This is a rehash of a comment I made at Thinking Christian earlier this week.
Theists at TC argue that our intuition is that free will is incompatible with determinism (or determinism plus randomness). Consequently, they argue that free will cannot be physical. However, I think they confuse two intuitions.
Let's distinguish two circumstances:
(1) Irrelevant Choice: a final state arrives, no matter what choice you make.
(2) Deterministic Choice: your choice was fixed by past states of affairs (your preferences and computing ability are fixed by the past).
Do you see a difference between these two?
In principle, cases (1) and (2) might occur from time to time whether the universe were physical or not.
Irrelevant Choice could occur under supernaturalism, e.g., if an asteroid is about to hit your house, your choices won't stop it under physicalism and won't stop it under supernaturalism.
Deterministic Choice is typically associated with physicalism, but could happen under some forms of supernaturalism too.
However, Irrelevant Choice does not always occur under supernaturalism, and does not always occur under deterministic physicalism. Under deterministic physicalism, I still make decisions and can often prevent things from happening by my desire to avoid a final state, even if my choice and action could have been forecast in the past. I am aware that my actions and thoughts are affecting the future, and this awareness deterministically alters my course.
I think theists confuse Irrelevant and Deterministic Choice. Under Irrelevant Choice, though I still wouldn't say that I don't have any agency, it might be fair to say that I don't have effective agency vis-a-vis the inevitable event. That is, my thinking process, whether deterministic or otherwise, cannot stop the event.
But Irrelevant Choice isn't what physicalism entails. At least, it entails it no more frequently than supernaturalism.
Physicalism often entails Deterministic Choice, but it doesn't deny agency, the self, or decision-making capability.
Here's one more way to see the difference between the two cases. In Irrelevant Choice scenarios, the final state is consistent with any choice you make. (For example, the surprise asteroid will impact no matter what you decide.) However, in general, under Deterministic Choice, the final state must be consistent with your choice.
I look forward to getting a response from the folks at TC.