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Schizo comments on Created Already In Motion - Less Wrong
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This is why it's always seemed to silly to me to try to axiomitize logic. Either you already "implement" logic, in which case it's unneccessary, or you don't, in which case you're a rock and there's no point in dealing with you.
I think this also has deeper implications for the philosophy of math -- the desire to fully axiomitize is still deeply ingrained despite Goedel, but in some ways this seems like a more fundamental challenge. You can write down as many rules as you want for string manipulation, but the realization of those rules in actual manipulation remains ineffable on paper.
Axiomatizing logic isn't to make us implement logic in the first place!
It's to enable us to store and communicate logic.
I wouldn't describe any typical human mind as implementing logic. Even those that are logical don't seem to think that way naturally or innately. But particular human minds have had much success thinking with 'axiomitized' logic.