It seems like it's a given that the laws of physics that govern our universe are consistent, and that inconsistency somehow is a reason to doubt an explanatory theory (such as famously Godel's spinning universes leading to an inconsistency that caused Einstein to doubt his own theory).
Along these same lines, if our universe was found to be inconsistent, what would that mean? How would it physically manifest?
Edit$^2$: My question was intended to be less phiosophical, and more about what kinds of explanatory or simplifying benefits allowing contradiction would give to attempted models of physics. Or if such a program has been attempted - because so far I don't see any apparent reason why we avoid it.
Edit$^3$: Really the answer to "what would that mean?" is a philosophical one, hence the long discussion that doesn't belong here, sorry. My opinion is that it may simply be a mathematical simplification similar to imaginary numbers that gives us a different and helpful perspective. But I don't know.