Linked Questions

(current answers neglect the fact that the set of all concepts( $C_{U}$) is a subset of U as all of them are physically encoded( symbolically represented by the physical events themselves(brains, ...

According to Gödel's Incompleteness theorems, there exist problems in any sufficiently powerful, consistent system of arithmetic that are undecidable form the axioms of said system. *What known ...

Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics? I work partially in Quantum Information Theory ...

According to Gödel's incompleteness theorem, no matter how many statements you prove, you will always have a set of statements not proved. Does this imply that some time in the future, scientific ...

Gödel's incompleteness theorems basically sets the fact that there are limitations to certain areas of mathematics on how complete they can be. Are there similar theorems in physics that draw the ...

I have been wondering about the axiom of choice and how it relates to physics. In particular, I was wondering how many (if any) experimentally-verified physical theories require the axiom of choice (...

I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics (...

Do Gödel's incompleteness theorems have any significance or application to axiomatic theories of classical mechanics like Newton's for example?

It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of "we can know, we must know." Three ...

Assuming we develop quantum computers one day, what would be theoretically the next step? Would it be string-theory based computers? How would these computers differ performance-wise (ie what can they ...

There is a lot of interesting debate over whether a "theory of everything" (ToE) is allowed to exist in the mathematical sense, see Does Gödel preclude a workable ToE?, Final Theory in Physics: a ...

Some time ago, I read something like this about the issue of "a final theory" in Physics: "Concerning the physical laws, we have several positions as scientists There are no ...

I see many learned contribution about the role of a Theory of Everything (TOE), what it might do or not do, what kind of answer it might provide, and what not. But I do not know what a TOE is, how I ...

Mathematical logic defines quite clearly what is true or false in math, and also that some theorems are impossible to prove. This resulted in some clear definitions of axioms set like Peano, ZF or ZFC,...

I will add a better phrased question here. Do we need to consider quantum foundations to form a quantum theory of gravity? The kind of foundational question I am thinking of is expressed in the ...