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I am especially intrigued by the argument made by Nicholas Argall. In that the question of whether P = NP or not is incomplete in and of itself.[1] I think this

I am especially intrigued by the argument made by Nicholas Argall. In that the question of whether P = NP or not is incomplete in and of itself.[1] I think this is very true on the basis that not all of these problems are the same or present the same criteria to solve. I think understanding these problems is going to require thinking from a different depth though. It's fun to me to think about and try to wrap my head around. I'm no expert but have a lot of fun with it. http://web.archive.org/web/20170817220728/http://www.win.tue.nl/~gwoegi/P-versus-NP/argall.txt http://web.archive.org/web/20170817220728/http://www.win.tue...

thethirdone 9y ago
The argument put forward in the link misrepresents Godel's theorem. > 6) Therefore, no consistent and complete definition of the set NP is possible Rationale: If we accept that the set NP can only be rigorously defined via a language, this conclusion follows from the premises above. This doesn't even make sense. Definitions do not change a languages completeness or consistency; they simply relate a new concept to previously defined concepts. > 7) Therefore, no consistent and complete statement of the problem of P=NP is possible Comment: A conclusion which is not only proven in this paper, but supported by the years of argument between mathematicians regarding the relevance of proposed answers to the problem. This is not supported from Godel's theorem. The fact that you need a non-complete system to be able to reason about something does not mean the theorem you want to prove is not provable. The main problem with the argument is that it works for other theorems that have been formally proven.