Does one have to be aware that one is exercising one's free will, in order to have free will?

Hard to see why, in my opinion. If (say) a free action is one that you undertake such that, at the moment of acting, it was at least logically, and perhaps even physically, possible that you either perform that action or not perform that action, those facts themselves at least seem to be independent of what your awareness is. What would be interesting is an argument that shows that only IF one is aware of the facts just described could those facts obtain ... but at the moment I don't see how to generate such an argument. Perhaps in the mix here is the thought in the other direction, a kind of old-fashioned argument for free will, that states that if one believes one is acting freely then one IS acting freely--or using our conscious experience of (or as of) acting in a way in which it seems to us that multiple options are logically and perhaps physically available as a sufficient condition for acting freely. (Your question concerned whether such awareness was a necessary condition, but here it is offered as a sufficient condition.) But that kind of strategy is very old fashioned, and doesn't seem very convincing to most people -- at best we may be aware of some/many of the causal factors that determine our behaviors/choices, but we hardly seem aware of the "alternate possibilities" that may or may not be open to us when we act--plus the fact that most people believe that there are many causal factors affecting our behavior of which we are not aware, so whatever we ARE aware of could hardly suffice to guarantee the freedom of our action .... so it seems to me that "awareness of alternate possibilities" is neither necessary nor sufficient for freedom ....

This entire answer presupposes a libertarian conception of freedom -- that freedom is/requires alternative possibilities. But you may get a very different sort of answer from compatibilists, who (perhaps) may be more inclined to give positive answers to both the necessary condition and sufficient condition version of your question ...

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