All mathematics is produced by physical objects (brains, computers). Therefore the laws of physics determine what theorems are possible, and mathematics has no existence independent of our universe.
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The limits of mathematical structure are not given by physics, but by mathematical structure itself. The Church Turing thesis is a physical law, but one that also applies to a-physical universes (if you arrange *anything* into a computer you can do constructive math on it).
I don't think you got my point. The Church-Turing thesis is a product of Church's and Turing's minds, and therefore it's a physical entity, whatever universes it might apply to or not. (And its universes can be realized in computers or in our imagination, i.e., physically.)
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Physicalism may or may not be true. If physicalism is not true (e.g., the universe is a computer game), then Turing's brain is not be a physical object, yet the Church Turing thesis stays the same.
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A computer game still needs a physical substrate to run?
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So, Pedro, what you're saying is you're a Kantian? Do you accept Kant's synthetic apriori judgements in regards to mathematics/arithemtic?
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Pedro might not be a Kantian in belief but in spirit. I think Kant gives logical entities independent, but self contained existence (mathematical entities exist only in mathematics). Kant was a pre-computation cognitive scientist, parsing high level concepts into natural language
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That is precisely the error.
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