mean the same. Ask yourself 
 first, "What is it?" and then "What kind of 
 it?"'
 
 DEFINITION. 91 
 
 ' But is it easy to get the genus and differentia ?' 
 asked Dyver. ' I saw the words botany, monarchy, 
 money, metal, college, in a paper how would you 
 do them ? ' 
 
 Never having dreamt of attempting to define 
 difficult words like these, I was astonished at the 
 simplicity of the process as then given. 
 
 ' Nothing easier,' he replied. ' As a last resource 
 you can always call everything " a thing;" e.g., a 
 whip = a thing for driving ; a ship = a thing for going 
 on the sea, and so on ; but you generally know some- 
 thing more about the words, as here. Botany, quid? A 
 science (genus). How different from other sciences? 
 " Concerned with plants " (differentia) ; and hence 
 the " quale quid, " or species, " A science concerned 
 with plants " = whole essence = connotation; ergo 
 this is the definition. So monarchy. Genus ? ' 
 
 1 Rule/ said Dyver. 
 
 < What kind of rule?' 
 
 ' The rule of one.' 
 
 'So money="a medium of exchange." Metal 
 = "a substance hard and bright." College="a 
 society of men formed for the pursuit of knowledge.' " 
 
 'May I try " barrister?" ' said I. 
 
 ' By all means.' 
 
 'A barrister is a man, genus (answer to what?), 
 and his differentia is " pleads at law," and so the 
 species," a man who pleads at law." Would this do ? '
 
 92 PICTURE LOGIC. 
 
 * Very well indeed.' You see now how definition 
 gives the genus -f differentia (= species.) Description 
 gives you the properties and accidents, e.g., " Man is 
 able-to-do-Euclid," or " Man is a biped." ' 
 
 ' But if the connotation shifts with the position of 
 the spectator, surely the properties and accidents 
 from one point of view are differentiae from another ? ' 
 said Dyver. 
 
 * Quite so ; before you begin to draw out your . 
 genus, &c., you must determine your point of 
 view. In the illustration above, the proposition 
 "Man has a certain chest, posture, &c.," is an accident 
 to the student who stands on the other side (so to 
 speak), and to whom the " rational qualities" of man 
 are the prominent ones ; while to the student who 
 regards man as " an animal of certain chest, posture, 
 &c.," the fact that " man is rational " is an accident. 
 Hence the definitions of one science become the 
 descriptions of another, for the definition = genus + 
 differentia, and the description = accidents or pro- 
 perties ; but the differentia becomes an accident or 
 property if you change your science, i.e. your point 
 of view, and so the definition becomes a description. 
 Do you understand ? ' 
 
 * Not clearly,' said I. 
 
 'You are in the train, sitting opposite a prob- 
 able native of the country through which you are 
 passing. You ask, " Is this good country here ? "
 
 DEFINITION. 93 
 
 He looks at you carefully in order to get some idea 
 of your occupation in life, that he may know the 
 point of view from which you regard things. You 
 look like a farmer. He replies, " Crops is fair." 
 You have a white necktie on. " Ah, sir, there's a 
 deal of drinkin'. " Perhaps you carry a hunting 
 crop. He says, " Not much covert, sir " ; or a mi- 
 croscope with roots in your pockets, he says, 
 " Beautiful flowers about ;" or, lastly, you may be a 
 weary traveller, and he will reply, " Poor accommo- 
 dation, sir." But should your appearance give him 
 no clue, he will reply, " Well, sir, that dippends upon 
 what you mean by country. Yer see, what would 
 make one man call a country good would be quite 
 secondary like to another man. It ain't essential like 
 to the man as looks at country from a 'untin' point 
 of view that there should be purty landscapes, 
 'owever, &c." In other words, given a class name (e.g., 
 man) with an infinite number of attributes, the promi- 
 nent attributes go to form the differentia, and all the 
 rest of the round (so to speak) sinks into the secondary 
 position of properties and accidents. Definition 
 gives the former; description the latter. Change 
 your point of view or science and your definitions 
 become descriptions. 
 
 *5. The rules of definition are not difficult to 
 remember. 
 
 (a) It must be essential (i.e. give the prominent 
 attributes).
 
 94 PICTUKE LOGIC. 
 
 (&) It must be adequate (i.e. sufficient to dis- 
 tinguish tke term from others). 
 
 (c) It must not be obscurum per obscurius, 
 
 i.e. explaining an unintelligible term by 
 terms if anything more unintelligible still; 
 as if to enlighten a rustic you defined 
 the soul " as a species of eutelechy of 
 a potential spiritual existence, my good 
 man," or a flea thus : " A flea, madam, 
 may be defined as an apterous hexa- 
 pod." 
 
 (d) It must not be "circulus in definiendo." 
 
 You must not in your definition come 
 round to the term defined, and use it 
 again. You must not say, " Metal is 
 a metallic substance." 
 
 (e) No metaphors allowed. You must not 
 
 define memory as " a storehouse of ideas." 
 A metaphor is an image borrowed from 
 one class of things and applied to another. 
 When I speak of a lady '* sailing " through 
 a ball-room, the image is borrowed from 
 ships. Metaphors are apt to mislead. 
 From the lady's " sailing " in a room we 
 might be led to imagine she could float 
 in deep water, and the experiment might 
 drown her ; showing how dangerous meta- 
 phors are. So Logic does not admit them 
 into definitions. Remember these rules
 
 DEFINITION. 
 
 95 
 
 by the examples of their violation. " Man is a biped ;' 
 " Man is an animal ; " " the soul j " " Metal ; ' 
 "Memory," thus: 

 
 96 PICTUEE LOGIC. 
 
 CHAPTER XV. 
 
 DIVISION. 
 
 * DIVISION gives the denotation of a term as defini- 
 tion gives the connotation. As there were five heads 
 under which to group all you need know about defi- 
 nition, so there are four heads here. Only under- 
 stand and you will find it easy to remember. 
 
 1. Various kinds of division. 
 
 2. Technical terms of division. 
 
 3. Division and dichotomy distinguished. 
 
 4. Rules of division. 
 
 * 1. When you break a "plate" you divide it 
 into parts, but each part is not a complete plate ; 
 whereas if you divide " plates " into soup plates, salad 
 plates, cheese plates, &c., each member of the divi- 
 sion is called a plate still. So if you divide " man " 
 into " arms, legs, &c." or into " Europeans, Africans, 
 &c." The first kind of division is called partition or 
 physical division ; the second, logical division. One 
 divides wholes into parts, the other classes into 
 classes. There is also metaphysical division or the 
 process of making abstract terms.' 
 
 1 What are abstract terms ? ' asked Dy ver. 
 
 * We have seen that the whole world around us
 
 DIVISION. 95 
 
 may be regarded as things and their qualities, or 
 individuals and their attributes. As a master of fact 
 we never see things and qualities apart. Every 
 quality we know of is always found in connection 
 with the thing which manifests it. We never see 
 " red " or " white " apart from " red thing," " white 
 thing." But by help of imagination we can picture 
 to ourselves " red " and " white " in the abstract. 
 Now an attribute viewed in connection with its indi- 
 vidual (con-cresco) l is said to be " concrete " ; but 
 viewed apart from its individual it is called "ab- 
 stract " (abs traho), and the process of abstraction is 
 called metaphysical division. So physical division 
 divides wholes into parts, metaphysical separates 
 individuals from attributes, and logical divides classes 
 into classes. 
 
 ' 2. The technical terms of division are the totuin 
 divisum, the membra dividentia, and the fundamen- 
 turn divisionis. The totum divisum is the whole 
 class to be divided. As in definition you take the 
 species and resolve it into its component genus and 
 differentia ; so in division you take a genus, and by 
 selecting some differentia or point of difference you 
 find all the species that are included in the genus. 
 The genus is then called the totum divisum ; the 
 point of difference, or the ground or source of the 
 
 1 Concrescere = ' to grow with.' Abstrahere = ' to draw away.' So to 
 speak, we draw away the green from the trees in bloom when we talk ot 
 ' greenness' the green and the tree grew together. 
 
 H
 
 98 PICTUEE LOGIC. 
 
 division, is called fundamentum divisionis ; and the 
 species obtained the membra dividentia. Given the 
 genus, "picture." Divide this. The question is 
 " upon what principle ? What is to be our funda- 
 mentum divisionis ? " Take as F. D. (fundamentum 
 divisionis) " manner of frame," and your M. D. (mem- 
 bra dividentia) become "pictures with gilt frames, 
 pictures with wooden frames, pictures with all other 
 frames ; " or, take as F. D. " material " and your 
 M. D. become " pictures in oil, pictures in water- 
 colour, pictures in all other material." Loosely 
 speaking, definition may be said to break up the 
 species into the genus and differentia of which it is 
 composed, while division, by the addition of dif- 
 ferentia, builds up the species out of its genus and 
 differentia.' 
 
 ' Please explain this further,' said I. 
 
 * Given the common term, " guns." Divide this. 
 You must select some point of difference if you want 
 to find the species which form this genus " guns." 
 Take as F. D. "manner of loading," and you get as 
 your species or membra dividentia " breech-loading 
 guns," " muzzle-loading guns ; " or, again, F. D. 
 number of barrels, and M. D. " double barrels " and 
 " single barrels." 
 
 < T. D., houses ; F. D., " material ; " M. D., houses 
 of brick, houses of stone, houses of all other material. 
 
 ' T. D., horses ; F. D., " use ; " M. D., hunters, 
 hacks, carriage horses, all other horses. 
 
 1 As there are as many definitions, so there are as
 
 DIVISION. 99 
 
 many divisions as there are points of view, for each 
 fresh point of view will start a fresh F. D. or source 
 of difference from which to form differentise. The 
 ordinary observer divides " animals " into " rational 
 and irrational," the moralist into " animals with a 
 conscience and without," the zoologist into " animals 
 with such and such teeth, breast, or posture," 
 the tailor into " animals to be clothed and not to be 
 clothed," and so on. Each is determined in his 
 choice of an attribute to stand as F. D. by the point 
 of view he takes. 
 
 ' 3. Dichotomy is a kind of division. Dichotomy 
 (Sifta Tfj.vG>) or the " cutting into two " always divides 
 a genus into two species. It selects an F. D. and 
 divides the class into one part that possesses an 
 attribute implied and another part that does not, e.g., 
 men : F. D. " nation," M. D. " Asiatics and not- 
 Asiatics." It depends upon the law of excluded 
 middle. It is more useful in matters of which we 
 know little. We should not divide the kings of 
 England by dichotomy into Norman and not-Nor- 
 man, and not-Norman into Plantagenet and not- 
 Plantagenet, &c., because we know all the names of 
 the houses. But in dividing mysterious things like 
 the " corns in a horse's foot," if we divided thus 
 
 CORNS 
 
 1 
 
 1 
 
 ! 
 
 Corns from 
 
 Corns from 
 
 Corns from 
 
 nature 
 
 bruises 
 
 shoeing, 
 
 
 H 2 

 
 100 PICTUEE LOGIC. 
 
 a corn might appear which was due to none of 
 these causes, and we should have no class to enroll 
 this new-comer in. Whereas, if we had divided 
 thus, 
 
 CORNS 
 I 
 
 From Not from 
 
 nature nature 
 
 From Not from 
 
 bruises bruises 
 
 From Not from 
 
 shoeing shoeing, 
 
 the new comer would be immediately enrolled in the 
 class of " not from shoeing," and our classification 
 would not have been found wanting. 
 ' 4. Learn by heart these rules : 
 
 (a) Each M.. D. must be a common term. 
 (6) The T. D. must be predicable of each M. D. 
 (c) The M. D.s taken together must equal the 
 T. D. or the division must be exhaustive. 
 (I) There must be only one F. D. 
 
 ' (&) Distinguishes logical from physical division. 
 You can't say this piece of a plate is a plate, but you 
 can say " soup-plates are plates." 
 
 ' (c) The membra dividentia taken together must 
 make up the whole genus divided, or the division 
 will not be exhaustive, i.e. will not have exhausted
 
 DIVISION. 101 
 
 the number of species in the genus. Divide the 
 cartridges in your pouch according to colour the 
 membra dividentia are blue and green cartridges. 
 After shooting away all the blue and green you find 
 several yellow ones, and so your division was not 
 exhaustive luckily, or your shooting must have 
 ended. 
 
 * (d) There must be only one F. D. or you have a 
 cross division. You may have several F. D.s, but 
 only one at a time. Thus 
 
 (See pp. 67-69. ' The FIGTIEB 
 
 lost scalene | 
 
 triangle.') j j 
 
 Curvilineal Eectilineal 
 
 Triangle Quadrilateral Polygon 
 (three-sided) (or four-sided) (or more than 
 four-sided) 
 
 I I 
 
 Scalene Equilateral Isosceles 
 
 (no sides equal) (three sides equal) (two sides equal) ; 
 
 where subdivisions take place, and there are three 
 different F. D.s in succession (nature of lines, number 
 of sides, equality of sides), but only one at a time. 
 A cross division would be to divide women into 
 sisters of mercy, Americans, spinsters, and loud 
 talkers, for in one division you have the F. D.'s " oc- 
 cupation," " nation," " marriage," and " manner of 
 speech." Eemember this :
 
 102 PICTUEE LOGIC. 
 
 ' " Your l M. D. is common, TeDious, exhaustive, 
 but never cross," i.e. 
 
 (1) The M. D. must be common terms. 
 
 (2) Each. M. D. must be a T. D. 
 
 (3) The division must be exhaustive (M. D. to- 
 
 gether = T.D.). 
 
 (4) No cross division (i.e. one F. D.). 
 
 1 ' It has been said that this is equally true -whether M. D. stands 
 for Membra Dividentia, as above, or Membra Dividentes, i.e., Doctors. 
 But Logic is only concerned with the former and less violent rending.'
 
 103 
 
 CHAPTEE XVI. 
 
 INFERENCE. 
 
 ' WE have now arrived at the third head, Syllogism. 
 Syllogism is a kind of inference. Inference, from 
 in and fero, means "the bringing in of new truth," 
 or the " bringing in" of the same truth in a new form 
 (for some say that in a syllogism we bring in no new 
 truth). Now we may " infer" from particulars to 
 universals, or from universals to particulars. From 
 " John is mortal, James is mortal," &c., we may 
 infer that " All men are mortal ;" or from " No two 
 straight lines can enclose a space," we may infer 
 that these two ramrods cannot enclose a space. The 
 first is called induction, the second deduction. Set- 
 ting aside inductive Logic as beyond our limits, we 
 subdivide deductive inference into immediate and 
 mediate. Immediate where we deduce one proposi- 
 tion directly from another, mediate where we do so 
 not directly, but by the help of a middle term. 
 Hence inference is thus divided : 
 
 INFERENCE 
 
 Inductive Deductive 
 
 I I 
 
 Immediate Mediate 
 
 (opposition, conversion, (the syllogism), 
 permutiition)
 
 104 
 
 PICTUEE LOGIC. 
 
 ' To begin with immediate inference, (i) Opposi- 
 tion, where the truth or falsity of one proposition is 
 inferred directly from the truth or falsity of another. 
 The four forms A E I are opposed in various 
 ways, and this you will remember by this figure : 
 
 Contrary j 
 
 
 "f> 
 
 For the opposition of 
 A and E is called contrary opposition 
 7 and is called sub-contrary opposition 
 A and I or E and is called subaltern opposition 
 A and OorE and Jis called contradictory opposition,, 
 
 The only case in which we can always infer the truth 
 or falsity of one proposition from another is contra- 
 dictory opposition, and you need remember nothing 
 more than the names of the rest. To prove an ad- 
 versary's statement false, use contradictory opposi- 
 tion. At first sight contrary opposition seems more 
 powerful. If he says, for instance, " All Englishmen 
 are black-bearded," you are strongly tempted to make 
 a sweeping retort, "No Englishmen are black-
 
 JKFEKENCE. 105 
 
 bearded ; " but if you do so, as a man who makes 
 too eager a lunge, you expose yourself, for he replies 
 " Jones, Smith, &c., i.e. some Englishmen, are so," 
 and he produces them. In the first instance you 
 should have replied, " Some Englishmen are not 
 black-bearded," and this would have refuted his 
 statement.' 
 
 ' How can you call it an opposition between / 
 and (" Some men are maniacs" " Some men are not 
 maniacs "), and still more between A and /and i/and 
 (" All men are mortal " " Some men are mortal : " 
 " No men are fishes " " Some men are not fishes ")' ? 
 asked Dyver. 
 
 * There is an opposition here, but only a very mild 
 one,' he replied. 
 
 * (ii) The inference called conversion makes the 
 predicate the subject and the subject the predicate, 
 and so gets a new proposition, e.g., " Some men are 
 bold leapers " " Some bold leapers are men." 
 
 * This change is sometimes dangerous. From " All 
 our loveliest companions are women " it would be a 
 grievous error to infer that " All women are our 
 loveliest companions." Or from " All dogs are ani- 
 mals that bite," that "All animals that bite are dogs," 
 i.e. that there are no other "animals that bite" beside 
 dogs. Here we must change the quantity, and say 
 from " All men are animals " not " All animals 
 are men " (for where would the bears be ?) ; but " Some 
 animals are men." . Where no change of quantity
 
 106 PICTURE LOGIC. 
 
 takes place it is called " simple conversion ;" where a 
 change takes place it is called " conversioper accidens." 
 A propositions are converted per accidens ; E simply ; 
 I simply ; not at all. There is one case, however, 
 in which A converts simply when the subject and 
 predicate are of the same size, so to speak, or co- 
 extensive. Thus, "All men are rational animals " 
 " All rational animals are men ;" but, as a rule, and 
 unless you know that they are coextensive, convert 
 A per accidens.' 
 
 * But if you are asked to convert things like, 
 " Talents are often misused, &c.," ' said Dyver. 
 
 ' It is easy enough, if you will only remember to 
 bring them to one of your four logical forms, A E 10, 
 before you attempt to convert them, and then you 
 know whether they are converted simply or per 
 accidens: e.g., 
 
 " Fixed stars are self-luminous." 
 
 This proposition is not recognised by Logic except 
 as an indefinite proposition. You must bring it to 
 one of the recognised forms of Logic (A E I 0}. If 
 you want it converted. 
 
