7 ms·

This 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

This 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 ago
Also 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 ago
  Wittgenstein's devastating critique of [Gödel 1931] came afterward. See the article referenced in this discussion.
  - monstersinF 6y ago
    Thanks 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 ago
      Unfortunately, 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 ago
Thanks! 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 ago
The 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

monstersinF 6y ago

Also 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 ago
Wittgenstein's devastating critique of [Gödel 1931] came afterward. See the article referenced in this discussion.
- monstersinF 6y ago
  Thanks 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 ago
    Unfortunately, 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 ago

Thanks! 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 ago

The 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