Buffy and Disjunction

I try to keep an eye out for uses of logical connectives, etc., in “everyday life” that I can use in logic classes. Here’s a nice use of excluded middle, in which neither disjunct is assertible, from “Two to go,” the penultimate episode of Buffy, Season Six. Or maybe it’s really an example of the failure of Ought(A ∨ B) → (Ougth A ∨ Ought B).

ANYA: She [Willow] tried to use you for a hood ornament, Xander! She doesn’t care if you live or die.

XANDER: Guess you two finally have something in common.

ANYA: I care if you live or die, Xander. I’m just not sure which one I want.

7 thoughts on “Buffy and Disjunction

  1. Somehow, I don’t follow how you are parsing this. Where does “ought” come from? Posted by Thad Coons

  2. Well, maybe you need a belief operator in there, too. Anya believes that it ought to be the case that: Xander lives or dies. But Anya neither believes that it ought to be the case that Xander lives, nor does she believe that it ought be the case that Xander dies. But I don’t want to undertake a detailed analysis of “care whether.” Posted by Richard Zach

  3. Did I ever tell you my favorite? It’s on the shopping carts at our local Albertson’s store: “Do not leave children unattended or permit to stand to up.”  Posted by Kai Wehmeier

  4. I would have parsed this differently, then, with the emphasis on “whether A or B” , in the case of Willow. In that case, or (P v ~P) -> R; which amounds to a verbose and emphatic statement of R.But a natural restatement would be “She doesn’t care if you live and she doesn’t care if you die” which may suggest a non-truth functional use of “or”.In Anya’s case, I would have taken the affirmation, “she believes” as more natural than “does not believe”. Posted by Thad Coons

  5. Wait, are you reading the “if” as a conditional, i.e., are you taking R to be “Willows doesn’t care”? That seems implausible to me. I’d think “care if” is a propositional attitude. There’s no conditional “if” in these sentences. Posted by Richard Zach

  6. I’m not sure if the “or” is used in a logical sense or not. Comparing this to the examples you gave, it does appear that “if” is synonymous with “whether”, which wouldn’t easily correspond to a conditional “if”. But since different verbs (to care, to be sure) can be used with this same construction (whether A or B), (if A or B), it appears that the “or” is the common “exclusive or” used to separate cases, rather than the “inclusive or” usually used in logic. Posted by Thad Coons

  7. I’d also say that the sentence isn’t actually a disjunction–maybe closer to the ‘ought’ reading. “I care” it seems to me must take a contrast set of alternatives: it means “I am not indifferent among the members of the set.” When we have just plain old “I care if P” presumably the implicit contrast is ~P–so this means the speaker prefers one of {P, ~P} to the other. But here ‘or’ means both alternatives are being stated explicitly: “I care if you live or die” means the alternatives are {you live, you die} and the speaker prefers one of them. Either the speaker prefers the hearer living to the hearer dying, or the speaker prefers the hearer dying to the hearer living. Hm. Then “I’m not sure which one I want” does turn out to be a refusal to assent to one of the disjuncts. But not for the obvious reason. Posted by Matt Weiner

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