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Physicalistic determinism would require that the entire physicalistic universe would be determined. Non-compatiblistic concepts of free will generally hold that our conscious self awareness and free will is the result of "something" that is not bound by physicalism (a "soul" for want of a better word). Well, since determinism only says what will happen with regard to physicalism, then an extra-physicalisitc component to consciousness could not have physicalistic effects, but it could have extra-physicalistic effects. Once someone accepts an extra-physicalistic input into human consciousness, then one would have no problem accepting extra-physicalistic outputs. As long as the effects of extraphysicalistic free will are exclusively extraphysicalistic then physicalistic determinism and free will are completely independent of one another and no argument against that kind of free will would seem to have any validity.

An example of a non-physicalistic output to a choice made by a non-physicalistic input (soul, consciousness, what have you) would be that if the universe existed as "many worlds" fulfilling all allowed possibilities, then the output of a non-physicalistic input could be the determination of which of the myriad of worlds you are conscious within.

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    Yes, they would, this option is called epiphenomenalism. However, the view of consciousness and free will as physically idle sidekicks to the body is rather unattractive. That they could counterfactually do something else in a parallel world is little consolation. Unless, of course, you mean that such parallel world actually exists, and consciousness can force its way into it by sheer will, but that would hardly be "extra-physicalistic".
    – Conifold
    Dec 19, 2021 at 7:08
  • @Conifold. Epiphenomenalism doesn't entail free will does it? SEP's description: "Epiphenomenalism is the view that mental events are caused by physical events in the brain, but have no effects upon any physical events". Or were you saying that epiphenomenalism can accommodate free will somehow? If so, I'm wondering how. Dec 19, 2021 at 10:13
  • @Conifold my pure conjecture here is a model that extraphysicalistic inputs could determine one thing: which path through many worlds your consciousness maintains awareness of. None of the individual many worlds would be altered in that process. In a sense, you would only be conscious of the one path that coincides with your free will, but since the mechanism is extraphysicalistic it could be affect by, but not deterministically bound by the path that your consciousness observes. I'm not really promoting this, just pointing out that there are models that avoid certain arguments against. Dec 19, 2021 at 15:55
  • Also, it seems that compatibilistic free will (one that only accepts physicalistic=real) is far more problematic than extraphysicalistic free will. I'm not sure that an extraphysicalistic model could be distinguished empirically from a compatabilistic model though. Your conclusion would depend on your presuppositions. Dec 19, 2021 at 16:00
  • @Futilitarian It's an old conception that goes back to ancient Stoics. There are things we cannot control (physical events) and there are things we can control (our attitudes). In Chrysippus's metaphor:"When a dog is tied to a cart, if it wants to follow it is pulled and follows, making its spontaneous act coincide with necessity, but if it does not want to follow it will be compelled in any case". And that is all the free will the dog gets.
    – Conifold
    Dec 19, 2021 at 21:12

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There are many dualist theories, none of which is confirmed as scientifically possible, because they all draw on things outside science.

I believe your example might be classified as a variant of psychophysical parallelism https://en.m.wikipedia.org/wiki/Psychophysical_parallelism

Note your example does not even require the physical world to be deterministic, so your question is not much related to determinism.

Your example with many worlds is unsatisfactory as it does not explain what causes all your bodies in all the possible world to move and act as they do. If your soul just picks one, what is driving all the versions of your body that your soul did not pick? If infinitely many versions of your soul can act in their worlds without any soul present, why bother with souls? Also it would seem unlikely that all souls pick the same world, so you'd have to assume that all people around you are soulless zombies.

This does not make your example impossible, dualism is a free-for-all playground, but you might prefer to look for something more happy. The majority of ordinary people in the USA (non philosophers) currently appears to believe the universe might as well be deterministic as far as it matters for daily life, yet also believes in an eternal soul.

The solution to combining both is too also believe that this is currently not understood by science, that it might be understood one fine day like so many other things that were discovered over time, or that it might remain a mystery forever.

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Determinism is only a theoretical concept. It is not a theory or a belief. It is neither true nor false nor possible.

Free will has many definitions. Depending on the definition it is either an obviously real phenomenon or equally obviously an illogical impossibility. No valid definition leaves the question of free will unanswered, subject to debate, possible.

So, neither is possible.

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