4 ms·
For state of the art on foundations of mathematics, see "Recrafting Foundations of Mathematics" https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.c
by ProfHewitt 6y ago
For state of the art on foundations of mathematics, see
"Recrafting Foundations of Mathematics"
https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021
- monstersinF 6y agoThis paragraph in that article is an incomplete sentence that ends hanging. Any idea what it intended to say? > “Monster” is a term introduced in [Lakatos 1976] for a mathematical construct that introduces inconsistencies and paradoxes. Since the very beginning, monsters have been endemic in foundations. They can lurk long undiscovered. For example, that "theorems are provably computational enumerable" [Euclid approximately 300 BC] is a monster was only discovered after millennia when [Church 1934] used it to identify fundamental
- monstersinF 6y agoAlso I don’t understand the impact of Wittgenstein‘a work on Godel’s discovery, could you clarify for me? What are the implications. The consensus I’ve read indicates it’s a misguided interpretstion
- ProfHewitt 6y agoWittgenstein's devastating critique of [Gödel 1931] came afterward. See the article referenced in this discussion.
- monstersinF 6y agoThanks for the response Professor. What do you make of the following article though? It concludes that the critique is not devastating to Gödel http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6.annotate http://wab.uib.no/agora/tools/alws/collection-6-issue-1-arti...
- ProfHewitt 6y agoUnfortunately, the author Timm Lampert did not quote the most powerful Wittgenstein proof that existence of I'mUnprovable means that mathematical foundations are inconsistent. Wittgenstein's more powerful version is much more devastating. As mentioned previously in this discussion, the following article explains why I'mUnprovable must not and does not exist in foundations: "Recrafting Foundations of Mathematics" https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021
- ProfHewitt 6y agoThanks! The complete sentence is as follows: For example, that “theorems are provably computational enumerable” [Euclid approximately 300 BC] is a monster was only discovered after millennia when [Church 1934] used it to identify fundamental inconsistency in the foundations of mathematics that is resolved in this article."
- ProfHewitt 6y agoThe Church/Turing Thesis is false because there are digital computations that cannot be implemented by a nondeterministic Turing Machine. See the following for more information: "Recrafting Foundations of Mathematics" https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021
- rq1 6y agoHi Carl. Thanks for sharing and your work in general. I always thought Godel results’ point is undecidability. Which (always?) arise with (StringTheoremsAreEnumerable and SomeKindOfCantorDiagonalReasoning). Where am I wrong? Do you have any historical writings to recommend about Wittgenstein/Gödel battle?
- ProfHewitt 6y agoYou are very welcome! In addition to the article linked in this discussion, see the following: Hao Wang. "Reflections on Kurt Gödel" MIT Press. 1987.
- rq1 6y agoThank you very much!
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