Lewis Carroll (Charles Lutwidge Dodgson) - Symbolic Logic

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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 Im 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.

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

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 ableshould 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:

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.

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

The chief alterations, since the First Edition, have been made in the Chapter on Classification (). 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 childs 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 hostthat, 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 biddenand 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