How to solve Blum's paradox
In An Essay on Free Will, Peter van Inwagen (1983: 93-95) produced a classic argument for incompatibilism, the claim that freedom and determinism are incompatible. Van Inwagen begins by assuming that, for any proposition p, it is a necessary condition of someone's being free with respect to p that she have a choice about whether p. He then goes on to argue that 'if determinism is true, then no one ever has any choice about anything' (1983: 95). In his rigorous presentation of this 'consequence' argument, van Inwagen uses 'Op' to abbreviate 'it is broadly logically necessary that p', and uses 'Np' to abbreviate 'p and no one ever has, or ever had, any choice about whether p'. The argument itself relies on the following two principles, Alpha and Beta: