



Produced by Tony Browne, Geetu Melwani, Greg Weeks, L.
Lynn Smith and the Online Distributed Proofreading Team
at http://www.pgdp.net






                                                                   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