Edit: My question is specifically about Godel's second incompleteness theorem. I get the significance of his first incompleteness theorem, which is of course completely amazing. According to the ...
Falsifiability is considered a positive (and often essential) quality of a hypothesis because it means that the hypothesis is testable by empirical experiment and thus conforms to the standards ...
Russell was active in philosophy (although no longer in math) for many years after the Godel's 1931 publication. Godel's paper were not obscure, and Russell would have been aware of their effect on ...
In a great answer, a community member gave the following proof sketch that the halting problem is undecidable: Proof that the halting problem is undecidable. If there were a computable procedure ...
Do Godel's incompleteness theorems support the idea that the examination of a 'system' should only be undertaken to arrive at the inconsistency?
Roughly, Gödel demonstrated that in a logical system, that contains a model or arithmetic, there are statements which may be true, but are unprovable within the system. If a statement is not ...
Smullyan (1991, 2001) has argued forcefully that Tarski's undefinability theorem deserves much of the attention garnered by Gödel's incompleteness theorems. That the latter theorems have much to ...
Godel's First Incompleteness Theorem states Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any ...
I found a throw-away critique of Kurt Gödel's Incompleteness Theorem in an essay about Deconstruction: The basic enterprise of contemporary literary criticism is actually quite simple. It is based ...