Sunday, July 26, 2009

Unkind Cuts, and different Sorites desiderata*

Is accepting the existence of a cut in the sorites series, into an extension and an antiextension, just like accepting the arbitrariness of other things in nature--the exact value of the gravitational constant, the maximum amount of money the government would spend to save an endangered child, the exact amount of poison that would kill you dead? Fine (1975) suggests that it is:

"I suspect that the temptation to say that [a sorites sentence] is true may have two causes. The first is that the value of a falsifying n appears to be arbitrary. This arbitrariness has nothing to do with vagueness as such. A similar case, but not involving vagueness, is: if n straws do not break a camel's back, neither do (n+1) straws."

Fara cites this as an attempt to answer "the Psychological Question":

"If the universally generalized sorites sentence is not true, why were we so inclined to accept it in the first place? In other words, what is it about vague predicates that makes them seem tolerant, and hence boundaryless to us?" (50)

She contrasts this with two other questions, "the Semantic Question" and "the Epistemological Question":

Semantic Question. If the universal generalization AxAy(Fx & Rxy -> Fy) is not true, then must this classical equivalent of its negation be true?: ExEy(Fx & Rxy & ~Fy) [called "The Sharp Boundaries Claim"].
(i) if Sharp Boundaries is true, how is its truth compatible with the fact that vague predicates have borderline cases?
(ii) If Sharp Boundaries is NOT true, what revision of classical logic/semantics must be made to accommodate this fact?

Epistemological Question. If AxAy(Fx & Rxy -> Fy) is not true, why are we unable to say which instance is untrue, even in the best epistemic situation?

Graff's response is that active consideration of a case (a particular value of x and y which bear the relation R to each other) raises the similarity of x and y to salience, so the boundary cannot fall between them.
The reason this seems odd to me is that active consideration of two shades seems to make one's ability to discriminate them sharper! This observation is compatible with the claim that one would never draw the F/~F line between them, but since active consideration brings their differences to the fore, it's counterintuitive.

***
Delia Graff Fara, "Shifting Sands." Phil. Topics, 2000.

Kit Fine, "Vagueness, Truth and Logic" Synthese. 1975.


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