Kygron Posted May 16, 2010 Share Posted May 16, 2010 In the real world a full self-reference is impossible (I can give my name but not my quantum state), if this were somehow incorporated into mathematics, would Godel's Incompleteness proof fail? It's based solely on self-reference, right? Merged post follows: Consecutive posts mergedIf you aren't able to answer, do you know of somewhere or someone else I can ask? Link to comment Share on other sites More sharing options...
the tree Posted May 18, 2010 Share Posted May 18, 2010 In the real world a full self-reference is impossible (I can give my name but not my quantum state),Mostly, there's a who-cares element to this. The Incompleteness Theorems are part of pure mathematics, which isn't overly bothered by the real world. Also, self reference doesn't need to absolutely detailed - a personal pronoun is self reference.if this were somehow incorporated into mathematics, would Godel's Incompleteness proof fail?A few more things would fail. Loads of objects are defined by how they relate to themselves. [imath]y=y'[/imath] look familiar to you?It's based solely on self-reference, right?Well, it's based on lots of things. Self reference is part of the conclusion of the second theorem - specifically that when it comes to describing consistency, it doesn't work. Which I think is kind of what you were getting at initially, a system cannot really evaluate itself, according to Gödel. Link to comment Share on other sites More sharing options...
bascule Posted May 19, 2010 Share Posted May 19, 2010 Self reference is part of the conclusion of the second theorem Self-reference is a huge part of both theorems. In the first theorem self-reference through Godel numbers plays an integral part. Godel numbers are how Godel managed to encode self-referential statements into the logic language of PM. Link to comment Share on other sites More sharing options...
ecoli Posted May 19, 2010 Share Posted May 19, 2010 Self-reference is a huge part of both theorems. In the first theorem self-reference through Godel numbers plays an integral part. Godel numbers are how Godel managed to encode self-referential statements into the logic language of PM. forgive me newbity, but the purpose of Godel numbers is to avoid contradictions involving self reference, no? Link to comment Share on other sites More sharing options...
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