I'm not sure I get what you mean by "truth". As the GP said, physics is about making useful predictions within constraints. Under whatever definition of truth you choose to use (it's hard to tell from your post), it would inherently require contradictions to abound. I certainly don't like any definition that allows us to derive contradictions, since that means we can derive anything, which is certainly pretty useless.
One of the biggest advances in scientific thinking in the 20th century is Popper's analysis of falsification and that induction doesn't exist (or at least doesn't really work). Philosophers have struggled for centuries to come to some understanding regarding when induction works and when it doesn't. Not letting scientific theories ever be "true" solved a LOT of problems, since once you prove something true, it can never be false-- and this isn't just a cop out; from a logical standpoint, proving something true and falsifying it are asymmetrical. To prove something true requires you to show validity for an infinite set of cases, whereas falsification only requires you to find one counterexample, and this is why designing experiments that can potentially falsify your theory is so useful (and also why string theory is criticized for not predicting anything that can be tested). Scientists have moved away from the old definition of truth (as you seem to understand it) for good reason.
Beware of the Turing Tar-pit in which everything is possible but nothing of interest is easy.