Godel has no idea what truth is so theorem meaningless
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From: byron on 9 Nov 2009 23:38 It has been pointed out by the australian philosopher colin leslie dean that godels theorem is meaningless http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf as it turns out that godel had no idea what makes a mathematical statement true as peter smith notes himself quote Gödel didn't rely on the notion of truth thus his incompletness theorem becomes meaningless quote http://en.wikipedia.org/wiki/G%C3%B6...s_theorems#Fir Gödel's first incompleteness theorem, perhaps the single most celebrated result in mathematical logic, states that: For any consistent formal, recursively enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true, but not provable in the theory, can be constructed.1 That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. And Peter smith notes godel is talking about true mathematical statements quote http://assets.cambridge.org/97805218...40_excerpt.pdf Godel did is find a general method that enabled him to take any theory T strong enough to capture a modest amount of basic arithmetic and construct a corresponding arithmetical sentence GT which encodes the claim The sentence GT itself is unprovable in theory T. So G T is true if and only if T cant prove it If we can locate GT , a Godel sentence for our favourite nicely ax- iomatized theory of arithmetic T, and can argue that G T is true-but- unprovable, So with out knowing what makes a mathematical statement true the incompleteness theorem is meaningless |