CANTORS PROOF?
I hope this isnt a stupid question.
Can someone explain to me why cantor’s infinity isnt trivial? Im not the only person in the world who thinks this. But as far as i can tell whether you adopt finitism or infinity is pragmatic utility not truth. And if you dig into Godel, Cantor or ZFC, its platonic and does not represent except loosely, language and science.
Arent we just extrapolating the platonic to the real? Isnt that an error? If thats true then gods exist too in the same form as mathematical objects. And if thats the case there is no discipline of science as we understsnd it.
All that exists are real numbers. Everything else is platonic.
The constraint that we place upon our theories is needed to compensate for observability, cognitive limits – mostly to short term
Memory – and for cognitive biases.
That we should avt as if our theories are unbounded is not because they are unbounded, it is because its useful to limit error.
I have to keep working on this a bit.
Source date (UTC): 2013-07-24 05:00:00 UTC
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