In Miami last year, I sat in on a few weeks of a seminar on philosophical issues about quantum mechanics, before I got too swamped with last-minute dissertation edits and whatnot to make the time. (Later, the professor did join me and some friends for an evening of drinking single malt and watching and making fun of "What The Bleep Do We Know?") On the first day, the professor went through a long and funny list of nonsense topics that might come to mind when one hears the phrase "philosophical issues about quantum mechanics" and announced that we wouldn't be talking about any of those. He then proceeded to list off a few "actually serious topics" we also wouldn't be going over, purely because of time constraints. One of the topics he listed off there was that of whether quantum results create a problem for classical logic.
A few minutes later, he moved on to describe the two path experiment we'd read about in a slightly whimsical way in the first chapter of David Albert's excellent book Quantum Mechanics and Experience. (The assignment was sent around by e-mail before the first day of class.) The punch line of the experiment, which establishes "superposition" (a term that often feels, at least from my non-physicist's perspective, more like a label slapped on the weirdness than anything particularly illuminating), goes like this:
Given the experimental evidence, it seems like we can absolutely rule out the possibility that the electron is passing through path A. Or path B.
....would seem to me to kind of create a problem for classical logic.
That's such a good note to end on that I was tempted to it there, but I should probably say some more.
As I've indicated before, the Hartry-Field-style "paracomplete" approach to the Liar Paradox--whereby we set up an elaborate formal apparatus and use it to reject that Liar sentences are true, reject that they're false, reject that they're neither, and so on--isn't particularly attractive to me, both because I think that better options are on the table and because of the difficulties its proponents face in saying anything particularly intuitively plausible about sentences like this one:
"This sentence would not be accepted by a being who accepted all true sentences."
...and, of course, my standard complaint about non-classical solutions to the Liar, which is that the Liar and Curry are obviously instances of the same phenomenon, and a solution to the Liar that doesn't apply to Curry is no better than a solution to the Simple Liar that doesn't apply to the Strengthened Liar.
All of that said, quantum superposition state weirdness does strike me as a much more promising application of parcompleteness. I think that Priest & Routley have an old paper suggesting a dialetheic approach to quantum mechanics, but that seems to get the intuitive situation exactly wrong. It's not that all the possibilities can be jointly ruled *in*, it's that they can all be jointly ruled *out.*
Moreover, the quantum analogy to my view of the Liar Paradox would fall completely flat. Claiming that any of the statements involved commit category mistakes is (a) incompatible with the claim that they can be empirically ruled out, and (b) hard to square with the way we talk about electrons that *aren't* in superposition states. It's meaningless to say that some ideas are yellow, or to deny it, since color talk just doesn't apply to ideas, but position talk clearly *does* apply to particles.
Now, I'm certainly not endorsing a paracomplete approach to quantum weirdness--I'm not ready to give up on classical logic just yet, and the empirical and conceptual issues involved in arguing about this one way or the other get pretty murky pretty fast--but I do think there's an obvious prima facie case for some such logical revision. (Even if I hold out hope for its defeat.) Notice, though, that, as I've been arguing in the last few posts, none of this remotely threatens Distribution.