> Many people believe that free will and determinism are not incompatible (compatibilists).

Could you explain how that works? I'm unfamiliar with that, but I suspect that they may be using a different definition of "free will" than I am familiar with.

> Personally, I'm not even sure introducing non-determinism matters much. What would it even mean? That beyond determinsitic actions defined by our precise history, we get a bit of randomness permuting the whole thing? Does that really make it any freer?

I think free will and randomness are both forms of non-determinism. Non-determinism doesn't prove free will, but it allows for the possibility that it might exist (and post people intuit that randomness could be indistinguishable from non-determinism).

To me, free will is the lack of external forces controlling my decisions and actions. That is, I can decide things for myself, even if those decisions are a deterministic product of my current state.

How are you defining it such that it must be non-deterministic and distinct from randomness? I don't really understand what that means. Assuming there's a single shared reality, what's the source of the non-determinism? Even if you say that's the free will itself, you'd be asserting that our "wills" are somehow capable of randomness.

> To me, free will is the lack of external forces controlling my decisions and actions. That is, I can decide things for myself, even if those decisions are a deterministic product of my current state.

Without some place in the sequence of events that isn't deterministic, I don't see how you can separate your current state from external forces. That is, if your decisions are a deterministic product of your current state and your current state is a deterministic product of other states before it (including states that existed before you did, such as your parents) then I don't see that as "the lack of external forces controlling my decisions and actions".

> How are you defining it such that it must be non-deterministic and distinct from randomness? I don't really understand what that means. Assuming there's a single shared reality, what's the source of the non-determinism? Even if you say that's the free will itself, you'd be asserting that our "wills" are somehow capable of randomness.

Part of the difficulty with talking about free will is that there isn't a clear definition of what it is. However, I do think I can say what it isn't--I think most people don't consider randomness or determinism to be free will. But I also think that it would be nigh impossible to distinguish randomness from free will without a clearer definition of free will.

The fallout of this belief is that I think we could disprove free will if we could prove determinism (but, I don't think we can prove determinism currently). But I don't think we can prove free will, even if we could disprove determinism (I don't think we can do that either). In order to prove free will we would have to disprove both determinism and randomness.

I think in the end we will find out that both interpretations of whether free will exists might be correct, but with determinism being more fundamental. Think about a deterministic machine learning algorithm with a fixed input of training data. The agent/algorithm learns by reacting to it's data input/environment, has goals in the form of a cost function it is actively trying to minimize, has options to adjust its neural weights depending on what it experiences, yet we know the system including the environment is predetermined from the moment we kick off the program. -Khatchig, from "Digital Physics" (the movie).