News for hackers. Stuff that matters.

A comment on 1931: Kurt Gödel shows limits of math, logic, computing, AI. Parent comment

Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by IngoBlechschmid on Thursday June 17, 2021 @06:30PM (#27545155)
This is not quite true, Gödel's incompleteness theorems can luckily be formalized in extremely weak fragments of Peano arithmetic such as primitive recursive arithmetic (PRA) with its very limited induction principle. :-)

The only position on the philosophy of mathematics I know which does not accept PRA is ultrafinitism.

[ Parent | on HN ]
Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by ProfHewitt on Monday June 21, 2021 @12:16PM (#27580646)
Problem with 1st-order PRA is that it is too weak to serve as

foundation of mathematics.

[ Parent | on HN ]
Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by erichahn on Friday June 18, 2021 @08:38AM (#27549670)
Can you provide a paper or book on this?
[ Parent | on HN ]