Buckle, who seem to have maintained implicitly not only that, in view of
the fact that the breadth of a geometrical line depends upon the
material out of which it is constructed, or upon which it is drawn, that
there ought to be a paste-board geometry, a stone geometry, and so
on;[119] but also that the foundations of logic are inductive in their
nature.[120] "We cannot," says Mill,[121] "conceive a round square, not
merely because no such object has ever presented itself in our
experience, for that would not be enough. Neither, for anything we know,
are the two ideas in themselves incompatible. To conceive a body all
black and yet white would only be to conceive two different sensations
as produced in us simultaneously by the same object--a conception
familiar to our experience--and we should probably be as well able to
conceive a round square as a hard square, or a heavy square, if it were
not that in our uniform experience, at the instant when a thing begins
to be round, it ceases to be square, so that the beginning of the one
impression is inseparably associated with the departure or cessation of
the other. Thus our inability to form a conception always arises from
our being compelled to form another contradictory to it."

FOOTNOTES:

[118] _Md._, N. S., vol. x., July, 1901, pp. 313-14.

[119] J. B. Stallo, _The Concepts and Theories of Modern Physics_, 4th
ed., London, 1900, pp. 217-27.

[120] _Ibid._, pp. 140-4.

[121] _Examination of the Philosophy of Sir William Hamilton_, vol. i.
p. 88, Amer. ed.

CHAPTER XLII

LAUGHTER

[It seemed advisable to give here[122] some views on laughter, most of
which were also held by Mr. R*ss*ll, though no written expression of his
views has yet been found. In a review[123] of M. Bergson's book on
_Laughter_,[124] Mr. Russell has remarked:

"It has long been recognized by publishers that everybody desires to be
a perfect lady or gentleman (as the case may be); to this fact we owe
the constant stream of etiquette-books. But if there is one thing which
people desire even more, it is to have a faultless sense of humour. Yet
so far as I know, there is no book called 'Jokes without Tears, by Mr.
McQuedy.' This extraordinary lacuna has now been filled. Those to whom
laughter has hitherto been an unintelligible vagary, in which one must
join, though one could never tell when it would break out, need only
study M. Bergson's book to acquire the finest flower of Parisian wit. By
observing a very simple formula they will know infallibly what is funny
and what is not; if they sometimes surprise their unlearned friends,
they have only to mention their authority in order to silence doubt.
'The attitudes, gestures and movements of the human body,' says M.
Bergson, 'are laughable in exact proportion as that body reminds us of a
mere machine.' When an elderly gentleman slips on a piece of orange-peel
and falls, we laugh, because his body follows the laws of dynamics
instead of a human purpose. When a man falls from a scaffolding and
breaks his neck on the pavement, we presumably laugh even more, since
the movement is even more completely mechanical. When the clown makes a
bad joke for the first time, we keep our countenance, but at the fifth
repetition we smile, and at the tenth we roar with laughter, because we
begin to feel him a mere automaton. We laugh at Molière's misers,
misanthropists and hypocrites, because they are mere types mechanically
dominated by a master impulse. Presumably we laugh at Balzac's
characters for the same reason; and presumably we never smile at
Falstaff, because he is individual throughout."

The review concludes with the reflection that "it would seem to be
impossible to find any such formula as M. Bergson seeks. Every formula
treats what is living as if it were mechanical, and is therefore by his
own rule a fitting object of laughter." Now, this undoubtedly true
conclusion has been obtained, as is readily seen, by a vicious-circle
fallacy which Mr. R*ss*ll would hardly have committed.--ED.]

FOOTNOTES:

[122] From a remark on p. 47 above, it is evident that Mr. R*ss*ll
intended to write some such chapter as this.

[123] _The Professor's Guide to Laughter, The Cambridge Review_, vol.
xxxii., 1912, pp. 193-4.

[124] _Laughter, an Essay on the Meaning of the Comic_, English
translation by C. Brereton and F. Rothwell, London, 1911.