 Subject. Predicate. 
 
 All fixed-stars are self-luminous. (A prop, per acciiens.) 
 Some self-luminous are fixed-stars. 
 
 i.e. Some self-luminous things are fixed stars. 
 
 " No one is always happy." 
 Logical form : 
 
 No men are always-happy. (E prop, simply.) 
 No always-happy are men. 
 
 i.e. No things always happy are men.
 
 INFERENCE. 107 
 
 " Some of the most valuable books are seldom read." 
 Logical form : 
 
 Scme-(of)-the-most-valuable-books-are-seldom-read. (I prop, simply.) 
 Some seldom-read are the-most-valuable-books. 
 i.e. Some of the things seldom read are the most valuable books. 
 
 " Every mistake is not culpable." 
 Logical form : Some mistakes are not culpable. (0, not at all.) 
 
 For it does not follow that " Some culpable things 
 are not mistakes ; " nevertheless if you wish to con- 
 vert an 0, you can change it to an I by saying, 
 " Some mistakes are not-culpable " and then it 
 converts simply.' 
 
 * I understand these simple cases, ' said I, ' but 
 how would you treat " He jests at scars who never 
 felt a wound " ? ' 
 
 ' Be careful about your subjects and predicates. 
 Remember the test questions, " What am I talking 
 of?" "What do I say about it?" What am I 
 talking of here? " He-who-never-felt-a-wound " 
 the subject ; and of him I say that he " jests at 
 scars." It becomes then in logical form ; 
 
 All who-never-felt-a-wound are people-who-jest-at-scars. 
 
 An A proposition, which is converted per accidens, 
 thus : 
 
 Some people- who-j est-at-scars are those-who-never-felt-a- wound ; 
 
 and this is obvious, for there are others who jest at 
 scars (e.g., hardy men) besides those who never felt a 
 wound.
 
 108 PICTURE LOGIC. 
 
 * Mistakes often arise from the predicate's position. 
 Always ask yourself the test questions, and put your 
 propositions into logical form before you attempt to 
 convert them. Here is another. " No one is free 
 who doth not command himself " = " No-men-who- 
 do-not-command-themselves are free," an E pro- 
 position converted simply. " Life every man holds 
 dear " = " All life is a thing which every man 
 holds dear," an A proposition per accidens. " Only 
 the brave deserve the fair" = "No not-brave, &c." 
 "Nothing is beautiful except truth" = "No not- 
 truth, &c.," and " Every little makes a mickle " be- 
 comes when converted " One of the things which 
 make a mickle is every little." 
 
 * (iii) Lastly, permutation (or immediate inference 
 by privative conception) infers one proposition from 
 another by changing the quality alone, e.g., 
 
 All men are mortal, 
 .'. No men are immortal. 
 No cowards are good soldiers 
 .'. All cowards are bad soldiers 
 
 Some investments arc made with risk, 
 .'. Some investments are not made without risk. 
 Some investments are not made without risk, 
 .'. Some investments are made with risk. 
 
 And Mr. Jevons makes this very clear by diagrams, 
 by help of which we might represent it thus :
 
 INFERENCE. 109 
 
 ' Where it is plain that no part of the included 
 class man can be outside the class mortals : . . No 
 men are immortal. 
 
 ' No cowards are good soldiers ; they are two sepa- 
 rate classes, and . . All cowards are not good (i.e. 
 bad) soldiers. 
 
 1 Here the two classes overlap one another ; and, 
 as some of the investments are things made with 
 risk, it is clear that the part of investments which 
 overlaps is not without the other circle, i.e. is not 
 without risk, and the last case is clear by the same 
 figure. 
 
 ' N.B. These diagrams also serve to illustrate the 
 two kinds of conversion. The first proves that from
 
 110 PICTUEE LOGIC. 
 
 " All men are mortals " you get " Some mortals are 
 men ; " the second, that from " No cowards are good 
 soldiers " you get " No good soldiers are cowards ; " 
 and the third, that if " Some investments are things 
 with risk," " Some things with risk are invest- 
 ments ; " and that if " Some investments are not 
 things with risk " you can infer nothing, for it does 
 not follow that " Some things with risk are not in- 
 vestments," for we happen to know that some things 
 with risk are investments.' 
 
 That night I had one of my Logic dreams. I 
 thought I was walking through a fair. A man was 
 shouting from a platform, ' This way for the real, 
 live, strugglin' propositions ! He very kind of hopo- 
 sition 'twixt them as differ in quantity or quality, or 
 both ! ' I entered and saw all kinds of fights going 
 on between things with small waists, like wasps. 
 
 The Fight of Propositions. 
 
 The spectators seemed to take very little interest in 
 the fighting, except when, as every now and then it 
 happened, a small animal engaged a large one and
 
 INFERENCE. Ill 
 
 threw him and mortally wounded him. Then they 
 shouted with delight. For the other combatants 
 made a very poor fight of it. The man told me that 
 what made them fight was that they differed in 
 quantity or quality, or both. Suddenly, I heard 
 shouts of * Contradictory, contradictory ! ' and, 
 hurrying to the spot, saw one of these mortal fights. 
 The smaller animal had ' Particular ' branded on its 
 back, the larger * Universal.' The spectators ap- 
 plauded loudly. 
 
 Death of the Universal. 
 
 Quitting this tent, I heard another man crying, 
 
 * Come and see the operations ! ' I entered a kind 
 of hospital ward. They were operating upon animals 
 similar to those I had seen fighting. They kept 
 cutting off their heads and their bodies, and sticking 
 them on again ; the heads where the bodies were and 
 
 o * 
 
 the bodies where the heads were. They don't seem 
 to feel it in the least,' I remarked to a bystander. 
 
 * Ah ! said he, they be E's and I's ; wait till you see 
 an A done.' Very soon an A did come, and they 
 had a severe struggle to convert him (for they called 
 the operation 'conversion '), and he lost so much blood 
 in the operation, that they all cried, " What a quantity 
 lost! Oh! what a quantity! " Certainly he looked
 
 112 PICTURE LOGIC. 
 
 much thinner after it, as if he had gone through . an 
 accident (per accidens). Last came an animal that 
 kept struggling so violently that the operator said, 
 ' I hope I don't hurt you? ' and he replied, ' O, not 
 at all ; ' at which the operator turned pale and let 
 him go at once. 
 
 After that they experimented on one of these 
 animals to show that the addition of a negative to 
 each end of them made no difference to them. They 
 hung one up by his waist, like a pair of scales, and 
 fastened something of equal weight to his head and 
 his body, so that the balance remained as before. 
 'There,' said the operator, 'that's permutation 
 change of quality alone.' At these words several of 
 his audience looked puzzled; but when he added 
 'otherwise denominated immediate inference by pri- 
 vative conception ' there was a wild rush to the door, 
 and I was carried along with the panic-stricken 
 crowd, and woke, repeating to myself, ' Opposition, 
 quantity or quality, or both, conversion, subject and 
 predicate, permutation, quality alone, and by this I 
 remember them always.'
 
 113 
 
 CHAPTEE XVII. 
 
 SYLLOGISM. 
 
 'MEDIATE deductive inference, or syllogism, is the 
 assertion of a third proposition in virtue of two 
 other propositions. Some say that only inductive 
 inference is entitled to the name of inference. We 
 shall regard the syllogism as an inference for reasons 
 we will afterwards state. Take the instance, 
 
 " All men are mortal, 
 Socrates is a man, 
 
 .'. Socrates is mortal.'* 
 
 'Here there are three terms. Socrates, man, 
 mortal. The term " man" occurs twice, for it is the 
 middle term through which Socrates and mortal 
 are compared. Hence the name " mediate infe- 
 rence." 
 
 ' Now there are three things to remember ahout 
 the syllogism. 
 
 (.4) The principle upon which it depends. 
 
 (B) The rules which test its validity. 
 
 (C) The canons of its figures. 
 
 ' (A) The principle upon which all syllogisms de- 
 pend is that " things which are equal to the same are 
 
 I
 
 114 
 
 PICTURE LOGIC. 
 
 equal to one another." In the above instance the 
 conclusion is " Socrates is mortal." Our object at 
 starting was to establish a comparison between 
 " Socrates " and " mortal." But it so happened that 
 we could not bring those two terms directly toge- 
 ther, and we employed the help of a third term. 
 You ha.ve a station at the foot of the Alps on the 
 north side, and another at the foot of the Alps on the 
 south side. You can't make a tunnel. How do you 
 effect a junction ? You must ascend to the summit, 
 and from the summit you must descend. So to effect a 
 junction between the terms " Socrates " and "mortal " 
 you must take " man " as a middle term. Thus : 
 
 The Syllogistic Alp. 
 
 Here we are asked to establish a comparison 
 between " Socrates " and " mortal." Unable to see
 
 SYLLOGISM. 115 
 
 through an intervening hill, we climb by ladder to 
 the point man, and then we can see both " Socrates" 
 and " mortal." From the conclusion, remember, we 
 get our names. The predicate of the conclusion is 
 the major term (for the predicate of a proposition is 
 generally a larger class including the subject, as 
 " mortal " is larger than Socrates), and the subject 
 of the conclusion is called the minor term. Hence, 
 major and minor premiss. The proposition which 
 connects the major term and middle term is called 
 the major premiss, and that which joins the minoi 
 and middle terms is called the minor premiss. The 
 former always comes first. Unless the principle that 
 " things which are equal to the same are equal to 
 one another " were true, it would not follow that 
 " Socrates " and " mortal," which are equal to the 
 same (" man "), would be equal to one another. 
 
 ' (B) The rules of the syllogism. We now know 
 that a syllogism consists of three propositions, con- 
 taining amongst them three terms : minor, major, 
 and middle. Out of the propositions A E I we 
 can frame a large number of such triplets, e.g., " All 
 animals can feel, all cats are animals, therefore all 
 cats can feel," which would be all A propositions, or 
 A A A ; " No angels are human, all women are 
 human, therefore no women are angels," which 
 would be E A E, &c.' 
 
 * But would they all be true or valid ? ' I asked. 
 
 t That we shall find out by the application of 
 
 i 2
 
 116 PICTUEE LOGIC. 
 
 rules. First of all, Douglas, look carefully at the 
 two syllogisms I have given you, and tell me if you 
 see anything wherein they differ from one another.' 
 
 ' To be sure/ said I ; ' one is about cats and the 
 other about angels.' 
 
 4 True; but that is a difference of matter. What 
 I want is a difference of form, and lest you should be 
 tempted by the flesh of the propositions, so to speak, 
 let us strip them of all but their bare bones ; let us 
 employ ciphers that in Logic we may not be misled by 
 the matter. Always use the same ciphers. A for 1 the 
 major term, B the middle, and C the minor. Thus : 
 
 A. 
 A. 
 A. 
 
 All animals can feel \ 
 All cats are animals 
 
 = ( ! ) " 
 
 Therefore all cats can ! 
 feel . . j 
 
 'All Bis A 
 All C is B 
 /. All C is A 
 
 (where B = animals, 
 C = cats, 
 A = things 
 that feel.) 
 
 E. 
 A. 
 E. 
 
 No angels are human \ 
 All women are human 1 .... 
 Therefore no women f ^ ' 
 are angels . .) 
 
 No A is B 
 All C is B 
 .'. No C is A 
 
 (where B = human 
 ,, C = women, 
 A = angels.p 
 
 Now do vou see any 
 
 difference 
 
 between these 
 
 two cipher syllogisms ? ' 
 
 * Yes,' said I ; ' the propositions that compose 
 them are different. In the first you have " all," 
 " all," " all," and in the second k < no," " all," " no." ' 
 
 * Precisely so, and syllogisms differing thus are 
 said to differ in mood. The syllogism A A A differs 
 in mood from E A E, and so moods mean the various 
 aiTangements of propositions in syllogisms. But 
 there is yet another difference.' 
 
 1 Do not confuse this A (MAJOR TERM) with Proposition A the first 
 of the four A E I O.
 
 SYLLOGISM. 11? 
 
 Neither of us could detect this until we were 
 told to mark the position of B, or the middle term in 
 the premisses, and then we saw that B was subject 
 in the major premiss (top proposition) of syllogism 
 (i), but predicate of major premiss of syllogism (ii). 
 
 * Here, then, is another point in which these 
 triplets of propositions, called syllogisms, may differ. 
 And as syllogisms differ in mood according to the 
 arrangement of their propositions, so they differ in 
 figure according to the position of the middle term in 
 those propositions. There can only be four figures. 
 Where the middle term is subject in the major and 
 predicate in the minor premiss, where it is predicate 
 in both, where it is subject in both, and where it is 
 predicate and subject ; e.g., take the mood A A A in 
 all the four figures : 
 
 A. All B is A 
 
 A. All C is*B j- Fig. I. 
 
 A. /. All C is A 
 
 A. All A is 
 
 A. AU C is IB (- Fig. II. 
 
 A. /. AU C is A 
 
 A. All B is A 
 
 A. All b is C } Fig. III. 
 
 A. /. All C is A 
 
 A. All A JsJB 
 
 A. All B is C f- Fig. IV. 
 
 A. /. All C is A 
 
 We know there can be only four figures ; the ques- 
 tion is, how many moods can we have in those four 
 figures. The four figures may be remembered by 
 the front of a collar. 1 As to moods, it is clear that 
 out of the four forms or propositions A E 1 a 
 large number of different triplets can be made. We 
 
 1 See next page. The figures are thus easily remembered ;\||X these 
 lines being taken from the position of the middle term as marked above. 
 For further remarks upon the figures see Appendix A (i.).
 
 118 PICTURE LOGIC. 
 
 may have A A A in all the four figures, and A A E, 
 A E E, and so on ; these will be all syllogisms, i.e. 
 triplets of propositions comparing two terms through 
 
 The Front of a Collar. 
 
 a third ; but whether they will be all valid syllogisms 
 is another question. Supposing we act upon the 
 conclusion we get from a syllogism and fall into 
 error, we should at once turn upon Logic and abuse 
 it. But Logic does not warrant as valid every com- 
 bination of the propositions AEIO in syllogistic 
 triplets.' 
 
 ' I don't quite understand,' said I. 
 
 ' Take the mood A A A in the second figure, and 
 tell me whether its conclusion is true : 
 
 A. all A is B 
 (fig. 2) A. all C is B 
 A. /. all C is A.' 
 
 * It seems right, as far as I can judge,' said I. 
 
 * By this syllogism a man might pray for a dissolu- 
 tion of his marriage on the ground that his wife was 
 married to a crocodile ; for 
 
 " All crocodiles are animals, 
 All men a.re animals, 
 Therefore all men are crocodiles." '
 
 SYLLOGISM. 119 
 
 ' In this shape it certainly sounds wrong,' said I. 
 
 ' Of course ; and there are many other of the pos- 
 sible moods which will be found to be not valid in 
 the same way. A mood not valid in one figure may be 
 valid in another. There are sixty-four possible moods. 
 How many of them can we admit into the four 
 figures as valid syllogisms ? That all the moods are 
 not valid in all the figures is clear from the above 
 instance, where the mood A A A in the second figure 
 is found to produce an unheard-of conclusion. By 
 what test shall we try pretenders to the name of 
 valid syllogisms? The answer is, by applying cer- 
 tain rules to them ; and if they do not violate these 
 rules, they are valid ; and if they do, they are not. 
 These rules are eight. Do not be alarmed ; they are 
 all eight wrapped up in four lines easily learnt. To 
 explain these rules : 
 
 ' (1) The middle term must be distributed at least 
 once. For unless it be used in its full extent once, it 
 may be used first for one part of itself, and second!)' 
 for another part of itself; e.g. 
 
 
 This whole figure represents the class " women ; " 
 parts of this class are " cooks " and " queens." 
 Hence :
 
 120 PICTUEE LOGIC. 
 
 All queens are women, 
 
 All female cooks are women, 
 
 . . all female cooks are queens. 
 
 Had the middle term " women " been once used in 
 its full extent, this false conclusion could not have 
 been drawn. 
 
 ' (2) You must only have three terms, otherwise the 
 principle of the syllogism is violated, " things which 
 are equal to the same" &c. An ambiguous middle 
 term is the same as two terms, thus : 
 
 All chests are boxes, 
 Part of me is a chest, 
 . . part of me is a box, 
 
 where " chest " means " box " in the major premiss, 
 and " breast " in the minor. 
 
 ' (3) Two negative premisses prove nothing. For if 
 we wish to compare two things through a third, and 
 neither of these two things is connected with the 
 third, we can draw no conclusion. From " Socrates 
 is not an elephant," and " Pugilists are not ele- 
 phants," I should be in no way helped as to the 
 question whether Socrates was a pugilist or not. 
 
 ' (4) Two particular premisses prove nothing. For 
 they would be 0, 0, which violates (3), or I, I, which 
 violates (1), or I, 0, which will be found to violate 
 (5).' 
 
 * (5) If either premiss be negative, the conclusion 
 must be negative. For if, after taking our middle 
 1 For further explanation see Appendix A (ii.).
 
 SYLLOGISM. 121 
 
 term as a medium of comparison, we say that one of 
 the two things to be compared is equal to the 
 middle term and the other is not, it follows that 
 the two things to be compared cannot be equal to 
 one another. If we want to compare " Socrates " 
 and " stone " through the medium " animal," we say 
 " Socrates is animal, stone is not animal," and the 
 conclusion must be negative, " . . Socrates is not 
 stone." 
 
 * (6) If either premiss be particular, the conclusion l 
 must be particular. I will prove this rule afterwards. 1 
 
 ' (7) Let no term be distributed in the conclusion, 
 unless it has been already distributed in the premisses. 
 Otherwise we argue from part to whole. Violation 
 of this rule, if it be in the case of the minor term, is 
 called " illicit process of the minor," or, if it be in 
 the case of the major term, " illicit process of the 
 major." 
 
 ' (8) Let not the conclusion, be negative, unless one 1 
 of the premisses is negative. For we could not say, 
 " Socrates is not stone " as a conclusion, unless 
 we had a " not " in one of our premisses ; e.g., 
 "' Stone is not animal," " Socrates is animal." * 
 
 ' Further explanation of these rules I do not think 
 to be necessary, but you can find it in the books of 
 Mr. Jevons or Mr. Fowler. For our purpose it will 
 be enough to remember them by heart, and this you 
 do by learning off these four hexameter lines : 
 
 1 For further explanation see Appendix A (ii.).
 
 122 PICTUKE LOGIC. 
 
 Distribuas medium, nee quartus terminus adsit, ( = Rules 1 and 2.) 
 
