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                                                                   pg-i

SYMBOLIC LOGIC

By Lewis Carroll
                                                                   pg-ii
                                                                   pg-iii
                                                                   pg-iv

A Syllogism worked out.

That story of yours, about your once meeting the sea-serpent, always
sets me off yawning;

I never yawn, unless when I'm listening to something totally devoid of
interest.

The Premisses, separately.

   .---------------.          .---------------.
    |( )    |    ( )|           |       |       |
    |  .---|---.   |           |  .---|---.   |
    |   |  (#)  |   |           |   |   |( )|   |
    |---|---|---|---|           |---|---|---|---|
    |   |   |   |   |           |   |   |( )|   |
    |  .---|---.   |           |  .---|---.   |
    |       |       |           |       |       |
   .---------------.          .---------------.

The Premisses, combined.

   .---------------.
    |( )    |    ( )|
    |  .---|---.   |
    |   |(#)|( )|   |
    |---|---|---|---|
    |   |   |( )|   |
    |  .---|---.   |
    |       |       |
   .---------------.

The Conclusion.

   .-------.
    |(#)|( )|
    |---|---|
    |   |   |
   .-------.

That story of yours, about your once meeting the sea-serpent, is totally
devoid of interest.

                                                                   pg-v


                           SYMBOLIC LOGIC


                              _PART I_

                             ELEMENTARY



                                 BY

                            LEWIS CARROLL


                           SECOND THOUSAND

                           FOURTH EDITION


                        _PRICE TWO SHILLINGS_


                               London
                     MACMILLAN AND CO., LIMITED
                   NEW YORK: THE MACMILLAN COMPANY
                                1897

                        _All rights reserved_


                                                                   pg-vi

                   RICHARD CLAY AND SONS, LIMITED,
                          LONDON AND BUNGAY

                                                                   pg-vii


ADVERTISEMENT.


An envelope, containing two blank Diagrams (Biliteral and Triliteral)
and 9 counters (4 Red and 5 Grey), may be had, from Messrs. Macmillan,
for 3_d._, by post 4_d._

       *       *       *       *       *

I shall be grateful to any Reader of this book who will point out any
mistakes or misprints he may happen to notice in it, or any passage
which he thinks is not clearly expressed.

       *       *       *       *       *

I have a quantity of MS. in hand for Parts II and III, and hope to be
able----should life, and health, and opportunity, be granted to me, to
publish them in the course of the next few years. Their contents will be
as follows:--

_PART II. ADVANCED._

Further investigations in the subjects of Part I. Propositions of other
forms (such as "Not-all x are y"). Triliteral and Multiliteral
Propositions (such as "All abc are de"). Hypotheticals. Dilemmas. &c.
&c.

_Part III. TRANSCENDENTAL._

Analysis of a Proposition into its Elements. Numerical and Geometrical
Problems. The Theory of Inference. The Construction of Problems. And
many other _Curiosa Logica_.

                                                                   pg-viii


PREFACE TO THE FOURTH EDITION.


The chief alterations, since the First Edition, have been made in the
Chapter on 'Classification' (pp. 2, 3) and the Book on 'Propositions'
(pp. 10 to 19). The chief additions have been the questions on words and
phrases, added to the Examination-Papers at p. 94, and the Notes
inserted at pp. 164, 194.

In Book I, Chapter II, I have adopted a new definition of
'Classification', which enables me to regard the whole Universe as a
'Class,' and thus to dispense with the very awkward phrase 'a Set of
Things.'

In the Chapter on 'Propositions of Existence' I have adopted a new
'normal form,' in which the Class, whose existence is affirmed or
denied, is regarded as the _Predicate_, instead of the _Subject_, of the
Proposition, thus evading a very subtle difficulty which besets the
other form. These subtle difficulties seem to lie at the root of every
Tree of Knowledge, and they are _far_ more hopeless to grapple with than
any that occur in its higher branches. For example, the difficulties of
the Forty-Seventh Proposition of Euclid are mere child's play compared
with the mental torture endured in the effort to think out the essential
nature of a straight Line. And, in the present work, the difficulties of
the "5 Liars" Problem, at p. 192, are "trifles, light as air," compared
with the bewildering question "What is a Thing?"

