this list escalates so quickly https://en.wikipedia.org/wiki/Copenhagenization
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Naïm Camille Favier 🎃
@ncf@types.pl
mastodon 4.8.0-alpha.2+glitchPhD student at Chalmers interested in univalent foundations, category theory and music.
Fuck genAI and everything it represents.
305 Followers
134 Following
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Joined May 25, 2023
i am not a mathematician or a computer scientist, i'm a linguist. it just so happens that i study the languages with which people express precise arguments and computations.
I've just added to my formalisation of @jemlord@mathstodon.xyz 's "Easy Parametricity" a short proof that every function of type (A : U) → A → A is the identity. Such a neat idea!
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@jeanas@mathstodon.xyz @totbwf@types.pl probably completely intractable unless we get rid of like half of Agda's induction features, i'm guessing
I had a pretty fucking cool dad.
Is there a name in category theory for the following situation? Two categories A and U with functors i : A → U and r : U → A such that for all X : U, irX retracts onto X (maybe naturally in X?). Like a "retraction up to retraction" or something.
I ask because the type theoretic version of that where A : U are nested universes is enough to set up Russell's paradox (well known).
Nausicaä of the Valley of the Wind (1984), in addition to being the greatest work of art ever made, contains a remarkably current (if not very subtle) metaphor for AI (hint: it is not the Sea of Decay).
A self-referential self-referential statement about self-referential statements:
I can make statements about myself, like this one.
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@de_Jong_Tom @ionchy @andrejbauer The typst documentation is the best I've seen. The language is also fairly well-designed.
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@jonmsterling@mathstodon.xyz @totbwf@types.pl @jeanas@mathstodon.xyz I think we need to be more precise about "translation to eliminators" here: of course IR doesn't admit a translation to eliminators relative to a type theory without IR (unless you restrict to small IR), but inductive-recursive types themselves can be specified in terms of eliminators, I think?
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@mei Being a decidable order is a proposition (if you don't know why, then... sub-puzzle!), so you can remove the truncation in "strong total order" when proving this.
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@mjd What annoys me most about this is that it seems like the only available way for beginners to learn about foundations, which leads to endless confusion about the thoroughly chaotic and unprincipled way that basic notions are encoded in material sets. Latest example to date but this happens every other week on MSE.
Most people still view type theory as a fringe topic or an advanced area of research, not something for beginners to learn, and this makes me very sad.
catfishing.net
#677 - 8/10 🎉
🐈🐈🐈🐈🐈
🐟🐈🐈🐟🐈
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@mevenlennonbertrand i think i had a similar realisation recently when i saw someone motivate the subformula property by saying "we don't have to guess anything in proof search". it really is not at all about subformulas and all about information flow...
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@wilbowma I think this is a useful post and I mostly agree with your conclusions, although I am not a fan of the structure.
I think you phrased every argument except your own in a way that is very easy to refute by making them about the technology (and not the AI industry), only presenting their "real" versions in the section about power. But this is what (most) people really mean by these arguments, and I think it sounds a bit disingenuous to pretend otherwise.
I also have other complaints that were already raised here, but overall thank you for writing this.
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@mevenlennonbertrand reference 2 has different authors in the text and in the bibliography
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@trebor@types.pl Nice, thanks! I indeed don't really need the categorical structure on A here (it doesn't even need to be a universe).
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@arianvp@functional.cafe i think you can configure DeArrow to show original titles untranslated
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@constantine @edwinb Yes, I think that's what threw me off. The sort itself is interpreted as a subterminal presheaf (so a functor Con → Ω) whose elements at Γ are maps Γ → φ. I wonder if you mean anything precise by "relativises".