One way is to show that, given a state of the universe, it is possible to determine the next state. From what I understand, this does not seem to be the case.
My instinct is that physics is performing a computation at optimal efficiency. Even if everything is deterministic, there is no other way to determine the outcome other than letting it play out.
In other words, even if a decision you made was bound to happen, there was no other way to find out what that decision would be beside letting you compute it.
So, your decisions can be both deterministic and unpredictable.
From this perspective, I don't think the existence or absence of randomness makes any difference on the question of free will.
This is not a limitation of technical prowess, this is a quality of quantum particles, of thermodynamics, etc.
My point is, if it is impossible to construct such an experiment, it means it is not a question within the domain of science. Science deals with hypothesis which can be realistically disproven.
Maybe. Determinism isn't dead, by any means. Depending on what model of quantum mechanics turns out to actually be correct, full determinism might be just fine. But even if one of the models that would invalidate full on determinism is correct, 'adequate determinism', similar to what Stephen Hawking believed in, might apply - the idea that the level any quantum fluctuations occur at makes it unlikely to result in any difference at the level that human thought, etc., operates at.
Universal predictability would definitely disprove free-will, but disproving universal predictability tells us nothing about free-will.
If determinism is correct, then given enough storage and computational power (or intelligence capable of doing this within their mind), an outside observer would be able to figure out every single action I would ever take before I took it.
If how my brain works is deterministic, and all of my encounters are able to be pre-determined, and those all deterministically shape my decisions and actions, then... how I can I possess libertarian free will?
0: https://upload.wikimedia.org/wikipedia/commons/4/45/Double-c...
To be clear, I think that free will--by definition--cannot exist in a purely deterministic universe. Any semblance of free will in such a universe would be purely illusory. It also cannot exist in a universe where events can only ever be some combination of random events and determined events. Randomness is also not free will.
Free Will would have to be some other special category of events that is neither determined not random. We don't have a word or phrase to describe what these events would be like other than "Free Will." However, lacking the vocabulary and math to describe it does not make it non-existent.
1) Events with no cause such as the beginning of the universe or broader multiverse, depending on your beliefs or 2) Infinite regressions of causal chains if you believe that the universe or God (or a god) has always existed or 3) Some combination of the above.
In all of these, somehow there can be uncaused effects, but in 1) and 3) some causal chains can just begin existing, like free will would require.
That is not even non-existent, more like a misconception which one comes out of by thoroughly examining what "feels" correct. Like Wittgenstein said one of the jobs of philosophy is to free us out of semantic knots. I see free will such a knot arising due to our conception of a separate self from the causality, leading us to project a conception of freedom which makes no sense when examined upon.
There are systems today that we can predict fully (i.e. we can predict what will happen faster than it can actually happen) that decades ago would have been unpredictable due to their chaotic nature. There are systems we cannot predict today that we will be able to in the future. Brains very well could be one of them.