In the Chapter on 'Propositions of Relation' I have inserted a new
Section, containing the proof that a Proposition, beginning with "All,"
is a _Double_ Proposition (a fact that is quite independent of the
arbitrary rule, laid down in the next Section, that such a Proposition
is to be understood as implying the actual _existence_ of its Subject).
This proof was given, in the earlier editions, incidentally, in the
course of the discussion of the Biliteral Diagram: but its _proper_
place, in this treatise, is where I have now introduced it.
                                                                   pg-ix
In the Sorites-Examples, I have made a good many verbal alterations, in
order to evade a difficulty, which I fear will have perplexed some of
the Readers of the first three Editions. Some of the Premisses were so
worded that their Terms were not Specieses of the Univ. named in the
Dictionary, but of a larger Class, of which the Univ. was only a
portion. In all such cases, it was intended that the Reader should
perceive that what was asserted of the larger Class was thereby asserted
of the Univ., and should ignore, as superfluous, all that it asserted of
its _other_ portion. Thus, in Ex. 15, the Univ. was stated to be "ducks
in this village," and the third Premiss was "Mrs. Bond has no gray
ducks," i.e. "No gray ducks are ducks belonging to Mrs. Bond." Here the
Terms are _not_ Specieses of the Univ., but of the larger Class "ducks,"
of which the Univ. is only a portion: and it was intended that the
Reader should perceive that what is here asserted of "ducks" is thereby
asserted of "ducks in this village." and should treat this Premiss as if
it were "Mrs. Bond has no gray ducks in this village," and should
ignore, as superfluous, what it asserts as to the _other_ portion of the
Class "ducks," viz. "Mrs. Bond has no gray ducks _out of_ this village".

In the Appendix I have given a new version of the Problem of the "Five
Liars." My object, in doing so, is to escape the subtle and mysterious
difficulties which beset all attempts at regarding a Proposition as
being its own Subject, or a Set of Propositions as being Subjects for
one another. It is certainly, a most bewildering and unsatisfactory
theory: one cannot help feeling that there is a great lack of
_substance_ in all this shadowy host----that, as the procession of
phantoms glides before us, there is not _one_ that we can pounce upon,
and say "_Here_ is a Proposition that _must_ be either true or
false!"----that it is but a Barmecide Feast, to which we have been
bidden----and that its prototype is to be found in that mythical island,
whose inhabitants "earned a precarious living by taking in each others'
washing"! By simply translating "telling 2 Truths" into "taking _both_
of 2 condiments (salt and mustard)," "telling 2 Lies" into "taking
_neither_ of them" and "telling a Truth and a Lie (order not specified)"
into "taking only _one_ condiment (it is not specified _which_)," I have
escaped all those metaphysical puzzles, and have produced a Problem
which, when translated into a Set of symbolized Premisses, furnishes the
very same _Data_ as were furnished by the Problem of the "Five Liars."
                                                                   pg-x
The coined words, introduced in previous editions, such as "Eliminands"
and "Retinends", perhaps hardly need any apology: they were
indispensable to my system: but the new plural, here used for the first
time, viz. "Soriteses", will, I fear, be condemned as "bad English",
unless I say a word in its defence. We have _three_ singular nouns, in
English, of plural _form_, "series", "species", and "Sorites": in all
three, the awkwardness, of using the same word for both singular and
plural, must often have been felt: this has been remedied, in the case
of "series" by coining the plural "serieses", which has already found
its way into the dictionaries: so I am no rash innovator, but am merely
"following suit", in using the new plural "Soriteses".

In conclusion, let me point out that even those, who are obliged to
study _Formal_ Logic, with a view to being able to answer
Examination-Papers in that subject, will find the study of _Symbolic_
Logic most helpful for this purpose, in throwing light upon many of the
obscurities with which Formal Logic abounds, and in furnishing a
delightfully easy method of _testing_ the results arrived at by the
cumbrous processes which Formal Logic enforces upon its votaries.

This is, I believe, the very first attempt (with the exception of my own
little book, _The Game of Logic_, published in 1886, a very incomplete
performance) that has been made to _popularise_ this fascinating
subject. It has cost me _years_ of hard work: but if it should prove, as
I hope it may, to be of _real_ service to the young, and to be taken up,
in High Schools and in private families, as a valuable addition to their
stock of healthful mental recreations, such a result would more than
repay ten times the labour that I have expended on it.

