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Title: Picture logic
An attempt to popularise the science of reasoning by the combination of humorous pictures with examples of reasoning taken from daily life
Author: Alfred James Swinburne
Release date: October 13, 2026 [eBook #79775]
Language: English
Original publication: London: Longmans, Green, and Co., 1887
Other information and formats: www.gutenberg.org/ebooks/79775
Credits: deaurider and the Online Distributed Proofreading Team at https://www.pgdp.net (This book was produced from images made available by the HathiTrust Digital Library.)
*** START OF THE PROJECT GUTENBERG EBOOK PICTURE LOGIC ***
[Illustration:
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.
]
PICTURE LOGIC
AN ATTEMPT TO POPULARISE THE SCIENCE OF
REASONING BY THE COMBINATION OF HUMOROUS PICTURES WITH
EXAMPLES OF REASONING TAKEN FROM DAILY LIFE
BY
ALFRED JAMES SWINBURNE, B.A.
QUEEN’S COLLEGE, OXFORD
[Illustration: The Lion of Human Understanding in the tangle of Logical
Knots assisted by the Mouse of Illustration]
WITH ORIGINAL ILLUSTRATIONS FROM DRAWINGS BY THE
AUTHOR ENGRAVED ON WOOD BY G. PEARSON
_FIFTH EDITION_
LONDON
LONGMANS, GREEN, AND CO.
AND NEW YORK: 15 EAST 16th STREET
1887
_All rights reserved_
INTRODUCTION.
It was at the beginning of a certain Long Vacation when my father sent
for me and delivered himself of the following 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
present 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 obscurity, 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 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 college. The result was that I
was ordered to select a tutor for two months in the Long Vacation and
pass my moderations 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 I 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 considerably 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 that never for a moment entered my head. ‘Old
Prac’ (as we called him afterwards) had such a smooth, comfortable way
of settling any difficulties I proposed--so reassuring 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 answered
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.
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 RECONCILIATION, AND ALSO HOW LOGIC IS MORE OF A 38
SCIENCE THAN AN ART
VI. LOGIC THE SCIENCE OF SCIENCES AND ART OF ARTS 43
VII. THE RELATION OF LOGIC TO LANGUAGE 48
VIII. ALL 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 PREDICABLES 79
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 155
APPENDIX B 162
APPENDIX C 163
A LIST OF USEFUL FACTS IN LOGIC 177
LIST OF ILLUSTRATIONS.
DESTRAWNEY OVERCOMES THE SPHINX _Frontispiece_
‘LOGIC’
NONPLUSSED 2
SCIENCE PRESERVED IN JARS 9
SUPERSTITION 11
THE BEGINNING OF SCIENCE 16
THE BEGINNING OF ART 17
ART 17
THE LOGICAL SAUSAGE MACHINE 35
TROJA FUIT 41
SINDBAD AND THE SAILOR 45
LOGIC PAYS 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 WISE’ 78
THE ESSENCE OF MAN 86
THE BIPED ANIMAL WHOSE SOLE METAL IS 95
MEMORY
THE FIGHT OF PROPOSITIONS 110
DEATH OF THE UNIVERSAL 111
THE SYLLOGISTIC ALP 114
THE FRONT OF A COLLAR 118
MOOD-HUNTING 126
CHAPTER I.
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 comprehend,
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 understand; 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
remembering the force of the expressions “long swim” or “unpleasant
cruise.” The neat and concise phrases you meet with in your treatises
on Logic are deceptive--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
instances that you do not understand as you read your treatises side by
side with my attempts at explanation.’
[Illustration: Nonplussed.]
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 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 complicated, and
letters in the ‘Field’ about the breeding 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 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, objects 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 attributes, 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
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 peculiarities; particular facts you may call them or phenomena
(from the Greek φαίνομαι, I appear or show myself), and the noting or
acceptation of these particular facts by the senses is knowledge. The
lion 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 something 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
peculiarities 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, attributes or phenomena not yet discovered or known
to exist. The man who first applied steam to locomotion 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.
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 universal
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”;[1] of a universal, “all” or “no.”’
I could not help thinking how learned I 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 knowledge, and the results attained to are called
generalisations, 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. ‘Remember 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 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 seeming 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 something
over and over again--about knowledge and triumphs. ‘Rather 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 particulars? to detect similarities and form universal
propositions, or uniformities, or laws, and lay by these laws in jars
for future use? to introduce neatness and order in that tangled medley
before you, that bewildering chaos of confusion?’ ‘Most certainly I
do, but I don’t quite see how you mean. I don’t pretend to be clever,
though.’
[Illustration: SCIENCE PRESERVED IN JARS.]
‘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 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 comprehensive 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 ornament; 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 I 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 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. ‘O please, Mr. Science,’
said she, ‘I’ve got a law at home that “all comets are signs of war,”
and as mother 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 particulars 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.
[Illustration: Superstition.]
‘You see those two hills beyond,’ he said, turning 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 chemistry and human conduct, and
they’re very difficult to get at. And as one of the chief advantages of
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.’
‘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 backward there.’
‘Or supposing,’ said I, ‘two men always visited your house together,
and at the sight of them the dog always exploded into barking, unless
you could 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.’
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 Encyclopædia 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, 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 observation 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 conditions
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 particular 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 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.
[Illustration: The Beginning of Science.]
‘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.
‘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 distinct 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 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.”’
[Illustration]
So he draws up these common elements in the form of laws, and teaches
them to his boy. ‘All correct sunsets have such and such rays,’ &c.
And the boy grows up, and carries out in a particular instance the
laws his father drew from particular instances, by painting a picture
of a particular sunset which obeys the laws his father drew; and if it
obeys all of them, it is said to be a very good painting 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; ‘the above
is obviously production.’
[Illustration: The Beginning of Art.]
‘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 criticism. 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 swimming are the particular movements
of the limbs by this or that swimmer. These are observed by the man of
science--their uniformities or common elements 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 particular sunsets you see in fig. i. and fig. iii. are
the beginning and the end.’
All of a sudden Dyver clutched his pencil convulsively, 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 leaving 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 the
figure, and Mr. Practical was highly pleased with it; and the more so
because he told us universal knowledge is always regarded as something
_higher_ than particular--we ‘ascend’ to it and _de_duce from it--and
we talk of particulars _de_pending upon or hanging from laws or
conditions.
[Illustration]
CHAPTER III.
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 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 unexpressed 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 indigestible; this is
cucumber; therefore it is indigestible,” a thought unexpressed also. Or
you may think, “All young ladies are charming companions; my neighbour
is a young lady; therefore my neighbour 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 remarks 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 ἕρκος ὁδόντων. 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
and call these laws the principles or conditions upon which correct
remarks or inferences depend--precisely as the botanist did 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.
