[HUM 3551] Whatever will be, will be

It is often said that the notion of free will is incompatible with causal determinism, namely, "the idea that every event is necessitated by antecedent events and conditions together with the laws of nature." But the notion of free will may also be incompatible with classical logic (more specifically, the principle of bivalence according to which, for any proposition p, either p is true or p is false), as Aristotle's discussion of the problem of future contingents suggests.

Consider the following proposition:

1. Neo will choose the red pill.

On the one hand, if (1) is true, then Neo will choose the red pill and there is nothing he can do about it. On the other hand, if (1) is false, then it is not the case that Neo will choose the red pill and, again, there is nothing he can do about it. Either way, Neo cannot help but choose the red pill if (1) is true, or not choose the red pill if (1) is false, which means that Neo cannot choose freely.

What do you make of this argument? Does it show that the notion of free will is incompatible with classical logic (specifically, the principle of bivalence)? If so, which, if any, should we give up?