December 25, 2004

The law of the excluded bowling alley

Thomas Shannon said that "[y]esterday was one of the worst days of my life". That's because the Bloomberg wire service reported that Shannon's bowling alley chain was partly owned by Yasir Arafat, or at least by "Palestine Commercial Services Co., a Ramallah, West Bank-based holding company" controlled by Arafat through his financial advisor Mohamed Rachid.

The AP wire service story quotes Shannon as saying "We don't choose to be affiliated with any political-based organization, especially one that may or may not have ties to things we find absolutely abhorrent."

There's an interesting point of interpretation here. What Shannon means, I guess, is that the question of whether the PA has ties to abhorrent things is a serious one, worth thinking about; or maybe he means to assert that such ties exist, while weakening the assertion so as to avoid offense or lawsuits. Weasel words like "may or may not [have property P]" are often used to flag uncertainty while still getting the idea out there. This is a perfect way to spread a rumor: "Madonna may or may not be pregnant".

Logically, this phrase offers perfect deniability while transmitting no information whatever. That's because it's necessarily true, no matter what P is. At least, "it's possible that P or it's possible that not P" is a theorem in just about anything worth calling a modal logic (given the "law of the excluded middle", which says that "P or not P" is always true, and the fact that if P is true, then P is possible, at least for alethic modality). So strictly speaking, I myself may or may not have ties to things Mr. Shannon finds absolutely abhorrent, and so may you. Not only Madonna, but also Geoff Pullum may or may not be pregant. In order to conclude that these statements are literally true, we don't need to learn anything more about my ties, your ties, Mr. Shannon's moral sentiments, or Geoff Pullum's physiological state.

There's a principle of relevance here. If you ask me why I don't trust X, and I say "well, I'm always uneasy about someone who may or may not be an embezzler", I'm communicating a fairly specific suspicion. Literally, it's true of every single one of us that we may or may not be an embezzler -- or drug dealer or a saint -- but the fact that I choose to raise the particular issue of embezzlement by X communicates something in and of itself.


Posted by Mark Liberman at December 25, 2004 11:57 AM