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?

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If you aren't able to answer, do you know of somewhere or someone else I can ask?

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.

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.

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?