 Utraque nee praemissa negans, nee particularis ; ( = Rules 3 and 4.) 
 
 Sectetur part em conclusio deteriorem, ( = Rules 5 and 6.) 
 
 Et non distribuat, nisi cum preemissa, negetve. 1 ( = Rules 7 and 8.) 
 ( = unless when the premiss does so.) 
 
 * How do you translate the third line ? ' asked 
 Djver. 
 
 ' " Let the conclusion follow the weaker part." 
 The negative is thought "weaker" than the affirma- 
 tive, and the particular than the universal. Thus 
 this line conveys rules (5) and (6). And before pro- 
 ceeding any further I must beg of you to learn these 
 four lines by heart, in order that you may move 
 amongst the syllogisms, armed, so to speak, with a 
 test, whereby you may prove their validity, and 
 dispel the false ones as evil spirits are dispelled by a 
 charm.' 
 
 1 Thus rendered by some young lady friends : 
 'Distribute the middle, and have only three ; 
 From two part, or neg. premisses proof cannot be; 
 Conclusion with part, or neg. premiss must t>, 
 A.nd be dist. or neg. only if premiss be so.'
 
 123 
 
 CHAPTEE XVIII. 
 
 SYLLOGISM. 
 
 ' WE are now ready to encounter all moods in all 
 figures ; and, by the help of our " Distribuas medium," 
 &c., to admit the true, and reject the false. Take 
 A A A in all four figures : 
 
 Fig. i. 
 
 A. All B.. is A 
 A. All C 'is B 
 A. /.AllCia A 
 [Violates no rule. Call it 
 "bArbArA."] 
 
 Fig. ii. 
 All A is : B 
 All C is iB 
 /. All C is A 
 
 [Violates "Distribuas medium" 
 for A props, do not dis- 
 tribute their predicate. Ke- 
 mcmber ASEBINOP. Call 
 this " undistributed middle."] 
 
 Fig. iii. 
 
 A. All B is A 
 
 A. All B is C 
 
 A. /. All C is A 
 [Violates " Et non distribuat nisi 
 cum praemissa." C is distri- 
 buted in conclusion but not in 
 premiss (ASEBINOP). Call 
 this "illicit process of the 
 minor."] 
 
 KB. For ASEBINOP refer back to the 
 propositions," pages 75-78. 
 
 Fig. iv. 
 All A is.B 
 AllBisC 
 .'. All C is A 
 
 [Illicit process of the minor, as 
 in fig. iii. Kemember ASE- 
 BINOP.] 
 
 ! Distribution of terms in
 
 124 PICTURE LOGIC. 
 
 Take E A E in all four figures : 
 
 Pig. i. Fig. ii. 
 
 E. No B.is A No A is 3 
 
 A. All C is B All C is iB 
 
 E. /. No C is A /. No C is A 
 
 [Violates no rule. Call it [Violates no rule. Call it 
 " cElArEnt."] " cEsArE."] 
 
 Fig. iii. Fig. iv. 
 
 E. No B is A No A is B 
 
 A. All iB is C All B"is"c 
 
 E. .'. No C is A /. No C is A 
 
 [Illicit process of the minor. [Illicit process of the minor.] 
 
 From part of C in premiss we 
 argue to whole of C in con- 
 clusion."] 
 
 Thus, amongst these eight possible moods, we have 
 found three valid ones Barbara, Celarent, and Cesare; 
 and by going through all the possible moods (which 
 you should do for practice), we should find the fol- 
 lowing valid ones : 
 
 Barbara, Celarent, Darii, Ferioque, prioris : (i.e. in fig. i.) 
 Cesare, Camestres, Festino, Baroko, secunda: (i.e. in fig. ii.) 
 Tertia, Darapti, Disarms, Datisi, Felapton (i.e. in fig. iii.) 
 
 Bokardo, Ferison, habet: quarto, insuper addit 
 Bramantip, Camenes, Dimaris, Fesapo, Fresison (i.e. in fig. iv.) 
 
 These hexameter lines should be learnt by heart, as 
 there is much contained in them.' 
 
 * We have not yet seen what I have much desired 
 to see,' said I * an illicit process of the major.' 
 
 1 A. All B is A All herrings are fishes 
 
 E. No B is C or No herrings are mackerel 
 
 E. .'. No C is A .*. No mackerel are fishes ; 
 
 and if ever you have to examine arguments, put them 
 first into ciphers, if possible, in fig. i. ; and then, by
 
 SYLLOGISM. 125 
 
 the help of " Distribuas," &c. and " ASEBINOP," you 
 will quickly find their weak point. Thus, in the 
 instance above, it is hard to find the flaw in the 
 herring-shape, but in the cipher-shape ASEBINOP 
 finds A undistributed in the major premiss, and dis- 
 tributed in the conclusion ; i.e. an argument from 
 part to whole.' 
 
 * I have found a mood here,' said Dyver, * which 
 seems right, and yet it isn't among that " Barbara, 
 Celarent " lot ; it is A A I in fig. i.' 
 
 ' You are quite right it is valid ; it is called " a 
 subaltern mood." There are five of them ; they are 
 really contained in the others. Thus A A I is con- 
 tained in A A A ; for if I can get the conclusion, 
 " all C is A," it contains the conclusion, " some 
 C is A." If from the premisses " all cats are anknals, 
 all animals can feel," I draw the conclusion " all cats 
 can feel," much more can I draw the " weakened 
 conclusion," " some cats can feel." 
 
 That night I had a strange dream. I thought 
 Mr. Practical told us he had four rooms which he 
 wished to stock with certain specimens. The names 
 of the rooms were ' Fig. i.,' ' Fig. ii.,' ' Fig. iii.,' and 
 ' Fig. iv ' He gave Dyver a kind of hand fire-screen, 
 with ' Distribuas medium,' &c. printed in large letters 
 upon it. He gave me a stout staff, with Truth 
 engraved on the handle, bidding me to knock on the 
 head anything that Dyver could not repel without
 
 126 PICTURE LOGIC. 
 
 violence. Then, with minute instructions as to the 
 kind of specimens we were to secure (' moods ' was 
 their name), and as to the manner of capturing the 
 right ones and getting rid of the wrong ones (for 
 they were very like one another), and with no small 
 delight on my part at the idea of a liberal use of my 
 staff, and, lastly, accompanied by a keen-scented 
 pointer named ( Asebinop,' we started before daylight, 
 and made for the land of moods. 
 
 Upon arriving there we saw hundreds of animals 
 of a most wonderful description each looked like 
 three gigantic wasps joined together one above 
 another; and there was a perfect hurricane of 
 ' ergos ' and * therefores,' which they kept hissing 
 with human voices. Suddenly ' Asebinop ' pointed ; 
 Dy ver grew pale, and I clutched my staff. Enveloped 
 in a cloud of darkness, a huge Form loomed before 
 us, and we heard a voice as of an irascible major in 
 hot argument saying over and over again, 'All 
 officers are exposed to temptations, no officers are 
 saints, therefore no saints are exposed to tempta- 
 tions.' A low growl from Asebinop, and the mood 
 (for such it was) caught sight of him for the first 
 time, and shuddered visibly. Meanwhile Dyver was 
 holding up his screen persistently, and shouting out 
 ' Dis-tribu|-as medi|-um, nec|,' &c., with painful stress 
 on the scanning, without any effect, however, upon 
 the monster, until he arrivel at the line ' Et non| 
 distribujat nisi) cum pree),' &c., when the form uttered
 
 SYLLOGISM. 127 
 
 a cry of pain, and seemed unable to move, being 
 fascinated by the screen. ' Now then, Douglas,' cried 
 Dyver, and with a blow of my club I finished the 
 illicit old wretch. After that we despatched an 
 ' illicit minor J in the same way, and after that an 
 ' undistributed middle.' This last was a horrid sight. 
 It was rolling about in an agony of pain, and gasping 
 out, f I must be right " all lotions are medicine," 
 and "all potions are medicine;" so lotions and potions 
 are the same ; and in swallowing iny lotion to cure 
 this indigestion, T must have been right, but the pain 
 is intense ! ' We heard afterwards that this mood 
 had argued itself into swallowing poison to cure its 
 indigestion. We owed much to ASEBINOP, though 
 sometimes he took no notice of a mood ; but Dyver's 
 distinct reading of the rules was a sure test always. 
 We secured many valid specimens, and brought them 
 home, and Mr. Practical read * Barbara, Celarent/ &c. 
 over them like a roll-call ; and when each mood had 
 answered to its name, he praised us highly for having 
 found them all; and, bidding them retire to their 
 several figures, wished them all ' good night,' and 
 retired.
 
 128 PICTURE LOGIC. 
 
 CHAPTER XIX. 
 
 SYLLOGISM CANON OP FIEST FIGUEE EEDUCTION. 
 
 ' I CAN'T understand how you call a syllogism a uni- 
 versal form of thought, when nobody ever speaks in 
 syllogisms.' said I. 
 
 * In ordinary writing or speaking,' replied Mr. 
 Practical, * part of the full form is suppressed, and 
 the order changed ; but to examine arguments it is 
 always better to restore them to their full and ori- 
 ginal form. These shortened forms are called 
 " Enthymemes " (from h and 6v/j,6s, because part is 
 suppressed, understood, or kept " in mind," but not 
 expressed). You get three kinds of enthymeme by 
 suppressing either the major premiss, or the minor, 
 or the conclusion. You may say either, " Socrates 
 is a man," .-. " Socrates is mortal," or "All men are 
 mortal, .-. Socrates is mortal," or "All men are 
 mortal, and Socrates is a man." The order of the 
 first two in conversation would be " Socrates is mor- 
 tal, because he is a man," and " Socrates is mortal, 
 because all men are so." As to the last, its order 
 would not be changed, and if you wish to see how 
 quickly men supply the missing conclusion (which is 
 " in the minds," sv Ovpols) go to the most illiterate
 
 SYLLOGISM. 129 
 
 costermonger and say, " All costermongers are 
 scoundrels, and you are a costermonger," and ob- 
 serve the result. We now pass to 
 
 ' (C). The canon of the first figure. A giance at all 
 the moods in the first figure shows us that they all 
 agree in having a universal major premiss and an 
 affirmative minor premiss. Hence what is called the 
 canon or law of the first figure, 
 
 (1) The major premiss must be universal. 
 
 (2) The minor affirmative. 
 
 ' There are also " canons " of the other figures. 1 
 but they are of less importance, and I refer you to 
 other books for them. The use of this first figure 
 canon is that by it we are enabled to be still more 
 sure of the validity of the moods in the remaining 
 figures. By a change that does not interfere willi 
 their validity we can reduce moods of figs, ii., iii., and 
 iv. to fig. i., when we can reassure ourselves as to their 
 validity by applying to them the canon of the first 
 figure. Take CESAEE (i.e. mood E AE in fig. ii.). 
 E. No A is B ~| ^ e wan * to bring this mood in 
 A. All C is IB I fig. ii. to a mood in fig. i., i.e. 
 E. . . No C is A J we wan t to make the middle 
 term come as subject, predicate, instead of predi- 
 cate, predicate (for herein consists the difference of 
 figure). Eemember conversion is our great instru- 
 ment here. If in the major premiss " No A is B " 
 we know by simple conversion that " No B is A," 
 and the reduction is complete, we have 
 
 * Appendix A (iii.). 
 K
 
 130 
 
 PICTUEE LOGIC. 
 
 1 E. No B is A 
 A. AllCisB 
 
 So the mood E A E in the se- 
 cond figure becomes the mood 
 E A E in the first figure, or Ce- 
 sare becomes Celarent. 
 Now apply our canon and we find it obeyed, and we 
 thus have an additional proof of the validity of 
 Cesare. Take FESAPO (i.e. E A in fig. iv.) : 
 1 E. No A is B 1 ^ e wan t the middle term 
 
 (B), subject, predicate, in- 
 stead of predicate, sub- 
 ject. We must change 
 both premisses. By simple conversion we make 
 " No B is A," but we must not convert an A pro- 
 position simply, we must employ conversion per acci- 
 dens, and it becomes " Some C is B." We now have 
 
 A. All B is C 
 
 O. .'. Some C is not A 
 
 E. No B is A 
 
 I. Some C is B 
 0. . . Some C is not A 
 
 Here the mood has changed 
 as well as the figure, and 
 FESAPO (or E A of the 
 fourth) becomes FEEIO 
 Apply the canon and you 
 
 (or EIO of the first). 
 will find it is obeyed. 
 
 1 Sometimes you have to change the premisses 
 when you do so remember you change your major and 
 minor terms. Take AEE of fig. ii. (Ca,mestres). 
 A. All A is .B\^'No C is B No B is C E 
 
 E. No C is 'B ^ \AllAifiiB { s tapiy, T^cT'M Ail ^ B A 
 
 E. .'. No C is A .'NoCisA /. No A is C... E 
 
 /. No C is A (by 
 simple conversion.) 
 
 Apply your canon and you will find it obeyed. 
 
 1 See note at the end of the chapter.
 
 SYLLOGISM. 131 
 
 ' Thus Camestres becomes Celarent. As you must 
 have noticed, the first letter in each of these strange 
 names in figs, ii., iii., iv. means that the mood when 
 reduced becomes a mood which begins with the same 
 letter in fig. i. The vowels of course mean the 
 mood. The letter " s " after the vowel means " sim- 
 ple conversion," and " p " per accidens in the process 
 of reduction. " M " (mutation) means change the 
 premisses, and " k " means " per impossible." All 
 these facts might have been gathered from observa- 
 tion and experiment, but it is a help to memory to 
 learn them thus as well.' 
 
 ' What does " per impossibile " mean ? asked 
 Dyver.' 
 
 ' Eeduction, as above exhibited, is called ostensive 
 or simple reduction, but there are two moods, 
 BAEOKO (second figure) and BOKAEDO (third 
 figure), which are beyond the power of simple reduc- 
 tion. The process by which they are proved to 
 furnish us with true conclusions is as follows (and 
 here you had better not attempt ciphers, but remem- 
 ber these instances and that will be quite enough). 
 If the conclusion they give is not true, it must be 
 false. Assume it to be false, and work on the 
 assumption till you are brought face to face with an 
 obvious absurdity, and then retrace your steps saying, 
 " After all our original conclusion was not false, but 
 true." (i.) Take BAEOKO (A 00, fig. ii.). 
 
 K 2
 
 132 PICTURE LOGIC. 
 
 A. All bantams are fowls, 
 0. Some birds are not fowls, 
 O. .*. Some birds are not 
 bantams. 
 
 If I declared this 
 conclusion to be un- 
 true, an opponent 
 might reply, "Very- 
 
 well, assume it false, and you will find you get a new 
 conclusion, which contradicts one of your premisses, 
 which, of course, you start by assuming to be true." 
 If " Some birds are not bantams " is false, its contra- 
 dictory, " All birds are bantams " is true. Substitute 
 this new truth for your original minor premiss, and 
 
 you get 
 
 All bantams are fowls, 
 
 All birds are bantams, 
 (from which two premisses it follows that) 
 .-. All birds are fowls. 
 
 ' But this new conclusion contradicts our old 
 minor premiss " Some birds are not fowls," which 
 we assumed to be true. Therefore we have come to 
 an absurdity, as we must do in any case if we 
 assume our first conclusion, " Some birds are not 
 bantams," to be false. 
 
 ' Therefore that first conclusion is true. 
 
 < (ii). So with BOKARDO (0 A 0, fig. iii.). Only 
 here you substitute your new truth for the original 
 major premiss : 
 
 0. Some policemen are not fools, 
 A. All policemen are in the Queen's service, 
 0. .'. Some of those who are in the Queen's ser- 
 vice are not fools.
 
 SYLLOGISM. 133 
 
 The new truth here will be, " All in the Q. S. 
 are fools." Substitute this for the original major, 
 and we get 
 
 All in the Q. S. are fools, 
 All policemen are in the Q. S., 
 . . All policemen are fools ; 
 
 and this new conclusion is antagonistic to our old 
 major premiss, " Some policemen are not fools," a 
 contradiction. Therefore our original conclusion 
 was not false but true. For by the law of excluded 
 middle a thing must be either true or false, and if 
 this conclusion isn't false it must be true.' 
 
 Note. Putting words for the ciphers above we should reduce thus : 
 E. No colliers can manage balloons, -| or fig. ii. may be 
 
 A. All good aeronauts can manage balloons, I reduced to fig. i. 
 
 E. /. No good aeronauts are colliers. J thus : 
 
 E. No people who can manage balloons are colliers, 
 A. All good aeronauts can manage balloons, 
 R .'. No good aeronauts are colliers. 
 
 E. No flirts are true women, -> or fig. iv. may be 
 
 A. All true women are dear to men, > reduced to fig. i. 
 
 0. .'. Some of the things dear to men are not flirts. J thus : 
 
 R No true women are flirts, 
 
 1. Some (i.e. one of the) things dear to men are true women, 
 O. .'. Some of the things dear to men are not flirts.
 
 134 PICTUEE LOGIC. 
 
 CHAPTER XX. 
 
 TRAINS OP REASONING SOBITES. 
 
 ' SYLLOGISMS may be " heaped " one above another 
 (<ra>po$, a heap) in a train of reasoning, called Sorites. 1 
 Thus : 
 
 All A is B, 
 
 All B is 0, 
 All C is D, 
 All D is E, 
 .-. All A is E. 
 
 ' This you may resolve into as many syllogisms 
 as there are premisses between the first premiss and 
 the conclusion. Always start with the second pre- 
 miss and the rest is easy 
 
 All B is C, All C is D, All D is E, 
 All A is B, All A is C, All A is D, 
 .-.All A is C. .-.All A is D. .-.All A is E. 
 
 * These syllogisms are called pro-syllogisms or 
 epi- syllogisms, according as you regard them as 
 prior or subsequent to one another. There are two 
 rules : 
 
 (1) Only one premiss (the first) can be particular. 
 