‘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 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 look of wonder steals slowly over every face.
The man proceeds to an inference. “Balloons is the most riskiest
travellin’, and I’m a goin’ by the Underground 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 cleverness 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.’
‘Could 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, 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_
adulterated, 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 adulterated.” What should I gain by such information? Should I
not, in a fit of anger at his cold, dull certainties, 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
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 inconsistent.
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
upon the oarsman if we blame his rowing, when we gave him a rotten
oar to start with, and he 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 logician, “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. Your remark, “All
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 confidence 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 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 conditions 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 OF 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 start with certain
plants and trees, and in Logic we start with “correct and incorrect
thoughts.” If anyone 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, I 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 answer for its truth, whereas if he said
“Comets are not comets,” I should declare the thought to be incorrect.
Of course the impression upon the senses and the decision of the reason
of our fellow-men is considered 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 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 versâ_, 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 things that nobody could understand,--and had
we really 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 proposition 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, hippopotamus, 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 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 all 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 pays exclusive
attention to the form, they are all propositions 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 logician 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 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 produces 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.’
‘I 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 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.
[Illustration: THE LOGICAL SAUSAGE MACHINE.]
On the left of the machine sat an old Professor, and on the right
of the machine there was an indescribable 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 following 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 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 painfully cramped for want of room.
‘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 of surprise at
seeing me. ‘Do you know the old boy sitting there says, “One of the
advantages, or practical 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 conducted me to the
Professor’s workshop, where I 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.
[Illustration]
CHAPTER V.
THE RECONCILIATION, AND ALSO HOW LOGIC IS MORE OF A SCIENCE THAN AN ART.
‘We can now proceed to reconcile the various definitions of Logic,’
resumed Mr. Practical. ‘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 equivalent 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 concerned 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
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?’ 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.’
‘I begin now to realise the meaning of the expressions. “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. Roughly 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 contradiction
or inconsistency in almost all cases as quickly as the Logician, though
he may not be able to say 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
application 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 wandering 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 basket on her
lap, swaying slowly from side to side, and took no notice of me. 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, “O, then! we 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 a’ready?
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 may be 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--practical 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.
[Illustration:]
CHAPTER VI.
LOGIC THE SCIENCE OF SCIENCES AND ART OF ARTS.
‘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 particulars,
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 universal
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 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; therefore 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 consciously, 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.
Thought 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 turning into mathematics; ‘but still I
don’t understand yet.’
[Illustration: SINDBAD THE SAILOR.]
‘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
specimens. Take botany. Thought lingers by a stream and gathers rushes.
“Rushes are light,” he remarks, 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 contradiction.”
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,
“Yonder’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 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
insensible, 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 contradiction 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 charge. Or,
again, when she 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 5_l._ to a friend, casting in
his teeth at least 100_l._ 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 95_l._ 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 well to aid the
memory as much as possible by understanding the derivation and meaning
of the names you meet with.’
CHAPTER VII.
THE RELATION OF 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
primarily connected with language, and so through errors arising from
the inability of language to express 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 further. Dyver retired to his corner and I to mine, and on the
following day we produced a couple of rough sketches.
This was Dyver’s relation of logic to language.
[Illustration: 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! But there is no help for it.
Alas! what mistakes and confusions will arise!’
And this was mine.
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
productions 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 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 daughter 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 been led into a _mésalliance_, and in the same
way had Logic been conversant with _several_ languages, and become
acquainted with their powers of misleading 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.
[Illustration: Logic in Trouble.]
CHAPTER VIII.
ALL THOUGHT IS COMPARISON.
‘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 language. 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 inference or syllogism are the results of comparison, we 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 “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 sensations 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, then, and under one or other of these
heads came 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 propositions 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 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.
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.
5. _Definition_, or propositions expressing the connotation of a term.
6. _Division_, or propositions expressing the denotation of a term.
III. _The inference or syllogism._*
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.
* 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.’
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 propositions; 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 content yourselves with these expressions, as
the question as to “What is the meaning of thing?” is beyond the sphere
of Logic.’
Dyver here took occasion to observe that he knew that individual meant
something incapable of further division, _i.e._ a simple whole; and
that attributes 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 ‘quality’ meant
the same as ‘individual’ and ‘attribute.’
‘Well, then, a term expresses either an individual 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” expresses a group of
soldiers, but you can’t call each soldier a “Black Watch;” whereas
“horse” expresses 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 attributes, it
is called either abstract (3rd finger) or attributive (4th finger), the
abstract term being a substantive, the attributive an adjective.’
‘Are there not several other kinds of terms?’ asked Dyver.
‘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 simplicity of our scheme of Logic.’
[Illustration: The Logical Hand.
1. Socrates.
2. The Black Watch.
3. A horse.
4. Whiteness.
5. White.
N.B.--The second finger the largest, and the common term the most
important.
]
CHAPTER X.
CONNOTATION AND DENOTATION.
‘Of the five terms, the common term is that with which we shall have
most to do. Let us 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. You
speak of trees, men, stones, birds; and your friend understands you to
mean by them four distinct things. They all have attributes, and if
those attributes 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, 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 defined 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 connotes
attributes and denotes individuals, and the five terms are thus said to
be connotative or denotative.
[Illustration: Denotative and Connotative Hand.]
‘The singular and collective have only denotation; the abstract and
attributive only connotation; and the common terms, both. For the
singular term is a mere mark arbitrarily imposed upon an individual,
_not_ in virtue of the possession of certain attributes, 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 manifested 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 attributes, 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 connotation,’ 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 John stoutly
refuses, and why? because the names “mare” and “cow” are common terms
awarded to certain animals in virtue of their possession 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 individuals,
while singular terms are only denotative.
‘You will see how the connotation of a common term increases as its
denotation decreases, and _vice versâ_; for the more attributes
required as a qualification 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 denotation 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 demand are now rejected as lacking the qualities implied
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. 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 advertisement. 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 thoughtlessness, 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_ the names are taken. The word “paper” (or
papyrus) originally meant “writing materials made of byblus;” it
gradually came to mean “writing material made of rags, straw, or
anything.” The denotation has thus grown by the admission of several
other kinds of writing material; and the connotation 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 attributes of “writing material” is admitted. On the
other hand, “physician” originally meant φυσικὸς, “a man who studied
nature.” It gradually came to mean “a man who studied nature in respect
of healing 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 connotation 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 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 connotation and denotation; for you have attributes, and
you’re a connotative term.’ ‘Alas! what mean these vile names?’ ‘Come
with me,’ said I, laughing, ‘and we will find your class.’ 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 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 Rectilineal 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 entrance.
The interior was divided into three compartments. 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!’
