Like the theory of gravity. Right.
I think the whole idea of "proof" is also contextual.
Laymen tend to think of the word "proof" as meaning that you need to prove something to them personally. Almost like a philosophical proof. You need to "convince" them unequivocally that something is true.
In science that kind of proof would be laughed at. There is no need for scientist to prove anything to philosophers or laymen. When scientists talk about proofs they are talking about them within the context of the "theory". And the theory is a well-structured logical formalism based on initial premises.
The problem with laymen and philosophers is that they refuse to believe the fundamental premises. Well, that's all fine and dandy. But the point of that is that if they don't accept the premises then they are basically rejecting the theory in the first place because a good theory always begins with premises.
For example, one of the premises of Einstein's theory of relativity is that nothing can travel faster than the speed of light. That's a premise. It's not provable. At best scientists can only say that they have never observed anything that can travel faster than the speed of light. However, once you accept that premise then the rest of the theory holds solid based on that premise.
So when a person talked about proofs there are basically two kinds of proofs. Scientific proofs, and philosophical "proofs". Personally I don't believe that it's possible to prove anything philosophically so the word doesn't even really apply to that type of thinking at all.
More to the point, "music theory" isn't a rigorous logical mathematical science. It's more like the study of English. There are probably more exceptions than rules.
What could you "prove" about music theory???
Going from the rules outward you might be able to think you've proved something. In other words, if you start with a scale and ask someone to give you all the triads for that scale you could prove whether what they gave you did or didn't satisfy the rules.
However, going from a composition back to music theory you'd be hard pressed to prove anything at all. Ultimately anything goes in music and the composer may not have even been thinking about music theory when he or she wrote the piece. In other words, the composer could have easily broken some of the "rules" of music theory. That leads back to the fact that there are more exceptions in music theory than rules.
On the other hand, if you can find an instance of something traveling faster than the speed of light then you could denounce the theory of relativity because you would have demonstrated that at least one of its premises is false.
So when it comes time to "prove or disprove" a theory of gravity, this can indeed be done from a scientific point of view. But from a philosophical point of view you can't prove or disprove anything. So when you talk about proving something you really need to specify the context in which you are attempting to prove or disprove it. If the word "premises" isn't involved then you may as well chuck the word "proof" too because without premises to support or deny you can't prove or disprove anything. All you are really trying to do is to "convince" someone of something, which isn't at all the same as proving something within the context of a logical formalism.
Like I say, Music Theory isn't really a logical formalism. its more like the study of a language. It just helps to offer some insight into to possible structures but doesn't dictate what is or isn't ultimately possible.
Gravity, on the other hand, says that if there is a massive object near you, you WILL feel the effect of the warped spacetime. That's an unequivocal prediction. It's either true or it isn't.
The bottom line is that the word "theory" has a differnet meaning in "Music Theory" than it does in a "Scientific Theory". These are two entirely different beasts.
Topic: term - ~music theory~