Peter van Inwagen argues (in 'The Incompatibility of Free Will and Determinism ', this journal, March 1975) that free will and determinism can be formally proven to be incompatible. Those of us who distrust formal proofs on such matters will be intrigued; but, I think, not convinced. The usual suspicion that something has gone wrong is again borne out.
Van Inwagen begins with definitions of determinism and free will (p. 186) which I shall accept here. Free will, in particular, is defined in terms of "the power or ability of agents to act otherwise than they in fact do" (p. 188); a minimum necessary condition of free will is that the agent could have done otherwise than he in fact did. And he presents a certain case of consideration. A certain judge, J, can prevent the execution of a certain criminal by raising his hand as a sign of clemency at a certain time, 'To' denotes an instant of time prior to J's birth, 'P0' the state of the world at To, 'P' the state of the world at T, 'L' the conjunction of all the laws of physics. And we will "suppose that the judge was unbound, uninjured, and free from paralysis; that he decided not to raise his hand at T only after a period of calm, rational and relevant deliberation ", etc. (pp. 190-1). He then presents the following sevenstep argument, the seventh of which is alleged to be a consequence of the first six, on any "relevant analysis of 'can', including the "wen.known 'conditional' analysis" (p. 189).
(1) (2) (3) (4) If determinism is true, then the conjunction of Po and L entails P. IfJ had raised his hand at T, then P would be false. If (2) is true, then if J could have raised his hand at T, J could have rendered P false. If J could have rendered P false, and if the conjunction of Po and L entails P, then J could have rendered the conjunction of Po and L false.