3 ms·
Veritasium missed that existence of the [Gödel 1931] proposition I'mUnprovable leads to inconsistency in foundations by the following simple proof: Ever
by ProfHewitt 5y ago
Veritasium missed that existence of the [Gödel 1931]
proposition I'mUnprovable leads to inconsistency in
foundations by the following simple proof:
Ever since Euclid, it has been a fundamental principle
that a theorem can be used in a proof (the principle of
TheoremUse), that is, {⊢((⊢Ψ)⇒Ψ)} [cf. Artemov and
Fitting 2019]. However, by [Gödel 1931],
⊢(¬I’mUnprovable⇔⊢I’mUnprovable). Consequently,
⊢(¬I’mUnprovable⇒I’mUnprovable) by TheoremUse.
• Therefore ⊢I’mUnprovable using
ProofBySelfContradiction {⊢((⊢(¬Ψ⊢Ψ)) ⇒ ⊢Ψ)} with
Ψ being I’mUnprovable.
• Thus, I’mUnprovable using TheoremUse {⊢((⊢Ψ)⇒Ψ)}
with Ψ being I’mUnprovable. Consequently,
⊬I’mUnprovable using ⊢(I’mUnprovable⇔⊬I’mUnprovable)
Having both ⊢I’mUnprovable and ⊬I’mUnprovable is a
contradiction in foundations.
- sillysaurusx 5y agoDear Professor Hewitt, I’m sorry for my comment at https://news.ycombinator.com/item?id=27537500 https://news.ycombinator.com/item?id=27537500. In hindsight, I realize now that it sounded like I was making fun of you. I didn’t intend to do that at all. I think your concerns about Wikipedia were surprising, and I only meant to express surprise. Thank you for taking the time to patiently explain to everyone your ideas about improbability. It takes a lot of courage to present an argument the way you’ve been doing in these threads. And you present your proofs in mathematical form here, which is rare, and worthy. (I’m posting this here simply because it’s your most recent comment, so that you’re likely to see it. I wasn’t quite sure where to put it.) Have a wonderful week.
- ProfHewitt 5y agoThank you very much sillysaurusx!
- sillysaurusx 5y ago(I meant “Your ideas about provability,” not “Improbability.” My phone changed it, so it probably sounded like nonsense. Point is, it seems to me that your ideas about the incompleteness theorem might be true, and I am surprised and impressed that you’re in here explaining to everyone mathematically why they might be true. I don’t have the expertise to judge, but I recognize excellence when I see it. And your explanations are clearly excellent, because if they were mistaken, someone could check your math and point out the mistake. But no one has done that, so it seems to me you might be correct, even though everyone seems to think it’s guaranteed you’re wrong.) If there’s somewhere I can follow your work in this area, I would be interested to see how it turns out. For example, if you’ve written a paper on this subject, or if there’s some place online where you post updates related to this. Either way, good luck!
- ProfHewitt 5y agoThanks for your perceptive remarks! The following article has more information: https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021 Also, there are further articles linked here: https://professorhewitt.blogspot.com/ https://professorhewitt.blogspot.com/ If interested, you can follow @ProfCarlHewitt on Twitter. For the really dedicated, there are few tickets left for sale at the upcoming "Theory and Practice of Actors" workshop at StrangeLoop 2021: https://www.thestrangeloop.com/2021/theory-and-practice-of-actors.html https://www.thestrangeloop.com/2021/theory-and-practice-of-a...
- YeGoblynQueenne 5y agoWell done, dude.