So I was trying to write something on metaphysical
vagueness, when I came across the following little puzzle. The aim was to turn
the few comments on Trenton
Merricks’s PPR paper in section 8 of my problem of the many paper into a full fledged discussion note. So I
started off by noting that the issue isn’t really whether all vagueness is
linguistic, because any representation, including pictures and (as Merricks
notes) thoughts can be vague. I then went to say that this doesn’t matter, and
that Merricks was right to focus on the linguistic case, when I suddenly had a
rather large fear that it does matter. Here’s why. Merricks spends a lot of
time fretting about whether the fact that (1) is indeterminate when Harry is a
borderline case of baldness.

(1) ‘Bald’
describes Harry.

Merricks claims that this is an instance of
metaphysical vagueness, because it is indeterminate whether a particular
object, the word ‘bald’, has a particular property, describing Harry. Set aside
concerns about whether describing Harry is a real property. There is a
huge issue remaining about just which object indeterminately has this
‘property’. It can’t be the word itself. It is not words themselves, but words
in languages, that describe (or don’t describe) people. So (1) should be ‘Bald’
in X describes Harry. But it is rather plausible that for every legitimate
substitution instance of X, we get a
sentence that is either determinately true or determinately false. There’s more
of a story to tell about how this avoids sliding into epistemicism, which is
Merricks’s response to a similar move he considers in the paper, but that story
can wait until the paper gets written.

The
real issue is that we can’t make the same move with pictures, because pictures
don’t represent with respect to a language. So imagine we start with a picture
of George Washington. Let’s start with this one:

This picture represents George Washington.
I could change it into a picture that didn’t represent Washington. The most
dramatic way to do this would be to replace every non-black pixel with a black
one. Let’s assume I did this slowly. (If I get some time this weekend I might
do just this, just to see the results in practice.) So we’d end up with
pictures that had causal origin in Washington, but whether they really were
pictures of Washington, well that would be hard to say. Indeed, whether they
were pictures of anything would be hard to say. Let a be the name for
one of these pictures. My claim is that it might be indeterminate whether $x(Represents(a, x)) is
true. I would have hoped that this wasn’t because of vagueness in ‘Represents’,
but I don’t really see any way out other than that. Any suggestions?