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PY4804 Philosophy of Logic Week 6: The Epistemic Theory of Vagueness

This document summarizes the epistemic theory of vagueness. [1] It presents the basic version which claims that borderline cases have sharp cutoff points but their status cannot be known. [2] It argues this view follows from assumptions that classical logic is valid and semantic relations like T-sentences hold. [3] It discusses Williamson's version and standard objections like denying T-sentences, and Williamson's replies defending the epistemic view.

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66 views3 pages

PY4804 Philosophy of Logic Week 6: The Epistemic Theory of Vagueness

This document summarizes the epistemic theory of vagueness. [1] It presents the basic version which claims that borderline cases have sharp cutoff points but their status cannot be known. [2] It argues this view follows from assumptions that classical logic is valid and semantic relations like T-sentences hold. [3] It discusses Williamson's version and standard objections like denying T-sentences, and Williamson's replies defending the epistemic view.

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Fred_Mayweather
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PY4804 Philosophy of Logic

Week 6: The Epistemic Theory of Vagueness


Agustı́n Rayo
ar29@st-andrews.ac.uk
November 5, 2003

1 The Position
1. Notation
If ‘bald’ doesn’t clearly apply to Harry and ‘not bald’ doesn’t clearly apply to Harry,
let us say that an attribution of ‘bald’ to Harry is a borderline attribution.

2. The basic version of epistemicism


A basic version of the epistemic theory of vagueness is given by the conjunction of
the following two claims:

(a) Sharp-cutoff points: each borderline attribution is either true or false


(b) Unknowability: true borderline attributions cannot be known to be true and
false borderline attributions cannot be known to be false.

3. Williamson’s version of epistemicism


Williamson adds the following two claims to (a) and (b) above:

(c) The safety Condition: if one knows that A is true in a situation α, then A must
be true in all situations sufficiently similar to α.
(d) The Fragility Thesis: The boundaries of vague predicates are sharp but unstable.

These are used to explain why [Unknowability] is true. But, of course, there might
be other explanations.

1
2 Why be an epistemicist?
1. Assumptions
[Sharp cutoff-points]—which is the only part of basic epistemicism which is controversial—
follows from two plausible assumptions:

(A1) The T-sentences hold (paradoxes aside)


(A2) Classical inferences are valid

2. The argument
Here’s how the argument goes:

(1) ‘Harry is bald’ is true iff Harry is bald


[by (A1)]

(2) ‘Harry is not bald’ is true iff Harry is not bald


[by (A1)]

(3) Either Harry is bald or Harry is not bald


[by (A2)]

(4) Either ‘Harry is bald’ is true or ‘Harry is not bald’ is true


[from (1), (2) and (3) by (A2)]

3. Why should one accept classical logic?


Here are some reasons Williamson gives:

• simplicity
• power
• past success
• integration with theories in other domains

4. The Sorites Paradox


Epistemicists have a straightforward answer to the Sorites Paradox. Since they be-
lieve in sharp cutoff-points, they can say that a premise of the form ‘If a man with n
hairs of his head is bald, then a man with n + 1 hairs on his head is bald’.

2
3 Standard Objections and Williamson’s Replies
1. Denying the T-sentences
Objection: why should one hold onto the T-sentences in the face of results as coun-
terintuitive as [Sharp cutoff-points]?
Reply: Given that ‘Harry is bald’ means that Harry is bald, what else could it take
for ‘Harry is bald’ to be true than for Harry to be bald?

2. Determinate Truth
Objection: Okay. The T-sentences hold for truth, but they don’t hold for definite
truth. Why not characterize borderline attributions as cases which are neither defi-
nitely true nor definitely false?
Reply: What does ‘definitely true’ mean, if not ‘knowably true’ ?

3. Supervenience I
Objection: The epistemicist would presumably want to claim that whether or not
Harry is bald supervenes on the number and distribution of hairs on his head.
Shouldn’t it follow that I could determine whether Harry is bald by counting the
hairs on his head and assessing their distribution?
Reply: It is one thing for an inference to hold necessarily and another for it to be
knowable a priori. The inference from ‘x is made of water’ to ‘x is made of H2 O’, for
example, holds necessarily, but is not knowable a priori. The inference from ‘x has
so many hairs and such-and-such a distribution’ to ‘x is bald’ is another such case.

4. Supervenience II
Objection: Isn’t it a consequence of the epistemic view that the truth of ‘Harry is
bald’ fails to supervene on our linguistic practice (together with, e.g. environmental
factors)?
Reply: No. Just because we can’t know what the supervenience relation is like, it
doesn’t follow that it’s not there.

4 Further Reading
(a) There is a required reading for Friday’s seminar:
• Williamson, T ‘Vagueness and Ignorance’ (1992), in Keefe and Smith Vague-
ness: A Reader, MIT Press, 1996.
(b) Enthusiasts could also look at:
• Chapters 7 and 8 of Williamson, T. Vagueness, Routledge, 1994.

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