Math's Fundamental Flaw

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Strong rec travisgriggs · 2021-11 · on “How imaginary numbers were invented [video]”

I love Veritasium. Derek has done a number of videos that are awesome like this. The videos are great and educational, but he also manages to subtly weave in an almost spiritual subtext to them as well. For example, in this one, you learn about imaginary numbers in some cool ways, history, how awesome e^ix is, etc, but also this yen-yang balance between embracing not only what is real but taking a chance on what is imaginary. Some of my other favorites: - [LINK] - [this video] - [LINK] - [LINK] - [LINK] I think he’s going to lose the $10,000 bet on the car though.

Recommends reggieband · 2021-05 · on “How inevitable is the concept of numbers?”

I'm not sure if it is what you want, but Intuitionism [1] is one area that challenges modern fashions in Mathematical thinking. It suffered greatly under the formalist approach lead by David Hilbert and still has little main-stream support despite Gödel and his incompleteness proofs. Veritasium's latest video on Gödel's incompleteness [2] gives a pretty fair account of how we settled on the current fashionable foundations of Math (including nods to Cantor and Hilbert). For a more formal history there is a book "The Philosophy of Set Theory" [3] that sketches out how we got to where we are. I have always been unsatisfied with the current foundations of math and their obtuse basis in Set Theor

Recommends littlecranky67 · 2021-06 · on “1931: Kurt Gödel shows limits of math, logic, computing, AI”

Veritasium recently released a very good video that explains Gödels incompletenes theorem such that even I could understand it: [this video]

Recommends simias · 2021-10 · on “Where do type systems come from? (2017)”

But what if the statement is "this statement can't be proven"? You haven't proven the statement, you've proven that it can't be proven. See [this video] for instance which is (IMO) a fairly good explanation of the proof and why you end up with something both true and not provable. Penrose's "Emperor's New Mind" also discusses this topic at length (within the context of whether human brains can be emulated). I wasn't convinced with his argument regarding AI but his overview of the problem of what's computable and what's not is rather good if a bit dense.

Recommends shagie · 2022-09 · on “Gödel, Escher, Bach: an in-depth explainer”

Veritasium - Math's Fundamental Flaw [this video] At 13:46 it gets into the "is there a way to prove every complete statement?" and furthermore goes into the Godel math for "there is no proof for the statement with Gödel number g" where that statement itself has a number "g". The entire video is a good watch though. And the related problem is that with Godel we don't know if math is consistent either.

Recommends pandoro · 2024-03 · on “The complete story of Gödel incompleteness”

It's very entry-level (my level :)) but I found Veritaseum's video about it really clear and instructive: [this video]

Recommends equanimitivity · 2024-04 · on “Philosophy is an art”

I used to think similarly, but learning about the proven incompleteness of sufficiently rigorous analytic systems has moved me towards appreciating less rigorous ways of interfacing with reality. Veritasium has a nice video on Godel’s incompleteness theorem. It’s quite ironic that it was mathematically provable that analytic systems can never be complete, and can’t be provably coherent. [this video]

Cites will_byrd · 2021-06 · on “William Byrd on logic and relational programming, miniKanren (2014)”

Hi YeGoblynQueenne, I always read your logicy comments and posts--thank you! > To clarify, that's incompleteness. Unsoundness is when an inference rule returns wrong results. Incompleteness is where it doesn't return all correct results. As you say, unification without an occurs check is unsound and Prolog's depth-first search is incomplete. Thank you. Yes, I misspoke. For anyone interested, this video gives a nice overview of soundness and completeness, in the context of logic: [this video] > I wanted to ask, because you brought it up in the interview, how does minikanren (or minikanrens?) handle the occurs check? You said that you are interested in trying to push the relational aspect as far as