 (2) Only one premiss (the last) can be negative. 
 
 1 Appendix B.
 
 TRAINS OF REASONING. 135 
 
 ' For if (1) be violated, you will find when you 
 expand your sorites into its full form that you have 
 a particular major in the first figure (contrary to 
 canon), and if (2) be violated you will find in the 
 same way that you have a negative minor in the first 
 figure (contrary to canon). 
 
 ' [If asked (as possibly you might be) what is the 
 regressive or Goclenian Sorites, remember it is the 
 reverse of the above. Begin with the last premiss 
 and write the train from last to first, and keep the 
 old conclusion, e.g., 
 
 All D is E, 
 
 All is D, 
 
 All B is C, 
 
 AU A is B, 
 .-. All A is E. 
 
 * The rules are reversed, too ; only one premiss 
 particular, the last ; only one negative, the first (the 
 same propositions being negative and particular as 
 before, you observe)].' 
 
 * Would it be enough,' asked I, * if you were 
 asked about the Goclenian Sorites to give a full 
 description of the ordinary Sorites, and then finish 
 up by saying, " Such is Sorites ; and the Goclenian 
 is not this, but the reverse," leaving the examiners 
 to draw upon their imaginations for your meaning.' 
 
 ' It would be a great deal better than leaving the 
 question out altogether,' he replied with a laugh.
 
 136 PICTUKE LOGIC. 
 
 CHAPTEE XXI. 
 
 HYPOTHETICAL SYLLOGISMS. 
 
 ' As jet our propositions have been only simple or 
 categorical. There are propositions which link 
 together a couple of simple propositions as simple 
 propositions link together a couple of terms. These 
 are called " complex or hypothetical propositions." 
 " Hypothetical " means " with something put under 
 or supposed " (VTTO ridrj^t, = sub-pono = suppose), or 
 " with a condition." Your father says, " I'll give 
 you a horse," that's one thing; but it is quite 
 another thing if he says, " I'll give you a horse IF 
 you pass your examination." The universal dislike 
 of IF's is proverbial, for they make all the difference 
 being the signs of " conditions." Now simple pro- 
 positions may be linked together in two ways : first, 
 where the truth of the consequent depends upon the 
 truth of the antecedent (antecedent and consequent 
 are the names of the two simple propositions when 
 linked together; the first, the antecedent; the 
 second, the consequent) ; and secondly, where the 
 truth of the consequent depends upon the falsity of 
 the antecedent. The first kind are called " conjunc- 
 tive," e.g., " If the weather is rainy my sponge is
 
 HYPOTHETICAL SYLLOGISMS. 137 
 
 damp" (their sign is "if"). The second kind are 
 called disjunctive, e.g., " Either Logic is deep or I am 
 dull" (their sign is "either or"). Hence we may 
 divide propositions in the following manner : 
 
 PROPOSITIONS 
 
 Complex or Simple or categorical 
 
 hypothetical (of which we have 
 
 | already spoken). 
 
 i i 
 
 Conjunctive Disjunctive. 
 
 ' Now syllogisms are composed of these hypothe- 
 tical propositions, and so borrow their names. We 
 have conjunctive and disjunctive hypothetical syllo- 
 gisms, i.e. syllogisms composed of such premisses. 
 Cases where both premisses are hypothetical we shall 
 discuss under " dilemma." For the present we shall 
 consider cases where one premiss is hypothetical and 
 one simple. 
 
 * I. Conjunctive Hypothetical Syllogisms. These ad- 
 mit of two valid conclusions out of the four possible 
 ones you get by amrming and denying the antecedent 
 and consequent. 
 
 (a) If the weather is rainy, my sponge is damp. 
 The weather is rainy, 
 .. my sponge is damp. 
 
 Amrming the antecedent for a minor premiss. 
 
 (6) If the weather is rainy, my sponge is damp. 
 
 The weather is not rainy. 
 
 No conclusion. 
 Denying the antecedent for a minor premiss.'
 
 138 PICTUEE LOGIC. 
 
 * Surely,' said I, ' it follows that " my sponge is 
 not damp." ; 
 
 ' No,' said he, ' for it may have fallen into the 
 bath. Suppose I say " If the ' Brighteyes ' are 
 going, I shall enjoy the ball;" it does not follow 
 that if they do not go, I shall not enjoy the ball, for 
 I may meet the " Lighttoes." ' 
 
 ' (c) If the weather is rainy, my sponge is damp. 
 My sponge is damp. 
 No conclusion. 
 
 Affirming the consequent for a minor premiss. 
 For though it follows that my sponge is damp if 
 the weather is wet, it does not follow that the 
 weather is wet because my sponge is damp. If the 
 wife weeps because the husband is condemned to 
 death, does it follow that the husband is condemned 
 to death because the wife weeps ? 
 
 ' (d] If the weather is rainy, my sponge is damp. 
 My sponge is not damp. 
 .*. the weather is not rainy. 
 
 Denying the consequent for the minor premiss. 
 Thus the conjunctive hypothetical syllogism admits 
 of two conclusions where you affirm the ante- 
 cedent called " constructive," and where you deny 
 the consequent called " destructive." 
 
 II. Disjunctive Hypothetical Syllogisms admit of 
 four conclusions, for you may affirm or deny ante- 
 cedent and consequent.
 
 HYPOTHETICAL SYLLOGISMS. 139 
 
 e.g., (1) Either Logic is deep, or I am dull. 
 Logic is deep. 
 ..I am not dull. 
 
 (2) Either Logic is deep, or I am dull. 
 
 Logic is not deep. 
 .. I am dull. 
 
 (3) Either Logic is deep, or I am dull. 
 
 I am dull. 
 
 .-. Logic is not deep. 
 
 (4) Either Logic is deep, or I am dull. 
 
 I am not dull. 
 .*. Logic is deep. 
 
 * The dilemma is a combination of conjunctive and 
 disjunctive premisses. As it is a difficult matter to 
 understand, I should advise you to remember the 
 three forms of it by their examples, and after your 
 examination go more deeply into the theory of it as 
 expounded in the books on Logic. There are : 
 
 (i.) The simple 1 constructive / Instance: "Science." 
 (ii.) The complex/ dilemma V Instance: "Politician." 
 iii.) The destructive dilemma. Instance: " Jesting at Scripture." 
 
 ' (i) The Simple Constructive Dilemma is of this 
 form: 
 
 If science lightens labour, it should be culti- 
 vated ; and if science invigorates the faculties, 
 it should be cultivated ; 
 
 But science does one, or the other ; 
 
 Therefore science should be cultivated.
 
 140 PICTURE LOGIC. 
 
 ' (ii) The Complex Constructive Dilemma is of this 
 form : 
 
 If a politician (who finds he is wrong) changes 
 his views, he is inconsistent; and if he does 
 not change them, he is not conscientious ; 
 
 He must either change them or not change them ; 
 
 Therefore he must be either inconsistent or not 
 conscientious. 
 
 ' (iii) The Destructive Dilemma is of this form : 
 
 If a man were wise, he would not jest at Scrip- 
 ture in fun ; and if he were good, he would not 
 do so in earnest ; 
 
 He must do it either in fun, or in earnest ; 
 
 Therefore he must be either not wise or not good. 
 
 These three (the substance of which is borrowed 
 from Mr. Jevons's book) will be quite enough to show 
 that you understand what dilemma means. A di- 
 lemma may be rebutted thus : 1st Dilemma. " Do 
 not enter into public affairs ; for if you say what is 
 just, men will hate you; and if you say what is 
 unjust, the gods will hate you. You must do one or 
 the other ; therefore you must be hated by gods or 
 by men." 2nd Dilemma. "Do enter into public 
 affairs ; for if you say what is unjust, men will love 
 you ; and if you say what is just, the gods will love 
 you ; therefore you must be loved by gods or men." 
 
 ' In the " Oxford Spectator " I saw a dilemma,' 
 said I, * which seemed conclusive. How would you
 
 HYPOTHETICAL SYLLOGISMS. 141 
 
 rebut this : " Examinations are useless ; for if you 
 know the questions already, they teach you nothing ; 
 and if you do not know the questions, they teach you 
 nothing; you must either know them or not know 
 them ; therefore examinations are useless ? " 
 
 To which Dyver replied, to my astonishment: 
 * Examinations are useful ; for if we do know the 
 questions, they teach us how to express our know- 
 ledge ; and if we do not know the questions, they 
 teach us what our weak points are (and it is not 
 their fault if we do not remedy them) ; we must 
 either know the questions or not know them ; there- 
 fore examinations must he useful.' 
 
 Mr. Practical expressed his approval, and I 
 began to think that if Mr. Practical taught Dyver 
 much more it would be a case of the young horse 
 running away with the ' coach ' altogether.
 
 142 PICTURE LOGIC. 
 
 CHA.PTEE XXII. 
 
 PEOBABLE REASONING. 
 
 * HITHEETO we have spoken of syllogisms with strictly 
 logical forms of propositions for their premisses, 
 when the conclusions are certain. There are two 
 kinds of reasoning which furnish us with conclusions 
 not strictly certain, but of sufficient weight to in- 
 fluence our actions in life self-infirmative, and self- 
 confirmative inference. By help of such probable 
 reasoning we are enabled to make syllogisms out of 
 propositions with the sign "most'' or "many," instead 
 of " all " or " some ; " and we can take into account 
 the force of such words as " probably," without (as in 
 strict Logic) thrusting them into the subject or 
 predicate. 
 
 ( (i.) Self-infirmative inference is where each fresh 
 fact weakens the conclusion, so that the more pre- 
 misses you have the less likely is it that the con- 
 clusion will be true. " Never go out of doors in a 
 severe frost," says the anxious mother, " because the 
 Humane Society's men are obliged to drink." 
 
 * But what has that to do with my " going out ? " 
 you ask.
 
 PROBABLE REASONING. 143 
 
 * " You know," she replies, " some of those who go 
 out in such times are tempted to skate, and some of 
 those who skate break the ice, and some of those 
 who break the ice are rescued by the Humane 
 Society's men, and some of these men drink to keep 
 themselves warm ; therefore, some of the men who 
 venture out in a severe frost may have to be rescued 
 by possibly intoxicated men." 
 
 1 You laugh at this argument, because every fresh 
 premiss weakens the conclusion. So with the words 
 " possibly," " probably," &c. 
 
 * By this process you can argue that men with 
 money are likely to commit suicide ; thus : 
 
 Men with money probably invest it ; 
 Men who invest probably speculate ; 
 Men who speculate possibly lose all ; 
 Men who lose all are probably pinched with 
 
 poverty ; 
 Men who are pinched with poverty probably 
 
 despair ; 
 
 Men who despair possibly commit suicide. 
 .-. To this extent men with money are likely to 
 
 commit suicide. 
 
 The amount of the probability may be estimated to 
 a fraction; but calculations of this sort seem to 
 belong rather to mathematics than Logic.' 
 . ' What a comfort ! ' I reflected. 
 
 * (ii.) Self-confirmative inference is where each 
 fresh fact strengthens the conclusion you wish to
 
 144 PICTURE LOGIC. 
 
 establish. It is called " circumstantial evidence/' 
 or a " chain " or " coil " of evidence. Many verdicts 
 are awarded in the Law Courts solely upon the 
 strength of this evidence, which amounts in some 
 cases almost to certainty. Each fact may be regarded 
 as the minor premiss of a syllogism, with a probable 
 major premiss and a probable conclusion. Given the 
 assertion " That our cook gave the joint to a follower, 
 when she said the dog ate it." It is required to 
 prove this assertion by circumstantial evidence for 
 nobody actually saw her give it. The evidence is as 
 follows : " The dog was a remarkably well-behaved 
 dog." " On the day of the mysterious disappearance 
 the kitchen blinds were kept down." " Certain other 
 articles (such as beer, tea, spirits, &c.), which dogs 
 would not eat or drink, vanished during the same 
 cookship," &c. Each of these facts becomes the 
 premiss of a syllogism ; thus : 
 
 I. 
 
 Well-behaved dogs probably are innocent of a 
 
 theft. 
 This was a well-behaved dog. 
 
 .-. The dog is probably innocent of the theft. 
 
 II. 
 
 The drawing of the blinds probably betokened 
 
 the presence of a follower. 
 The blinds were drawn. 
 
 ..A follower was probably present.
 
 PEOBABLE REASONING. 145 
 
 Tf a follower was present, probably the dog is 
 
 innocent of the theft. 
 
 A follower was probably present. 
 Therefore the dog is probably innocent of the 
 
 theft. 
 
 III. 
 
 If tea, spirits, &c. disappeared also, the dog 
 
 is probably innocent of the theft. 
 Tea, spirits, &c. did disappear. 
 Therefore the dog is probably innocent of the 
 
 theft. 
 
 Every syllogism has the same conclusion, you 
 observe ; and every fact thus becomes a link in the 
 chain of evidence. You may find instances for your- 
 selves in the newspapers. This evidence is also 
 called " Self-corroborative," from "robur," strength. 
 * And here 1 may mention an exception to the 
 rule " Ex duobus particularibus nihil sequitur," or 
 "two particular premisses prove nothing" (Eule 4 
 of the Syllogistic Rules) ; for there is one case in the 
 third figure where two particular premisses do prove 
 Bomethinar; e.g., 
 
 " Most pins are good ; 
 Most pins are cheap. 
 ..*. Some cheap things are good."'
 
 146 PICTURE LOGIC. 
 
 OHAPTEE XXIII. 
 
 THE FALLACIES. 
 
 * A FALLACY (fallo, to deceive) is an argument which 
 seems to be true, but is really false. The fallacies 
 have been classed under two heads : material (extra 
 dictione) and formal (in dictione), i.e. fallacies arising 
 from mistakes in the matter and the form. For the 
 mistakes in matter Logic is not responsible (see 
 "'Matter and Form of Thought"). But we shall 
 adopt Mr. Fowler's arrangement. (N.B. Learn off 
 this scheme, and read through the explanation that 
 follows). 
 
 I, Assumption of a false premiss. 
 Achilles and the tortoise. 
 
 II. Neglect of the laws of deductive inference. 
 
 Illicit major. 1 
 ,, minor. 
 
 Undistributed middle. 
 Petitio principii (begging the question). 
 
 HL Ignwatio elencki, or irrelevancy. 
 
 Argumentum ad hominem...(" early rising "). 
 t , populum.,.(" weeping wife"). 
 
 baculum...(" religious persecution") 
 
 1 For several instances ot these see Appendix A (ii\
 
 THE FALLACIES. 
 
 IV. Ambiguity of language. 
 
 Ambiguous (analogous, equivocal, &c.) words... (" box, 
 
 muzzle, &c."). 
 
 Composition and division... (" 3 and 2 odd and even "). 
 Fallaciae accidentis [2]...(" mad dog's bite "). 
 Paronymous terms... (" drunk once, drunk ever"). 
 Fallacia pluriiim interrogationum...("Have you left off 
 
 poaching yet ? "). 
 Amphibolia, or amphibology... (" The duke yet lives that 
 
 Henry shall depose"). 
 Fallacy of accent... (" and they saddled him "). 
 
 ' (I.) Is a mathematical difficulty, and strictly 
 speaking is out of the sphere of Logic. A tortoise 
 starts so many yards ahead of the fleet Achilles, and, 
 according to mathematical calculations, Achilles 
 never overtakes the tortoise. For when the tortoise 
 has advanced a few yards, Achilles has gained so 
 much that there is only half the distance between 
 them, and presently only a quarter, and then one- 
 eighth, and then one-sixteenth, and so on, the frac- 
 tion becoming smaller and smaller, but never quite 
 vanishing, so Achilles could never (according to 
 this) catch the tortoise quite. The logicians in 
 despair cried, " Solvitur ambulando," or " Walk it 
 and see ; " a better answer would have been, " Logic 
 has nothing to do with the complications and diffi- 
 culties and errors of the matter." (See " Form and 
 Matter of Thought"). 1 Under this head come all 
 fallacies of the matter. 
 
 * (II.) These have already been explained except 
 the petitio principii. "Begging the question" is 
 proving the conclusion you wish to establish by 
 
 1 P. 26 and p. 29. 
 L 2
 
 148 PICTUEE LOGIC. 
 
 assuming that conclusion to be true before you have 
 proved it to be true. There is the simple form of it. 
 " A man is a man," says a lady. " Why ? prove it," 
 say you. " Because he is a man," she retorts. It 
 may be by a synonym (a like name). " The air is 
 dry." " Why ? " " Because the atmosphere is dry." 
 Under this head comes the " argument in a circle," 
 for you move in circles when you prove your state- 
 ments by making them your premisses as well as 
 your conclusion, e.g., " Fire is hot, because it burns," 
 says your lecturer, and presently, when asked, " But 
 why does fire burn ? " he blandly replies, " Because 
 it's hot, of course." In long speeches such argu- 
 ments pass unnoticed, especially in a language like 
 the English, compounded of Saxon, Norman, and 
 Latin where there are so many different words all 
 meaning the same forming excellent covert for 
 fallacies of this kind to hide themselves in. 
 
 ' III. Ignoratio elenchi, or irrelevancy, means 
 ignorance of the exact point to be refuted. Your 
 arguments are irrelevant when they miss the point 
 to be assailed, and batter down some unoffending, 
 innocent, unguarded point. Argumentum ad ho- 
 minem misses the theory and assaults the man. Its 
 object is to find a flaw, not in the theory advocated, 
 but in the person advocating. When Mr. Gladstone 
 advocated the theory of Disestablishment of the Irish 
 Church opponents condemned the idea simply be- 
 cause its holder "once thought differently," in other
 
 THE FALLACIES. 149 
 
 words, galloping by the fortified heights of the 
 theory, they levelled their batteries at the weak 
 flesh from whence it emanated. They made the 
 inconsistency of the person a proof of the inefficiency 
 of the measure. And so when a late riser speaks in 
 glowing terms of early rising and its benefits, people 
 laugh. The point to be assailed may be weak or 
 strong, but the Logician must not swerve from that 
 point.' 
 
