The Strong Free Will Theorem (2009) [pdf]

You are assuming your conclusion. If free will exists, it might exist outside the current understanding of physics. Most likely, it does (if it exists!)

> it disallows the idea of a decision being undetermined and free to decide

That doesn't compute. A decision doesn't do deciding. A decider decides decisions. Any phenomena of "will" necessarily implies contingency on a prior. To ask for non-contingency is to ask for freedom _from_ will.

Yep. This is what I mean by my second paragraph -- when I believe something else to be free-willed is exactly when I cannot predict its actions, but believe it to be capable of doing so (i.e., it believes itself to have free will). So, a pachinko ball, while its haphazard movement is unpredictable by me, does not have free will, because it does not have the capability to predict its own movement. Nor does an individual ant, since I can predict its actions in response to chemical stimuli, regardless of whether it can.

Whereas myself... I know people in general can have a variety of responses to any given stimuli. But I know exactly what response I will have to a stimuli that has just occurred. From my point of view, I am very free-willed! After all, I'm "choosing" one out of a multitude of possible responses to this stimuli. But really, my "choice" is determined by physics, and the illusion of free will is exactly that I -- as the sole entity with the capability to observe my own internal state -- can predict my response, and no-one else can.

I think also, an additional factor is that of volition: the actions I take should somehow derive from, and act to fulfill, what I consider to be my (chemically deterministically determined) desires. Otherwise I might perceive "someone else" to be in control of my person.

I'd say dualism absolutely solves this problem, or at least can provide the tools to do so.

(I say all of this as a devil's advocate, and nothing more)

Imagine that heaven exists, and is a kind of meta-universe that our reality is a subset of. It has access to a higher order of systems than those within its subset, and they can say things about truth that the reality subset cannot (because of incompleteness; a system sufficiently powerful to say all true things is unable to prove all of them). Things that we cannot write proofs about, that we must accept as axioms (for example, in the space of ethics and morality) may be trivially expressible in the higher-order logic of meta-heaven.

Say now too that the dualistic, non-material constituent, the Soul, exists in this meta-heaven. It has access to this higher-order reasoning, and can make causal decisions according to it. However, to its physical coupling in the reality subset, these decisions will appear to be random and non-causal. They will be the outcome of nothing from within the universe. Manifestation of Free Will and Randomness can be considered to be indistinguishable in this sense, from the perspective of something inside the system that they are operating on.

It still pushes the problem 'up' one level, but who knows what the physics of a meta-heaven looks like. We can't even imagine it, in the way that a computer can't imagine its own halting. Hence all the talk of ineffability in the older dogmas of the world.

> This does not mean free will is anywhere to be found in one of those intermediate layers

The problem here is that you're carrying some preconceptions of what free will means into this debate. The whole point of the free will debate is to define free will and figure out what it means.

Think of it this way, you can define a term in two ways: via denotative or connotative definitions. Incompatibilists push a connotative definition of free will, where they say, "free will must have such and such properties, oh and look! humans don't have those properties, therefore people don't have free will". They have been wrong every single time they've claimed a property was necessary.

By contrast, most people typically reason with denotative definitions saying, "that thing I do when I make a choice free from coercion, that's free will". And then we explore precisely what this means and what properties this requires.

As for it being just a heuristic, I'm not sure that's accurate. Take a sorting algorithm and point out precisely which step actually does the sorting. Well that's nonsense isn't it? Every step is essential to a sorting algorithm, and removing any single step breaks the sorting property.

Your god of the gaps argument is essentially trying to do the same thing with free will: you can't point to any specific brain state and say that's free will in action, but the ensemble is what produces what we recognize as free will. All brain states we see when a decision is being made are essential to making a free choice.