WAYNE STATE UNIVERSITY
IN "It's Actual, so It's Possible" 1 Norwood Russell Hanson argues in the following way. Many philosophers are inclined to accept at once two "philosophical principles": one of these is the principle that all true propositions are logically possible, i.e., self-consistent; the other is the principle that "a proposition whose negation is consistent cannot entail another whose negation is inconsistent--save in that 'degenerate' case wherein a necessary proposition is said to be strictly implied by any proposition whatever" (p. 71). We may restate these two principles as follows:
A. If P is true, then P is logically possible. B. If P is logically contingent, then P entails no necessary propositions. These two principles, Hanson argues, are prima facie inconsistent. For it can be demonstrated that:
C. If P is logically contingent, then "P is logically possible" is necessary. (And from C it follows that "P is logically possible" is either necessarily true or necessarily false.) Now consider some contingent proposition P: by the first principle P (or "P is true") entails "P is possible." By principle C however, "P is possible" is necessary; hence a necessary proposition is entailed "by a contingent one, which contradicts principle B. Hanson then goes on to suggest a way out of the difficulty.
I want to point out a mistake in Hanson's argument for C; and I shall argue further that the solution he proposes to the problem arising from the incompatibility of A, B, and C is quite unacceptable. Now the fact that Hanson's piece is written in dialogue form might create certain difficulties of interpretation. I am assuming throughout that the views expressed by Socrates are Hanson's and that Socrates' argument on pages 71-72 is offered as a genuine proof of principle C.
Socrates' (or Hanson's) proof for C is a reductio ad absurdum; he proposes eo deduce a contradiction from the negation of "P is logically possible" (where P is a contingent proposition) thereby showing that "P is logically possible" is necessary (again, where P is contingent). So he begins by assuming at step (1) of the proof the proposition that P is not logically possible and adds at step (2) the proposition that P is contingent (p. 71). He then deduces a contradiction. But the deduction of a contradiction from the conjunction of these two propositions is hardly astonishing, since "P is con-