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I don't consider Godel's theorem to be philosophy. Its status is similar to Cantor's theorem stating that reals are uncountable. Surely is inspired by philosoph
by sold 14y ago
I don't consider Godel's theorem to be philosophy. Its status is similar to Cantor's theorem stating that reals are uncountable. Surely is inspired by philosophy and has philosophical consequences, but it is a part of mathematics. Trivia: Godel used the Chinese remainder theorem in his proof http://mathoverflow.net/questions/19857/has-decidability-got-something-to-do-with-primes http://mathoverflow.net/questions/19857/has-decidability-got.... I acknowledge that philosophy can be inspiration for mathematics, but this is rather unsatiating, as very many things can be.
In the meantime, I found a very good defense of philosophy here: http://www.ditext.com/russell/rus15.html http://www.ditext.com/russell/rus15.html
- fatbird 14y agoYou might not, but philosophers certainly do--I learned it in my philosophy classes on logic. I also learned there about Cantor's diagonalization proof. More generally, in the early 20th century there was a huge overlap between mathematics and philosophy. You had Russell and Whitehead's Principia Mathematica, you had the Vienna Circle, you had Carnap and logical positivism... It's really not possible to cleanly categorize Goedl's proof into either math or philosophy--they weren't disjunct categories then, and they're not now, either. More importantly, if you approached any of those figures and asked whether they were separate things, they'd have thought the question nonsensical. Philosophy was, and still is, the home of logic in the academy, and the fact that logic and math frequently seem like different sides of the same coin doesn't settle the issue either way.