Note 234 — Chapter VIII

Dr Wolf holds in opposition to the view here expressed that on the supposition in question all the ordinary immediate inferences remain valid. This conclusion is based on the doctrine that Some S is P does not imply that if there is any S there is also some P. “All S is P and Some S is P, it is true, do not imply that ‘if there is any P there is also some S.’ But then Some P is S does not necessarily imply that either. There can, therefore, be no objection, on that score, against inferring, by conversion, Some P is S from All S is P or Some S is P. With the vindication of conversion all the remaining supposed illegitimate inferences connected with it are also vindicated. We may, therefore, conclude that to let no propositional form as such necessarily imply the existence of either its subject or its predicate in no way affects the validity of any of the traditional inferences of logic” (Studies in Logic, p. 147). I have dealt with Dr Wolf’s position in the note on page 216; and it is unnecessary to repeat the argument here. If importance is attached to concrete examples, I may suggest, as an example for conversion, All blue roses are blue (a formal proposition which must be regarded as valid on the existential supposition under discussion); and, as an example for inversion, All human actions are foreseen by the Deity. There are, moreover, certain difficulties connected with syllogistic and more complex reasonings that need a brief separate discussion, even when the case of conversion has been disposed of.