Lack of Freewill doesn't mean lack of choice

[Half_Man_Half_Wit]

@Mijin

Imagine someone with a pen and paper using your function to work out whether I’ll drink coffee or tea. At some point on that piece of paper will be written, whether explicitly or implicitly, “It’s getting a bit late for coffee, I’ll have a tea” if those were my conscious thoughts prior to choosing tea.
It’s a wholly incorrect framing to imagine my conscious thoughts as not being relevant to the choice.

I gave that argument short shrift earlier, but it’s an issue worth considering. First, as @Max_S has pointed out, in that form, it doesn’t quite work: situations in which there are closed form solutions to the underlying dynamics can ‘leapfrog’ any particular intermediate states and directly calculate later ones. So, for a two-body problem in gravitational dynamics, I can calculate the relative position at any point in time without taking any account of intermediate positions.

But that isn’t the case anymore for more complex situations—generally, situations that can be used to model universal computation: then, the task of finding the state at any given point in time is equivalent to the halting problem, and hence, in general unsolvable. Thus, no such closed-form solutions exist, and we’re left with having to work out the dynamics step by step. This is sometimes termed ‘computational irreducibility’. So here’s a version of the argument I’ve used before:

@Half_Man_Half_Wit

For systems of sufficient complexity—which, suggestively, are systems at just the same level of complexity such that there are independent propositions about that system, namely the threshold of universal computation, which will be elaborated on when we get to the third requirement—any explanation of their behavior at a given point depends on the entire history of that system, in the sense that we can only ‘predict’ that system’s behavior by explicit, step-by-step simulation. But that’s effectively just the same as taking that system, or perhaps a copy of it, and watching what it does—that is, what the system does is an indispensable element of accounting for the system’s behavior.

Now suppose that such a system meets a point where it has two options, A or B, which are both logically compatible with all the facts about the universe at a given point in time. Then, when it chooses A, due to its irreducibility, any account of its choosing A will include the system making that choice—that is, there is nothing else but the system making that choice that accounts for the outcome A. This, I believe, is the truest notion of freedom that makes sense.

But I don’t really believe this argument works anymore. For one, there’s some heavy lifting done by the notion of a ‘copy’ of the system—in general, this will be what’s computationally termed a ‘reduction’, i.e. a problem in the same problem-class whose solution can be used to (efficiently) find a solution of another. But it’s not at all clear whether what we’re computing really amounts to some version of ‘the system making that choice’—there will be a map from the computation to that system, but it’s questionable whether that map suffices to proclaim identity.

But more seriously, the above depends on an implicit premise that any unavoidable feature of a process must be relevant to its outcome—which is simply false. So if I boil potatoes, the burbling sound the water makes is unavoidable in the process, but doesn’t actually contribute to getting the potatoes done. The waste heat produced is unavoidable to the operation of any machinery, but doesn’t actually, say, move my car forward.

So even if something equivalent to you making a decision occurs in every possible account of that decision being made, that doesn’t mean that therefore, your decision is relevant to what happens after. It could be just ‘waste cogitation’, an ineluctable by-product, but not itself efficacious in bringing it about. And indeed, that’s what the fact that your decision doesn’t actually hold any sway over the outcome—doesn’t actually pick one option over the other, the way a random coin flip would do—is pointing to.

@Mijin

I am not aware of whether there are other interpretations of “slice” in the block universe, but since different observers can disagree on the order of events (and neither perspective is more correct), I very much doubt that a film reel set of spatial slices through time is going to make any sense.

Well, it’s perfectly possible to formulate general relativity in a way that starts with a foliation of the universe into 3-surfaces—this is the ADM formalism. So this gets you a ‘slicing’ of the universe that would work for a ‘film reel’ type of analogy. (Relatedly, the shape dynamics of Julian Barbour takes as its dynamical content three-dimensional geometries—‘shapes’—and can be shown to be equivalent to the ADM formulation—it’s what the above ‘Snapverse’ is based on.)

@Pseudonym

determinism = events are only caused by previous events

vs.

indeterminism = some events aren’t caused by previous events

I don’t think it’s helpful to entangle the notions of causality and determinism like this—they’re logically perfectly independent ideas. Determinism can be true in a universe in which there are no causal relations, such as a block universe, or the collection of ‘snapshots’ I have called the ‘Snapverse’ above, or in which causal relations—if one should call them thus—never obtain between successive moments, but only between some fundamental substrate, e.g. Malebranche’s god. A simulated universe likewise seems deterministic from the inside, but there are no causal relations between its objects, but the motions of objects supervene on the computational processes of the underlying system.

On the other hand, it’s quite possible, and has been gaining traction recently, to think about causality in a probabilistic fashion, as in interventionist accounts—where A could be a cause of B even if the relationship between the two isn’t deterministic, but the occurrence of A simply increases the probability of the occurrence of B.