                                                                L. C.

29, BEDFORD STREET, STRAND.
    _Christmas, 1896._

                                                                   pg-xi


INTRODUCTION.

_TO LEARNERS._

[N.B. Some remarks, addressed to _Teachers_, will be found in the
Appendix, at p. 165.]


The Learner, who wishes to try the question _fairly_, whether this
little book does, or does not, supply the materials for a most
interesting mental recreation, is _earnestly_ advised to adopt the
following Rules:--

(1) Begin at the _beginning_, and do not allow yourself to gratify a
mere idle curiosity by dipping into the book, here and there. This would
very likely lead to your throwing it aside, with the remark "This is
_much_ too hard for me!", and thus losing the chance of adding a very
_large_ item to your stock of mental delights. This Rule (of not
_dipping_) is very _desirable_ with _other_ kinds of books----such as
novels, for instance, where you may easily spoil much of the enjoyment
you would otherwise get from the story, by dipping into it further on,
so that what the author meant to be a pleasant surprise comes to you as
a matter of course. Some people, I know, make a practice of looking into
Vol. III first, just to see how the story ends: and perhaps it _is_ as
well just to know that all ends _happily_----that the much-persecuted
lovers _do_ marry after all, that he is proved to be quite innocent of
the murder, that the wicked cousin is completely foiled in his plot and
gets the punishment he deserves, and that the rich uncle in India (_Qu._
Why in _India_? _Ans._ Because, somehow, uncles never _can_ get rich
anywhere else) dies at exactly the right moment----before taking the
trouble to read Vol. I. This, I say, is _just_ permissible with a
_novel_, where Vol. III has a _meaning_, even for those who have not
read the earlier part of the story; but, with a _scientific_ book, it is
sheer insanity: you will find the latter part _hopelessly_
unintelligible, if you read it before reaching it in regular course.
                                                                   pg-xii
(2) Don't begin any fresh Chapter, or Section, until you are certain
that you _thoroughly_ understand the whole book _up to that point_, and
that you have worked, correctly, most if not all of the examples which
have been set. So long as you are conscious that all the land you have
passed through is absolutely _conquered_, and that you are leaving no
unsolved difficulties _behind_ you, which will be sure to turn up again
later on, your triumphal progress will be easy and delightful.
Otherwise, you will find your state of puzzlement get worse and worse as
you proceed, till you give up the whole thing in utter disgust.

(3) When you come to any passage you don't understand, _read it again_:
if you _still_ don't understand it, _read it again_: if you fail, even
after _three_ readings, very likely your brain is getting a little
tired. In that case, put the book away, and take to other occupations,
and next day, when you come to it fresh, you will very likely find that
it is _quite_ easy.

(4) If possible, find some genial friend, who will read the book along
with you, and will talk over the difficulties with you. _Talking_ is a
wonderful smoother-over of difficulties. When _I_ come upon
anything----in Logic or in any other hard subject----that entirely
puzzles me, I find it a capital plan to talk it over, _aloud_, even when
I am all alone. One can explain things so _clearly_ to one's self! And
then, you know, one is so _patient_ with one's self: one _never_ gets
irritated at one's own stupidity!

If, dear Reader, you will faithfully observe these Rules, and so give my
little book a really _fair_ trial, I promise you, most confidently, that
you will find Symbolic Logic to be one of the most, if not _the_ most,
fascinating of mental recreations! In this First Part, I have carefully
avoided all difficulties which seemed to me to be beyond the grasp of an
intelligent child of (say) twelve or fourteen years of age. I have
myself taught most of its contents, _viva voce_, to _many_ children, and
have found them take a real intelligent interest in the subject. For
those, who succeed in mastering Part I, and who begin, like Oliver,
"asking for more," I hope to provide, in Part II, some _tolerably_ hard
nuts to crack----nuts that will require all the nut-crackers they happen
to possess!
                                                                   pg-xiii
Mental recreation is a thing that we all of us need for our mental
health; and you may get much healthy enjoyment, no doubt, from Games,
such as Back-gammon, Chess, and the new Game "Halma". But, after all,
when you have made yourself a first-rate player at any one of these
Games, you have nothing real to _show_ for it, as a _result!_ You
enjoyed the Game, and the victory, no doubt, _at the time_: but you have
no _result_ that you can treasure up and get real _good_ out of. And,
all the while, you have been leaving unexplored a perfect _mine_ of
wealth. Once master the machinery of Symbolic Logic, and you have a
mental occupation always at hand, of absorbing interest, and one that
will be of real _use_ to you in _any_ subject you may take up. It will
give you clearness of thought----the ability to _see your way_ through a
puzzle----the habit of arranging your ideas in an orderly and
get-at-able form----and, more valuable than all, the power to detect
_fallacies_, and to tear to pieces the flimsy illogical arguments, which
you will so continually encounter in books, in newspapers, in speeches,
and even in sermons, and which so easily delude those who have never
taken the trouble to master this fascinating Art. _Try it._ That is all
I ask of you!

