Toby Meadows

A thread that is probably misguided. Let's call it: An ordinary language response to a structuralist problem in philosophy of mathematics. It's not very catchy.

Five-year postdoc at Oxford in Logic and the Philosophy of Mathematics. Deadline May 1. chch.ox.ac.uk/vacancies/care…

Just arrived. After so much work, I am so glad finally to see this in print!

@AcerFur Thanks!

@TobyMeadows My understanding is a greater amount of world knowledge is more desirable in other scientific fields than necessarily reasoning capabilities. This model seems like it may be bigger and knows more. There are lots of knowledge-based science benchmarks out there.

FWIW, I think GPT-5.4 Pro is better on science in general, but would say it's worse on math than 5.2 Pro. Maybe some mathematicians could chip in their thoughts there.

Anyone got a copy of this, "The Proceedings of the Bertrand Russell Memorial Conference" (Uldum, 1971)?

Douglas Blue, Paul Larson, Grigor Sargsyan: The failure of square at all uncountable cardinals is weaker than a Woodin limit of Woodin cardinals arxiv.org/abs/2602.13077 arxiv.org/pdf/2602.13077 arxiv.org/html/2602.13077

Congratulations to Farmer Schlutzenberg on being selected as the recipient of the 7th Hausdorff Medal of the European Set Theory Society for his paper “On the consistency of ZF with an elementary embedding from V_{λ+2} into V_{λ+2}”, Journal of Mathematical Logic, 2025.

I prove something that is obviously true but it takes a while and is kinda fun.

@hanuljeon95 @dimenerno *posets

@hanuljeon95 @dimenerno n extra predicate V which (schematically) satisfied ZFC and assume that generics for all posted in V exist in the "true" universe in which we are working. But there's no accounting for taste so others may disagree.

오랜만에 블로그에 엄청 긴 글을 올렸습니다! 아무래도 논리학 블로그에 강제법 다루는 글이 없는 건 좀 그래서 날잡고 썼어요 dimenerno.github.io/2026/01/28/for…

@dimenerno @hanuljeon95 I think you may be onto something, but one hurdle for this analysis is that Russell invented type theory.

@hanuljeon95 비트겐슈타인이 유형론이고 러셀이 집합론입니다. 이 단상의 동기는, 러셀과 비트겐슈타인이 “There exists at least one entity in the universe"가 참인(증명가능한?) 문장인지를 두고 논쟁한 것인데, 비트겐슈타인이 우주에 관한 진술은 유의미하지 않다고 주장한 것으로 압니다. 유형론에 관점에서

@MccallumRupert @Wenitte1 Not sure it's worth writing up. It'll never get past the structuralistas of phil math who'd referee it.

@MccallumRupert @Wenitte1 I thought I did. But you wouldn't be the first person not to see that. The presentation of the idea still needs work.

A thread that is probably misguided. Let's call it: An ordinary language response to a structuralist problem in philosophy of mathematics. It's not very catchy.

@MccallumRupert @Wenitte1 Then maybe demure from what you cannot defend?

@TobyMeadows @Wenitte1 All right. Well, I would certainly need to try to defend it at greater length rather than just making an off-the-cuff remark on X.

@MccallumRupert @Wenitte1 My proposal is to provide a way for people who would like to be able to refer to THE natural numbers to be able to do so in a formally coherent way. I think a lot of ink has been wasted on this problem and it has a quite boring answer. But that's my view.

@TobyMeadows @Wenitte1 I take it your proposal does indeed require endorsing truth-value realism about first-order arithmetic?

@MccallumRupert @Wenitte1 Well. Yes. Most of them are big.

@TobyMeadows @Wenitte1 I'm basically just saying some natural numbers are very big. Which I agree may not seem all that deep. But I mean, like, really, really, REALLY big.