I think it can't be the case because the brain is a chaotic system. But hiding behind chaotic behavior to preserve "free will" is farcical, isn't it? We can't know how the pendulum[0] will swing next, so we can say that it's got free will?
Well, chaos theory is explicitly not a denial of determinism, and speaks more to our ability to precisely measure state and accurately model it than anything else. The more precisely you can can measure state, the longer the Lyapunov time, and the longer we can accurately predict the future states of the system.
There are systems today that we can predict fully (i.e. we can predict what will happen faster than it can actually happen) that decades ago would have been unpredictable due to their chaotic nature. There are systems we cannot predict today that we will be able to in the future. Brains very well could be one of them.
It's not "farcical". If you could prove that physical states are deterministic, you could prove that there is no free will. That statement makes no claims whatsoever about what it means that physical states are not known to be deterministic. In other words, it could have been useful as proof negative of free will, but not as proof positive. And that's okay.
Wheter "free will" exists or not seems like a technicality, tied to whether the Universe is deterministic or not. Whether or not it's deterministic, a brain must still go through its thought processes to come up with any decision. The only difference that non-determinism makes is that the decision may randomly go one way or the other based on low-level fluctuations. Thinking and decision making still occurs even if the Universe is deterministic.
To be clear, I think that free will--by definition--cannot exist in a purely deterministic universe. Any semblance of free will in such a universe would be purely illusory. It also cannot exist in a universe where events can only ever be some combination of random events and determined events. Randomness is also not free will.
Free Will would have to be some other special category of events that is neither determined not random. We don't have a word or phrase to describe what these events would be like other than "Free Will." However, lacking the vocabulary and math to describe it does not make it non-existent.
>Free Will would have to be some other special category of events that is neither determined not random. We don't have a word or phrase to describe what these events would be like other than "Free Will." However, lacking the vocabulary and math to describe it does not make it non-existent.
That is not even non-existent, more like a misconception which one comes out of by thoroughly examining what "feels" correct. Like Wittgenstein said one of the jobs of philosophy is to free us out of semantic knots. I see free will such a knot arising due to our conception of a separate self from the causality, leading us to project a conception of freedom which makes no sense when examined upon.
I think this is some kind of supernatural "free will", and no mechanism has been found for such a thing in science. It's associated with mind–body duality, souls, homunculi inside the body, that kind of thing.
It doesn't have to be super natural either, though. By the nature of it's existence, the universe proves that there can be chains of events spawned that completely undermine our current treatment of causality. A realistic model must include at least one of the following:
1) Events with no cause such as the beginning of the universe or broader multiverse, depending on your beliefs or 2) Infinite regressions of causal chains if you believe that the universe or God (or a god) has always existed or
3) Some combination of the above.
In all of these, somehow there can be uncaused effects, but in 1) and 3) some causal chains can just begin existing, like free will would require.
There are systems today that we can predict fully (i.e. we can predict what will happen faster than it can actually happen) that decades ago would have been unpredictable due to their chaotic nature. There are systems we cannot predict today that we will be able to in the future. Brains very well could be one of them.