CHAPTER XLIII

"GEDANKENEXPERIMENTE" AND EVOLUTIONARY ETHICS

The "Gedankenexperimente," upon which so much weight has been laid by
Mach[125] and Heymans,[126] had already been investigated by the White
Queen,[127] who, however, seems to have perceived that the results of
such experiments are not always logically valid. The psychological
founding of logic appears to be not without analogy with the surprising
method of advocates of evolutionary ethics, who expect to discover what
_is_ good by inquiring what cannibals have _thought_ good. I sometimes
feel inclined to apply the historical method to the multiplication
table. I should make a statistical inquiry among school-children, before
their pristine wisdom had been biassed by teachers. I should put down
their answers as to what 6 times 9 amounts to, I should work out the
average of their answers to six places of decimals, and should then
decide that, at the present stage of human development, this average is
the value of 6 times 9.

FOOTNOTES:

[125] See, e.g., _E. u. I._, pp. 183-200.

[126] _G. u. E._, vol. i.

[127] See Appendix T.

APPENDIXES

A. LOGIC AND THE PRINCIPLE OF IDENTITY.

_T. L. G._, p. 45: "'Contrariwise," continued Tweedledee, "if it was so,
it might be; and if it were so, it would be: but as it isn't, it ain't.
That's logic."

_S. B._, p. 159: The Professor said: "The day is the same length as
anything that is the same length as _it_."

_S. B._, p. 161: Bruno observed that, when the Other Professor lost
himself, he should shout: "He'd be sure to hear hisself, 'cause he
couldn't be far off."

B. SYNTHESIS OF CONTRADICTORIES.

_T. L. G._, p. 71: "'What a beautiful belt you've got on!' Alice
suddenly remarked.... 'At least,' she corrected herself on second
thoughts, 'a beautiful cravat, I should have said--no, a belt, I mean--I
beg your pardon!' she added in dismay, for Humpty-Dumpty looked
thoroughly offended, and she began to wish she hadn't chosen that
subject. 'If only I knew,' she thought to herself, 'which was neck and
which was waist!'"

C. EMPIRICAL PHILOSOPHERS AND MATHEMATICS.

_T. L. G._, p. 79: "'... Now if you had the two eyes on the same side of
the nose, for instance--or the mouth at the top--that would be _some_
help.'

"'It wouldn't look nice,' Alice objected. But Humpty-Dumpty only shut
his eyes and said: 'Wait till you've tried.'"

_T. L. G._, p. 72: "'And if you take one from three hundred and
sixty-five, what remains?'

"'Three hundred and sixty-four, of course.'

"Humpty-Dumpty looked doubtful. 'I'd rather see that done on paper,'
he said."

D. NOMINAL DEFINITION.

_T. L. G._, p. 73: "'When _I_ used a word,' Humpty-Dumpty said in rather
a scornful tone, 'it means just what I choose it to mean--neither more
nor less.'

"'The question is,' said Alice, 'whether you _can_ make words mean
different things.'

"'The question is,' said Humpty-Dumpty, 'which is to be master--that's
all.'"

E. CONFORMITY OF A PARADOXICAL LOGIC WITH COMMON-SENSE.

_T. L. G._, p. 100:

  "But I was thinking of a plan
  To dye one's whiskers green,
  And always use so large a fan
  That they could not be seen."
                                   (Verse from White Knight's song.)

F. IDEALISTS AND THE LAWS OF LOGIC.

_T. L. G._, p. 52-3: Tweedledee exclaimed: "'... if he [the Red King]
left off dreaming about you [Alice], where do you suppose you'd be?'

"'Where I am now, of course,' said Alice.

"'Not you!' Tweedledee retorted contemptuously. 'You'd be nowhere. Why,
you're only a sort of thing in his dream!'

"'If that there King was to wake,' added Tweedledum, 'you'd go
out--bang!--just like a candle!'

"'I shouldn't!' Alice exclaimed indignantly. 'Besides, if _I'm_ only a
sort of thing in his dream, what are _you_, I should like to know?'

