(I see you've been downvoted. Not by me.)

If we don't have the freedom to choose our desires, then on what basis is it reasonable to call decision that take those non-freely-chosen desires into account "free will"?

If Jewishness is inherited from one's mother, and a person's great^200000-grandmother [EDITED to fix an off-by-1000x error, oops] was more like a chimpanzee than a modern human and had neither ethnicity nor religion as we now understand them, then on what basis is it reasonable to call that person Jewish?

If sentences are made up of letters and letters have no meaning, then on what basis is it reasonable to say that sentences have meaning?

It is not always best to make every definition recurse as far back as it possibly can.

David Deutsch's book [...] also [...]

I have read both books. I do not think chapter 7 of TFoR shows that theories with high predictive power but low explanatory power are impossible, but it is some time since I read the book and I have just now only glanced at it rather than rereading it in depth. If you reckon Deutsch says that predictive power guarantees explanatory power, could you remind me where in the chapter he does it? Or, if you have an argument that starts from what Deutsch does in that chapter and concludes that predictive power guarantees explanatory power, could you sketch it? (I do not guarantee to agree with everything Deutsch says.)

Do you distinguish between "will" and "desire"?

I seldom use the word "will" other than in special contexts like "free will". Why do you ask?

What are they [sc. necessary conditions for free will that a compatibilist might state]?

One such might be: "For an action to be freely willed, the causes leading up to it must go via a process of conscious decision by the agent."

[...] not free at all. It is exactly as free as the first case.

Meh, OK. So let me remind you that the question we were (I thought) discussing at this point was: are there clearer-cut satisfactory criteria for "free will" available to incompatibilists than to compatibilists? Now, of course if you say that by definition nothing counts as an instance of free will then that's a nice clear-cut criterion, but it also has (so far as it goes) nothing at all to do with freedom or will or anything else.

I think you're saying something a bit less content-free than that; let me paraphrase and you can correct me if I'm getting it wrong. "Free will means unpredictability-in-principle. Everything is in fact predictable in principle, and therefore nothing is actually an instance of free will." That's less content-free because we can then ask: OK, what if you're wrong about everything being predictable in principle; or what if you're right but we ask about a hypothetical different world where some things aren't predictable in principle?

Let's ask that. Imagine a world in which some sort of objective-collapse quantum mechanics is correct, and many things ultimately happen entirely at random. And let's suppose that whether or not the brain uses quantum effects in any "interesting" way, it is at least affected by them in a chaos-theory sort of way: that is, sometimes microscale randomness arising from quantum mechanics ends up having macroscale effects on what your brain does. And now let's situate my two hypothetical examples in this hypothetical world. In this world, of course, nothing is entirely predictable, but some things are much more predictable than others. In particular, the first version of me (deciding whether to take the bribe on the basis of my moral principles and preferences and so forth, which ends up being very predictable because the bribe is small and my principles and preferences strong) is much more predictable (both in principle and in practice) in this world than the second version (deciding, at gunpoint, on the basis of what I will now make a quantum random number generator rather than a coin flip). In this world, would you accordingly say that first-me is choosing much less freely than second-me?

The only difference between the two cases is your awareness [...]

I don't think that's correct. For instance, in the second case I am coerced by another agent, and in the first I'm not; in the first case my decision is a consequence of my preferences regarding the action in question, and in the second it isn't (though it is a consequence of my preference for living over dying; but I remark that your predictability criterion gives the exact same result if in the second case the random number generator is wired directly into my brain so as to control my actions with no conscious involvement on my part at all).

You may prefer notions of free will with a sort of transitive property, where if X is free and X is caused by Y1,...,Yn (and nothing else) then one of the Y must be free. (Or some more sophisticated variant taking into account the fact that freedom comes in degrees, that the notion of "cause" is kinda problematic, etc.) I see no reason why we have to define free will in such a way. We are happy to say that a brain is intelligent even though it is made of neurons which are not intelligent, that a statue resembles Albert Einstein even though it is made of atoms that do not resemble Einstein, that a woolly jumper is warm even though it is made of individual fibres that aren't, etc.