Note 450 — Chapter IX

Sigwart holds that, in order properly to understand the value of the syllogism, we should take as our type the conditional (or, as he expresses it, the hypothetical), rather than the categorical, syllogism. We need, he says, but glance at any mathematical or physical text-book to assure ourselves that by far the greater number of propositions which are used as major premisses are hypothetical in nature, if not in expression. “Propositions such as ‘two circles which intersect have no common centre’ are hypothetical in nature; the proposition states the condition upon which the predicate is denied.… It is the same with the formulae of analytical mechanics; these and others of the same description are hypothetical judgments, and inferences are made in accordance with them by substituting definite values for the general symbols” (Logic, § 55). Sigwart perhaps attaches undue importance to the mere question of form. If our major premiss is unconditionally universal, and is understood to be so, it does not affect the character of the reasoning whether we adopt the categorical mode of expression or the conditional. Sigwart’s reason for dwelling on the hypothetical force of the major premiss is to be found largely in the trivial nature of the examples that it has been customary to give of the purely categorical syllogism.