"'Ditto,' said Tweedledum...; 'you know very well you're not real.'

"'I _am_ real!' said Alice, and began to cry."

_T. L. G._, p. 97: "'How _can_ you go on talking so quietly, head
downwards?' Alice asked, as she dragged him out by the feet, and laid
him in a heap on the bank.

"The Knight looked surprised at the question. 'What does it matter where
my body happens to be?' he said. 'My mind goes on working all the same.
In fact, the more head downwards I am, the more I keep inventing new
things.'"

_T. L. G._, p. 98: "'... Everybody that hears me sing--either it brings
the _tears_ into their eyes, or else----'

"'Or else what?' said Alice, for the Knight had made a sudden pause.

"'Or else it doesn't, you know.'"

G. DISTINCTION BETWEEN SIGN AND SIGNIFICATION.

_T. L. G._, pp. 98-9: "'The name of the song is called "_Haddocks'
Eyes_."'

"'Oh, that's the name of the song, is it?' Alice said, trying to feel
interested.

"'No, you don't understand,' the Knight said looking a little vexed.
'That's what the name is _called_. The name really _is_ "_The Aged Aged
Man_."'

"'Then I ought to have said "That's what the _song_ is called"?' Alice
corrected herself.

"'No, you oughtn't: that's another thing. The _song_ is called "_Ways
and Means_": but that's only what it's _called_, you know!'

"'Well, what _is_ the song, then?' said Alice, who was by this time
completely bewildered.

"'I was coming to that,' the Knight said. 'The song really _is
"A-sitting on a Gate_"....'"

H. NOMINALISM.

_A. A. W._, p. 70: "'Then you should say what you mean,' the March Hare
went on.

"'I do,' Alice hastily replied; 'at least--at least I mean what I
say--that's the same thing, you know.'

"'Not the same thing a bit!' said the Hatter. 'Why, you might just as
well say that "I see what I eat" is the same thing as "I eat what I
see."'

"'You might just as well say,' added the March Hare, 'that "I like what
I get" is the same thing as "I get what I like"!'

"'You might just as well say,' added the Dormouse, which seemed to be
talking in its sleep, 'that "I breathe when I sleep" is the same as "I
sleep when I breathe"!'

"'It _is_ the same thing with you,' said the Hatter; and here the
conversation dropped,..."

I. UTILITY OF SYMBOLIC LOGIC.

_A. A. W._, p. 92: "'I quite agree with you,' said the Duchess, 'and the
moral of that is--"Be what you would seem to be"--or if you'd like it
put more simply--"Never imagine yourself not to be otherwise than what
it might appear to others that what you were or might have been was not
otherwise than what you had been would have appeared to them to be
otherwise."'

"'I think I should understand that better,' Alice said very politely,
'if I had it written down: but I can't quite follow it as you say it.'

"'That's nothing to what I could say if I chose,' the Duchess replied,
in a pleased tone."

J. MISTAKE AS TO THE NATURE OF CRITICISM.

_T. L. G._, p. 105: "'She's in that state of mind,' said the White
Queen, 'that she wants to deny _something_--only she doesn't know what
to deny.'

"'A nasty, vicious temper,' the White Queen remarked; and then there was
an uncomfortable silence for a minute or two."

K. A CRITERION OF TRUTH.

_H. S._, p. 3:

  "Just the place for a Snark! I have said it twice:
  That alone should encourage the crew.
  Just the place for a Snark! I have said it thrice:
  What I tell you three times is true."

_H. S._, p. 50:

  "'Tis the note of the Jubjub! Keep count. I entreat;
  You will find I have told it you twice.
  'Tis the song of the Jubjub! The proof is complete,
  If only I've stated it thrice."

L. UNIVERSAL AND PARTICULAR PROPOSITIONS.

_T. L. G._, p. 40: The Gnat had told Alice that the Bread-and-butterfly
lives on weak tea with cream in it; so:

"'Supposing it couldn't find any?' she suggested.

"'Then it would die, of course.'

"'But that must happen very often,' Alice remarked thoughtfully.

