Note 320 — Chapter I

A case similar to that adduced by Jevons is dealt with in the Port Royal Logic (Professor Baynes’s translation, p. 211) as follows:—“There are many reasonings, of which all the propositions appear negative, and which are, nevertheless, very good, because there is in them one which is negative only in appearance, and in reality affirmative, as we have already shewn, and as we may still further see by this example: That which has no parts cannot perish by the dissolution of its parts; The soul has no parts; therefore, The soul cannot perish by the dissolution of its parts. There are several who advance such syllogisms to shew that we have no right to maintain unconditionally this axiom of logic, Nothing can be inferred from pure negatives ; but they have not observed that, in sense, the minor of this and such other syllogisms is affirmative, since the middle, which is the subject of the major, is in it the attribute. Now the subject of the major is not that which has parts, but that which has not parts, and thus the sense of the minor is, The soul is a thing without parts, which is a proposition affirmative of a negative attribute.” Ueberweg also, who himself gives a clear explanation of the case, shews that it was not overlooked by the older logicians; and he thinks it not improbable that the doctrine of qualitative aequipollence between two judgments (i.e., obversion) resulted from the consideration of this very question (System of Logic, § 106). Compare, further, Whately’s treatment of the syllogism, “No man is happy who is not secure; no tyrant is secure; therefore, no tyrant is happy” (Logic, II. 4, § 7).