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. Thanks!

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I'm sure that Stephen Maitzen

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 that gets past is no longer up-down polarized. Since diagonally polarized light has a component along the left-right axis, there's no puzzle about why some light is able to pass all three filters. The proportions are given by Malus's laws, which was formulated at the beginning of the 19h century.

Now there's a more intriguing phenomenon that emerges when we do the same experiment with an ensemble of single photons. Each photon either passes a filter or it doesn't; no "partial passage." On the simple standard story, if a photon gets past a filter, it emerges polarized along the axis of the filter. Note: if we accept this story, the filter changes the photon. There's no contradiction in saying that a photon that once was polarized in one direction is now polarized in another. The probability that a photon will pass a filter is a simple function of the angle between the incoming polarization and the orientation of the filter. Now we get the pattern you describe exhibited statistically. As the number of photons gets large, the proportions among the photon counts will mirror the intensities in the wave version of the experiment. But nothing I've said here conflicts in any way with classical logic.

All this said, there is a debate about whether quantum mechanics has implications for logic. The majority opinion, both among physicists and philosophers of physics, is that quantum mechanics doesn't conflict with classical logic. The issues are technical and subtle and beyond the scope of what can be said here. My take: quantum mechanics may call for enlarging the range of logical relations that we consider, but there is nothing like a knock-down argument for this conclusion, and in particular no simple example that could settle the case.

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