"'It always happens,' said the Gnat."

M. DENOTING.

_T. L. G._, p. 43: Tweedledum and Tweedledee were, in many respects,
indistinguishable, and Alice, walking along the road, noticed that
"whenever the road divided there were sure to be two finger-posts
pointing the same way, one marked 'TO TWEEDLEDUM'S HOUSE' and the other
'TO THE HOUSE OF TWEEDLEDEE.'

"'I do believe,' said Alice at last, 'that they live in the same
house!...'"

N. NON-ENTITY.

_T. L. G._, p. 87: "'I always thought they [human children] were
fabulous monsters!' said the Unicorn....

"'Do you know [said Alice], I always thought Unicorns were fabulous
monsters, too! I never saw one alive before!'

"'Well, now that we _have_ seen each other,' said the Unicorn, 'if
you'll believe in me, I'll believe in you. Is that a bargain?'"

_T. L. G._, pp. 80-1: "'I see nobody on the road,' said Alice.

"'I only wish _I_ had such eyes,' the [White] King remarked in a fretful
tone. 'To be able to see Nobody! And at that distance, too! Why, it's as
much as _I_ can do to see real people by this light!'"

_A. A. W._, p. 17: "And she [Alice] tried to fancy what the flame of a
candle looks like after the candle is blown out, for she could not
remember ever having seen such a thing."

_A. A. W._, p. 68: "... This time it [the Cheshire Cat] vanished quite
slowly, beginning with the end of the tail, and ending with the grin,
which remained some time after the rest of it had gone.

"'Well! I've often seen a cat without a grin,' thought Alice; 'but a
grin without a cat! It's the most curious thing I ever saw in all my
life!'"

_A. A. W._, p. 77: "... The Dormouse went on,...; 'and they drew all
manner of things--everything that begins with an M.'

"'Why with an M?' said Alice.

"'Why not?' said the March Hare.

"Alice was silent.

"... [The Dormouse] went on: '--that begins with an M, such as
mouse-traps, and the moon, and memory, and muchness, you know you say
things are "much of a muchness"--did you ever see such a thing as a
drawing of a muchness?'

"'Really, now you ask me,' said Alice, very much confused, 'I don't
think----'

"'Then you shouldn't talk,' said the Hatter."

O. OBJECTS OF MATHEMATICAL LOGIC.

_T. L. G._, p. 93: "'I was wondering what the mouse-trap [fastened to
the White Knight's saddle] was for,' said Alice. 'It isn't very likely
there would be any mice on the horse's back.'

"'Not very likely, perhaps,' said the Knight, 'but, if they _do_ come, I
don't choose to have them running all about.'

"'You see,' he went on after a pause, 'it's as well to be provided for
_everything_. That's the reason the horse has all these anklets round
his feet.'

"'But what are they for?' Alice asked in a tone of great curiosity.

"'To guard against the bites of sharks,' the Knight replied."

P. THE PRINCIPLE OF PERMANENCE.

_T. L. G._, p. 106: "'Can you do Subtraction? [said the Red Queen] Take
nine from eight.'

"'Nine from eight I can't, you know,' Alice replied very readily 'but--'

"'She can't do Substraction,' said the White Queen."

_A. A. W._, p. 56: [Said the Pigeon to Alice]: "'... No, no! You're a
serpent; and there's no use denying it. I suppose you'll be telling me
next that you never tasted an egg!'

"'I _have_ tasted eggs certainly,' said Alice, who was a very truthful
child; 'but little girls eat eggs quite as much as serpents do, you
know.'

"'I don't believe it,' said the Pigeon; 'but if they do, why then
they're a kind of serpent, that's all I can say.'

"This was such a new idea to Alice, that she was quite silent for a
minute or two, which gave the Pigeon the opportunity of adding, 'You're
looking for eggs, I know _that_ well enough; and what does it matter to
me whether you're a little girl or a serpent?'

"'It matters a good deal to _me_,' said Alice hastily;..."

