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Sometimes ‘and’ is not a truth-functional connective

February 24, 2010, 2:51 pm

This nonsense from Clark Hoyt cracked me up. The NYT reported that James O’Keefe “made his biggest national splash last year when he dressed up as a pimp and trained his secret camera on counselors with the liberal community group Acorn.” O’Keefe dressed as a pimp. O’Keefe trained his secret camera on counselors. When he filmed, though, he dressed in khakis and an oxford.

[Hoyt replied to this criticism by saying]—with emphasis in the original— that “The story says O’Keefe dressed up as a pimp and trained his hidden camera on Acorn counselors. It does not say he did those two things at the same time.”

Really brings me back. In grad school, I taught introductory logic courses, and one of the standard things we did was cover basic propositional logic and natural deduction. The idea is to teach formal logic by showing students how to work in an artificial language made of up of atomic propositions (symbolized with p, q, etc.) and truth-functional connectives (&, v, -, etc.). A connective is truth-functional just in case the truth value of a compound sentence made with this connective is determined entirely by the truth values of the component sentences and the way the connective works. For example, suppose we’re dealing with “&” in our artificial language. p&q is true just in case p is true and q is true: that is, all you need to know is the truth values of p and q, and you’ll know what the truth value of p&q is.

And here the Hoyt-type examples come in. I used to use examples where temporal relations mattered to suggest that the artificial language “&” is not really the same as the ordinary-language “and.” It’s kind of like a crude approximation. A classic:

(i) John and Mary got married and had a baby

is different from

(ii) John and Mary had a baby and got married

The natural language version either says or suggests that the events happened in that order, while our “&” doesn’t care about that– all that matters is the truth values of “John and Mary got married” and “John and Mary had a baby.” The lesson to take from this is that our artificial language is different from spoken English in just this way: only the artificial connectives are truth-functional. It’s great to see this old chestnut of a point in the news. Next: Clark Hoyt wonders about justified true belief!

(There are some debates about whether the ordering is just an implicature or part of the truth conditions of the ordinary language sentence. Some people will die in the last ditch arguing for the the truth-functionality of the English “and,” but, if the best the public editor can do is to say “we didn’t print something false; we printed something that was, strictly speaking, true, that we knew ordinary readers would misunderstand,” well, he’s still lousy.)

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