Yes You Can Tell The Difference Revisited
- From: Kropotkin <not@xxxxxxx>
- Date: Mon, 02 Jun 2008 04:35:39 GMT
I've spent way too much time thinking about the issues raised in the
³Tell the Difference² thread. I thought I would share my conclusions,
for what they are worth.
First, let me try to pinpoint what's at issue here. (Dictionary
definitions aren't nearly sharp enough to cut any hay on this sort of
thing.)
We often encounter sentences that seem to be straightforward
affirmations of aesthetic value, eg: ³BWV1043 is a great piece of
music². This is a very common way of speaking: what are we to make of
it? Judging by its surface grammar, this sentence, call it S, is a
simple predication: of the object BWV1043 is predicated the quality
greatness. Those who want to say that beauty is subjective, ³in the eye
of the beholder², must claim that this surface grammar is misleading.
They might say that sentences like S are always false, or perhaps
neither true nor false, because the predicate is defective and fails in
reference. Or they might try to preserve more of the semantic
appearances here - for instance, the conviction with which S is often
uttered - by offering to supply a more subtle and accurate deep grammar
for S. Perhaps S does have truth conditions - which are often met - but
they must be relativized and the apparent predication eliminated. The
sort of suggestion the subjectivist contributers to the thread seem to
have in mind, is that, very roughly speaking, S could be taken to mean
something like ³ BWV1043 gives me great aesthetic pleasure² (where
presumably we can specify without appeal to aesthetics the sort of
pleasure involved). The details of the semantic proposal don't matter
for now; the point is that the subjectivist owes us some such story.
Not only that, but we are also owed an explanation of why we must
complicate our semantics in this way (for in semantics as in
everything, the simpler theory wins).
Now, despite all the verbiage in the thread, I can find only one
attempt (by ³Wilbur Slice²) to provide such an explanation (and not
even the beginnings of an attempt to make good on the semantic debt).
The proposed explanation begins with a challenge: if there really are
qualities such as seem to be predicated in S, then how do we measure
them? By what procedures can we verify S? Since we pretty clearly
cannot meet this challenge, the subjectivist concludes that S cannot be
taken at face value.
It is revealing to see why this argument fails by issuing a similar
challenge in the domain of mathematics - the bastion of objectivity if
there is one. What makes mathematics objective, everyone learns in
grade school, is that mathematical conclusions can be conclusively
proved. Consider the sentence ³Proof P is valid². Again, by its surface
grammar, a simple predication. But what of the predicate ³valid²? How
can we measure validity? But what procedures can we verify that
something is valid? Now of course we can formalize mathematical proof
to some extent. There are even computer programs that can check
validity, right? But this is a bit like writing a program to check for
parallel fifths in counterpoint: it shows nothing but what it shows. We
judge a formalism by the degree to which it reproduces our practice,
and none of the hard questions - like, do we allow proof by
contradiction? - can be answered formally. (The are more technical
limitations of formalism that fall out of Godel's theorems, but we can
neglect those here.)
In fact, the only way to teach someone to judge mathematical validity -
the only ³procedure² we have - is to show them a bunch of proofs that
we accept and hope they eventually ³get it². If they don't, we flunk
them. This might suggest the mathematics is more about social
conformity than ultimate reality. But I've never known a mathematician
who would entertain that thought for a minute - they all believe that
validity is part of our perception of the beauty of Plato's heaven.
Which brings us back to beauty in music. The situation is just the same
as with mathematics: there is no measurement, there are no procedures;
either you get it or don't.
It might be urged that judgments of mathematical beauty are more stable
and unanimous than judgments of musical beauty. But they are not as
unanimous as commonly thought by non-professionals - cf., the issue of
proof by contradiction alluded to above, or more currently, the issue
of computer-aided proof. Obversely, the lack of consensus on aesthetic
value is much over-rated: consensus comes, it just comes slowly. There
are still accredited professionals who have their doubts about the
axiom of choice (and hence most of the math we teach engineering
students); I don't know of any accredited professionals who have doubts
about the value of Bach, Beethoven, et al.
I'm not contending that aesthetic subjectivism is wrong, just that
aesthetics doesn't suffer by comparison with mathematics. Or, mutatis
mutandis, by comparison with empirical science: just ask what
constitutes ³scientific² confirmation? Considered human social
consensus is how we judge objectivity; maybe we could subjectivize
objectivity with a semantics that relativizes the truth conditions for
sentences like S and its mathematical and scientific analogs to that
consensus. Hmm, sound good to me - if I can work out the details, I'll
get back to y'all.
.
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