 ' But when a holder is attacked instead of his 
 theory,' said Dyver, ' do we not often find that a 
 man says one thing and does another, and ought \, e 
 not rather to believe what he does than what he 
 says ? ' 
 
 * True ; but we cannot "practice what we preach." 
 As a Logician you have only to ask, " Is the theory 
 good or bad ? " and all questions of persons should 
 be set aside. The argument " ad populum " appeals 
 to the feelings rather than the judgment of an 
 audience. When a prisoner at the bar brings his 
 weeping wife and children to excite pity he is missing 
 the point, so to speak ; for the point he ought to aim 
 at is to prove his own innocence, the point he does 
 aim at is to win their pity. The argument " ad 
 baculum," declining to face the argument, lays hold 
 upon the voice that pleads it, and by force compels 
 it to hold its peace. It is the refutation of those who 
 are strong of hand, but weak of head, for it crushes 
 theories by brute force. Religious persecution is an 
 instance.'
 
 150 PICTURE LOGIC. 
 
 ' That reminds me,' said I, ' of the fox and the 
 serpent and the man. There was once a man who 
 found a wounded serpent and put it into his bosom. 
 And as soon as the serpent revived it bit the man's 
 bosom. And the man called it an " ungrateful 
 monster ; " upon which a long argument arose 
 between the two as to whether the man or the ser- 
 pent was the more ungrateful animal on the whole. 
 Appeals were made to various animals (old cows, 
 hunters, &c.) without any abatement of the hot dis- 
 cussion, until the fox was consulted. " If you wish 
 this fierce argument to come to an end," said the 
 fox to the serpent, " be so good as to enter into 
 this bag, and you will be so convinced that you will 
 never utter another syllable." Upon the serpent's 
 ready obedience, the fox tied up the neck of the bag, 
 and handing it to the man said, " Stamp on him," 
 and so the argument was ended.' Mr. Practical was 
 highly pleased at this, and continued. 
 
 ' IV. All fallacies arising from ambiguous use of 
 language. Equivocal and analogous words are in- 
 stances. Remember this any word may be used in 
 one sense or more than one sense. If it is used in one 
 sense, it is said to be univocally used, as " butter " 
 (there are very few of these). If in more than one 
 sense, there may be a connection between the several 
 senses, or there may not. If there is, it is said to be 
 analogously used, as " muzzle," in its three senses of 
 " part of a gun," " part of a dog," " a gag " (all have
 
 THE FALLACIES. 151 
 
 something to do with the mouth). If there is not, it 
 is said to be equivocally used, as box in its three 
 senses of a " chest," a " tree," a " blow " (no con- 
 nection between these). Hence ambiguous middles 
 in syllogisms, as " The people here are the church ; 
 the stones built up here are the church ; . . the people 
 here are the stones built up here." 
 
 * The fallacy of composition is arguing from what 
 is true of things taken separately to what is true of 
 things taken together; e.g., from " two and three are 
 even and odd" to argue "five is odd and even." 
 And division is the converse, from " five is odd " to 
 argue "two and three are both odd." Or from 
 " Jones and his wife were happy when single " to 
 argue " Jones and his wife are happy together ; or 
 from " Jones and his wife are miserable together " to 
 argue that " Jones and his wife were miserable when 
 single." 
 
 ' The fallacies accidentis are two, (I) the argu- 
 ment " a dicto simpliciter ad dictum secundum quid ; " 
 (2) the argument " a dicto secundum quid ad dictum 
 simpliciter." Which formidable expressions simply 
 mean arguing from what is true as a general rule 
 to what is true under particular circumstance, and 
 from what is true under particular circumstances 
 to what is true as a general rule. 
 
 * Now as a general rule " it is a bad thing to cut 
 off a man's arm," but under certain circumstances 
 (bite of a mad dog, for instance) it is not bad. Ac-
 
 152 PICTUEE LOGIC. 
 
 cording to the first of the above fallacies, one would 
 persist in saying, " Do not cut off his arm never 
 mind what has happened do not cut it off, for it's a 
 bad thing for a man to have his arm cut off." 
 According to the second fallacy one would say, " Let 
 us cut off all the arms of all men, for once upon a 
 time I knew a man (who had been bitten by a mad 
 dog) who gained great advantage from losing his 
 arm." 
 
 ' The fallacy of paronymous terms is exemplified 
 when you say, " Job Turnips is a drunkard," because 
 he has been once or twice drunk ; or " a thief,'* 
 because he has once or twice stolen. 
 
 ' The fallacia plurium interrogationum is the fal- 
 lacy of risking two questions in one. For instance, 
 take the question of a barrister examining a pri- 
 soner : " Have you left off poaching yet ? " when the 
 unfortunate man criminates himself by saying, " Lor' 
 bles yer, yes, this six months or more." For the 
 barrister asked him two questions in one : " Did you 
 ever poach ? " and " Have you left off yet ? " mean- 
 'ng only to discover whether the man ever poached 
 at all. 
 
 ' The fallacy of amphibolia, or amphibology is a 
 purely grammatical one, and is the name given to 
 such doubtful passages as " The duke yet lives that 
 Benry shall depose." Where you do not know 
 whether it is the duke who shall depose Henry, or 
 Eenry the duke.
 
 THE FALLACIES. 153 
 
 'The fallacy of accent is a mere matter of em- 
 phasis. For instance, if you lay stress upon the 
 pronoun " him " in the following words, " Saddle me 
 the ass. And they saddled him," you convey a 
 wrong impression. 
 
 Lastly, there are two fallacies not mentioned 
 in the scheme above ; that of " non-causa pro- 
 causa " (as to say, " A comet shone, therefore there 
 will be war "), where you take for a cause that 
 which is not really so ; 1 and the fallacy of the con- 
 sequent (fallacia consequentis or " non-sequitur ") , 
 e.g., " he is an animal ; ergo he is a man." 
 
 1 This fallacy is the one referred to by the words, ' Post hoc, sed 
 non propter hoc,' as the man said when he stumbled after partakiug 
 freely of a well-known light wine.
 
 APPENDIX A. 
 
 (i.) WITH regard to the four figures in the Syllogism 
 remember that 
 
 Fig. I. is most useful for the discovery or proof of pro- 
 perties of a thing. 
 
 Fig. II. is most useful for the discovery or proof of dis- 
 tinctions between things. 
 
 Fig. III. is most useful for the discovery or proof of 
 instances or exceptions. 
 
 Fig. IV. is most useful for the discovery or exclusion of 
 the different species of a genus. (Lambert. ) 
 
 And this is because : 
 
 (1) Fig. I. can prove (i.e. have for its conclusion) A, E, 
 I, or O. 
 
 (2) Fig. II. can prove (i.e. have for its conclusion) E and 
 O only (i.e. negatives only , for as in this figure the middle 
 term is predicate (i.e. predicate in both premisses) unless 
 one of the premisses were negative, the middle term would 
 be undistributed. 
 
 .*. One of the premisses must be negative. 
 .'. The conclusion must be negative. 
 
 (3) Fig. III. can prove (i.e. have for its conclusion) I or 
 only (i.e. particulars only). 1 
 
 1 By working out the six moods in Fig. III. you will find an illicit 
 minor in each case if you make the conclusion universal. For pr .ctice work 
 them out. Ste Appendix A (iv.).
 
 156 
 
 APPENDIX. 
 
 (4) Fig. IV. proves E, I, 0, and is of little use because its 
 work can be done more easily by Fig. I. 
 
 N.B. From this it is plain that Fig. III. is the best for 
 the purpose of overthrowing an adversary's conclusion, as it 
 furnishes us with material for the establishment of a con- 
 tradictory opposition (see p. 104). 
 
 (ii.) There are three rules (4), (6), and (8), which require 
 further explanations : 
 
 Eule (4). ' Two particular premisses prove nothing.' I 
 and O are the only forms of particular propositions. Two 
 particular premisses must therefore be either I, I ; or O, O ; 
 or I, O ; or O, I. 
 
 Take these four combinations in all figures : 
 
 Fig. i. 
 I. Some B is A 
 
 I. Some C is'fi 
 No conclusion. 
 
 Fig. ii. 
 Some A is : B 
 
 Some C is B 
 No conclusion. 
 
 Fig. iii. 
 Some .B is A 
 
 Some : B is C 
 
 Fig. iv. 
 Some A is B 
 
 Some B is C 
 
 No conclusion. | No conclusion. 
 
 For by l ASEBINOP it is plain that the Middle Term 
 (B) is not once distributed in any of these .'. There can be 
 no conclusion. 
 
 O. Some B, is not A 
 
 0. Some C is not'B 
 No conclusion. 
 
 Some A is not . B 
 
 Some C is not : B 
 No conclusion. 
 
 Some ;B is not A 
 
 Some : B is not C 
 No conclusion. 
 
 Some A is not B 
 
 Some B'is cot C 
 No conclusion. 
 
 In all these there are two negative premisses, which give 
 no conclusion (p. 130). 
 
 I. Some B is A 
 
 O. Some C is not"*B 
 No conclusion. 
 
 Some A is ;B 
 
 Some C is not ;B 
 No conclusion. 
 
 Some ;B is A 
 
 Some ; B is not C 
 No conclusion. 
 
 Some A is B 
 
 Some B'' is not C 
 No conclusion. 
 
 In all these (by Rule (5) p. 130) the conclusion, if there 
 be any, must be negative, and by Rule (6) particular. 
 
 In all four figures it will be ' .*. Some C is not A. 1 
 
 1 For Asebinop, see pp. 78 and 126. It only means that an A prop, dis- 
 tributes its subject, E both subji-ct and predicate, I neither, predicate.
 
 APPENDIX. 167 
 
 By ASEBINOP we know all four to be cuses of Illicit Major 
 (p. 1245), i.e. the term A is used in its full sense in the 
 conclusion, but only in a partial sense in the premisses and 
 this is arguing from part to whole. 
 
 0. Some B is not A 
 
 1. Some C is B 
 No conclusion. 
 
 Some A is not j B 
 
 Some C is ; B 
 No conclusion. 
 
 Some : B is not A 
 
 Some : B is C 
 No conclusion. 
 
 Some A is not B 
 
 Some B' is C 
 No conclusion. 
 
 For here we find that in figs. i. and iii. the Middle Term 
 (B) is undistributed ; and in figs. ii. and iv. there will be an 
 ' Illicit Major ' as above. 
 
 N.B. ' No conclusion ' means ' No valid conclusion.' 
 
 Rule (6). ' If either Premiss be particular, the conclusion 
 must be particular.' 
 
 For, so to speak, universal conclusions are expensive 
 luxuries to their premisses ; premisses of small quantity can- 
 not afford them. To keep up a universal conclusion both 
 premisses must be at their full or universal stage in point of 
 quantity, and any diminution at once tells sensibly upon their 
 conclusion. Two universal premisses can sustain a universal 
 conclusion ; but impoverish one of your premisses, without 
 making a corresponding reduction in your conclusion, and 
 you will find that Illicit Major or Minor has eaten away, 
 like a canker, the truth of your Reasonings. This is best seen 
 by going through all possible combinations of Particular and 
 Universal Premisses (the combination of two particulars is by 
 Rule (4) invalid): 
 
 These are ,,,,,,. Of 
 
 these (Q) and () are invalid by Rule (3), p. 120. We have 
 
 now to show that none of the remaining six moods, or parts 
 of moods, can have a universal conclusion (i.e. A or E) in any 
 of the figures.
 
 158 
 
 APPENDIX. 
 
 Fig.i. 
 A. All Bis A 
 
 I. Some C is B 
 
 All A is ;B 
 Some C is ; B 
 
 Pig. ill. 
 All ;B is A 
 
 Some 'B is C 
 
 Fig. iv. 
 All A is /B 
 
 Some B'IS C 
 
 Here in figs. ii. and iv. the middle is undistributed 
 (ASEBINOP), and there is no conclusion. In figs. i. and iii. 
 the conclusion cannot be E by .Rule (8) (which will be ex- 
 plained below) ; and it cannot be A, or in both figures you 
 would have Illicit Minor. 
 
 Fig. i. 
 A. All Bis A 
 
 O. Some C is not B 
 
 Fig. ii. 
 All A is jB 
 
 Some C is not B 
 
 Fig. iii. 
 All :B is A 
 
 Some : B is not C 
 
 Fig. iv. 
 All A is B 
 
 Some 15 i* not C 
 
 In all these the conclusion, if universal at all, must be 
 universal neg. (E) by Rule (5). Now supposing E to be the 
 conclusion in each, we have in fig. i. Illicit Minor and Major 
 together (ASEBINOP); in fig. ii. Illicit Minor; in fig. iii. 
 Illicit Major ; and in fig. iv., the middle being undistributed, 
 there can be no conclusion at all. 
 
 I. Some B is A 
 A. All C is B 
 
 Some A is B 
 All C is JB 
 
 Some ;B is A 
 All 'B is C 
 
 Some A is B 
 All B is C 
 
 In all of these the conclusion, if universal at all, must be 
 A by Rule (8). In figs. i. and ii. there are no conclusions at 
 all, the middle being undistributed. In figs. iii. and iv. if 
 the conclusion be A, you get illicit minors in both. 
 
 O. Some B is not A 
 A. All C is B 
 
 Some A is not ;B 
 
 All C is 
 
 B 
 
 Some :B is not A 
 All te is C 
 
 Some A is not B 
 All B'is C 
 
 Here in fig. i. there is no conclusion (undist. mid.). In 
 the rest, the conclusion, if universal at all, must be E (Rule 5), 
 which would involve, in fig. ii. Illicit Major ; in fig. iii. Illicit 
 Minor ; in fig. iv. both together (ASEBINOP). 
 
 E. No B is A 
 I. Some C is'B 
 
 No A is .B 
 Some C is : B 
 
 No ; B is A 
 Some B is C 
 
 No A is B 
 Some B is C 
 
 In all these the conclusion, if universal at all, must be E 
 (Rule 5). This would involve an Illicit Minor in all four 
 figures (ASEBINOP).
 
 APPENDIX. 159 
 
 I. Some B is A 
 E. No C is B 
 
 Some A is : B 
 No C is : B 
 
 Some B is A 
 No ^B is C 
 
 Some A isJB 
 No B is C 
 
 In all these, the conclusion, if universal at all, must be E 
 (Rule 5). This would involve Illicit Major in all four figures 
 (ASEBINOP). 
 
 Eule (8). ' Let not the conclusion be negative unless one 
 of the premisses is negative.' 
 
 The necessity of this is evident from a consideration of 
 the principle upon which all Syllogism depends. For in it 
 two things are compared with one another through the medium 
 of a third thing. The comparison of the 1st thing with the 
 3rd thing makes one premiss ; the comparison of the 2nd 
 thing with the 3rd thing makes another premiss ; and the 
 comparison of the 1st and 2nd thing which results is the 
 conclusion. Now if this conclusion expresses dissimilitude, 
 i.e. is negative, it is clear that in one or other of the premisses 
 there must have been dissimilitude expressed before, else 
 whence could this dissimilitude have sprung? for the conclu- 
 sion is only a summary of what was contained in the premisses ; 
 in other words, if the conclusion is negative (i.e. expresses 
 dissimilitude between its subject and prsedicate) one of the 
 premisses must have been negative before it. 
 
 N.B. The following are instances in words as opposed to 
 ciphers. 
 
 Violations of (Rule 4) : 
 
 ^ , Kg.i. 
 
 ' Fishes fly ; fishes do not fly. I. Some fishes fly. 
 This proves the futility of all - = J I. Some things that don't fly aie 
 knowledge.' fishes. 
 
 No conclusion. 
 
 ' Lancashire is lovely, old \ ( Fig. U. 
 
 women are lovely too. So Lan- [ j I- Some of Lancashire is lovely, 
 cashire must be an old woman or | " j I. Some old women are lovely. 
 Logic is untrue ! ' No conclusion.
 
 160 
 
 APPENDIX. 
 
 ' Inspectors are stern, and In- 
 spectors are mild, at the same time 
 and place. So "stern "and "mild" 
 must be the same thing.' 
 
 ' Some ladies must be addicted I 
 to drink, for they are thirsty, and L 
 thirsty people are often addicted 
 to drink.' 
 
 Some eagles have no wings ; ' 
 for all birds are not eagles, and 
 there are other winged things 
 besides birds.' 
 
 ' Silence and speech are the I 
 same things ; for sometimes one is r 
 not seemly, sometimes the other.' j 
 
 ' Carpenters can't be hand- 
 some, for tall men are often hand- 
 some, and it isn't every carpenter 
 that is tall.' 
 
 ' Some cabmen are honest, for I 
 all men can't be dishonest, and > . 
 cabmen are men.' 
 
 Violations of (Eule 6) : 
 
 ' We must eat cook's children, 
 for we eat cook's productions ; I 
 dumplings are her productions, j 
 and we eat them.' 
 
 ' How wretched must all men 
 under petticoat government be! 
 For all henpecked men are under 
 petticoat government, and how 
 miserable are some henpecked 
 men ! ' 
 
 Fig. ill. 
 
 I. Some inspectors are stern. 
 I. Some inspectors are mild. 
 No conclusion. 
 
 Fig. iv. 
 
 I. Some ladies are thirsty. 
 I. Some thirsty people are addicted 
 to drink. 
 
 No conclusion. 
 
 I Fig.i. 
 
 J O. Some birds are not eagles. 
 
 1 0. Some winged things are not birds. 
 
 I No conclusion. 
 
 / Fig. ii. 
 
 0. Some silence is not seemly. 
 ] 0. Some speech is not seemly. 
 No conclusion. 
 
 IFig. i. 
 I. Some tall men are handsome. 
 0. Some carpenters are not tall men. 
 No conclusion. 
 
 I Fig. iii. 
 
 j 0. Some men are not dishonest. 
 j I. Some men are cabmen. 
 \ No conclusion. 
 
 i Fig.i. 
 
 A. All dumplings are to be eaten. 
 I. Some of cook's productions are 
 dumplings. 
 .'. All cook's productions must be 
 eaten. 
 
 Fig. iii. 
 
 I. Some henpecked men are miser- 
 able. 
 A. All henpecked men are under 
 
 petticoat government. 
 .'. All under petticoat government 
 are miserable. 
 
 N.B. In both of these a particular conclusion would 
 have passed as valid.
 
 APPENDIX. 
 
 161 
 
 fThe Major Premiss must be 
 
 J universal. 
 
