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A comment on Does Gödel Matter?. Parent comment

Re:Does Gödel Matter? by cchooper on Monday December 22, 2008 @10:32AM (#406453)
The second theorem tells us that we can't prove the consistency of set theory without using an even more powerful system. This doesn't mean that set theory is inconsistent, it just means that we can't prove its consistency in any meaningful way. So yes, Gödel indeed shows that there are no 'ultimate axioms' that contain everything of interest in mathematics.
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Re:Does Gödel Matter? by mstoehr on Monday December 22, 2008 @11:31AM (#406507)
Although it does lead to a mathematically uninteresting paradox: if you let A be the axioms of set theory and you add an axiom P which states that A proves x and not x, (i.e. set theory is inconsistent) then A' = A and P is still consistent.
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Re:Does Gödel Matter? by d0mine on Monday December 22, 2008 @01:51PM (#406699)
For clearity: A' = (A and P)
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Re:Does Gödel Matter? by cchooper on Tuesday December 23, 2008 @05:04AM (#407439)
Ah, that makes a lot more sense now!
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