godel

Their goal was to encapsulate mathematical truth 'algorithmically' (in a computable way) and Godel showed this wasn't possible.

In the form Godel proved it, the theorem doesn't require any semantic assumptions.

I'm pretty sure if you are talking about proofs having to do with a determined, computation system, Godel applies.

I remember thinking about this after reading Godel esher bach.

What Godel showed was that there is no first order system capable of encapsulating all true statements in the integers (the model we all know and love).

>> I remember thinking about this after reading Godel esher bach.

They didn't know before Godel that the natural numbers we all grew up with couldn't be modeled properly with a recursively enumerable set of axioms but that's what they wanted and were looking for.

See Manin's discussion of "Godel's argument" and particularly step (c) on p.255 of his book.

I don't 'stomach' higher math (experimentalist), but thought Hofstadter did a good job in "Godel, Escher, Bach".

"Do you contain the Godel number of the proof that Peano arithmetic is consistent?" Yes.

Godel's Completeness Theorem has absolutely nothing to do with his Incompleteness Theorem, and the "completeness" it talks about is very different from the "incompleteness" the other theorem talks about.

Bigfoot might 0.0137384 exist.) The universe gives us Fermi paradoxes and dark energy and Godel's incompleteness theorem.

You are confused by the implications and meanings of the results of Godel.

It's been proved for this logic once and for all by Godel.