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I'm inclined to agree with you, with a few caveats. I do think ZFC isn't the superlative candidate for foundations. That being said, most mathematicians don't r
by throwawaymath 7y ago
I'm inclined to agree with you, with a few caveats. I do think ZFC isn't the superlative candidate for foundations. That being said, most mathematicians don't really think about the foundations of mathematics often (if ever). They use ZFC's set theory because it's a succinct, versatile and useful notation which is frankly very easy to learn.
In that sense there's a compelling argument that a revised set theory might be called for, in the sense that it could be a better fit for the way most mathematicians use set theory in practice. But since Leinster's set theory is axiomatically equivalent to ZFC without regularity, there's also a compelling argument that it's not worth it unless it's significantly more expedient or easy to learn.