Again, that’s just one of the possible interpretations of indeterminacy—that the universe goes and flips a coin, so to speak, determining the outcome of every ‘undetermined’ situation for you. But that’s not necessarily how things work—the chess player has a certain chance of making a move, but whatever move they make is due to their choosing. Now, you might say that this choosing is itself just a process that’s either deterministic or involves an indeterministic element, but that just pushes back the question one step. The point remains: chance could just as well mean openness to different possible continuations as it could mean a random draw. The laws of physics don’t say; all we do know is that at certain junctures, the current state of the world plus the laws of physics don’t uniquely specify the next move, so to speak. You propose that at such point, some black-box mechanism flips a coin or rolls a die, but that’s a metaphysical hypothesis on your part.
The will, of course. Now, you might say: but then, the will itself is either determined, or set by chance. But again, that just pushes the question back one step. Somebody intent on defending free will won’t disagree on that—the disagreement is where things bottom out, so to speak. You say events occur either causally, or by appeal to whatever it is that determines random outcomes; the defender of free will holds that, at least sometimes, they occur due to being willed. Each of these is a black box—neither stands on more solid footing.
In fact, it’s easy to prove that a universe that has the resources of producing (genuinely) random outcomes has the resources of producing freely willed outcomes: both depend on the same infinitary powers. Consider Thomson’s lamp: it’s switched on after a second, off after half a second, on again after a quarter, and so on. What is its state after two seconds? Clearly, it can’t be on: for every time that it has been switched on, it also has been switched off. And for the same reason, it can’t be off! But it must be in either of these states (those being the only states available to it). So whatever state it is in can’t be a function of its history.
Randomness works the same way. An algorithmically random bit is formally independent (from a certain axiom system, say)—it’s an undecidable proposition. In fact, it’s equal to solving a particular instance of the halting problem—something that’s impossible for a computer, in general. But a general procedure to solve the halting problem is the following: you simulate the first step of the process in one second, the second step in half a second, the third step in a quarter… And so on. After two seconds, you know whether the process halts, and have thereby generated a random bit.
But the same process can be used to produce freely willed outcome. For if nothing but the will determines the will, we’re locked in an infinite regress: my will to eat a peanut butter sandwich must be made either peanut-butter-willing or non-peanut-butter willing; so for my decision to eat a peanut butter sandwich to be free, the fact that my will is peanut-butter-willing must be free, likewise. Thus, it must be set by my will—which must therefore be peanut-butter-willing-willing, rather than non-peanut-butter-willing-willing, and freely so. And so on. So, we again have an infinite regress at hand—but all of the infinitely many rungs of the ladder can be set by a process equivalent to the one I described giving rise to a random bit.
So you might say, well, actually, there’s no randomness in the universe, there’s just pseudo-randomness. But then, the same infinity crops up at two (superficially) distinct places: first, either the chain of causality is infinite, or it isn’t. If it isn’t, it must have started somewhere—but then, that starting place can’t be causally determined (perhaps it’s some random initial condition—which leads us back to where we were). But more importantly, in any given instance of causation, we’re faced with the same regress: if matters of fact A made it so that matters of fact B obtain, what made it so that matters of fact A are matters-of-fact-B-causing?
So in any case, we bump up against an infinite gap. Which really is no wonder: the question of how things happen is outside of the domain of scientific reasoning; it only describes their regularities. The way things connect is an input into the process, and trying to turn that process on its own input leads to self-referential circularity: the origin of the regresses we’ve seen. Claiming that because these methods are insufficient for this sort of analysis, there must be no ‘there’ there, is essentially to claim that the Earth must be flat, because all our maps are: limitations on the models we use do not imply equivalent limitations on the things modelled.
The difference between the free-will proponent and the free-will opponent then is just what notions they’re willing to accept as ‘basic’: causality, chance, or free will. Neither is in any way in a better position here.
