Talk:WikiJournal of Science/Can each number be specified by a finite text?

PDF available: File:Definable.pdf. It is hyperlinked, which is not visible here; download it and open in an appropriate pdf viewer. Boris Tsirelson (discuss • contribs) 19:26, 21 December 2018 (UTC)

The PDF is now updated, it corresponds to this version of the preprint. Boris Tsirelson (discuss • contribs) 20:18, 7 April 2019 (UTC)

Self-published on arXiv. Boris Tsirelson (discuss • contribs) 03:26, 26 September 2019 (UTC) Discussions broke out the same day (and died out the next day) on Twitter and Reddit.

--
 * (Uncanny as this is similar to something I was planning to tweet about - but this article will be a lot better than anything I could have written.)  (@sigfpe).
 * My mind is being blown by section 8, the value of Chaitin's constant depends on which model of ZFC you're in!  (@luqui)
 * I thought it was trivially true. Thanks for sharing. Another pdf in my todo read list. On the other side the concept of "definable" is quite fuzzy in my mind. Hopefully the doc would clarify my misconceptions a little.  (@DuduRyer)


 * So in fact we can't say that not every real is definable, because we can't even ask the question. [...] The problem is that it's impossible to define what it means for a formula to hold true of a given real number.  (Oscar_Cunningham)
 * Great article. Also interesting to see so many commenters miss the point. Let me try to summarize...
 * Alice: There are uncountably many reals, but only countably many definitions in any finite language, so undefinable reals must exist. I win!
 * Bob: By Lowenheim-Skolem, there's a countable model of ZFC. Moreover, there's a model of ZFC whose every member is definable. You were saying?
 * Alice: Wait, doesn't ZFC prove that reals are uncountable?
 * Bob: Sure it does. You're just mixing up levels. The reals of that model do have a one-to-one mapping with the integers, but that mapping isn't part of the model.
 * Alice: That's a pathological model then!
 * Bob: But you can't tell it from a normal one using ZFC. That's what being a model means.
 * Alice: Ok, screw this ZFC bullshit. My argument works in truth.
 * Bob: If your system of truths about reals is non-contradictory, then by Lowenheim-Skolem it has a countable model too. And I don't think it could prove the existence of reals undefinable in that system.
 * Alice: What's then the status of my argument?
 * Bob: I'd have to say it's neither true nor false. You know how the consistency of {union of all your truths} feels like a truth, but can't be part of the union? The existence of undefinable numbers is in the same kind of limbo. Philosophy of math is weird.  (want_to_want)

--
 * [...] "defining" something is a delicate process. There's a potential difference between a definition in English words and one in mathematical symbols.   (avocadro)
 * If an issue like this is resolved in the paper, don't tell me. I'm gonna go read it now before I say anything else potentially wrong/misinformed.   (point_six_typography)
 * Read it to find out what the subtleties are!   (completely-ineffable)
 * Premise 2 is too vague to a be a theorem, as it depends heavily on what counts as a “definition”. This is what the article is challenging.   (CheekySpice)
 * "exercises are waiting for you"   (jmdugan)

Boris Tsirelson (discuss • contribs) 19:56, 24 October 2019 (UTC)

Plagiarism check

 * ✅: False positive of 43% possible, from http://jdh.hamkins.org/the-universal-definition/. This is an extended quotation in a footnote, and is properly cited.  Maknongan (discuss • contribs) 12:31, 24 March 2019 (UTC)

First review
Summary of author revisions

Posthumous reviews
Responses to invitations to comment with the information that the author has passed away and querying whether A) the paper is publishable in its current form, and B) whether it needs any additional foreword to clarify any outstanding issues.