                                                                L. C.

29, BEDFORD STREET, STRAND.
    _February 21, 1896._

                                                                   pg-xiv
                                                                   pg-xv

CONTENTS.


=BOOK I.=

=THINGS AND THEIR ATTRIBUTES.=


CHAPTER I.

_INTRODUCTORY._

                                                               PAGE
'=Things='                                                       1

'=Attributes='                                                   "

'=Adjuncts='                                                     "


CHAPTER II.

_CLASSIFICATION._

'=Classification='                                               1 1/2

'=Class='                                                        "

'=Peculiar=' Attributes                                          "

'=Genus='                                                        "

'=Species='                                                      "

'=Differentia='                                                  "

'=Real=' and '=Unreal=', or '=Imaginary=', Classes               2

'=Individual='                                                   "

A Class regarded as a single Thing                               2 1/2

                                                                   pg-xvi
CHAPTER III.

_DIVISION._


Sec. 1.

_Introductory._

'=Division='                                                     3

'=Codivisional=' Classes                                         "


Sec. 2.

_Dichotomy._

'=Dichotomy='                                                    3 1/2

Arbitrary limits of Classes                                      "

Subdivision of Classes                                           4


CHAPTER IV.

_NAMES._

'=Name='                                                         4 1/2

'=Real=' and '=Unreal=' Names                                    "

Three ways of expressing a Name                                  "

Two senses in which a plural Name may be used                    5


CHAPTER V.

_DEFINITIONS._

'=Definition='                                                   6

Examples worked as models                                        "

                                                                   pg-xvii
=BOOK II.=

=PROPOSITIONS.=


CHAPTER I.

_PROPOSITIONS GENERALLY._


Sec. 1.

_Introductory._

Technical meaning of "some"                                      8

'=Proposition='                                                  "

'=Normal form=' of a Proposition                                 "

'=Subject=', '=Predicate=', and '=Terms='                        9


Sec. 2.

_Normal form of a Proposition._

Its four parts:--

  (1) '=Sign of Quantity='                                       9

  (2) Name of Subject                                            "

  (3) '=Copula='                                                 "

  (4) Name of Predicate                                          "


Sec. 3.

_Various kinds of Propositions._

Three kinds of Propositions:--

  (1) Begins with "Some". Called a '=Particular=' Proposition:
      also a Proposition '=in I='                               10

  (2) Begins with "No". Called a '=Universal Negative='
      Proposition: also a Proposition '=in E='                   "

  (3) Begins with "All". Called a '=Universal Affirmative='
      Proposition: also a Proposition '=in A='                   "
                                                                   pg-xviii
A Proposition, whose Subject is an Individual, is to be
regarded as Universal                                            "

Two kinds of Propositions, 'Propositions of Existence',
and 'Propositions of Relation'                                   "


CHAPTER II.

_PROPOSITIONS OF EXISTENCE._


'=Proposition of Existence ='                                   11


CHAPTER III.

_PROPOSITIONS OF RELATION._


Sec. 1.

_Introductory._

'=Proposition of Relation='                                     12

'=Universe of Discourse=,' or '=Univ.='                          "


Sec. 2.

_Reduction of a Proposition of Relation
to Normal form._

Rules                                                           13

Examples worked                                                  "


Sec. 3.

_A Proposition of Relation, beginning with "All",
is a Double Proposition._

Its