CHAPTER XI.
PROPOSITIONS.
‘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
prædĭco means “to assert.”’
‘Oughtn’t the (i) to be long?’ asked Dyver, ‘and doesn’t it come from
_præ_ and _dico_, to foretell.’
‘No! there are two words; prædīco, “to say before” (in the sense of
time), and prædĭco, “to say before” (in the sense of place, _i.e._
publicly); and prædĭco is equivalent to κατηγορέω, and means “to
assert, or declare;” hence predicate.
‘Take an instance. “The sun is bright.” Sun, subject--is,
copula--bright, predicate.’
‘Then in “Fair was her form,”’ said I; ‘fair, subject--was, copula--her
form, predicate?’
‘No! remember the questions you are to ask 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 together 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._ | _Copula._ | _Predicate._
The sun | is | bright.
Fires | are | burning.
The ‘Faraday’ | is not | a-ship-that-will-convey-
| | the-telegraph-cable.
The-sound-of-the- | |
waves-on-the-shore | is | 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 ancients 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 mistakes 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 proposition. Now, may the
words “possibly, &c.,” be joined to the copula? No. All words of this
description 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 carriages. It is unreasonable to suppose
that they are to be allowed to travel on the coupling chain--however
full the carriages may be they must squeeze in somewhere, or not go at
all.
[Illustration: The Great Logic Branch.]
‘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 copulæ affirm or deny
the predicate of the subject. We may say,
“All or no Cretans are liars,”
or
“Some Cretans are or are not 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. 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” O
A and I from AffIrmo, 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.’
CHAPTER XII.
DISTRIBUTION OF 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
full extent are said to be “distributed.” In the proposition, “All
foxes are sly” the subject is distributed, _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.
‘To apply this distinction to our five terms, we find singular and
collective terms are always distributed (_e.g._, “Socrates is ill,”
where “All of Socrates” is meant) and abstract and attributives may be
treated as common terms, and for common terms in propositions 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 proposition is “all”
or “no,” and “all” or “no” attached to the subject of a proposition
proves 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.
‘(2) All negatives distribute their predicate; for in every negative
proposition we may suppose ourselves 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
becomes “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.
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 proposition;
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” referred to do not belong
to that class.’
‘I can’t quite see how the particular negative distributes 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 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 distribute
both its subject and predicate; I (particular affirmative) obeys
neither and distributes neither; O (particular negative) must obey (2)
and distribute its predicate.
‘Remember this by the word A s E b I n O p (A subject, E both, I
neither, O predicate).’
[Illustration: ‘A Word to the Wise.’]
CHAPTER XIII.
HEADS OF PREDICABLES.
‘The 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.
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 differentia 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
attributes “made of apple, made of suet, &c.,” are the differentiæ; for
they are that which makes one class of dumpling differ from another,
and part of the connotation 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 indigestion after them.’
‘True; but if “apple dumplings” are so made that they cease to be
entitled to the name, you can’t 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 dumplings
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 proposition_. 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)
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
connotation varies according to the point of view you choose to take.
‘1. The genus answers the question “What?” (τί; quid?). The species,
the question “What kind?” (ποῖον τί; 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,
irrational, 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
which never stands as a genus (the summum genus and the infima
species). Man is a species of animal, 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 regarded as an infima species.
SUBSTANCE (or thing)
|
---------------------------------------------
| |
Corporeal Incorporeal substance
substance = BODY (as air)
|
---------------------------------------------
| |
Animate Inanimate body
body = LIVING BEING (stones)
|
---------------------------------------------
| |
Sensible Insensible living being
living being = ANIMAL (plants)
|
---------------------------------------------
| |
Rational Irrational animal
animal = MAN (brute creation)
|
---------------------------------------------
| |
Socrates Plato Others
‘Suppose you are being cross-examined thus:--“You speak of Plato.
What is Plato?” “A man.” “What is a man?” “A rational animal”
(genus “animal;” differentia, “rational”). “What then 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 explanation or unfolding into simpler elements. It’s a ‘summum
genus,’ and I can’t answer any more.”
‘2. The connotation varies according to the point of view taken. We
have already shown how connotation (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 attributes thus selected
are not _all_ the attributes possessed by the individuals (for it
would be a hopeless task to enumerate them all), but only a few of
them. Nevertheless, 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 prominent. 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.
‘According to all these “his” 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) beast.’”
‘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. Real (ampliative or accidental) propositions tell you
something _more_ than you necessarily knew, if you knew the meaning of
the 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 abiding 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 may be divorced.’
[Illustration: THE ESSENCE OF MAN.]
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 or
substance,” the summum genus, can’t be defined; and so sweet, bitter,
harsh, &c. “What is love?” asks your unsusceptible 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 understand 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. (_b_) 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 depends 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 kingdoms 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
“important-for-the-time-being” attributes are the connotation, and the
prominence depends upon the position 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 differentiam._ If you are asked
to define words in examination remember this. Always make your genus,
find your differentia, add the two, and you get genus + differentia
= species = whole essence, connotation, intension, 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?”’
‘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 something
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?’
‘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?’
‘Very well indeed.’ You see now how _definition_ gives the genus +
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
differentiæ 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 properties;
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 probable native of the
country through which you are passing. You ask, “Is this good country
here?” 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 microscope with roots in your pockets, he says, “Beautiful flowers
about;” or lastly, you may be a weary traveller, and he will reply,
“Poor accommodation, 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 prominent
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).
(_b_) It must be _adequate_ (_i.e._ sufficient to distinguish the
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 hexapod.”
(_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 metaphors are. So Logic does not admit them into
definitions. Remember these rules by the examples of their
violation. “Man is a biped;” “Man is an animal;” “the soul;”
“Metal;” “Memory,” thus:--
[Illustration: The biped animal whose sole metal is memory]
CHAPTER XV.
DIVISION.
‘Division gives the denotation of a term as definition gives the
connotation. As there were five heads under which to group all you need
know about definition, so there are four heads here. Only understand
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 division
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.’
‘What are abstract terms?’ asked Dyver.
‘We have seen that the whole world around us 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 individual
(con-cresco)[2] is said to be “concrete”; but viewed apart from its
individual it is called “abstract” (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 totum divisum, the membra
dividentia, and the fundamentum 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 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
fundamentum divisionis?” Take as F. D. (fundamentum divisionis) “manner
of frame,” and your M. D. (membra 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 differentia, 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.
‘As there are as many definitions, so there are as 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 differentiæ. 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 (διχα τέμνω) 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-Norman, 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
|
+------------+------------+
| | |
Corns from Corns from Corns from
nature bruises shoeing,
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
|
+------+------+
| |
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.
(_b_) 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.
(_d_) There must be only one F. D.
