In the short story/paper "Sylvan's Box" by Graham Priest the author tries to argue that it's possible to talk meaningfully about a story with internally inconsistent elements. However, I realized afterward that if one truly was in possession of a box that was simultaneously empty and not empty there would be no way to keep the inconsistency from leaking out. Even if the box was tightly closed it would both bend spacetime according to its empty weight and also bend spacetime according to its un-empty weight. Opening the box would cause photons and air molecules (at the least) to being interacting and not interacting with the contents. Eventually a hurricane would form and not form over the Atlantic due to the air currents caused (and not caused) by removing the lid. In my opinion If there is any meaning to be found in a physical interpretation of the story it's that inconsistency everywhere would explode from any interaction with an initial inconsistency, probably fairly rapidly (at least as fast as the speed of sound).

I'd be interested to know what other people think of the physical ramifications.