- Either it is true that all events are causally determined (determinism) or it is false that all events are causally determined (indeterminism).
- If determinism is true, then there is no real choice, for a choice is an event, and all events are causally determined.
- If indeterminism is true, then there is no real choice, for a choice is an event, and events are either causally determined or not determined at all.
- If there is no real choice, there is no free will.
- Therefore, if determinism is true or indeterminism is true, there is no free will.
- Therefore, there is no free will.
I have thought for a while that the solution lies in this word "determined". It's at least sometimes glossed as semantically empty. That is, "causally determined" just means "caused". If that's true, though, then (2) and (3) are false. (2) is false because even if an event is caused, its causes may only contribute to its likelihood of occurring. So, there can still be room for real choice, in that any particular choice is only made more likely, but not guaranteed, by the causal history. If we conceive of agency as a source of causes (which, plausibly, it is), then choice, although in part caused by external circumstances, is also caused by an internal event which "flows from" the agent. So, the causal influence of the external circumstances can be overwhelmed or swamped by the internal influence of the agent's own will. By the same token, (3) would turn out to be false, because (3) suggests that at least some events are causally determined -- and, as said, if "causally determined" means "caused", then this leaves room for free will.
However, if there is supposed to be a difference between "causally determined" and "caused", then why is the possibility that an event is caused (such as by having its probability increased by its causes, including agency) being ruled out in favour of the (apparently stronger) requirement that events are causally determined?
In short, once we accept that there is a difference between a cause determining (or guaranteeing) its effect and an effect being caused, we can allow that an agent has a will that itself exerts causal influence. At least sometimes, agents will not choose what they do, and will be under the sway of external circumstances. (We've all experienced something like that at various points in our lives.) However, at least sometimes, agents will choose what they do, by exerting their own internal influence over events.
Really, this requires accepting two metaphysical committments. First, the world is not deterministically causal, but is probabilistically causal. Second, agency is a form of causal influence. (Which, I should note, can itself be caused: it is "free" in the sense that its "actions" are not determined by its causal history, but only influenced.)