The godel tag has no wiki summary.
6
votes
6answers
338 views
What's the big deal with Godel's second incompleteness theorem?
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 ...
-1
votes
2answers
157 views
Relation of Gödel's incompleteness theorems and Karl Popper falsification
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 ...
9
votes
1answer
268 views
Did Russell understand Godel's incompleteness theorems?
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 ...
4
votes
2answers
293 views
What are the philosophical implications of the Halting Problem?
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 ...
3
votes
3answers
192 views
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 ...
10
votes
1answer
400 views
When it is correct to use Tarski's undefinability theorem versus Godel's incompleteness theorem?
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 ...
12
votes
4answers
1k views
What are the philosophical implications of Godel's First Incompleteness Theorem?
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
...
38
votes
5answers
2k views
Is Kurt Gödel's Incompleteness Theorem a “cheap trick”?
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 ...