_A. A. W._, p. 75: "'But why [asked Alice] did they live at the bottom
of a well?'

"'Take some more tea,' the March Hare said to Alice, very earnestly.

"'I've had nothing yet,' Alice replied in an offended tone, 'so I can't
take more.'

"'You mean you can't take _less_,' said the Hatter: 'it's very easy to
take _more_ than nothing.'"

Q. MATHEMATICIANS' TREATMENT OF LOGIC.

_A. A. W._, p. 74: The Hatter had told of his quarrel with Time, and of
Time's refusal now to do anything he asked: "'... It's always six
o'clock now!'

"A bright idea came into Alice's head. 'Is that the reason so many tea
things are put out here?' she asked.

"'Yes, that's it,' said the Hatter, with a sigh: 'it's always tea time,
and we've no time to wash the things between whiles.'

"'Then you keep moving round, I suppose?' said Alice.

"'Exactly so,' said the Hatter: 'as the things get used up.'

"'But what happens when you come to the beginning again?' Alice ventured
to ask.

"'Suppose we change the subject,' the March Hare interrupted, yawning.
'I'm getting tired of this.'"

_A. A. W._, p. 99: "'And how many hours a day did you do lessons?' said
Alice, in a hurry to change the subject.

"'Ten hours the first day,' said the Mock Turtle, 'nine the next, and so
on.'

"'What a curious plan!' exclaimed Alice.

"'That's the reason they're called lessons,' the Gryphon remarked,
'because they lessen from day to day.'

"This was quite a new idea to Alice, and she thought it over a little
before she made her next remark. 'Then the eleventh day must have been a
holiday.'

"'Of course it was,' said the Mock Turtle.

"'And how did you manage on the twelfth?' Alice went on eagerly.

"'That's enough about lessons,' the Gryphon interrupted in a very
decided tone...."

R. METHOD IN MATHEMATICS AND LOGIC.

_A. A. W._, p. 71: "'Two days wrong!' sighed the Hatter. 'I told you
butter wouldn't suit the works!' he added, looking angrily at the March
Hare.

"'It was the _best_ butter,' the March Hare meekly replied.

"'Yes, but some crumbs must have got in as well,' the Hatter grumbled;
'you shouldn't have put it in with the bread-knife.'

"The March Hare took the watch and looked at it gloomily: then he dipped
it into his cup of tea, and looked at it again: but he could think of
nothing better to say than his first remark, 'It was the _best_ butter,
you know.'"

S. VERDICT THAT LOGIC IS PHILOSOPHY.

_A. A. W._, pp. 119-23: "... 'Consider your verdict,' he [the King] said
to the jury, in a low trembling voice.

"'There's more evidence to come yet, please your Majesty,' said the
White Rabbit, jumping up in a great hurry: 'this paper has just been
picked up.'

"'What's in it?' said the Queen.

"'I haven't opened it yet,' said the White Rabbit, 'but it seems to be a
letter written by the prisoner to--to somebody.'

"'It must have been that,' said the King, 'unless it was written to
nobody, which isn't usual, you know.'

"'Who is it directed to?' said one of the jurymen.

"'It isn't directed at all,' said the White Rabbit, 'in fact there's
nothing written on the _outside_.' He unfolded the paper as he spoke,
and added, 'It isn't a letter, after all: it's a set of verses.'

"'Are they in the prisoner's handwriting?' asked another of the jurymen.

"'No they're not,' said the White Rabbit, 'and that's the queerest thing
about it.' (The jury all looked puzzled).

"'He must have imitated somebody else's hand,' said the King. (The jury
brightened up again.)

"'Please your Majesty,' said the Knave, 'I didn't write it, and they
can't prove that I did: there's no name signed at the end.'

"'If you didn't sign it, said the King, that only makes the matter
worse. You _must_ have meant some mischief, or else you'd have signed
your name like an honest man.'

"There was a general clapping of hands at this: it was the first really
clever thing the King had said that day.

