Picture logic : an attempt to popularise the science of reasoning ... online

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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,