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”.