‘(_b_) 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 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--
[Sidenote: (See pp. 67-69. ‘The
lost scalene
triangle.’)]
FIGURE
|
+-------------------+-------------------+
| |
Curvilineal Rectilineal
|
+------------------+----------------+
| | |
Triangle Quadrilateral Polygon
(three-sided) (or four-sided) (or more than
| four-sided)
+--------------------+--------------------+
| | |
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 “occupation,” “nation,” “marriage,” and
“manner of speech.” Remember this:--
‘“Your[3] 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. together = T. D.).
(4) No cross division (_i.e._ one F. D.).
CHAPTER 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. Setting aside
inductive Logic as beyond our limits, we subdivide deductive inference
into immediate and mediate. Immediate--where we deduce one proposition
_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
|
+-----------------+------------------+
| |
Immediate Mediate
(opposition, conversion, (the syllogism).
permutation)
‘To begin with immediate inference. (i) _Opposition_, where the truth
or falsity of one proposition is inferred directly from the truth or
falsity of another. The four forms _A_ _E_ _I_ _O_ are opposed in
various ways, and this you will remember by this figure:--
[Illustration]
For the opposition of
_A_ and _E_ is called contrary opposition
_I_ and _O_ is called sub-contrary opposition
_A_ and _I_ or _E_ and _O_ is called subaltern opposition
_A_ and _O_ or _E_ and _I_ is called contradictory opposition.
The only case in which we can always infer the truth or falsity of
one proposition from another is contradictory opposition, and you
need remember nothing more than the names of the rest. To prove an
adversary’s statement false, use contradictory opposition. 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-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 _I_ and _O_ (“Some men are
maniacs”--“Some men are not maniacs”), and still more between _A_ and
_I_ and _E_ and _O_ (“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 animals 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 takes place it is called “_simple conversion_;”
where a change takes place it is called “_conversio per accidens_.”
_A_ propositions are converted per accidens; _E_ simply; _I_ simply;
_O_ 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 coextensive. 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_ _I_ _O_, 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_ _O_). If you want it converted.
_Subject._ _Predicate._
All--=fixed-stars=--are--=self-luminous=. (A prop. per accidens.)
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.
“Some of the most valuable books are seldom read.”
Logical form:--
Some-=(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=. (O, not at all.)
For it does not follow that “Some culpable things are not mistakes;”
nevertheless if you wish to convert an _O_, 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-jest-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.
‘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_ proposition
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” becomes 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 are 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:--
[Illustration]
‘Where it is plain that no part of the included class man can be
outside the class mortals: ∴ No men are immortal.
[Illustration]
‘No cowards are good soldiers; they are two separate classes, and ∴ All
cowards are not good (_i.e._ bad) soldiers.
[Illustration]
‘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 “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
investments;” 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 investments,” 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! Hevery kind of hoposition ’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.
[Illustration: 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 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 applauded loudly.
[Illustration: 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 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 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 privative 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.’
CHAPTER 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 inference.”
‘Now there are three things to remember about the syllogism.
(_A_) 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 depend is that “things
which are equal to the same are 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 together,
and we employed the help of a third term. You have 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:--
[Illustration: The Syllogistic Alp.]
Here we are asked to establish a comparison between “Socrates” and
“mortal.” Unable to see 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 minor 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, containing amongst them three terms:
minor, major, and middle. Out of the propositions A E I O 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.
‘That we shall find out by the application of 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.’
‘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 the major term[4], B the
middle, and C the minor. Thus:--
A. All animals can feel } { All B is A (where B = animals,
A. All cats are animals } = (i.) { All C is B where C = cats,
A. Therefore all cats } { ∴ All C is A where A = things
can feel } that feel.)
E. No angels are human } { No A is B (where B = human,
A. All women are human } = (ii.) { All C is B where C = women,
E. Therefore no women } { ∴ No C is A where A = angels.)
are angels }
Now do you 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 “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 arrangements of propositions in syllogisms. But there
is yet another difference.’
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:--
Fig. I. Fig. III.
A. All B is A A. All B is A
└────┐ │
A. All C is B A. All B is C
A. ∴ All C is A A. ∴ All C is A
Fig. II. Fig. IV.
A. All A is B A. All A is B
│ ┌────┘
A. All C is B A. All B is C
A. ∴ All C is A A. ∴ All C is A
We know there can be only four figures; the question is, how many moods
can we have in those four figures. The four figures may be remembered
by the front of a collar.*
* See illustration. The figures are thus easily remembered; ╲║╱, these
lines being taken from the position of the middle term as marked above.
For further remarks upon the figures see Appendix A (i.).
[Illustration: The Front of a Collar.]
As to moods, it is clear that out of the four forms or propositions A
E I O a large number of different triplets can be made. We 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 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 combination of the
propositions A E I O 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
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 dissolution of his marriage
on the ground that his wife was married to a crocodile; for
“All crocodiles are animals,
All men are animals,
Therefore all men are crocodiles.”’
‘In this shape it certainly sounds wrong,’ said I.
‘Of course; and there are many other of the possible 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 certain 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 secondly for another part of itself; _e.g._
WOMEN
+-----+-------+------+
|COOKS| |QUEENS|
+-----+-------+------+
This whole figure represents the class “women;” parts of this class are
“cooks” and “queens.” Hence:--
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_ elephants,” 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 O, O,
which violates (3), or I, I, which violates (1), or I, O, which will be
found to violate (5). (_For further explanation see Appendix A (ii.)_)
‘(5) _If either premiss be negative, the conclusion must be negative._
For if, after taking our middle 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 must be
particular._ I will prove this rule afterwards. (_For further
explanation see Appendix A (ii.)_)
‘(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 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.” (_For further
explanation see Appendix A (ii.)_)
‘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:--
Distribuas medium, nec quartus terminus adsit, (= Rules 1 and 2.)
Utraque nec præmissa negans, nec particularis; (= Rules 3 and 4.)
Sectetur partem conclusio deteriorem, (= Rules 5 and 6.)
Et non distribuat, _nisi cum præmissa_, negetve.[5] (= Rules 7 and 8.)
(= unless when the premiss does so.)
‘How do you translate the third line?’ asked Dyver.
‘“Let the conclusion follow the weaker part.” The negative is thought
“weaker” than the affirmative, and the particular than the universal.
Thus this line conveys rules (5) and (6). And before proceeding 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.’
CHAPTER 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. ∴ All C is A
Violates no rule. Call it “bArbArA.”
Fig. ii.
All A is B
│
All C is B
∴ All C is A
Violates “Distribuas medium”--for A props. do not distribute their
predicate. Remember 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 præmissa.” C is distributed in
conclusion but not in premiss (ASEBINOP). Call this “illicit process
of the minor.”
