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Your statement that we will never get to the bottom may be true, but the reasoning is flawed. Gödel's incompleteness theorems are about mathematical theories,
by smokel 12y ago
Your statement that we will never get to the bottom may be true, but the reasoning is flawed.
Gödel's incompleteness theorems are about mathematical theories, not about physical theories. It may well be that for physical understanding a very limited arithmetic is sufficient. Also, there may be statements that are unprovable, but these might turn out to be irrelevant to sufficiently understanding the universe.
Also, an axiom, by definition, can not be proven. The things that are proven are theorems, statements, etc. An axiom is an assumption.
Eventually, it all depends on what level of understanding you want. But Gödel's theorems have little to do with that.
- mkaziz 12y agoDo you not have to start off with a set of axioms though? Assumptions that will never be proven?
- dfox 12y agoFrom the mathematical point of view, physics is about finding smallest set of axioms from which you can mathematically derive complete theory of universe's behavior. Validity of such axioms is in turn validated by experiments (by testing whether results match theory derived from given axioms)
- dllthomas 12y agoIt is true that they will never be "proven", but that doesn't mean we can't build a tremendous confidence in them through experimentation. (Which is to say "I agree", but I wanted to put a slightly different spin on it.)
- sp332 12y agoThe incompleteness theorem describes a tradeoff: A system of axioms cannot be both consistent and complete. But that seems irrelevant, since you could make a system that describes all of physics while not being either consistent or complete. https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Background https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
- eli_gottlieb 12y agoScientific reasoning is inductive, not deductive. When doing inductive reasoning you are allowed to update your belief in your axioms based on the empirical evidence you see. In fact, the theorem showing how to do so (Bayes' Theorem) is so utterly elementary we teach it in the first probability course everyone takes.