Post #2668009
2026-05-07 17:01 UTC
@mc@mathstodon.xyz hm, no references to Lawvere’s ETCS (1964) or its recent presentation by Leinster in Rethinking Set Theory (2014) https://arxiv.org/abs/1212.6543
A educated hobbyist’s opinion: the problem with set theory as traditionally presented is not that it’s too powerful, although it may be that, too; it’s that for most mathematics other than set theory itself, it demands awkward, low-level encodings.
Replies (1)
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@cdrichards@mathstodon.xyz 2026-05-07 17:17
@mc@mathstodon.xyz I want to ask, who is the customer for this product. “Core” mathematicians should be able to ignore foundations, and I assume they mostly do. Set theorists are fine, thanks. For non-set theorists interested in foundations, a set that includes me, the literature shows lots of ways to mix and match axioms if e.g. you don’t like arbitrary choice, or if Replacement gives you a bad vibe. I do see some value in narrowing the gap between math-as-encoded (in a foundational system) and math-as-practiced, but that’s not what’s happening here, AFAICT.