Fig. iv.
All A is B
┌────┘
All B is C
∴ All C is A
Illicit process of the minor, as in fig. iii. Remember ASEBINOP.
N.B.--For ASEBINOP refer back to the “Distribution of terms in
propositions,” pages 75-78.
Take E A E in all four figures:--
Fig. i.
E. No B is A
└─────┐
A. All C is B
E. ∴ No C is A
[Violates no rule. Call it “cElArEnt.”]
Fig. ii.
No A is B
│
All C is B
∴ No C is A
[Violates no rule. Call it “cEsArE.”]
Fig. iii.
E. No B is A
│
A. All B is C
E. ∴ No C is A
[Illicit process of the minor. From _part_ of C in premiss we argue
to _whole_ of C in conclusion.]
Fig. iv.
No A is B
┌───┘
All B is C
∴ No C is A
[Illicit process of the minor.]
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
following valid ones:--
Barbara, Celarent, Darii, Ferioque, _prioris_: (_i.e._ in fig. i.)
Cesare, Camestres, Festino, Baroko, _secundæ_: (_i.e._ in fig. ii.)
_Tertia_, Darapti, Disamis, Datisi, Felapton (_i.e._ in fig. iii.)
Bokardo, Ferison, habet: _quarta_ 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.’
‘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 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 distributed 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 contained 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 animals, 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 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; Dyver 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 temptations.’ 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 ‘Dīs-trĭbŭ|-ās mĕdĭ|-um,
nēc|,’ &c., with painful stress on the scanning, without any effect,
however, upon the monster, until he arrived at the line ‘Et non|
dīstrĭbŭ|āt nisi| cūm prǣ|,’ &c., when the form uttered 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’ 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, ‘I must be right--“all lotions are medicine,” and “all potions are
medicine;” so lotions and potions are the same; and in swallowing my
lotion to cure this indigestion, I 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.
[Illustration: MOOD-HUNTING.]
CHAPTER XIX.
SYLLOGISM--CANON OF FIRST FIGURE--REDUCTION.
‘I can’t understand how you call a syllogism a universal 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
original form. These shortened forms are called “Enthymemes” (from ἐν
and θυμός, 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 mortal, 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,” ἐν θυμοῖς) go to the most illiterate costermonger and say,
“All costermongers are scoundrels, and you are a costermonger,” and
observe the result. We now pass to
‘(C). _The canon of the first figure._ A glance 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 premiss must be affirmative.
‘There are also “canons” of the other figures, (_Appendix A (iii.)_)
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 with 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 CESARE (_i.e._ mood E A E in fig. ii.).
E. No A is B
A. All C is B
E. ∴ No C is A
We want to bring this mood in fig. ii. to a mood in fig. i., _i.e._ we
want to make the middle term come as subject, predicate, instead of
predicate, predicate (for herein consists the difference of figure).
Remember conversion is our great instrument 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
E. No B is A
└─────┐
A. All C is B
E. ∴ No C is A
So the mood E A E in the second figure becomes the mood E A E in the
first figure, or Cesare 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 O
in fig. iv.):--
E. No A is B
┌───┘
A. All B is C
O. ∴ Some C is not A
We want the middle term (B), subject, predicate, instead of predicate,
subject. We must change both premisses. By simple conversion we make
“No B is A,” but we must not convert an A proposition simply, we must
employ conversion per accidens, and it becomes “Some C is B.” We now
have--
E. No B is A
└──────┐
I. Some C is B
O. ∴ Some C is not A
Here the mood has changed as well as the figure, and FESAPO (or E A O
of the fourth) becomes FERIO (or E I O of the first). Apply the canon
and you will find it is obeyed.[6]
‘Sometimes you have to change the premisses when you do so _remember
you change your major and minor terms_. Take A E E of fig. ii.
(Camestres).
A. All A is B No C is B No B is C ...E
│ ╳ │ └─────┐
E. No C is B All A is B { but E converts } All A is B ...A
{ simply, hence:-- }
E. ∴ No C is A ∴ No C is A ∴ No A is C ...E
∴ No C is A (by
simple conversion.)
Apply your canon and you will find it obeyed.
‘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 “simple conversion,” and “p” per accidens in the
process of reduction. “M” (mutation) means change the premisses, and
“k” means “per impossibile.” All these facts might have been gathered
from observation and experiment, but it is a help to memory to learn
them thus as well.’
‘What does “per impossibile” mean? asked Dyver.’
‘Reduction, as above exhibited, is called ostensive or simple
reduction, but there are two moods, BAROKO (second figure) and BOKARDO
(third figure), which are beyond the power of simple reduction. 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 remember
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 BAROKO (A O O, fig.
ii.).
A. All bantams are fowls,
O. Some birds are not fowls,
O. ∴ Some birds are not bantams.
If I declared this conclusion to be untrue, 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 contradictory, “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_ (O A O, fig. iii.). Only here you substitute
your new truth for the original major premiss:--
O. Some policemen are not fools,
A. All policemen are in the Queen’s service,
O. ∴ Some of those who are in the Queen’s service are not fools.
‘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.’
CHAPTER XX.
TRAINS OF REASONING--SORITES.
‘Syllogisms may be “heaped” one above another (σῶρος, a heap) in a
train of reasoning, called Sorites. _See Appendix B._
Thus:--
All A is B,
All B is C,
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 premiss 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.
‘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 C is D,
All B is C,
All 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.
CHAPTER XXI.
HYPOTHETICAL SYLLOGISMS.
‘As yet 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_” (ὑπὸ τίθημι = 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 propositions 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 “conjunctive,” _e.g._, “If the weather is rainy
my sponge is 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).
|
+-----+-------+
| |
Conjunctive Disjunctive.
‘Now syllogisms are composed of these hypothetical propositions, and so
borrow their names. We have conjunctive and disjunctive hypothetical
syllogisms, _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 admit of two valid
conclusions out of the four possible ones you get by affirming and
denying the antecedent and consequent.
(_a_) If the weather is rainy, my sponge is damp.
The weather _is_ rainy,
∴ my sponge is damp.
Affirming the antecedent for a minor premiss.
(_b_) If the weather is rainy, my sponge is damp.
The weather is _not_ rainy.
No conclusion.
Denying the antecedent for a minor premiss.’
‘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 antecedent called “constructive,” and
where you deny the consequent called “destructive.”
II. _Disjunctive Hypothetical Syllogisms_ admit of four conclusions,
for you may affirm or deny antecedent and consequent.
_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 } constructive { Instance: “Science.”
(ii.) The complex } dilemma { 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 cultivated; and if science
invigorates the faculties, it should be cultivated;
But science does one, or the other;
Therefore science should be cultivated.