 (in.) Rules of fag. 11. are s ~ ,. ., -r> . , 
 
 ] One of the Premisses must be 
 
 L negative. 
 
 f The Minor Premiss must be 
 
 fi". iii. < affirmative. 
 
 ] The conclusion must be 
 L particular. 
 Fig. iv. can be more clearly arranged as fig. i. 
 
 (iv.) The moods of fig. iii. are Darapti, Disarms, Datisi, 
 Felapton, Bokardo, Ferison (see p. 124). 
 
 A. All B is A. 
 A. All B is C. 
 I .. Some C is A. 
 
 E. No B is A. 
 
 A. All B is C. 
 O. Some C is not A. 
 
 I. Some B is A. 
 A. All B is C. 
 I. .'. Some C is A. 
 
 O. Some B is not C. 
 A. All B is C. 
 
 O Some C is not A. 
 
 A. All B is A. 
 I. Some B is C. 
 I. Some C is A. 
 
 E. No B is A. 
 I. Some B is C. 
 0. Some C is not A. 
 
 In all of these a universal conclusion involves an ' illicit 
 minor.' So the 3rd fig. only gives particular conclusions. 
 Putting two of the above into words, we get : 
 
 P All fishes live in the water. 
 53 All fishes can swim. 
 j.*. Some of the things that can 
 H swim live in the water. 
 
 It would not be right to infer 
 that ' all things that can swim live 
 in tlie water,' for even swimming 
 masters do not live there always. 
 
 2 Some persons can preach. x , It would be ^ ^ conclu(ie 
 
 All persons think they can II tfaat a]J thc s that think lfa 
 
 g. '.Some of thepersons that thmk " can can ^ 
 
 55 they can preacli, can preach .) \
 
 162 
 
 APPENDIX B. 
 
 AN instance of Sorites would be : 
 All fleas are animals. 
 
 All animals sustain life by assimilating food. 
 All that lives by assimilating food is liable to hunger 
 All that is liable to hunger may be half famished. 
 /. All fleas way be half famished. 
 
 Here A = Fleas. 
 
 B = Animals. 
 
 C = ' Sustaining life by assimilating food.' 
 
 D = ' Liable to hunger.' 
 
 E = ' May be half famished.' 
 And the Sorites may be resolved as in the .cipher-form
 
 163 
 
 APPENDIX C. 
 
 TURNING back to p. 103 we find inductive inference put aside. 
 Induction or inductive inference starts from particulars and 
 works towards universals. The process is fully explained 
 under the heading 'What is Science?' (pp. 4 to 13; read 
 carefully) for all science is inductive (p. 184, ' Method '). As 
 deduction has its forms and rules (discovered by Logic), so 
 induction has its forms and rules (discovered by Logic) ; and 
 we have inductive as well as deductive logic. The mind of 
 man is as carefully controlled in its journey (/ut'0ocioc) from 
 the particular facts up to the universal laws, as it is in its 
 journey from the universal law down to the particular facts. 
 (See illustration, p. 45.) Let us consider : 
 
 1. Induction what it is. 
 
 2. The principles upon which induction ultimately depends, 
 
 as deduction depends upon its principle, p. 113 (-4.). 1 
 
 3. The processes required for induction (observation and 
 
 experiment). 
 
 4. The ' methods ' in Induction corresponding to the syllo- 
 
 gistic laws in Deduction. 
 
 1 This principle of syllogism is founded on the three great laws 
 upon which all deductive reasoning depends (Laws of Thought, p. 
 160). The principles of inductive inference are not founded upon these 
 three self-evident axioms. Consequently we do not find the same cer- 
 tainty about our conclusions in induction as we have in deduction. For 
 the principles of the syllogism are laws, the violation of which is incon- 
 ceivable, whereas the principles of induction are laws, whereof the 
 violation is not inconceivable. For the principles of induction are 
 generalisations from experience, and not like those of dtduction part of 
 our nature, which we found but did not make. 
 
 11 2
 
 1G4 APPENDIX. 
 
 ( 1) Induction has been called an ' argument from the 
 known to the unknown,' or ' generalisation from experience,' 
 or 'inference from particular facts to universals.' (Pp. 4-13 
 give the process.) For by induction the old man ascends 
 from the particular objects he lets fall to the universal laws 
 of gravity. Most of the laws which deduction brings down 
 to particular facts have been by induction raised from parti- 
 cular facts beforehand. For induction precedes deduction 
 except in cases where the laws were implanted in us by nature, 
 and even then induction in a sense precedes ; for by it we 
 find those implanted laws (though we do not make them) before 
 we can bring them down to particular facts. 
 
 Now, induction may be thus subdivided (starting with 
 arguments from the known to the known, and Avorking towards 
 arguments from the known to the unknown) l : 
 
 Induction 
 
 Perfect (or Improper.) 
 
 Imperfect 
 
 for Proper.) 
 
 From 
 known 
 to 
 known, 
 
 0-.<7- 
 officers 
 
 Traduction. 
 (Solomon.) 
 
 Colligation 
 of Facts. 
 (The Floods.) 
 
 Parity of 
 Reasoning. 
 (Ab uno 
 disce omnes.) 
 
 Induction 
 per sim- 
 plicem 
 enumera- 
 tionem. 
 (Swans.) 
 
 Scientific 
 Induction. 
 (Flling 
 Bodies.) 
 
 army.) 
 
 In arguing from particular facts to universal laws you may 
 know all the particular facts or you may not. If I say all 
 the officers in the British army weigh more than six stone. 
 after having gone through the Army List, and caused each 
 officer to be weighed, I am not in my calculation stating more 
 
 1 The four subdivisions of perfect induction are arranged according 
 as they resemble more or less closely imperfect induction. Parity of 
 reasoning might almost be called imperfect induction ; colligation is 
 nearer than traduction ; traduction and ' from known to known ' are the 
 pure cases of perfect induction.
 
 APPENDIX. 165 
 
 than I had already stated in my particular premisses. But 
 supposing some of our officers were stationed in parts wheie 
 j.iO means of weighing existed, and I persisted in my conclusion, 
 then I should be slating something more in the conclusion 
 than I had already stated in my particular premisses. Then 
 there would be that ' leap in the dark ' which, according to 
 some, takes away the certainty of induction and makes it im- 
 perfect instead of perfect ; according to others, is the very 
 ' soul ' of induction, and makes it proper, instead of improper, 
 For if you know all your particulars, you gain in the cer- 
 tainty of your conclusion while you lose in its originality 
 (so to speak), for it only tells you what you already knew. 
 Whereas if you do not know all the particulars, but under the 
 impulse of what you do know hazard a conclusion for the rest, 
 you gain in the originality of your conclusion, but you lose in 
 its certainty ; for the particulars you never saw may be un- 
 like those you did see, and this would upset your conclusion. 
 If you read that each of the kings of England was above four 
 years old when he began to reign, your conclusion to the 
 effect that ' all the kings of England were above four years 
 old when they began to reign,' teems with certainty, but lacks 
 interest. But if, after enumerating your racing experiences, 
 you come to the conclusion that ' all gentlemen of the turf are 
 honourable men,' your conclusion, while teeming with origi- 
 nality (and the bigger the leap the more pleasurable the 
 sensation for we have as strong a tendency to jump with 
 the mind as crickets and fleas with the body see pp. 6 and 
 10), lacks certainty. A merit and a fault, then, attach to 
 each of these two cases ; where you do know all the parti- 
 culars, and where you do not, and so two names have been 
 given to each case, the former being called ' perfect induc- 
 tion ' by those who valued its certainty, but ' improper ' by 
 those who looked for something more in the conclusion than 
 they already had in the premisses ; the latter being called 
 4 imperfect induction ' by those who looked for certainty, but
 
 166 APPENDIX. 
 
 proper ' by those who valued the fresh information given by 
 a conclusion which did something more than re-echo the 
 words of its premisses. For rich discoveries in science we are 
 indebted to induction proper (or imperfect), but we must not 
 forget the less brilliant aid of induction proper (or perfect). 
 The ' leap in the dark ' like riding across unknown country, 
 contrasted with trotting along roads has its dangers as well 
 as its charms. Glorious discoveries, like that of the steam- 
 engine, are doubtless the results of such a leap in induction 
 proper, but how many a man has bitterly rued the day when, 
 rejecting the safer argument, he chose the more brilliant one, 
 and from the narrow premisses of his happy experience, ' This 
 married man has peace and that and that, &c.,' leapt in 
 the dark, cried ' all married men have peace,' and took him 
 a wife ! 
 
 Perfect (or improper] induction also includes traduction, or 
 arguing from particulars to particulars, e.g., Solomon was the 
 wisest man, Solomon was a married man, .*. the wisest man was 
 a married man. Also Colligation of facts, closely resembling 
 the argument from the known to the known as above described, 
 only here our conclusion is a general conception or universal 
 idea rather than a law. Kepler wished to find out the curve 
 described by the planet Mars in its course. He marked all its 
 particular positions, and, when the course was completed, 
 ' read off,' so to speak, an ellipse from his marks. So a man 
 when the floods are out at Oxford, after visiting every side of 
 Oxford is enabled to say ' the floods surround Oxford.' Sup- 
 posing he did not visit every side of Oxford, and still came to 
 the same conclusion, his induction would be ' proper ' instead 
 of ' improper.' Mr. Mill gives the instance of a sailor who 
 views undiscovered land, and after sailing all round concludes 
 that it is an island. Mr. Mill says this is no inference, for it 
 ' brings in ' no new truth (p. 103). At all events it ' brings 
 in ' truth in a new shape, and, as Dr. Whewell observes, the 
 sailor who joins his disconnected observations in one universal
 
 APPENDIX. 167 
 
 idea, may be as truly said to ' bring in ' something new as the 
 jeweller who strings together the pearls of a necklace ; the 
 pearls were all there before, but the uniting thread is new. 
 
 Lastly, there is the argument from parity of reasoning, e.g., 
 the propositions of Euclid. We take a single instance of a 
 triangle, and show that any two sides of it are together greater 
 than the third, and from this single instance we lay it down as 
 true of all triangles, that any two of their sides are greater than 
 the third. In walking nobody denies that, ' cseteris paribus,' ' 
 it is a short cut if you can cut off a corner. Now here we 
 argue from the known to the unknown, for no one has seen all 
 triangles, and yet there is such a strong likeness between all 
 triangles, that in a sense we know all if we know one ; Ab 
 uno disce omnes.' Hence there is so much certainty about 
 this inference that it ranks as a perfect induction. Example 
 (p. 180) to be a safe inference, must only deal with cases 
 where a strong resemblance exists between the particular in- 
 stances, as in geometrical figures. 
 
 We now come to induction proper (or imperfect). This 
 is an argument from the known to the unknown, as well as 
 from the particular to the universal. ' This and that and the 
 other swan all the swans we've seen or heard of (Socrates 
 might have said) ' are white. .*. All swans are white.' ' This 
 and that and the other body, when let fall, fall towards the 
 earth, even though, from the revolutions of the earth, they have 
 to fall upwards. .*. All bodies fly towards the earth.' ' This 
 and that and the other application of fire to powder result in 
 explosion. .*. All do.' And now to distinguish the two kinds 
 of induction proper, notice that two of these conclusions are far 
 more certain than the first. We know that black swans have 
 
 1 It would not be shorter if you had a broad river in the -way. 
 
 ' Caeteris paribus ' means ' all other things being the same.' A good 
 swimmer ewims a mile in shorter time than a bad swimmer, ' all other 
 things being the same,' i.e. if they both have the same conditions of 
 swimming. But ' caeteris ' not ' pari'uus,' or let one tow a boat and the 
 other not, and the bad swimmer may win the prize.
 
 168 APPENDIX. 
 
 been discovered since the days of Socrates, but we feel con- 
 vinced that bodies will fly towards the earth as long as the 
 earth lasts, and explosions will follow the application of fire to 
 powder as long as tire burns. The explanation of this differ- 
 ence is the secret of scientific induction. For a long time 
 men were content with inductio per simplicem enumerationem, 
 i.e., with saying ' all the swans we know or have heard of are 
 white. .*. All swans are white.' 
 
 Scientific induction begins with a demand for something 
 more reliable as a guide to our action, and this something is 
 found in the test of what is called cause or causation. Does 
 the swan depend upon his whiteness for being a swan ? Could 
 he be a swan without being white ? Yes ; there are black 
 swans. But could application of fire to powder be an appli- 
 cation of fire to powder without an explosion? No, we 
 should at once say, there is something wrong with the powder; 
 it can't be true powder. 
 
 To borrow Mr. Fowler's exhausted pump instance. A 
 guinea and a feather in an exhausted air-pump fall in equal 
 times. 
 
 /. These and all other bodies will, under the same cir- 
 cumstances, do likewise. 
 
 (2) Now here is an inference grounded on two assump- 
 tions. 
 
 1. That everything has a cause (law of causation ). 
 
 2. That like causes are followed by like effects 'Jaw of 
 
 uniformity of nature). 
 
 We know that in an exhausted air-pump there can be 
 nothing to act upon this guinea and this feather unless it be 
 the action of gravity, or that attraction to the centre of the 
 earth which keeps all our feet upon the spinning globe though 
 our heads may be downwards. We assume that everything 
 has a cause. .*. This fall in equal times must be due to a 
 cause, and the only cause present is the action of gravity. 
 
 .*. The action of gravity is the cause of the fall.
 
 APPENDIX. 169 
 
 Again, before inferring that the case will be the same with 
 a shilling, a watch-key, a marble, &c., we must assume that 
 like causes (e.g., the action of gravity here) are followed by 
 like effects (e.g., falls of shilling, watch-key, or marble). 
 
 Hence, underlying every scientific induction are found 
 these two assumptions or principles as already stated in a note 
 (p. 163). 
 
 Thus scientific induction, not content with a mere enu- 
 meration of facts, founds upon the principle of causation some 
 more reliable basis of operations. 
 
 (3) Imagine man in the infancy of the sciences (cf. pp. 
 9, 10), face to face with a tangled web of hopelessly complicated 
 phenomena; causes and effects mixed myriads together. His 
 innate love of order prompts him to arrange, and group, and 
 classify ; to put things together. He finds that some things 
 always appear side by side, while others appear in succession, 
 like always following like. As a student of scientific induc- 
 tion he will confine his attention to the sequences rather than 
 the co-existences, as likely to produce more certain laws. He 
 Is not unarmed in this battle with nature. His instruments 
 or weapons are observation and experiment. By the former 
 he watches phenomena as they occur ; by the latter he changes 
 their surroundings and sees what happens then. Thus observ- 
 ation is natural ; experiment artificial. The astronomer ob- 
 serves the movements of the stars and makes laws ; the botanist 
 observes the growth of plants and makes laws ; and these laws 
 are certain in proportion as they express the relations between 
 cause and effect. But the plurality of causes (or the fact that 
 the same effect may be produced by several causes, e.g., death 
 by all kinds of things), and the intermixture of effects (or the 
 fact that effects may be produced partly by one thing, partly 
 by another, as water is produced by the mixture of two gases), 
 baffle mere observation, and experiment is called in to ' isolate 
 the phenomena,' as in the air-pump the action of gravity is 
 isolated. By experiment we can produce in our laboratories
 
 1 70 APPENDIX. 
 
 the lightning in the shape of electrical sparks without the 
 danger or difficulty of watching it in the storm. To find the 
 effect of a given cause, experiment is better than observation ; 
 but to find the cause of a given effect, observation is better than 
 experiment. 1 
 
 It is easy to see that the more complicated the phenomena 
 the more difficult it is to distribute and arrange right causes 
 with right effects, and so to produce laws. In astronomy and 
 geometry much has been done, and they are called deductive 
 sciences because all their phenomena have been grouped and 
 classified under a few simple laws. In chemistry (read care- 
 fully pp. 12, 13), it is very hard to isolate the phenomena. 
 In physiology it is still more so. To reduce human action to 
 laws of cause and effect in a social science, 2 is a hopeless task 
 for the same reason. The ancient philosophers not receiving 
 from their fathers the results of previous observation and ex- 
 periment as we do, unaided by all the triumphs of modern 
 invention, were compelled either to give up the attempt of 
 making laws altogether, or else to make theories and force the 
 facts into subjection to them, and call these theories laws. 
 Now hypotheses (see p. 182) are assumptions to explain phe- 
 nomena but only assumptions, and they only become laws by 
 standing the test of verification. Given the phenomena of 
 movements of the sun, winds, and rivers. The ancients said 
 'a priori' (p. 185), 'things that more are living beings. 
 These move. .'. These are living beings.' They spun out their 
 theories and applied them to the facts, instead of starting with 
 the facts and working upwards. As the spider spins his web, 
 so they their theories out of themselves ; whereas they should 
 have flown from fact to fact like the bee. ' Hypotheses non 
 fingo,' cries a wise man. But hypotheses, like wine, must not 
 be condemned because some people are intoxicated with them. 
 
 1 This is important. Think it out and illustrate it by instances from 
 your own experience. 
 
 2 Statistics are ' observation systematised* for this purpose.
 
 APPENDIX. 171 
 
 Alany great discoveries have been preceded by several tenta- 
 tive hypotheses, which would not stand the test of verification. 
 Hypotheses are valuable enough if only subjected to impartial 
 and rigid verification. The following summary of Mr. Fowler's 
 rules should be remembered with regard to observation and 
 experiment : 
 
 1. Precision. Exact time at which an event occurs should 
 
 be noticed, &c. Hence all kinds of instruments 
 watches, thermometers, dials, &c. 
 
 2. Waste no time with immaterial circumstances. Set aside 
 
 everything which you know to have nothing to do 
 with the effect you are trying to find the cause of ; 
 e.g., if you're a doctor and see your patient is worse, 
 don't ask him if he feels better. 
 
 3. Vary the circumstances of the phenomenon as much as 
 
 possible. You do not feel well at Oxford. This is 
 the phenomenon. You say to yourself, ' Probable 
 cause wine.' But before you can be certain, you 
 must take the same wine at several other places; 
 e.g., Brighton, Scarborough, &c. ; and you will often 
 find that the wine is not the cause, but the climate or 
 some other thing. This rule especially applies to ob- 
 servation. 
 
