SeanMCoincon comments on Logical Pinpointing - Less Wrong

62 Post author: Eliezer_Yudkowsky 02 November 2012 03:33PM

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Comment author: SeanMCoincon 16 July 2015 09:58:48PM 1 point [-]

"The axioms aren't things you're arbitrarily making up, or assuming for convenience-of-proof, about some pre-existent thing called numbers. You need axioms to pin down a mathematical universe before you can talk about it in the first place. The axioms are pinning down what the heck this 'NUM-burz' sound means in the first place - that your mouth is talking about 0, 1, 2, 3, and so on."

Ok NOW I finally get the whole Peano arithmetic thing. ...Took me long enough. Thanks kindly, unusually-fast-thinking mathematician!