In an answer to a question about logic, Prof Maitzen says he is unaware of any evidence that shows classical logic fails in a real-life situation.
Perhaps he has never heard of an example from physics that shows how classic logic does not work in certain restricted situations?
A polarizing filter causes light waves that pass through it to align only in one direction (e.g., up-down or left-right). If you have an up-down filter, and then a left-right filter behind it, no light gets through.
However, if you place a filter with a 45 degree orientation between the up-down and left-right filter, some light does get through.
It seems to me that classic logic cannot explain this real-world result.
I'm sure that Stephen Maitzen will have useful things to say, but I wanted to chime on in this one. You have just given a perfectly consistent description of what actually happens in a simple polarization experiment that I use most every semester as a teaching tool. Classical logic handles this case without breaking a sweat. But there's another point. You've described the phenomenon in terms of light waves. That's fine for many purposes, but note that the wave version of the story of this experiment comes from classical physics, where (for the most part at least) there's no hint of logical paradox. The classical explanation for the result is that a polarizing filter doesn't just respond to a property that the light possesses. It also changes the characteristics of the wave. Up-down polarized light won't pass a left-right filter, but if we put a diagonal filter between the two, the classical story is that the intermediate filter lets the diagonal component of the wave pass, and when it does, the light...