"'That _proves_ his guilt, of course,' said the Queen, 'so, off
with----'

"'It doesn't prove anything of the sort!' said Alice. 'Why, you don't
even know what they're about!'

"'Read them,' said the King.

"The White Rabbit put on his spectacles. 'Where shall I begin, please
your Majesty?' he asked.

"'Begin at the beginning,' the King said very gravely, 'and go on till
you come to the end: then stop.'

"There was dead silence in the court, whilst the White Rabbit read out
these verses:

  "'_They told me you had been to her,
  And mentioned me to him;
  She gave me a good character,
  But said I could not swim._

  _He sent them word I had not gone
  (We know it to be true):
  If she should push the matter on,
  What would become of you?_

  _I gave her one, they gave him two,
  You gave us three or more;
  They all returned from him to you,
  Though they were mine before._

  _If I or she should chance to be
  Involved in this affair,
  He trusts to you to set them free
  Exactly as they were._

  _My notion was that you had been
  (Before she had this fit)
  An obstacle that came between
  Him, and ourselves, and it._

  _Don't let him know she liked them best,
  For this must ever be
  A secret kept from all the rest,
  Between yourself and me._'

"'That's the most important piece of evidence we've heard yet,' said the
King, rubbing his hands, 'so now let the jury----'

"'If any one of them can explain it,' said Alice (she had grown so large
in the last few minutes that she wasn't a bit afraid of interrupting
him), 'I'll give him sixpence. _I_ don't believe there's an atom of
meaning in it.'

"The jury all wrote down on their slates, 'She doesn't believe there's
an atom of meaning in it,' but none of them attempted to explain the
paper.

"'If there's no meaning in it,' said the King, 'that saves a world of
trouble, you know, as we needn't try to find any. And yet I don't know,'
he went on, spreading out the verses on his knee and looking at them
with one eye; 'I seem to see some meaning in them after all. "_-- said
I could not swim_"; you can't swim, can you?' he added, turning to the
Knave.

"The Knave shook his head sadly. 'Do I look like it?' he said. (Which he
certainly did _not_, being made entirely of cardboard.)

"'All right, so far,' said the King; and he went on muttering over the
verses to himself: ''_We know it to be true_'--that's the jury, of
course--'_If she should push the matter on_'--that must be the
Queen--'_What would become of you?_' What indeed!--'_I gave her one,
they gave him two!_' why, that must be what he did with the tarts, you
know----'

"'But it goes on, '_They all returned from him to you_,'' said Alice.

"'Why, there they are!' said the King, triumphantly pointing to the
tarts on the table. 'Nothing can be clearer than that. Then
again--'_Before she had this fit_'--you never had fits, my dear, I
think?' he said to the Queen.

"'Never!' said the Queen furiously, throwing an inkstand at the Lizard
as she spoke. (The unfortunate little Bill had left off writing on his
slate with one finger, as he found it made no mark; but he now hastily
began again, using the ink that was trickling down his face, as long as
it lasted.)

"'Then the words don't _fit_ you,' said the King, looking round the
court with a smile. There was a dead silence.

"'It's a pun!' the King added in an angry tone, and everybody laughed.

"'Let the jury consider their verdict,' the King said, for about the
twentieth time that day.

"'No, no!' said the Queen. 'Sentence first--verdict afterwards.'

"'Stuff and nonsense!' said Alice loudly. 'The idea of having the
sentence first!'

"'Hold your tongue!' said the Queen, turning purple...."

T. "GEDANKENEXPERIMENTE."

_T. L. G._, p. 61: "Alice laughed. 'There's no use trying,' she said:
'one _can't_ believe impossible things.'

"'I daresay you haven't had much practice,' said the [White] Queen.
'When I was your age, I always did it for half-an-hour a day. Why,
sometimes I've believed as many as six impossible things before
breakfast.'"

_Printed in Great Britain by_

UNWIN BROTHERS, LIMITED, THE GRESHAM PRESS, WOKING AND LONDON

End of Project Gutenberg's The philosophy of B*rtr*nd R*ss*ll, by Various