I think that it's a fundamental mistake to assume that free will somehow requires what Patricia Churchland called a "causal vacuum". Free will isn't behavior that occurs without a cause, it's behavior that has a particular kind of cause. Namely behavior that's the result or our own motives, understanding and decision processes. All of these can and probably do have neurological correlates.
It's important to recognize that causality isn't necessarily the same thing as determinism. Causality says that every event has a preceeding cause. Determinism says that the state of the universe at time A determines the state of the universe at time B. My speculation is that that at least some of that causal determination is probabilistic. In other words, causality defines a range of possible outcomes and assigns likelihoods of each one occurring. And as the time interval between A and B increases, those indeterminacies might increase as well, and the probabilities with which accurate predictions can be made of B from A decrease towards chance.
My speculation is that the path that the evolution of the universe has taken is fundamentally unpredictable. In other words, if we ran the 'big bang' all over again, with all of the same initial conditions (as close as they can be physically specified, which might not be entirely precise if things like quantum indeterminacy hold), the evolution of the universe would likely follow an entirely different trajectory the second time. Things might turn out very different.
I should add that when I use words like 'my' and 'myself', I'm not talking about 'the human soul' or Descartes' 'mind substance' or anything like that. I use those words to refer to my own on-board cognitive and volitional process.
Are my internal states caused? Sure. I think that they almost certainly are.
Are they determined? Probably 'yes' with a high degree of accuracy if we are talking about the states and experiences that immediately preceeded them, but probably less accurately if we are talking about how things were a week ago or ten years ago. And I don't really buy the idea that everything I think and do now was already determined long before I was born.
Defining 'free-will' is difficult. We all have an intuition of what it means, but putting that into words is hard. Perhaps the best way to approach it is descriptively, by following how people use the idea and what they typically mean by it in real life.
I'll say that an action of mine is a free act of my own will if it resulted from my own purposes, goals, ideas, evaluations and decisions. In other words, an act of mine is free if the decision to do it arose inside me, so to speak, from a suitable employment of my own internal decision processes, and wasn't imposed on me from outside by some external force. That's typically what people mean when they say, as they might in a court of law, 'He acted of his own free will'.
That doesn't mean that causal processes can't be how those decisions are made. Nor does it mean that our inner states don't determine our behavior. Moving my arm by free-will isn't the same thing as watching it jerk convulsively. The exercise of free-will demands that my moving my arm be the result of my own decision. And that decision isn't just a random event, it needs to have arisen as the result of my own beliefs, goals and purposes. Far from being inconsistent with local determinism, free-will seems to demand it.
It's only when people start insisting that all of our behavior is fully determined by the external environment, by things entirely other than ourselves, that the free-will problems start to arise.
What William James called the 'iron block' kind of hard determinism seems to do violence to the idea of free-will by insisting that while it may seem like my acts are the result of my own decisions, which in turn arose from my own desires, evaluations and beliefs, that all of these were in fact determined by the state of reality long before I ever appeared. Put another way, the details of my internal deliberations and the results that they give rise to were totally imposed on me by the causal force of the universe outside me.
My own belief is that the probabilistic sort of determinism might not pose nearly as much of a challenge to my kind of idea of free-will. That's because while our inner decision processes might indeed be entirely naturalistic and causal in nature, the decisions and actions they result in might not have been precisely determined by the rest of the universe outside us at all. The nature of the surrounding universe might indeed suggest that we're more or less likely to do some things than others, but few adherents of free-will would really care to dispute that. In order to explain precisely why people make the choices they make, simply describing their external environment will rarely if ever be sufficient. The inquirer will have little choice but to look at what's happening inside the person's head.
