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Re:Complexity No Bar to AI by monstersinF on Sunday February 21, 2021 @05:15PM (#26217808)
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

Re:Complexity No Bar to AI by ProfHewitt on Monday February 22, 2021 @11:37PM (#26233867)
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

Re:Complexity No Bar to AI by ProfHewitt on Monday February 22, 2021 @11:18PM (#26233770)
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."

Re:Complexity No Bar to AI by monstersinF on Sunday February 21, 2021 @06:19PM (#26218365)
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
Re:Complexity No Bar to AI by ProfHewitt on Monday February 22, 2021 @11:20PM (#26233779)
Wittgenstein's devastating critique of [Gödel 1931] came afterward.

See the article referenced in this discussion.

Re:Complexity No Bar to AI by monstersinF on Tuesday February 23, 2021 @09:13PM (#26245806)
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-arti...

Re:Complexity No Bar to AI by ProfHewitt on Tuesday February 23, 2021 @10:23PM (#26246236)
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