1858, pp. 188-9). On the whole, I conclude that Hamilton's treatment of the subject is so doubtful and confusing that it had better not be studied in an elementary course of reading. De Morgan, in the paper just referred to, gives some remarks about the history of the doctrine of intension and extension, and speaks of Hamilton as a logician who has ' recently contended for the revival, or rather the full introduction, of the distinction of extension and comprehension.' He correctly names the Port Royal Logic as being the first modern work to insist on the distinction, though the use made of it is not very extensive.' But he names only one other work, the Institutiones Philosophica of J. Bouvier (3rd Ed. Mans, 1830), as describing this distinction. De Morgan's reading of modern logic was not extensive. Not to mention the familiar Watts' Logic, in which the doctrine is frequently dwelt upon (see Part I. Chap. III. Section 3; Chap. VI. Section 10, and elsewhere), I find the matter excellently explained in 1816 in the brief manual of the American logician, Levi Hedge (pp. 42-44). In Murray's Manual, formerly much used in Dublin and Glasgow, the subject is fully explained, and in the clearest possible manner, in the Commentary of John Walker on Chapter II. This is in fact one of the best pieces of logical exposition which I know. Walker remarked that he had treated the point fully, because he regarded it as absolutely necessary to the understanding of the subsequent pages, which were often puzzling to students not familiar with the distinction between the comprehension and extension of a term. With some regret I must hold, then, that the pretensions of Hamilton in this matter are mistaken and unfounded. The whole subject of extension and comprehension or intension has been investigated with much care and profundity of thought by the American logician, Professor C. S. Peirce, in the memoir already referred to (see p. 127). This memoir should be studied by those who wish to acquire a thorough understanding of logical principles and relations. 6. It is asserted by some logicians that the predicate of a proposition must be interpreted in intension while the subject is regarded in extension. Give your opinion upon this point, and explain the bearing of the question upon recent logical controversies. [c.] I should answer this question to the effect that a proposition being, conformably to the opinion of Condillac, necessarily of the nature of an equation, it is absurd to suppose that things can be equated to their own qualities or circumstances. A proposition in extension expresses the identity of a thing or class of things with the same thing or class under another designation. As De Tracy says (Idéologie, vol. iii. p. 529), 'Dans tout jugement, les deux idées comparées sont nécessairement égales en extension.' A proposition in intension expresses an identity between the attributes of the one member and those of the other. The subject may be pursued in my Essay on Pure Logic, or the Logic of Quality apart from Quantity, 1864, passim ; in J. S. Mill's Logic, Book I. Chapter V.; and in Dr. Martineau's review of Samuel Bailey on the Theory of Reasoning, in his Essays Philosophical and Theological, 1869, vol. ii. CHAPTER XV QUESTIONS ON INTENSION 1. 'Christian,' 'animal,' 'Episcopalian,' 'organised,' 'man.' Arrange these terms (1) in the order of extension, beginning with the most extensive; and (2) in the order of comprehension, beginning with the most comprehensive. [L.] 2. Arrange the following in the same manner :-General, animal, composer for the pianoforte, Roman, historian of his own campaigns, conqueror of Gaul. (See De Morgan, Third Memoir, pp. 20, 21.) 3. Arrange in order of extension and intension such of the terms given in Question 1 of Chapter II. as are the names of subaltern, genera, and species, and can be arranged in a series. 4. Analyse the following terms in the counter quantities or wholes of extension and intension: Man, government, law, triangle, vegetable. [L.] 5. Show that the analysis of an intensive equals the synthesis of an extensive whole. [c.] 6. Invent a syllogism in Barbara, and state it both in the extensive and in the intensive forms. [L.] 7. What is the place of the Major and Minor Terms in the conclusion of (a) an extensive, and (b) an intensive (comprehensive) syllogism? 8. Can the distinction of extension and intension be made to apply to the inductive syllogism? [c.] 9. Select from pp. 91 to 98 examples of the moods Celarent, Cesare, and Camenes, and state them in the intensive form. 10. What is the difference of meaning of genus and species in extent and intent? Is the extent of a notion always less as the intent is greater, and vice versâ? II. Interpret the following propositions in extension and intension :: A libel is a malicious and injurious statement. He who believes himself to be always right in his opinion claims infallibility. It is impossible to be and not to be. He that can swim needs not despair to fly. CHAPTER XVI HYPOTHETICAL, DILEMMATIC, AND OTHER KINDS OF ARGUMENTS 1. SOME attempt will be made in the subsequent chapters on the Elements of Equational Logic to illustrate the actual and possible variety of assertions and arguments. But it will be convenient to give here a few examples of hypothetical and other arguments in the less common forms. Several subtle questions arising out of the hypothetical form of assertion are also considered with some care; but it has not been thought necessary to treat all the various forms of disjunctive and dilemmatic arguments which will be found described in almost identical terms in numerous text-books. 2. If virtue is voluntary, vice is voluntary; but virtue is voluntary; therefore so is vice. [w.] A valid Constructive Hypothetical syllogism, equivalent to the following categorical one in Barbara : Beings who can be virtuous at will can also be vicious at will; Men can be virtuous at will; Therefore, they can be vicious at will. |