QM may give us reason for believing that determinism is false. (Actually, even this claim is problematic, but it at least has some plausibility. If we think the world behaves as QM says it does, and think that QM implies that some events are irredeemably chancy, then it seems to follow that that the state of the world at one time doesn't deterministically fix how things must be at later times.) But even if QM gives us reason for believing that determinism is false , that doesn't establish that we do have free will. For the claim that there are irredeemably chancy events plainly doesn't show anything about whether we are in control of our destiny in any interesting sense. It could still be that "free will" is an illusion, that everything that happens to us is as the result of happenings quite out of our control, and our supposedly free decisions are like the froth on the wave, doing no serious causal work. It's just that that underlying causality is chancy. Of course,...

It is not entirely straightforward to come up with a cogent statement of determinism. But perhaps something along the following lines will do: our world is a deterministic one if the laws of nature are such that, given the past and current state of the world, there is only one possible way its future state can evolve. If you prefer that in "possible world" talk, then the idea is that the actual laws are such that any other possible world which shares these same laws, and whose past and present duplicates that of the actual world, will also be a future duplicate. Thus understood, the claim that our world is a deterministic one is a claim about the shape of the laws of nature governing the world. Do they, so to speak, uniquely fix what will happen next (given the past and current state of the world); or do they allow e.g. for irreducibly chancy events? And that is surely an empirical question. We can't settle from the armchair whether (i) we live in a "classical" world where the laws make the world...

A footnote to Eddy Nahmias's very helpful answer. What should we learn from all the complexities of the debates which he touches on? We could say: The ins and outs of the debates just go to show that our concept of "free will" is a very complicated and sophisticated one, although one of which it is difficult to command a clear view. We need to do more careful analytic work to explore how this pivotally important concept works. But another line is: We can now begin to see that talk of "free will" muddles together quite a variety of different things we might care about (such as the capacity to act on our desires, the capacity for self-control, having desires we reflectively identify with, absence of interference by others, etc.). There isn't a unitary concept here, and undifferentiated talk of "free will" isn't very helpful. Some of us incline to the second line, taking our cue from e.g. Daniel Dennett's provoking and characteristically very readable 1984 book, Elbow Room: The Varieties of...