February 02, 2004

Schmendrick's Paradox

While ranting against de re attitudes (as opposed to ascriptions), I discussed the truth conditions of ascriptions such as

(1) Brian wants Brian to win the election,
where the second "Brian" is taken to be de re. I remarked that you get a paradox if you propose that
(U) (1) is true iff, for some term X, Brian has a desire "I want X to win the election," and X refers to Brian (as used by him in the context of thinking.

Here's how. I'm going to replace "want" with "say," to avoid uglinesses concerning the language of thought and the like. So the proposed semantics for de re interpretations is:

(S) "X said of Y that he is phi" is true iff X said, "B is phi," for some term "B" which refers to Y in the context of X's utterance [and grant me my goofy use of quotation marks, OK? I don't think it makes a difference]

Now suppose Schmendrick, one of the minor Hebrew prophets, gets up before the people and says, "Malchiah is a sinner. The judges are sinners. Those who sneer at the prophets are sinners. And verily, I say unto you,

(P) He who stands before you today, and says not of himself that he is a sinner, he is a sinner."

Nobody else stands before the people that day. Does the phrase

(N) He who stands before you today, and says not of himself that he is a sinner

refer to Schmendrick?

Well, suppose (N) does refer to Schmendrick. Then, according to (S), when Schmendrick uttered (P), he said "N is a sinner" and N referred to Schmendrick. That means that Schmendrick did say of himself that he's a sinner. So (N) can't refer to Schmendrick.

Suppose (N) does not refer to Schmendrick (and, let's take it, none of the other terms he used referred to him either). Then Schmendrick did stand before the people--and he was the only one--and he did not utter "X is a sinner" for any X that refers to himself. By (S), he stood before the people and did not say of himself that he is a sinner; and he was the only person to do so (since no one else stood before the people that day). So (N) does refer to Schmendrick.

Some notes:
(1) It doesn't matter whether Schmendrick is a sinner or not.
(2) I don't actually think this paradox is very profound. I'd be happy to take care of it by a version of the revision theory. [Some of my old profs might not like the juxtaposition of those two sentences!]
(3) Some people might take the moral to be that definite descriptions can never be the basis for de re ascriptions, but only directly referring terms such as indexicals, demonstratives, and proper names. I don't find this appealing--if Alice says "The Vice President looks scary," do we really want to deny that Alice said that Dick Cheney looks scary? I suppose we could say that it is literally false but pragmatically acceptable that Alice said that Dick Cheney looks scary--but I really don't think there's much reason to privilege substitution of directly referring terms over subsitution of definite descriptions salva reference. And if you forbid substitution of directly referring terms, you're where I want you, allowing only descriptions de dicto.
(4) Some people might take the moral to be that definite descriptions can only be the basis for de re ascriptions when the holder of the attitude is acquainted with the referent of that description as the referent of the description. So Alice knows Dick Cheney as the Vice President, but Schmendrick doesn't know himself as the person who didn't say of himself that he was a sinner.--Well, all right. (I think David Kaplan held a view like this at some point.)
(5) This paradox is a lot like that put forth by Benoit de Cornulier in "Paradoxical Self-Reference," Linguistics and Philosophy 2 (1978) p. 435. (No link because Utah doesn't pay Kluwer's ridiculously high subscription prices.) I discovered the paradox independently--through the time-honored method of building a formal system for the semantics of quotation, and then discovering that my definitions were inconsistent. I discovered the de Cornulier paper because it's entirely contained, the way most maps of Maryland contain maps of Delaware, within my Xerox of Alexander P.D. Mourelatos's classic "Events, Process, and States" (same volume, pp. 415-434).

Posted by Matt Weiner at February 2, 2004 03:25 PM