A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points · HackerPapers discussions

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — HN submission

Tue, 12 May 2026 07:36:36 GMT

Universal Approach to Self-Referential Paradoxes (2003)

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — HN submission

Mon, 03 Mar 2025 06:29:26 GMT

A Universal Approach to Self-Referential Paradoxes - Noson S. Yanofsky [2003]

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — mentioned by doomrobo

Thu, 07 Sep 2023 02:30:43 GMT

It turns out that these are all kind of the same, the Liar's Paradox, Russell's Paradox, the Halting Problem, etc. And indeed the they rely on a "diagonal map" i.e., a map x -> (x, x) in the construction. This was a great read, if you want a mathematical take on it, and some generalization too. https://arxiv.org/abs/math/0305282v1

Paper and discussion history. A mention is not an endorsement.

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — mentioned by zozbot234

Sun, 18 Jun 2023 07:51:45 GMT

It is a formalization of Cantor's diagonal argument - in fact, of "diagonal arguments" more generally. See http://arxiv.org/abs/math/0305282 for an expository treatment.

Paper and discussion history. A mention is not an endorsement.

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — mentioned by myWindoonn

Fri, 16 Jul 2021 00:34:50 GMT

Hi, Lawvere pummelled your position into the ground a while ago: http://tac.mta.ca/tac/reprints/articles/15/tr15.pdf Your critique involves repeatedly crossing the boundary between the inside and outside of the system in question; Lawvere works entirely inside the system, and shows that the paradoxes of self-reference arise from our interpretations. https://arxiv.org/abs/math/0305282v1 explains with many examples. Hi downvoters: Use your words when somebody is wrong. Your downvotes aren't helpful here for finding the truth.

Paper and discussion history. A mention is not an endorsement.

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — mentioned by ajkjk

Thu, 14 May 2020 23:16:35 GMT

Oh, wow, this is a very stimulating comparison. My summary is that all of these are structurally the same: * programs with recursion that either halts or not -- is there a partial order on states of a recursive algorithm such that some state is eventually terminal? * threads with resource dependencies that either deadlock or not -- is there a partial order on resource acquisition so that eventually some operation is unblocked? * garbage collection of memory references -- is there a partial order on resource ownership such that some element is eventually unowned? * Russell's paradox…

Paper and discussion history. A mention is not an endorsement.

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — mentioned by lidHanteyk

Sun, 12 Apr 2020 04:30:37 GMT

It isn't what you're looking for, but perhaps Lawvere's generalization of Gödel's work is sufficiently geometric for you [0][1][2]. [0] https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem [1] http://tac.mta.ca/tac/reprints/articles/15/tr15.pdf [2] https://arxiv.org/abs/math/0305282

Paper and discussion history. A mention is not an endorsement.

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points — mentioned by throwaway000002

Sun, 08 Nov 2015 15:48:10 GMT

Wow Peter, thanks for that. I like their analysis. It reminded me of a great article I read years ago that dealt with the issue of self-referential paradox. In fact, at the time I tried applying the techniques therein towards the surprise examination, however I didn't get anywhere. It's a paper by Noson Yanofsky entitled "A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points" (http://arxiv.org/abs/math/0305282) I think you'll enjoy reading it. I read the paper on a long train ride loved working out how given "Ann believes that Bob believes that Ann believes that…

Paper and discussion history. A mention is not an endorsement.