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Ritalin comments on Proofs, Implications, and Models - Less Wrong
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Meditation:
It has been claimed that logic and mathematics is the study of which conclusions follow from which premises. But when we say that 2 + 2 = 4, are we really just assuming that? It seems like 2 + 2 = 4 was true well before anyone was around to assume it, that two apples equalled two apples before there was anyone to count them, and that we couldn't make it 5 just by assuming differently.
Two cups of water plus two cups of sugar does not equal four cups of sugar water. ;)