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 is the ontology of infinity (i.e. the unending process, of which the “number”
, is one example)?
There are no unending processes outside of our imagination. Infinity is just a useful approximation.
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Don’t know how you know that. You’re privileging the reality of thing described over that of the description. Descriptions aren’t actually real. Yes, maybe
is strictly imaginary, but maybe is really real and stuff is just a quantization thereof.Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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What about rethinking the relation between contingency and infinity? If infinity was nothing but an approximation, would we actually be able to 'imagine' the possibility of something "more than infinite"? I would not say so. It can't be only physical objects that produce all m.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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What is aleph1 the approximation of if aleph0 already exceeds the number of entities in the universe?
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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One finds it exceedingly difficult to hubristically consider Cantor's rigorous explication of degrees of infinity as being a mere "useful approximation." It is also interesting that beyond a certain degree of infinity, logic begins to break down and collapses into contradiction.
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Consider also the infinite digits of π, something quite outside the realm of human imagination. It would be quite the result were it to prove to be a normal number. The most recent achievement is 50 trillion digits. 5 years earlier, the achievement was 22 trillion digits.
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Actually, infinity is extremely real and it's the scalar invariant curvature of a black hole.
Kiitos. Käytämme tätä aikajanasi parantamiseen. KumoaKumoa
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