Bertrand Russell came up with this apparent contradiction. I don't know what title he gave it, if any, so the node title is my own invention. (This is the same Russell who came up with Russell's Paradox.)

Physics is based on Common Sense*.
But Physics shows that Common Sense is wrong **.
If Common Sense is wrong, then we shouldn't use it,
But if we don't use Common Sense, we don't get Physics in the first place.

Okay, so it's not really a problem, and certainly not a paradox. I doubt that Russell meant for it to be taken seriously. But it's still an interesting thought.

* Which is to say, we use the Scientific Method, Induction, and Deduction because they sound reasonable to us. All this is clearer if you have read some G.E. Moore (I wouldn't suggest it). In philosophy, 'common sense' means very obvious things, like 'My Hand Is Real', or 'Time Is Real'.

** Don't believe me? Check out quantum mechanics with its double-slit experiment, and the Theory of Relativity with its Twin Paradox. These theories very much go against our common sense views of the universe.