3 ms·
Your statement 2 of Gödel's second result is false because Gödel's second result is false for foundational theories. Foundational theories can in fact prove t
by ProfHewitt 5y ago
Your statement 2 of Gödel's second result is false because
Gödel's second result is false for foundational theories.
Foundational theories can in fact prove their own consistency.
However, the self-proof of consistency is not very convincing
because the proof is valid even if the theory is inconsistent.
Fortunately, there is another way to prove consistency by
showing that a theory has a mathematical model.
See the following for an overview:
https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021
- mcprwklzpq 5y agoThank you. I downloaded this paper a month ago to read it eventually. Your comment made me read it yesterday and i have a question. By using the type system would we exlude potentially consistent theories? Is it similar to how limitimg ourselves to a decidable language instead of a turing complete one would prevent us from writing potentially never halting programms that could still halt?