 1 4. Isolate the phenomenon. This is a rule for experiment. 
 You bathe in sea-water. Your head aches afterwards. 
 It may be the cold or the salt that is the cause of your 
 pain. Isolate the cold by bathing in fresh water, and 
 you will find out which it is. 
 
 N.B. The word ' cause ' is loosely used for any of the cir- 
 cumstances which precede a phenomenon. The phenomena 
 (' any things that appear or can be observed by the senses ') 
 which go to form that tangled web above described may be 
 regarded, supposing their orderly arrangement to be completed, 
 
 1 Kemember these four by the word VIEW, v vary, i isolate, E exact, 
 
 w
 
 172 APPENDIX. 
 
 as rows of soldiers one behind the other, each front rank to 
 the row behind becoming a rear rank to the row in front 
 in other words, each set of phenomena becoming antecedents to 
 the set in front of them and consequents to the set behind. 
 
 Often many antecedents combine to produce a consequent, 
 and strictly speaking all these antecedents taken together are 
 the cause of the effect. We speak of ' pulling the trigger ' as 
 the cause of the explosion of a gun, but it is only the occasion 
 or last cause. No explosion could have taken place, had it 
 not been for the powder, the cap, the barrel, &c. All these 
 are 'causally connected,' or ' part-causes of the effect.' A cause 
 may be defined as a ' necessary and indispensable antecedent.' 
 
 The above applies rather to physical or mechanical causes. 
 Efficient causes are those where the movement starts, so to 
 speak ; e.g., the movement of the steam-engine is caused by 
 the revolution of the wheel, which is caused by the working ot 
 the piston-rod, which is caused by the elasticity of the steam, 
 which is caused by the water heated by fire, which is caused 
 by the match applied by man. 
 
 Now this last agent, man, might or might not have applied 
 the match, but the rest of the causes had no choice about it. 
 They passed on the impetus mechanically. They were physical 
 causes. The man was an efficient cause. A great question 
 the freedom of the will hinges upon this distinction. Whether 
 man is the efficient or physical cause of his actions. If he is 
 only a physical cause, a social science would be possible. 
 
 (4) The Methods. ' Felix qui potuit rerum cognoscere 
 causas.' Man rules by obeying nature. By finding what effects 
 come from what causes, he can saddle those causes and bridle 
 them (so to speak), and make them his beasts of burden. But 
 he must study them carefully first, or they will crush him to 
 atoms. Inductive logic provides him with these methods of 
 experimental enquiry, as deductive logic gives him the rules 
 of the syllogism. To make these methods clearer we shall 
 give the examples first.
 
 APPENDIX. 173 
 
 I. The Method of Agreement. You are an inductive logi- 
 cian. The savages of some new island come to you and 
 beseech you to discover the cause of the madness which is 
 raging amongst them. You tell them to bring you instances. 
 They bring a dozen madmen. You find these men have 
 several points in common ; they have all of them always been 
 nervous, delicate, and worn with anxiety ; among other things 
 they have all been bitten by a dog. You cannot isolate your 
 phenomena you cannot separate the nervousness, &c., and 
 the bite. You cannot be sure which is the cause of the mad- 
 ness. You bid them bring you other instances of the same 
 madness, but differing in everything else except that they have 
 this madness. They bring all kinds of instances ; mad horses, 
 mad squirrels, &c. ; and you find that the instances of the 
 madness are so many and so vaiious that they may be said to 
 have only one circumstance in common a bite ; in fact, the 
 only thing you can say of them all is that they have been 
 bitten by a dog. 
 
 You conclude that the bite is the cause or the effect of the 
 madness. But you know the bite came first, so it must be the 
 cause. This put into formal language becomes : l ' If two or 
 more instances of the phenomenon under investigation have 
 only one circumstance in common, the circumstance in which 
 all the instances agree is the cause or the effect of the given 
 phenomenon.' 
 
 Here phenomenon = madness ; instances = men, horses, 
 squirrels, &c. ; circumstances in common = bite. 
 
 The principle of this is that whatever can be cut out with- 
 out affecting the phenomenon is not causally connected with it. 
 
 II. The Method of Difference. You have two guns of 
 precisely the same value and workmanship. One ' kicks,' 8 and 
 the other does not. Your man tells you that the reason is 
 that one's a badly made gun. But after a careful investigation 
 
 1 From Mr. Mill's Logic. 
 
 * If you use this instance, for ' kick ' road ' recoil ' throughout.
 
 174 APPENDIX. 
 
 you find that the two guns, the kicker and the non-kicker, 
 are precisely the same except in one thing have every cir- 
 cumstance in common except one viz., that the non-kicker is 
 cleaned daily and the kicker is not cleaned daily. You con- 
 clude that the want o daily cleaning is the cause of the kick- 
 ing of the gun. Put into formal language this becomes : 
 
 ' If an instance in which the phenomenon under investi- 
 gation occurs, and an instance in which it does not occur, have 
 every circumstance in common save one, that one being pre- 
 sent only in the former, the circumstance in which alone the 
 two instances differ is the effect, or the cause, or an indispensable 
 part of the cause, of that phenomenon.' 
 
 Here the instance in which the phenomenon under investi- 
 gation occurs is the ' kicking ' gun ; the instance in which it does 
 not occur is the ' non-kicker;' the circumstance in which alone 
 the two instances differ is the matter of cleaning; and the phe- 
 nomenon is ' kicking.' 
 
 The principle of this is that whatever cannot be cut out 
 without affecting the phenomenon is causally connected with it. 
 
 III. The Joint Method of Agreement and Difference. An 
 officer who has seen much service finds that on certain days 
 he is subject to twinges of rheumatism. Some of these days 
 are fine, some wet, some cloudy, some clear, some in the sum- 
 mer, some in the winter, some in the town, some in the country; 
 in fact these days of suffering have only one circumstance in 
 common an east wind. On the other hand the days when he 
 feels no twinges are of all kinds also, they also differing in 
 everything except one thing, i.e. having only one circumstance 
 in common the absence of an east wind. The officer con- 
 cludes that the east wind is the cause of the twinges. This 
 put formally becomes : 
 
 ' If two or more instances in which the phenomenon undi-r 
 investigation occurs have only one circumstance in common, 
 while two or more instances in which the phenomenon does 
 not occur have nothing in common save the absence of that
 
 APPENDIX. 175 
 
 circumstance, the circumstance in which alone the two seta of 
 instances differ is the effect or the cause or some indispensable 
 part of the cause of that phenomenon.' 
 
 Here the first set of instances are the wet, fine, cloudy, &c. 
 days, with an east wind. 
 
 The second set are the various days without an east wind. 
 
 In the first set rheumatism (the phenomenon) occurs ; in 
 the second it does not. The first set have only one thing 
 in common an east wind ; the second set only one thing in 
 common no east wind, 
 
 IV. The Method of Concomitant Variations. I rub two 
 sticks together ; the more I rub the hotter they grow, the less 
 I rub the cooler they grow. Therefore the friction is the 
 cause of the heat. 
 
 'Whatever phenomenon varies in any way whenever 
 any other phenomenon varies in some particular way is either 
 a cause or an effect of that phenomenon, or is connected with 
 it through some fact of causation.' 
 
 V. There is also a Method of Residues. ' Subduct from 
 any phenomenon such part as is known by previous inductions 
 to be the effect of certain antecedents, and the residue of the 
 phenomenon is the effect of the remaining antecedents ; ' e.g., 
 A man is taken seriously ill after bathing and oi-ertiring 
 himself and drinking bad wine. Take away that part of his 
 illness which is due to wine and the exhaustion, the residue is 
 caused by the bathing. 
 
 N.B. (i.) is the method for observation. 
 
 (n.) is the method for experiment (the best of all the 
 methods). 
 
 (in.) for cases where you cannot isolate your phenomenon. 
 
 (iv.) for cases where the causes are pei-manent. We c;m 
 modify heat 1 or the action of gravity, but so long as we are in 
 the world we cannot exclude them. 
 
 1 If we could banish the heat altogether, the sticks might be brought 
 to that most useful method of difference. But many causes are perma-
 
 176 APPENDIX. 
 
 (v.) most fertile in unexpected results. 
 
 Remember these methods by their instances. ' Even mad 
 creatures recoil from twingey old officers hot as two sticks 
 rubbed together, and seriously ill from various causes.' Or 
 by the hexameter and pentameter : 
 
 Agreement, difference, first apart, then taken together, 
 Concomitant variations and a fifth Residues. 
 
 FINIS. 
 
 Note. The inductive syllogism runs as follows : 
 This, that, and the other body fall to the ground. 
 This, that, and the other body are all bodies. 
 .*. All bodies fall to the ground. 
 
 This form is true enough, if we know all the instances. 
 (i.e. in perfect induction). In imperfect induction our minor 
 premiss is faulty, and our conclusion therefore not quite certain. 
 
 Archbishop Whately puts induction into a syllogism in 
 Barbara by making a major premiss of the law of the uni- 
 formity of nature. 
 
 What | belongs to this, and that, and the other body | be- 
 longs to all. 
 
 Falling earthwards | belongs to this, that, and the other 
 body.) 
 
 .'. Falling earthwards belongs to all. 
 
 Of course this is valid ; the uncertainty of imperfect in- 
 duction is, however, latent in the major premiss, which is only 
 a generalisation from experience. Perfect induction seems to 
 possess the certainty of deduction. 
 
 nent, and concomitant variations becomes a valuable method. The 
 whole N.B. is important.
 
 177 
 
 A LIST OF USEFUL FACTS IN LOGIC. 
 
 ABSOLUTE terms (opposed to relative terms) mean terms 
 which are ' loosed from ' (absolve) any connection with other 
 tenns (e.g., water) ; whereas relative terms have reference to 
 frefero), or suggest other terms (e.g., father [and son] husband 
 [and wife]). The pairs are called correlatives. You can think oi 
 ' water ' by itself ; but you can't think of ' father ' without also 
 thinking of ' son.' 
 
 A^AXOGY. 1 An argument whereby from similarity between 
 any two objects in points known we argue to further resemblance 
 in points unknown, e.g., moon and earth are two objects with 
 known points of similarity (clouds, mountains, shape, &c.). The 
 earth is inhabited ; by analogy it follows that the moon is inha- 
 bited also. The value of analogy depends upon the number of 
 points of resemblance known, as compared with the points of dif- 
 ference known, or the points of which nothing is known : e.g. f 
 given two men ; only known point of resemblance is ' both bar- 
 risters.' One we know succeeds ; but it would be a weak argu- 
 ment of an analogy to say .*. ' the other succeeds also.' But given 
 two fast men, with very many points of resemblance. One we 
 know repents in after life. It would be a strong argument of 
 analogy to say, ' .*. the other repents.' 
 
 A PRIORI. | (gee Method0 
 
 A POSTERIORI. J 
 
 ARGUMENTUM AD JUDICIUM means ' an appeal to the common 
 sense of mankind.' Argumentum ad ignorantiam, f an argument 
 founded on the ignorance of adversaries.' Argumentum ad vere- 
 cundiam, 'an appeal to our respect for some great authority.' 
 Argumentum a concesso, ' a proof derived from a proposition already 
 
 1 For 'analogous, equivocal, and uni vocal' words see p. 150-1. 
 
 N
 
 178 PICTURE LOGIC. 
 
 conceded.' Argumentum a fortiori,^ ' arguing that you are right in 
 a case which is stronger and better than one in which you were 
 already allowed to be right.' 
 
 ATTRIBUTE (See Metaphysics). 
 
 AXIOM. A proposition accepted on its own merits, so to speak, 
 which does not require proving itself, but from which we can 
 prove other proposi tions : e.g., ' The whole is greater than its part ' 
 (See Empiricism). 
 
 CATEGORIES. A list of ' summa genera ' (or ' highest classes ') 
 given by Aristotle. Everything was said to belong to one or other 
 of these genera, ' substance, quantity, quality, relation, action , 
 passion, place, time, position, habit, or state.' 
 
 CAUSE means that without which a thing could not exist. 
 Thus, there are four causes ; remember them by a statue. Take 
 away the stuff a statue is made of and there is no more statue ; 
 the material is called the material cause. Take away the shape 
 and you destroy the statue ; the shape or form = the formal cause. 
 Let there be no maker, and the statue can't be made. The maker 
 = the efficient cause. Let there be no aim or object in that 
 maker's work, and the statue is a mass of confusion. The end or 
 aim of the thing is its final cause. Hence there are four things 
 without which a statue ceases to be a statue, and these are the 
 four causes. 
 
 CONCEPTION (See Faculties). 
 
 CONCEPTUALIST (See Nominalist). 
 
 CONTRADICTORY (See Terms). 
 
 DIALECTIC. The art of discoursing. Also the old name of 
 Logic. Several other meanings. 
 
 DICTUM DE OMNI ET NULLO. This means to say that what is 
 true of a class is true of each individual in the class. Now to 
 those who hold that classes are merely the sum of individuals 
 composing them, this assertion is a truism. But to those who 
 hold that there is something more in a class than the mere list of 
 its individuals, it becomes an important truth. 
 
 DILEMMA. Remember the three instances of Dilemma thus : 
 ' Science makes the Politician jest at Scripture (See Chapter on 
 Hypothetical Syllogisms, p. 139). 1 
 
 EMPIRICAL (snirttpii, experience). Empirical knowledge is 
 knowledge derived from experience. The knowledge of the old 
 
 1 E.g., even dogs can't digest nails, a fortiori dyspeptic invalids can't.
 
 A LIST OF USEFUL FACTS IN LOGIC. 179 
 
 huntsman, or the old sailor is often empirical. They know what 
 to do in each particular case, not because they have any principles 
 or laws to act upon, but simply because they have an instinctive 
 inclination to act in a certain way under certain circumstances. 
 ' What do you do if a squall strikes the sail the wrong side ? ' you 
 ask your sailor friend. ' Well, Sir,' he replies, ' I don't know what 
 I does I couldn't tell you but when the squall comes I does it 
 quite natural/ He has no principles consciously elaborated from 
 the observation of particular facts, his knowledge is purely ' empi- 
 rical.' A famous dye was lost not long ago by the death of the 
 man who mixed the colours. ' Tell us,' said his employers, ' the 
 principles upon which you mix, that the dye may not perish when 
 you die.' ' Alas,' replied he, ' I know not how I do it. I can mix 
 it myself, but I could not show another person how to mix it. 
 The principles upon which he acted, the ' why ' and the ' where- 
 fore ' and the * how ' he knew not ; his knowledge was purely 
 empirical. 
 
 EMPIRICISM is the technical name given to the theory that all 
 our principles or laws are derived from experience. All men allow 
 that some are. Such laws as ' the sun rises daily ' are derived 
 from experience or the observation of particular facts. But there 
 are other laws which seem far deeper and more fundamental, such 
 as ' The whole is greater than its part.' We can easily imagine a 
 breach of the law, ' the sun rises daily ; ' but we can't imagine a 
 part greater than its whole. Hence it is supposed that by nature 
 certain laws are implanted in us to be apprehended by our reason 
 and intellect, as particular facts are apprehended by our senses. 
 Of this deep and fundamental character are the laws of thought. 
 Nevertheless it is still true that in the science of thought we start 
 with particulars ; for though the laws of thought already existed, 
 we did not know them ; we found them, though we did not make 
 them ; on our voynge of discovery we stalled with particulars and 
 landed at laws (so to speak), though we did not make the laws 
 any more than Columbus was making America when he started on 
 hia voyage of discovery. Empiricism would maintain that we 
 make all our laws as we make all our laws of nature ; e.g., the 
 laws of tides, sun, wind, &c., whereas others would maintain that 
 laws, whereof the breach is inconceivable, are part of our nature, 
 and found rather than made.
 
 180 PICTUKE LOGIC. 
 
 EXAMPLE. Analogy takes two instances as its grormdwork. 
 Induction takes more than two or several. Example takes one. 
 By example we take one member of a class to represent the whole 
 class, and argue from the individual to the class ; e.g., l Tyrants 
 are cruel.' Why ? ' Because Pisistratus (a tyrant) was cruel,' i.e. : 
 
 P. was cruel. 
 
 P. was a tyrant. 
 
 . * . all tyrants are cruel. 
 
 The syntax of grammar abounds with instances. Care must be 
 taken in this dangerous inference that the individual fairly repre- 
 sents the class. 
 
 EXPEKLMENTTTM CKTicis. 'An experiment which decides be- 
 tween two rival theories, and shews which is to be adopted, as a 
 finger-post shews which of the two roads is to be taken.' Crosses 
 
 are often erected in Roman Catholic countries at the cross-roads, 
 or places where two or three roads meet. Hence also ' a crucial 
 instance,' one which at once shows you which of two contending 
 theories you are to adopt. 
 
 FACT. A word used in many senses, strictly means 'what is 
 done or made.' Sometimes it is opposed to universal proposition, 
 and sometimes to what is theoretical. Generally we speak of the 
 facts of a case as the data (or ground, or material given), upon 
 which we are to build up our inferences and theories. Facts would 
 then mean all that is intuitively apprehended by sense or reason. 
 And remember that at both ends of the domain of proof (traversed 
 by the roads or paths called method) are ultimate and simple 
 propositions which are called facts (see Method). 
 
 FACULTIES OF THINKING. Sensation is the faculty by which 
 we are conscious of the presence of anything, without knowing 
 anything except that our senses are affected (e.g., child with dog, 
 in ' Thought is Comparison '). When we are not only aware of 
 the presence of a phenomenon, but also recognise it, we have at- 
 tained to perception. Conception is the forming of concepts in the 
 mind resulting from sensation and perception ; it employs imagi-
 
 A LIST OF USEFUL FACTS IN LOGIC. 181 
 
 nation (or the making of pictures or images in the mind). 
 Generalization is a faculty by which we ascend to universals 
 (ideas or propositions), which we apprehend by reason. By in- 
 tuition, we know anything that we know without the aid of proof 
 (see Method). 
 
 FIGURE OP SPEECH. A fallacy, which comes under amphi- 
 bolia e.g., ' When we run we tread heavily upon what we run 
 on ; sometimes we run on empty stomachs ; . * . sometimes we 
 tread heavily upon empty stomachs.' 
 
 GENERALIZATION. (1.) Opposed to specialization (see Conno- 
 tation of a Term). 
 
 (2.) Either the process or the result of our innate tendency to 
 gather and group the like with the like. 
 
