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Arithmetic existed long before its axiomatization. Arithmetic was useful and no one stumbled upon contradictions in it. So it was natural to suppose that it can
by red75prime 7y ago
Arithmetic existed long before its axiomatization. Arithmetic was useful and no one stumbled upon contradictions in it. So it was natural to suppose that it can be described by some axiomatic system. Peano found it.
- kevin_thibedeau 7y agoIt is a system for modeling concepts invented by man. Everything that falls out of such a system is a product of the invention. Numbers don't inherently exist. Everything derived from that concept can't be a "discovery".
- red75prime 7y ago> Numbers don't inherently exist How do we know that it is true?
- kevin_thibedeau 7y agoThey are symbols that we assign arbitrary meaning to. They are useful because of the axiomatic framework constructed to support them.