Bakkot comments on Proofs, Implications, and Models - Less Wrong
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Nor is it obvious how multiplication of apples should work. Apples might be considered an infinite cyclic abelian monoid, if you like, but it's beside the point - the point is that once you know what axioms they satisfy, you now know a whole bunch of stuff.
Well, if you have a row of 3 apples, and you get another three rows, you'll have 9 apples. But multiplying 3 apples by 3 apples would result in 9 apples^2; and I don't know what those look like.