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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Just as offensive and questionable as: “All physical objects result from information processing in human brains, and therefore human brains determine what physical objects are possible, and physics has no existence independent of our psychology,” no?
No. All the mathematics we know is produced by our brains and computers. That's a fact. As for physical objects, we don't know what they're produced by.
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Are we certain that (mathematical) thoughts are the result of brain information processing?
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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It's a trope maybe that mathematics is discovered and not created but it does support the idea that constructive mathematics is as real as a physical object. When viewed via that lens it would push back on your idea that mathematics is a creation of a computational entity.
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Do you think mathematical objects exist in the physical universe, or that they are abstract relational properties over patterns of information? Eg. I don't think that there are circles in the physical universe. Mathematics is about discoveries in the space of automatic creations.
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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).
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Btw I think of physicalism as the hypothesis that our universe is directly emergent over a causally closed layer of automata; the alternative would be that our universe is being arbitrarily simulated in a symbolic computer. Mathematics would always be the same.
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But our perception of physical objects is intrinsically linked to how they behave. According to physics that is
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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This is faulty reasoning. You're putting your answer in by claiming that this is a fact. Instead, this is precisely the difficult question if this is a fact.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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*interpreted by* not produced. Ditto for physical objects.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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All the mathematics *we know* is not all the mathematics.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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That is very very very much, not a fact.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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