Note 352 — Chapter III

Hamilton (Logic, I. p. 433) takes a curious position in regard to the doctrine of reduction. “The last three figures,” he says, “are virtually identical with the first.” This has been recognised by logicians, and hence “the tedious and disgusting rules of their reduction.” But he himself goes further, and extinguishes these figures altogether, as being merely “accidental modifications of the first,” and “the mutilated expressions of a complex mental process.” A somewhat similar position is taken by Kant in his essay On the Mistaken Subtilty of the Four Figures. Kant’s argument is virtually based on the two following propositions: (1) Reasonings in figures 2, 3, 4 require to be implicitly, if not explicitly, reduced to figure 1, in order that their validity may be apparent; for example, in Cesare we must have covertly performed the conversion of the major premiss in thought, since otherwise our premisses would not be conclusive; (2) No reasonings ever fall naturally into any of the moods of figures 2, 3, 4, which are, therefore, a mere useless invention of logicians. On grounds already indicated, both these propositions must be regarded as erroneous. A further error seems to be involved in the following passage from the same essay of Kant’s: “It cannot be denied that we can draw conclusions legitimately in all these figures. But it is incontestable that all except the first determine the conclusion only by a roundabout way, and by interpolated inferences, and that the very same conclusion would follow from the same middle term in the first figure by pure and unmixed reasoning.” The latter part of this statement cannot be justified in such a case as that of Baroco.