Note 240 — Chapter VIII

Dr Wolf (Studies in Logic, p. 132) denies the validity of this reasoning. He admits apparently that the existential propositions SPʹ = 0 and Either S = 0 or SPʹ > 0 are not contradictories; but he denies that on the supposition under discussion SaP and SPʹ = 0 are equivalent. His main ground for taking this view is that SaP carries with it the implication If there are any S’s they are all P’s, while SPʹ = 0 does not carry with it any such implication. This position has been already criticized in section 157. Dr Wolf relies partly upon concrete examples, but in so doing he complicates the discussion by introducing modal forms of expression. Thus for the proposition “Some successful candidates do not receive scholarships,” we find substituted in the course of his argument “If there are any successful candidates then some of them do not (or need not) receive scholarships,” and the insertion of the words in brackets yields a proposition which, although an inference from the original proposition, is not really equivalent to it, unless the original proposition is itself interpreted modally. Later on Dr Wolf explicitly alters the whole problem by assuming that what is under consideration is a modal schedule of propositions. Thus he goes on to say, “What SaP and SeP really express severally is the necessity and the impossibility of S being P”; and for the purpose of contradicting SaP and SeP, “SiP and SoP need mean no more than S may be P and S need not be P.” The question how far SaP and SeP should be interpreted modally is discussed elsewhere. All I would point out here is that it is a distinct question from that raised in the text, which is a question relating to the traditional schedule of propositions interpreted assertorically. The whole question of existential import is indeed one that cannot be discussed to any purpose until the character of the schedule of propositions under consideration has been defined. From the mixing up of schedules and interpretations nothing but confusion can result. In the following section the opposition of modals will be briefly considered in connexion with their existential import.