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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What about statements which are true but unprovable?
Those are a consequence of assuming infinity exists, which it doesn't outside our minds (and Godel's, in particular).
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I don't think they are artifact. For the sake of argument, how we can contemplate things that don't exist?
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Precisely because they exist in our minds, being physically created by our brains. Otherwise we couldn't contemplate them.
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The statement “outside our minds” is incoherent. Our minds are just a particular swirling of the ripples in the quantum pond. It’s a local phenomenon that you can say is either emergent or basic. Nature is self-describing. So you have the real using the “non-real”.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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