Evan Washington

https://mathstodon.xyz/@eewash

I'm a philosopher interested in applying formal tools like logic and category theory to philosophical problems. I also like comic books and movies

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Last Notes

2026-04-26 01:34:22 UTC

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This framing seems rather bizarre to me. I'll try to explain why:
Okay, so the theory of groups isn't categorical. And neither is set theory.
But (1) you don't need Gödel's incompleteness theorem to see this? And (2) we know of theories which *are* categorical, so it's not entirely naive to imagine that we might manage to cook another up.
(3) Even if you shouldn't be surprised in the case of sets (and I'm not so sure about that), I think you *should* be surprised in the case of arithmetic.
We know exactly what the intended model is. We might hope that it's more like writing down axioms for one particular group rather than for all groups.
But consider the complete theory of true arithmetic (i.e. Th(N) in the language of Peano arithmetic). Gödel's theorem does tell us something about this theory (that we cannot effectively axiomatize it) but nothing (directly) about its categoricity. And of course, there are *many* other countable models of Th(N), basically as many as possible.

2024-09-13 19:35:46 UTC

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yeah! that's better!

2024-09-12 21:14:59 UTC

here to start a fight: to be a number is to be an element of a ring