That implies that there is a priviledged truth. If two theories are completely indistinguishable by any conceivable experiment, then I would consider them both to be equally "true".
Would it be reasonable to claim that if different mathematics give the same answer in all cases, then it is really only different forms of a single mathematic?
They could produce different answers for cases that don't occur in nature. For example you can find many polynomials that go through a given point set (all possible observations you can make) but disagree wildly outside of the point set.
Define "completely different" please.
The two mathematical representation of quantum mechanic were completely different until it was shown that they were equivalent..
Yes that's what it implies. There's a privileged truth and we don't get to know it. Don't feel bad, though.
You can describe the laws of physics like little gremlins who follow a book of laws that happens to be the laws we know, and the predictions and observations we have will match the gremlins theory.
It doesn't make the existence of tiny gremlins real.
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Indeed. Plus, there's another subtle moment in science. It just creates models which are good at matching observations and making predictions.
Many mutually conflicting models can be created to describe the same properties of the same system.
We have no way of ever finding the "truth".
That implies that there is a priviledged truth. If two theories are completely indistinguishable by any conceivable experiment, then I would consider them both to be equally "true".
https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
How would they not be the same if they are indistinguishable by any experiment?
By using completely different mathematics.
Would it be reasonable to claim that if different mathematics give the same answer in all cases, then it is really only different forms of a single mathematic?
They could produce different answers for cases that don't occur in nature. For example you can find many polynomials that go through a given point set (all possible observations you can make) but disagree wildly outside of the point set.
Define "completely different" please. The two mathematical representation of quantum mechanic were completely different until it was shown that they were equivalent..
Yes that's what it implies. There's a privileged truth and we don't get to know it. Don't feel bad, though.
You can describe the laws of physics like little gremlins who follow a book of laws that happens to be the laws we know, and the predictions and observations we have will match the gremlins theory.
It doesn't make the existence of tiny gremlins real.