‘(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 Scripture 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
dilemma 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 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
knowledge; 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; therefore
examinations must be 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.
CHAPTER XXII.
PROBABLE REASONING.
‘Hitherto 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 influence 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 prædicate.
‘(i.) _Self-infirmative inference_ is where each fresh fact weakens the
conclusion, so that the more premisses you have the less likely is it
that the conclusion 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.
‘“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.”
‘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 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.
If 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 yourselves in the newspapers. This evidence is also called
“Self-corroborative,” from “robur,” strength.
‘And here I may mention an exception to the rule--“Ex duobus
particularibus nihil sequitur,” or “two particular premisses prove
nothing” (Rule 4 of the Syllogistic Rules); for there is one case in
the third figure where two particular premisses do prove something;
_e.g._,
“Most pins are good;
Most pins are cheap.
∴ Some cheap things are good.”’
CHAPTER 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. (_see Appendix A (ii)._)
Illicit minor.
Undistributed middle.
Petitio principii (begging the question).
III. _Ignoratio elenchi, or irrelevancy._
Argumentum ad hominem...(“early rising”).
Argumentum ad populum...(“weeping wife”).
Argumentum ad baculum...(“religious persecution”).
IV. _Ambiguity of language._
Ambiguous (analogous, equivocal, &c.) words...(“box, muzzle, &c.”).
Composition and division...(“3 and 2--odd and even”).
Fallaciæ accidentis (2)...(“mad dog’s bite”).
Paronymous terms...(“drunk once, drunk ever”).
Fallacia plurium...(“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 fraction 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 difficulties
and errors of the matter.” (See “Form and Matter of Thought” p. 26 and
p. 29). 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 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 statements 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 arguments 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 hominem 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 because its holder “once thought differently,” in other 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
we 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.’
‘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 serpent was the more
ungrateful animal on the whole. Appeals were made to various animals
(old cows, hunters, &c.) without any abatement of the hot discussion,
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 instances. 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 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 connection
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 fallaciæ accidentis are two, (1) the argument “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
circumstances, 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. According 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 fallacy of asking two
questions in one. For instance, take the question of a barrister
examining a prisoner: “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?” meaning 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 Henry shall depose.” Where you do not know whether it is the duke
who shall depose Henry, or Henry the duke.
‘The fallacy of accent is a mere matter of emphasis. 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-causâ” (as to say, “A comet shone, therefore there
will be war”), where you take for a cause that which is not really
so;[7] and the fallacy of the consequent (fallacia consequentis or
“non-sequitur”), _e.g._, “he is an animal; _ergo_ he is a man.”
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 properties of a
thing.
Fig. II. is most useful for the discovery or proof of distinctions
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
prædicate (_i.e._ prædicate 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 O only
(_i.e._ particulars only).[8]
(4) Fig. IV. proves E, I, O, 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 contradictory opposition (see p.
104).
(ii.) There are three rules (4), (6), and (8), which require further
explanations:--
Rule (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. | Fig. ii. | Fig. iii. | Fig. iv.
| | |
I. Some B is A | Some A is B | Some B is A | Some A is B
└────┐ | │ | │ | ┌────┘
I. Some C is B | Some C is B | Some B is C | Some B is C
| | |
No conclusion. | No conclusion. | No conclusion. | No conclusion.
For by ASEBINOP[9] 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 | Some A is not B | Some B is not A | Some A is not B
└────────┐ | │ | │ | ┌────────┘
O. Some C is not B | Some C is not B | Some B is not C | Some B is not C
| | |
No conclusion. | No conclusion. | No conclusion. | No conclusion.
In all these there are two negative premisses, which give no conclusion
(p. 130).
I. Some B is A | Some A is B | Some B is A | Some A is B
└────────┐ | │ | │ | ┌───┘
O. Some C is not B | Some C is not B | Some B is not C | Some B is not C
| | |
No conclusion. | No conclusion. | No conclusion. | 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_.’
By ASEBINOP we know all four to be cases of Illicit Major (p. 124-5),
_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.
O. Some B is not A | Some A is not B | Some B is not A | Some A is not B
└────┐ | │ | │ | ┌────────┘
I. Some C is B | Some C is B | Some B is C | Some B is C
| | |
No conclusion. | No conclusion. | No conclusion. | 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 cannot 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 (AI), (AO), (IA), (OA), (EI), (EO), (IE), (OE). Of these (EO)
and (OE) 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.
Fig. i. | Fig. ii. | Fig. iii. | Fig. iv.
A. All B is A | All A is B | All B is A | All A is B
└─────┐ | │ | │ | ┌───┘
I. Some C is B | Some C is B | Some B is C | 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 explained below); and it cannot be A, or in
both figures you would have Illicit Minor.
Fig. i. | Fig. ii. | Fig. iii. | Fig. iv.
A. All B is A | All A is B | All B is A | All A is B
└─────────┐ | │ | │ | ┌───┘
O. Some C is not B | Some C is not B | Some B is not C | Some B is 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 | Some A is B | Some B is A | Some A is B
└───┐ | │ | │ | ┌─────┘
A. All C is B | All C is B | All B is C | 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 | Some A is not B | Some B is not A | Some A is not B
└───┐ | │ | │ | ┌─────────┘
A. All C is B | All C is B | All B is C | 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 | No A is B | No B is A | No A is B
└─────┐ | │ | │ | ┌──┘
I. Some C is B | Some C is B | Some B is C | 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).
I. Some B is A | Some A is B | Some B is A | Some A is B
└──┐ | │ | │ | ┌────┘
E. No C is B | No C is B | No B is C | 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).
* * * * *
Rule (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 conclusion 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 prædicate) 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):--
} { Fig. i.
‘Fishes fly; fishes do not fly.} {I. Some fishes fly.
This proves the futility of all} = {I. Some things that don’t fly are
knowledge.’ } { fishes.
} { No conclusion.
‘Lancashire is lovely, old } { Fig. ii.
women are lovely too. So } = {I. Some of Lancashire is lovely.
Lancashire must be an old woman} {I. Some old women are lovely.
or Logic is untrue!’ } { No conclusion.
‘Inspectors are stern, and } { Fig. iii.
Inspectors are mild, at the same } = {I. Some inspectors are stern.
time and place. So “stern” and } {I. Some inspectors are mild.
“mild” must be the same thing.’ } { No conclusion.
} { Fig. iv.
‘Some ladies must be addicted } {I. Some ladies are thirsty.
to drink, for they are thirsty, and} = {I. Some thirsty people are addicted
thirsty people are often addicted } { to drink.
to drink.’ } { No conclusion.
