Kurt Godel's incompleteness theorem pertains to mathematical or computational propositions. Godel's incompleteness theorem (results) only showed that for any formal axiomatic system, there is always a statement about natural numbers which is true, but which cannot be proven in the system.

Godel's theorem applies to axiomatic systems that contain undecidable propositions and are (therefore) incomplete. An axiom is a rule or a statement that's accepted as true without proof. An axiom is also called a postulate. Godel's theorem applies to deduction from axioms, which is one way of logical thinking (but it's not the only way) nor is it a method of finding answers in other fields because (even though) there are axiomatic formulations of parts of physics, Godel's results ignores the fact that it's not the way reasoning is applied to other disciplines. Godel's theorem merely established that there are some propositions about numbers which we can't prove formally.

'The Principles of Mathematics Revisited' by Jaakko Hintikka is a good source of information about Godel's theorem, he says the result "casts absolutely no shadow on the notion of truth. All that it says is that the whole set of arithmetical truths cannot be listed, one by one, by a Turing machine."

This is actually an argument that is related to axioms and number theory (period) questions within axiomatic systems that are testable by the rules of arithmetic. Godel's results have been used incorrectly in many arguments (one is that artificial intelligence is impossible or machines cannot think) They argue that intelligence can't be reproduced by computational machines, and none of them could be as intelligent as we are. No one has ever presented any evidence that any of this is true, but there is evidence it's not true.

SINGULARITY PROJECTS
home.mchsi.com/~deering9/projects.html
creating the future
Artificial General Intelligence Research Institute

The AGIRI is a small team of individuals committed to explicitly working toward the grand goal of true artificial general intelligence.

They are designing, building, and testing the Novamente AI Engine. Novamente means "new mind".

This program is under development, and ambitions for it are large indeed. They intend for Novamente to be the world's first real Artificial General Intelligence - the first piece of software with roughly human-level general thinking power ... and then after that, through consistent goal-directed self-modification, thinking power on a substantially and increasingly superhuman level.