Online Papers - Brian Weatherson

Vagueness and Pragmatics 467
supervaluational theory, we can only properly say that a is F if a is F on all 19 precisifications,
and that is what it is for a to be determinately F on that theory. On degree
of truth theories, we can assert that a is F iff a is F to a very high degree, and that is
what it is for a to be determinately F on that theory. In short, the pragmatic content
of ‘a is F ’ is that a is determinately F , or, for short, �F a. Note that on the epistemic
theory, this is the subjective pragmatic content, while on the supervaluational
and degree of truth theories it is the objective pragmatic content. This reflects the
differences between the ways the theories understand determinate truth. This point
acquires some importance soon, so we will return below to what epistemicists might
take the objective pragmatic content of ‘a is F ’ to be. For now we will focus on those
theories where �F a is the objective pragmatic content of ‘a is F ’. On those theories,
COP predicts that objective pragmatic content of (3) and (4) will be (12) and (13)
(3) Louis is bald or Louis is not bald.
(12) � (Louis is bald) or � (Louis is not bald).
(4) It is not the case that Louis is bald and that he is not bald.
(13) It is not the case that � (Louis is bald) and that � (Louis is not bald).
Note that on almost any theory of vagueness one cares to consider, if Louis is a
penumbral case of baldness, then (12) will be false and (13) true. (12) is false because
Louis’s penumbral status makes both � (Louis is bald) and � (Louis is not bald) come
out false. Hence if COP is true, speakers should decline to assent to (3), but should
assent to (4). Since they do, this is good news for COP.
We have not said how COP should apply to quantified sentences. These are a little
harder to incorporate into the theory than sentences that are formed by familiar
propositional connectives because the logical form of these sentences is less transparent.
I will assume 20 that quantified noun phrases are restricted quantifiers. Hence the
logical form of (14) will be (15).
(14) Q Fs are Gs
(15) [Qx: Fx] Gx
Although COP as it stands is silent on quantified sentences, we can naturally generalise
it. And the natural thing to say, given COP, is that if the logical form of (14) is
(15) then its objective pragmatic content is (16).
(16) (Qx) [� Fx : � Gx]
This lets us explain one of the consequences of supervaluationism that is, if anything,
more surprising that its endorsement of the law of excluded middle. The following
presentation of the puzzle is due to Jamie Tappenden. Let P(n) abbreviate ‘A
man with exactly n cents is poor’. “Since the supervaluation deems the conditional
19 Or perhaps most. Little will turn on this here, but the ability of supervaluational theories to handle
various paradoxes (such as the Sorites and the problem of the many) might depend on just how this
principle is framed. For salient discussion on this point see Lewis (1993b).
20 Following Barwise and Cooper (1981), Higginbotham and May (1981) and, most directly, Neale (1990)