What if much of the mathematics we know isn't actually true? Perhaps there isn't even any objective notion of mathematical truth, and no consistent formal system has any better claim to soundness than any other. How could we tell? (1/6)
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At least consistency is a necessary constraint for a theory. Consistency of a theory is a claim about ℕ. So for consistency to be meaningful, ℕ must refer to some structure, about which claims can be meaningful, though establishing truth of non-Σ_1 sentences is difficult. (2/6)
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Gödel's ontological proof shows that God exists. (3/6)
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Therefore ZFC is sound, since God put ZFC in our minds, and would not deceive us. (4/6)
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And there is a true universe of sets, created by God. (5/6)
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Also, minds are not mathematical objects. (6/6)
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Replying to @ModelOfTheory
Only mathematical objects are mathematical objects
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Replying to @StoryOfSystem
Yes, of course. But to use this fact to conclude that minds are not mathematical objects, one first must establish that minds are not mathematical objects.
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Replying to @ModelOfTheory
Notions of mathematical object that involve spending "a lot" of time in Agda Follow up: Could mind be a mathematical object even if minds aren't?
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What distinction are you making between mind and minds?
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Replying to @ModelOfTheory
Mind as the substance, minds as its many instantiations in reality. Like water and drops
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