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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Cantor's theorem implies that there are sets having cardinality greater than the infinite cardinality of the set of natural numbers. What is the law of physics that demands that ?
Cantor's theorem is a product of Cantor's mind, and therefore of physics. Infinity exists only in our imagination, and that's why it exists.
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Physics laws does not like infinities of infinities
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They allow us to formulate them, which is all that's needed.
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Not sure you've really dealt with Cantor's theorem & actual infinities objection. Diagonal procedure happens in minds, obvi, but what about these mathematical objects? Are numbers real? Worry you're begging the question w/ the "minds reduce to brains" reply to ontological issues.
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Are sets real? Apart from my beliefs about their ontological status. Benaceraff has a trio of articles that stymie this reduction of mathematics to brain states.
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Laws of physics at what scale? At our own scale, reality is ruled by the forces of gravity & electromagnetism; at subatomic level there is no gravity & electromagnetism has to deal of strong and weak nuclear forces, instead. Logic is pure symbolism, figure without ground.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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Cantor's theorem is a formulation of a Mathematical truth. While the formulation was produced by Cantor's mind, the Mathematical truth wasn't.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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