‘Some eagles have no wings; } { Fig. i.
for all birds are not eagles, and } = {O. Some birds are not eagles.
there are other winged things } {O. Some winged things are not birds.
besides birds.’ } { No conclusion.
} { Fig. ii.
‘Silence and speech are the } = {O. Some silence is not seemly.
same things; for sometimes one is } {O. Some speech is not seemly.
not seemly, sometimes the other.’ } { No conclusion.
‘Carpenters can’t be handsome, } { Fig. i.
for tall men are often handsome, } = {I. Some tall men are handsome.
and it isn’t every carpenter } {O. Some carpenters are not tall men.
that is tall.’ } { No conclusion.
} { Fig. iii.
‘Some cabmen are honest, for } {O. Some men are not dishonest.
all men can’t be dishonest, and } = {I. Some men are cabmen.
cabmen are men.’ } { No conclusion.
Violations of (Rule 6):--
} { Fig. i.
‘We must eat cook’s children, } {A. All dumplings are to be eaten.
for we eat cook’s productions; } = {I. Some of cook’s productions are
dumplings are her productions, } { dumplings.
and we eat them.’ } {∴ All cook’s productions must be
} { eaten.
‘How wretched must all men } { Fig. iii.
under petticoat government be! } {I. Some henpecked men are miserable.
For all henpecked men are under} = {A. All henpecked men are under
petticoat government, and how } { petticoat government.
miserable are some henpecked } {∴ All under petticoat government
men!’ } { are miserable.
N.B.--In both of these a particular conclusion would have passed as
valid.
(iii.) Rules of fig. ii. are
The Major Premiss must be universal.
One of the Premisses must be negative.
Rules of fig. iii. are
The Minor Premiss must be affirmative.
The conclusion must be particular.
Fig. iv. can be more clearly arranged as fig. i.
(iv.) The moods of fig. iii. are Darapti, Disamis, Datisi, Felapton,
Bokardo, Ferison (see p. 124).
A. All B is A. | I. Some B is A. | A. All B is A.
A. All B is C. | A. All B is C. | I. Some B is C.
I. ∴ Some C is A. | I. ∴ Some C is A. | I. Some C is A.
E. No B is A. | O. Some B is not C. | E. No B is A.
A. All B is C. | A. All B is C. | I. Some B is C.
O. Some C is not A. | O Some C is not A. | O. 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:--
DARAPTI.
All fishes live in the water. } { It would not be right to infer
All fishes can swim. } = {that ‘all things that can swim live
∴ Some of the things that can } {in the water,’ for even swimming
swim live in the water. } { masters do not live there always.
DISAMIS.
Some persons can preach. } { It would be wrong to conclude
All persons think they can. } = {that all the persons that think they
∴ Some of the persons that think} {can preach, can preach.
they can preach, can preach. } {
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 may 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.
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 (μέΘοδος) 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 (_A._).[10]
3. _The processes required for induction_ (observation and
experiment).
4. _The ‘methods’ in Induction corresponding to the syllogistic laws
in Deduction._
(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
particular 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 working towards arguments from the known to the
unknown)[11]:--
Induction
|
+--------------------+----------+
| |
Perfect (or Improper.) Imperfect (or Proper.)
| |
| +-----+---------+
| | |
| Induction Scientific
| per simplicem Induction.
| enumerationem. (Falling
| (Swans.) Bodies.)
+----------+----+-----+--------------+
| | | |
From Traduction. Colligation Parity of
known (Solomon.) of Facts. Reasoning.
to (The Floods.) (Ab uno
known, disce omnes.)
(_e.g._
officers
in
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 than I had already stated in my particular
premisses. But supposing some of our officers were stationed in parts
where no means of weighing existed, and I persisted in my conclusion,
then I should be stating 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 _imperfect_ 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 certainty 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 unlike 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 originality (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 particulars, and where
you do not, and so two names have been given to each case, the former
being called ‘perfect induction’ 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
‘imperfect induction’ by those who looked for certainty, but ‘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.’ Supposing 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 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, ‘cæteris paribus,’[12] 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 instances, 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 been discovered since the days of Socrates,
but we feel convinced 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 fire burns. The explanation of this difference 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 application 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 circumstances, do
likewise.
(2) Now here is an inference grounded on two assumptions.
1. That everything has a cause--(law of causation).
2. That like causes are followed by like effects--(law 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.
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 enumeration 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
induction 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 observation is natural; experiment artificial. The
astronomer _observes_ 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 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.[13]
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 carefully 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,[14] is a hopeless task
for the same reason. The ancient philosophers not receiving from their
fathers the results of previous observation and experiment 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
phenomena 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
move 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.
Many great discoveries have been preceded by several tentative
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 observation.
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.
Remember these four by the word VIEW. V vary, I isolate, E exact, W
waste.
N.B. The word ‘cause’ is loosely used for any of the circumstances
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, 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 of 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.
I. _The Method of Agreement._ You are an inductive logician. 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 madness. 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 various 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:[15]--‘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 without 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,’[16] 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 you find that the two guns, the kicker and
the non-kicker, are precisely the same except in one thing--have every
circumstance in common except one--viz., that the non-kicker is cleaned
daily and the kicker is not cleaned daily. You conclude that the want
of daily cleaning is the cause of the kicking of the gun. Put into
formal language this becomes:--
‘If an instance in which the phenomenon under investigation occurs,
and an instance in which it does not occur, have every circumstance
in common save one, that one being present 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 investigation 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 phenomenon 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 summer, 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 concludes that the
east wind is the cause of the twinges. This put formally becomes:--
‘If two or more instances in which the phenomenon under 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 circumstance, the circumstance in which alone
the two sets 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 overtiring 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.
(II.) is the method for experiment (the best of all the methods).
(III.) for cases where you cannot isolate your phenomenon.
(IV.) for cases where the causes are _permanent_. We can modify
heat[17] or the action of gravity, but so long as we are in the world
we cannot exclude them.
(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 uniformity of nature.
What =belongs to this, and that, and the other body= belongs 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 induction is,
however, latent in the major premiss, which is only a generalisation
from experience. Perfect induction seems to possess the certainty of
deduction.
A LIST OF USEFUL FACTS IN LOGIC.
Absolute terms (opposed to relative terms) mean terms which are ‘loosed
from’ (absolvo) any connection with other terms (_e.g._, water);
whereas relative terms have reference to (refero), or suggest other
terms (_e.g._, father [and son]--husband [and wife]). The pairs are
called correlatives. You can think of ‘water’ by itself; but you can’t
think of ‘father’ without also thinking of ‘son.’
ANALOGY. 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 inhabited also. The value of analogy depends upon the
number of points of resemblance known, as compared with the points of
difference known, or the points of which nothing is known: _e.g._,
given two men; only known point of resemblance is--‘both barristers.’