 GENERIC PROPERTY. ' That which belongs to the whole of a 
 genus:' e.g., 'hunger' is a generic property of 'man,' because it 
 belongs to all the other species that go to make up the genus 
 ' animal ' to which the ' species ' man belongs. Whereas ' cooks 
 his food ' is a specific property, for it belongs only to the species 
 ' man.' Both are properties, for both follow from the connotation 
 of man, ' rational animals.' 
 
 GRAMMAR is the science which is concerned with language 
 primarily, whereas logic is only concerned secondarily with 
 language. The grammatical analysis of the sentence, ' She stoops 
 to conquer,' is into pronouns, verbs, &c., &c., but the logical 
 analysis is into subject copula predicate. For ideas and not 
 words are the important things to logic. Also rhetoric, or the 
 science and art of persuading, differs from logic. For rhetoric 
 persuades, logic convinces. In rhetoric, a fallacy which escaped 
 notice would be no flaw, whereas in logic all fallacies are flaws. 
 Rhetoric appeals to the feelings, logic to the intellect ; and rhe- 
 toric relies upon the warmth of sympathy, while logic only re- 
 cognises the cold, calm intellect. Hence rhetoric is the more 
 popular, but logic the more true. 
 
 HYPOTHESES (or suppositions, VTTO rid ij jui, sub ponoi) are the con- 
 jectures hazarded by men who seek to establish laws from the 
 observation of particular tacts. If an hypothesis is right it becomes 
 a law. I see several mad dogs at different times. I am anxious 
 to establish a law as to the course of mad dogs. I hazard au
 
 182 PICTURE LOGIC. 
 
 hypothesis by saying, ' Happy thought ! mad dogs run in circles.' 
 A neighbour acts upon this theory, gets bitten, and dies. I reject 
 this false hypothesis and select others, hoping to find one that 
 accounts for all the particulars. I end with ' The course of mad 
 dogs is a straight line if possible,' and many of my neighbours 
 are saved by attention to this hypothesis, which passes into a law, 
 or valid induction, as soon as it is found to stand the test of appli- 
 cation to particulars. So Kepler rejected about twenty hypothe- 
 ses before he found the true one as to the orbit or course of the 
 planets ; and the true hypothesis became at once a law. 
 
 INDIVIDUAL. The name given to that which is incapable of 
 logical division, being a single object, as opposed to a class or 
 group of objects. 
 
 INFERENCE. There are two kinds of immediate inference not 
 yet mentioned, (i.) Inference by added determinants, which is of 
 this form: 'The horse is a beast; .'.the noble horse is a noble 
 beast.' Care must be taken, for from ' The mouse is an animal ' 
 it does not follow that 'A huge mouse is a huge animal.' (ii.) 
 Inference by complex conception of the form : ' The horse is a 
 beast;. '.the stride of the horse is the stride of a beast.' Care 
 must be taken here also, for from 'Misers are men,' it does not 
 follow that ' The most liberal of misers are the most liberal of 
 men.' 
 
 INTENTION (for Intension see Connotation of Terms). A word 
 is said to be of the first intention when it is the name of a thing ; 
 of the second intention when it is the name of the name of a 
 thing. Thus, man, animal, &c., are names of things, while 
 species, genus, &c., are the names we give to these names of 
 things. "We call 'animal' the 'genus,' 'man' the 'species,' 
 and thus we name again (second intention) what were already the 
 names (first intention) of things. 
 
 LAWS or THOUGHT. The three great laws upon which all 
 thinking is found ultimately to depend are : 
 
 I. The law of identity. Whatever is, is. This we assume in 
 every syllogism, for if one premiss changed while we were ex- 
 amining the other no conclusion could be drawn. In the old 
 instance, when I seek to establish a connection between ' Socrates ' 
 and ' mortal,' after asserting ' Socrates is a man,' I may (so to 
 speak) turn my back upon ' Socrates ' in my attempt to find out
 
 A LIST OF USEFUL FACTS IN LOGIC. 183 
 
 how 'man and mortal ' stand to one another, intending to return 
 to ' Socrates ' as soon as I have found this out If ' Socrates ' 
 changes while my back is turned, what conclusion can I draw ? 
 3n the contrary, by this law I know that if he is mortal he is, 
 and I need not fear to leave that premiss while I busy myself 
 with the other. 
 
 II. The law of contradiction. 'A. thing cannot both be and 
 not be.' A man can't be both tall and not tall at the same time. 
 Of course, ' not tall ' means everything that isn't called ' tall,' or 
 you might say ' he is of middle height \(which really means he is 
 not tall). Upon this law, remember, opposition is based. Con- 
 tradictory opposition would be powerless without this law. So also 
 would reduction ' per impossible.' (See Reduction of Figures, 
 p. 133.) 
 
 III. The laio of excludtd middle, or that which excludes a 
 middle state. ' A thing must either be or not be.' Upon this 
 law depends dichotomy. (See Division.) N.B. Keep distinct 
 ideas of the laws of thought, the principle of the syllogism, the 
 rules of the syllogism, and the canons of the figures. 
 
 METAPHYSICS. We divided all the universe into two parts. 
 The ego, or person observing (subjective), and the non-ego, or ob- 
 jects observed (objective). We spoke of the attributes of these 
 objects, as though each object was a something underlying its at- 
 tributes, as our own souls and wills underlie our actions. To that 
 underlying something (which we can't see, but imagine to be at 
 the root of those attributes, as our own ' selves ' are at the root 
 of our actions) is given the name of noumenon (yovptvov, the 
 thinking part), or substance as opposed to phenomenon* (the part 
 seen), or attribute. This mysterious something, this substratum, 
 baffles all human powers of search. We think it lies somewhere 
 behind the attributes, so we carefully remove the attributes one 
 after another, and, wonderful to tell, when all the attributes are 
 removed, there is nothing left at all ! e.g., a tree take away all 
 its attributes, ' shape, height, size, hardness,' &c., and you have 
 nothing left. Still (by analogy from ourselves) we speak and 
 think of objects as substance underlying attributes. Now, the 
 science which is conversant with these inscrutable substances is 
 metaphysics, or ontology. 
 
 NOMINALISTS, REALISTS, CONCEPTTTALISTS. We saw that after 
 a time the infant would start at the name of ' dog ' without the 
 
 , I show mysel
 
 184 PICTURE LOGIC. 
 
 presence of a dog. Imagination enables us to picture to ourselves 
 4 a dog ' which is not this or that dog, but simply a specimen pos- 
 sessing the necessary attributes and no more. Now, with regard 
 to this perfect specimen, this type dog, with all the essential but 
 none of the accidental qualities of ' dog,' the realist holds that it 
 actually exists (though out of our view) as a model or pattern 
 after which all dogs are fashioned, but to the perfection of which 
 type canine frailty cannot attain. The conceptualist says, ' Yes, it 
 exists, but only in our minds, by help of imagination. For seeing 
 many dogs, we gather into one imaginary dog all the essential 
 attributes, and this forms our conception " dog." ' The nominalist 
 says, ' That which we picture to ourselves as " dog " exists neither 
 in the mind nor out of it ; it is merely " this or that dog " some 
 particular dog we have seen, that we have photographed (so to 
 speak) in our souls. Thus the realists believe in the objective 
 existence of general notions (or common terms). The conceptual- 
 ists in their subjective existence, and the nominalists allow them 
 no existence at all.' 
 
 METHOD (/<' oaoc). All our knowledge comes either from 
 intuition or from proof. There are the universals at the top, so to 
 speak, and the particulars at the bottom ; and the first we appre- 
 hend by reason or intellect, the second by sense. Between these 
 two extremes, which we accept upon intuition, comes a group of 
 facts accepted upon proof or inference. Our ' whys ' and ' be- 
 causes ' are obliged to stop when they reach the upper or lower 
 bounds, beyond which no proof can go. Now in the pursuit of 
 knowledge, as we pass through the domain of proof, we may travel 
 by two grand routes. We may either start with the universal 
 fact and journey southwards, or we may start with the particular 
 fact and journey northwards. And the roads or routes are called 
 fj.iQoSoi (o'floc) or ' ways after something.' The journey downwards 
 is called the deductive, or the d, priori, or the synthetic method, 
 and the upward journey the inductive, or the a posteriori, or the 
 analytical method. The former is also called the method of in- 
 struction, the latter the method of discovery. An instance of the 
 first would be proving that these two slate pencils couldn't enclose 
 a space by starting with the universal proposition, ' two straight lines 
 can't enclose a space.' (For this is one of the ' bounds ' of proof that 
 is accepted on intuition. If any one said* ' Why can't they ? ' you'd
 
 A LIST OF USEFUL FACTS IN LOGIC. 185 
 
 answer, ' Because they can't, and there's an end of it ; ' for it is one 
 of the upper side ' bounds '). An instance of the second would 
 be to prove that 'all bodies are attracted to the centre of the 
 earth from such propositions as ' this book falls ' (Suppose some 
 one said, ' Prove it falls ' after you've seen it fall, you'd answer 
 Can't you believe your eyes ? ' which means that it is a fact ac- 
 cepted upon intuition or sense one of the lower-side ' bounds ' of 
 proof). [As to Logic, in so far as we start with particulars to find 
 the laws, it's inductive, and in so far as those laws of thought 
 already existed, and we found and did not make them, it's de- 
 ductive.] The truths at the upper end are said to be 'notiora 
 naturae,' or better known in themselves and simpler ; those at the 
 lower end are ' notiora nobis,' better known to us, but more com- 
 plicated. Now as universal truths are simpler, so they are said to 
 be prior to particular truths. Hence a priori and a posteriori, though 
 generally we learn particulars first (as a child calls every man 
 papa). Smith is coming from Leicestershire to hunt with me. 
 A priori Smith is a ' good goer,' for ' all Leicestershire men are 
 good goers.' But Smith prefers the roads when he comes. A 
 posteriori, then, Smith is not a good goer. Synthesis is 'piecing 
 together ' and analysis ' breaking up.' I am anxious to know 
 what this pudding is made of. I may either take simple ele- 
 ments, ' currants,' ' flour,' &c., and ' piece together ' till I arrive at 
 the particular pudding in question, or I may send for Drug, the 
 chemist, and we may analyse the pudding till we get at the simple 
 elements of which it is composed. So with the proposition 
 ' Socrates is mortal,' I may either take simple elementary proposi- 
 tions and piece them together as premisses until I arrive at this 
 conclusion, or I may take the proposition to start with, and eye it 
 narrowly until I find the simple elementary propositions of which 
 it is an instance. In one case I start with the universal, in the 
 other with the particular. Thus a priori and deductive and syn- 
 thetical may be regarded as the same, and posteriori, analytical, 
 and inductive as their opposites. 
 
 OBJECTIVE (Metaphysics). 
 
 PRACTICAL UTILITY OF LOGIC. (1) As an abstruse study, it 
 braces the faculties of the mind. The harder the whetstone, the 
 keener the knife ; and when you come to cut wood afterwards it's 
 easy. So it ia with less abstruse questions after Logic.
 
 186 PICTURE LOGIC. 
 
 (2) It exposes fallacies. These recur. The foxhunter, who 
 has seen many a fox drawn from a covert, is more likely to tell me 
 whether there will be a fox in yonder untried covert than a raw 
 novice, though neither may have seen the covert before. In 
 Logic the covert is a wordy speech, the fox the fallacy, and the 
 old foxhunter the cold logician. When the mob is on the point 
 of ' stones and fire ' with delight at a speech, the logician is mut- 
 tering ' accursed fallacy ! ' 
 
 (3) It is the study of the highest part of man, and man is the 
 highest thing in the world. Such a study must elevate and 
 ennoble us. 
 
 PROPOSITION. Indefinite propositions, where the quantity is 
 not specified, as ' girls are shy.' Tautologons, where the predicate 
 simply repeats the subject, and no information is given. Eggs are 
 
 egg 8 - 
 
 PSYCHOLOGY. The science of the whole inner nature of man ; 
 i.e. of the whole mind or soul. Its object is to arrange and group 
 these phenomena and find their laws. One of its results is 
 that the mind or soul is broadly divided into three parts. The 
 purely intellectual, the purely animal, and the combination ot 
 the two, or the union of reason and desire. Other sciences 
 then step in, take these three results, and produce further 
 improvements and arrangements. The science of ethics takes ofl 
 the union of reason and desire, as its subject-matter ; and Logic in 
 the same way takes the purely intellectual part. Thus psychology 
 provides Logic with its material, as the art of making oars pro- 
 vides the art of rowing with material to work upon, or the science 
 of Euclid the science of land-measurement. 
 
 QUANTIFICATION OP PREDICATE. An attempt to quantify the 
 predicate as we do the subject. It is better not to adopt it : 
 
 (1 ) Because too troublesome. 
 
 (2) too unusual a form. 
 
 (3) makes one proposition into two. 
 
 RATIOCINATION. A grand name for syllogistic inference. 
 
 REALIST (See Nominalist). 
 
 RHETORIC (See Grammar). 
 
 SECUNDI ADJACENTIS. ' Brutus lives ' is said to be a proposi- 
 tion secnndi adjacentis (i.e. with copula lost in Terb). Brutus 
 is brave, is tertii adjacentis with copula distinct.
 
 A LIST OF USEFUL FACTS IN LOGIC. 187 
 
 SUBSTANCE (Metaphysics). 
 
 SYLLOGISM. Valuable as an inference, because it brings in 
 truth in a new way, if it does not bring in new truth : moreover 
 it is of the greatest assistance to the memory, as it dispenses with 
 the recollection of innumerable particulars. 
 
 The principle of syllogism has these corollaries 1 (propositions 
 following from itself, crowning it, so to speak) : 
 
 (1) Terms whereof both agree with the same middle term 
 
 agree with one another. 
 
 (2) Terms wherof one agrees and one does not agree 
 
 with the same middle term do not agree with one 
 another. 
 
 (S) Terms whereof neither agrees with the same middle 
 term may or may not agree with one another. 
 
 TERMS (irregular). Categorematic terms are of the form 
 ' house, horse.' Syncategorematic, ' of, to, from.' ' Grateful,' 
 ' ungrateful ' are positive and negative terms (presence and absence 
 of a quality). ' Dead ' is a privative term (loss of a quality). ' Less 
 and greater ' are opposites (< equal ' intervenes). ' Negatives ' are 
 also called ' contradictories.' 
 
 TROTSM = a tautologous proposition ; e.g., whatever is, is. 
 
 This list Mr. Practical gave us as a bricklayer gives a series of 
 dabs of mortar to fill up all crevices. He entreated us to read it 
 over ' the night before the battle,' which I did with the zeal of a 
 Roman Catholic soldier counting his beads, and the result was 
 such as to exceed my wildest hopes. Both Dyver and myself 
 passed with colours flying, Dyver being gently rebuked for giving 
 up in a pass examination papers that would have carried off high 
 honours, and I being complimented on the fact ( that I seemed to 
 understand well what I wrote, and that it was refreshing to read 
 papers that came from the writer's head ; and were not a string of 
 phrases from books learnt off, but never understood.' 
 
 The triumphant entry at home, the proud honours of a 
 conquering hero, the affable condescension towards a world of 
 inferiors who had never read Logic, or passed a public examina- 
 tion, the earnest desire of the female part of the family that the 
 Dver-wrought brain that had soared to, and faced, and fought, and 
 
 1 Corolla a little crown.
 
 18S PICTURE LOGIC. 
 
 mastered the mighty problems of that dimly awful monster Logic, 
 and passed through the anguish and tribulation and torture of an 
 Oxford examination, should have entire, absolute, and undisturbed 
 rest and enjoyment for months to come: all these things, as 
 likely to work upon the feelings, I leave to rhetoricians to de- 
 scribe; for my part, under the strong influence of my logical 
 teaching, I am disposed to cultivate the cold demeanour of the 
 logician, and to this end I habitually amuse myself by detecting 
 fallacies in the conversation of my father's friends, as they sip their 
 port after dinner, the exposition of which errors does not seem 
 so agreeable to them as it ought, though they are compelled to 
 acquiesce, my father nodding to them, as much as to say, ' Take 
 care, I expect he's right. He passed his examination very well in 
 Logic, you know.' For there is an undefined panic among them 
 at the very idea of Logic as it seems to me, at least : and, failing 
 this, as a last resource I can always call any of their assertions 'A 
 flagrant instance of violation of the principles of constructive, con- 
 junctive, hypothetical syllogisms,' and this produces a dead 
 silence at once. 
 
 PRINTED BY 
 
 6POTTISWOODE AND CO., NBW-STEKKT HyUAHK 
 LONDON
 
 1888. 
 
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 16 A Selection of Educational Works. 
 
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 SWINBURNE'S PICTURE LOGIC. 
 
 FOURTH EDITION. 
 
 'It seemed to me that you 
 had put the matter in an amusing 
 form, and had not at all destroyed 
 the accuracy of your logical 
 teaching hy mixing it with 
 
 humour When any suitable 
 
 opportunity occurs I shall always 
 be happy to recommend your 
 Picture Logic as an amusing and, 
 as far as I have observed, correct 
 introduction to the study.' 
 
 Prof. JKVONS (Jevons' Logic). 
 
 'The Author of this clever 
 and really humorous book has 
 
 achieved a distinct novelty 
 
 It will most materially assist the 
 struggling learners who have 
 been left in the dark by technical 
 
 text-books The dullest of 
 
 undergraduates will find enough 
 here to help him triumphantly 
 to floor any paper.' 
 
 The WORLD. 
 
 'I again recommended your 
 Picture Logic to my class last 
 winter.' 
 
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 'Such persons may, having 
 mastered Mr. SWINBURNE'S dis- 
 sertations, gain by them more 
 than they had reason to expect.' 
 ATHENAEUM. 
 
 ' The rules laid down in the 
 text are generally sound.' 
 
 DAILY NEWS. 
 
 ' Like such imperishable 
 works as " Philosophy in Sport 
 made Science in Earnest," Picture 
 Logic leads the reader pleasingly 
 from familiar subjects upon 
 which he has not much reflected 
 to truths, the existence, appre- 
 ciation, and application of which 
 never once entered his thoughts.' 
 MORNING POST. 
 
 London, LONGMANS & CO.
 
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