I have heard that the only argument we have at the moment for the existence of free will rests on quantum mechanics, however I'm not entirely sure how this works. Could you please help me with an example of how quantum mechanics expresses our free will?

QM may give us reason for believing that determinism is false. (Actually, even this claim is problematic, but it at least has some plausibility. If we think the world behaves as QM says it does, and think that QM implies that some events are irredeemably chancy, then it seems to follow that that the state of the world at one time doesn't deterministically fix how things must be at later times.)

But even if QM gives us reason for believing that determinism is false, that doesn't establish that we do have free will. For the claim that there are irredeemably chancy events plainly doesn't show anything about whether we are in control of our destiny in any interesting sense. It could still be that "free will" is an illusion, that everything that happens to us is as the result of happenings quite out of our control, and our supposedly free decisions are like the froth on the wave, doing no serious causal work. It's just that that underlying causality is chancy.

Of course, compatabilists will also argue the other way about: even if determinism is true, that doesn't establish that we don't have free will either. But that's another story.

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