PeterDonis said:
This claim is also false. Apparently you haven't fully grasped what I said before: the free will theorem is irrelevant if determinism is true. It only applies to the case where determinism is false. So the theorem can't possibly impose any constrains on what physical mechanisms are present if determinism is true.
The free will theorem is a clear refutation of determinism. Conway and Kochen makes this clear in their lectures. Here's how Conway ended 1 lecture.
He says there's no reason to believe in determinism because there's no evidence for it. Here's a full lecture:
Saying determinism is logically possible is meaningless. It's just saying determinism can't be disproved but neither can solipsism. Neither can Aliens living underground on Europa. Neither can the simulation hypothesis. These things are logically possible but there's no evidence to support these things as a true description of reality. This is why Kochen says it's not about theories anymore but it's about how the universe works.
“It’s not about theories anymore -- it’s about what the universe does,” said Kochen, a professor of mathematics and the associate chair of the Department of Mathematics. “And we’ve found that, from moment to moment, nature doesn’t know what it’s going to do. A particle has a choice.”
https://www.princeton.edu/news/2009/03/23/high-powered-mathematicians-take-free-will
This debate isn't about semantics of the term free will. This debate is about those who support determinism providing a shred of evidence that a physical mechanism can exist as an element of reality that determines the choice of the Experimenter before a measurement occurs.
bhobba already said this mechanism is too complex for us to know. That's like saying U.F.O.'s are Alien spacecraft but it's too complex for us to know.
It's clear that Conway and Kochen are doing 2 things with the free will theorem as it pertains to determinism.
1. They say determinism can't be disproved therefore it's logically possible. This is just common sense. You can't disprove determinism anymore than you can disprove the existence of Aliens. This doesn't mean there's any evidence to support it. This is why they talked about determinism and solipsism in the paper.
2. The free will theorem makes a physical mechanism that's an element of reality prior to measurement something that's as close to impossible as it gets. They clearly show any such mechanism can't be an element of reality prior to measurement. They say:
The fact that they cannot always predict the results of future experiments has sometimes been described just as a defect of theories extending quantum mechanics. However, if our physical axioms are even approximately true, the free will assumption implies the stronger result, that no theory, whether it extends quantum mechanics or not, can correctly predict the results of future spin experiments. It also makes it clear that this failure to predict is a merit rather than a defect, since these results involve free decisions that the universe has not yet made.
Wow, and this why I keep asking for evidence of a physical mechanism that can predict the choice of the Experimenter and the history of the particle prior to measurement. Determinism can't be true unless you provide evidence that such a mechanism exists.
It also says:
We remark that the Free Will assumption, that the experimenters’ choice of directions is not a function of the information accessible to them, has allowed us to make our theorem refer to the world itself, rather than merely to some theory of the world.
And again:
It follows that we cannot prove our Free Will assumption – determinism, like solipsism, is logically possible. Both the non-existence of free agents in determism and the external world in solipsism are rightly conjured up by philosophers as consistent if unbelievable universes to show the limits of what is possible, but we discard them as serious views of our universe.
We discard them as serious views of our universe. Again, saying something is logically possible requires meeting a very low bar. You can say this about almost any theory with no evidence is logically possible. But they make it crystal clear that there can't be a physical mechanism that can predict these future events prior to measurement if their physical Axioms are even approximately true.