One we know succeeds; but it would be a weak argument 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.’ (For
‘analogous, equivocal, and univocal’ words see p. 150-1.)
A PRIORI. (See Method.)
A POSTERIORI. (See Method.)
ARGUMENTUM AD JUDICIUM means ‘an appeal to the common sense of
mankind.’ Argumentum ad ignorantiam, ‘an argument founded on the
ignorance of adversaries.’ Argumentum ad verecundiam, ‘an appeal to
our respect for some great authority.’ Argumentum a concesso, ‘a proof
derived from a proposition already 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.’ (_E.g._, even
dogs can’t digest nails, _à fortiori_ dyspeptic invalids can’t.)
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
propositions: _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).
EMPIRICAL (ἐμπειρία, experience). Empirical knowledge is knowledge
derived from experience. The knowledge of the old 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 ‘empirical.’ 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 ‘wherefore’ 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 voyage of discovery we started 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 his 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.
EXAMPLE. Analogy takes two instances as its groundwork. 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._, ‘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 represents the
class.
EXPERIMENTUM CRUCIS. ‘An experiment which decides between 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.
[Illustration]
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 attained to _perception_.
_Conception_ is the forming of concepts in the mind resulting from
sensation and perception; it employs _imagination_ (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 intuition, we know anything that we know without the aid of
proof (see Method).
FIGURE OF SPEECH. A fallacy, which comes under amphibolia--_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 Connotation 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 rhetoric relies upon the warmth of sympathy,
while logic only recognises the cold, calm intellect. Hence rhetoric is
the more popular, but logic the more true.
HYPOTHESES (or suppositions, ὑπὸ τίθημι, _sub pono_) are the
conjectures hazarded by men who seek to establish laws from the
observation of particular facts. 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 an 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 application to particulars. So Kepler
rejected about twenty hypotheses 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 OF 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 examining 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 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?
On 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. Contradictory opposition would be
powerless without this law. So also would reduction ‘per impossible.’
(See Reduction of Figures, p. 133.)
III. _The law of excluded 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 objects observed
(objective). We spoke of the attributes of these objects, as though
each object was a something underlying its attributes, 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_ (νούμενον, the thinking part), or substance as opposed
to _phenomenon_[18] (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, CONCEPTUALISTS. We saw that after a time the
infant would start at the name of ‘dog’ without the presence of a
dog. Imagination enables us to picture to ourselves ‘a dog’ which is
not this or that dog, but simply a specimen possessing 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 conceptualists in
their subjective existence, and the nominalists allow them no existence
at all.’
METHOD (μέθοδος). 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 apprehend 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 ‘becauses’ 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 μέθοδοι
(ὅδος) or ‘ways after something.’ The journey downwards is called the
deductive, or the _à priori_, or the synthetic method, and the upward
journey the inductive, or the _à posteriori_, or the analytical method.
The former is also called the method of instruction, 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 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 accepted 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 deductive.]
The truths at the upper end are said to be ‘notiora naturæ,’ or better
known in themselves and simpler; those at the lower end are ‘notiora
nobis,’ better known to us, but more complicated. Now as universal
truths are simpler, so they are said to be prior to particular truths.
Hence _à priori_ and _à 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 elements, ‘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 propositions 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
_à priori_ and deductive and synthetical may be regarded as the same,
and _à 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 is with less
abstruse questions after 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 muttering ‘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.’ _Tautologous_, where the predicate
simply repeats the subject, and no information is given. Eggs are eggs.
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 of 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 off 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
provides the art of rowing with material to work upon, or the science
of Euclid the science of land-measurement.
QUANTIFICATION OF PREDICATE. An attempt to quantify the predicate as we
do the subject. It is better not to adopt it:
(1) Because too troublesome.
(2) Because too unusual a form.
(3) Because 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 proposition secundi
adjacentis (_i.e._ with copula lost in verb). Brutus is brave, is
tertii adjacentis with copula distinct.
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[19] (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 whereof one agrees and one does not agree with the same
middle term do not agree with one another.
(3) 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.’
TRUISM = 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 examination, the earnest desire of
the female part of the family that the over-wrought brain that had
soared to, and faced, and fought, and 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 describe; 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, conjunctive, hypothetical
syllogisms,’ and this produces a dead silence at once.
FOOTNOTES:
[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. 74.
[2] Concrescere = ‘to grow with.’ Abstrahere = ‘to draw away.’ So to
speak, we draw away the green from the trees in bloom when we talk of
‘greenness’--the green and the tree grew together.
[3] ‘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.’
[4] Do not confuse this A (MAJOR TERM) with Proposition A--the first of
the four A E I O.
[5] 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
go, And be dist. or neg. only if premiss be so.’
[6] Putting words for the ciphers we should reduce thus:
E. No colliers can manage balloons, } or fig. ii. may be A. All good
aeronauts can manage balloons, } reduced to fig. i. E. ∴ No good
aeronauts are colliers. } thus:--
E. No people who can manage balloons are colliers, A. All good
aeronauts can manage balloons, E. ∴ 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. O. ∴ Some of the things dear to men
are not flirts. } thus:--
E. No true women are flirts, I. Some (_i.e._ one of the) things dear to
men are true women, O. ∴ Some of the things dear to men are not flirts.
[7] This fallacy is the one referred to by the words, ‘Post hoc, sed
non propter hoc,’ as the man said when he stumbled after partaking
freely of a well-known light wine.
[8] 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 practice
work them out. See Appendix A (iv.).
[9] For _Asebinop_, see pp. 78 and 126. It only means that an A prop.
distributes its subject, E both subject and prædicate, I neither, O
prædicate.
[10] 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 certainty
about our conclusions in induction as we have in deduction. For the
principles of the syllogism are laws, the violation of which is
inconceivable, 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 deduction part
of our nature, which we found but did not make.
[11] 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.
[12] It would not be shorter if you had a broad river in the way.
‘Cæteris paribus’ means ‘all other things being the same.’ A good
swimmer swims 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 ‘cæteris’ not ‘paribus,’ or let one tow a boat and the
other not, and the bad swimmer may win the prize.
[13] This is important. Think it out and illustrate it by instances
from your own experience.
[14] _Statistics_ are ‘observation systematised’ for this purpose.
[15] From Mr. Mill’s Logic.
[16] If you use this instance, for ‘kick’ read ‘recoil’ throughout.
[17] If we could banish the heat altogether, the sticks might be
brought to that most useful method of difference. But many causes are
permanent, and concomitant variations becomes a valuable method. The
whole N.B. is important.
[18] From φαίνομαι, I show myself.
[19] Corolla--a little crown.
PRINTED BY
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LONDON
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