[hist-analytic] The Two Color Problem, Putnam, and the Synthetic A Priori
Baynesr at comcast.net
Baynesr at comcast.net
Tue Nov 3 14:26:48 EST 2009
"But if two determinate colors are conceded to be
distinguishable, it _follows logically_ that
nothing possesses both of them at the same place
at the same time." (ETK p. 66)
He adds that this is "very easily proved." (ETK p. 66). The
reason he gives is:
If we take 'DC' as 'determinate color', and
DCxt=A for 'the determinate color of x at t = A'
then on a proposal by Stephen Schwartz we have:
(A)(B)(DC(a) & DC(B) & Distinguishable (A,B) -> ~(A=B)
Bruce says that "the impossibility of DC(xt) = A
& DC(xt) = B & Distinguishable (A, B) follows
ALMOST IMMEDIATELY by conditional proof" (ETK p. 66).
Now the problems I have with this are:
1. I don't think it can be "very easily proved." If
it can, then Bruce will simply state the proof in
the sort of format Danny provided in his clarifying
remarks. So we need to see exactly how this proof
is supposed to work. Nothing is obvious, especially
with so many symbols and definitions. So let's see
2. I'm not sure there are such things as determinate
colors; try laying down conditions for partitioning
the class of red objects.
Putnam spends a great deal of time and introduces
numerous postulates in arriving at an understanding
of what a determinate shade is. He knew this was
crucial. It is. So what IS a determinate shade?
3. Even if the proof goes through, it misses the point.
We all agree that a thing can't be red and green all
over at the same time. That is not the issue. The
issue is whether this is synthetic a priori, relying
on the structure of intuitions or some such thing,
or whether it is analytic. Why should I believe that
'(A)(B)(DC(a) & DC(B) & Distinguishable (A,B) -> ~(A=B)'
is analytic? And if it is not analytic, why should I
reject self evidence as the basis for the claim that
nothing can be red and green all over etc.? Indeed
why should I believe this premise to be true? Can't
be self evidential because this is exactly what Bruce
seems to be denying.
4. Putnam has a lot of gizmos for stating the meaning
of one essential relation: 'exactly the same color as'.
Without this relation, i. e. his "basic idea" (this being the
idea upon which the proposed proof here is based), there
is no proving analyticity of the thesis.
Now these considerations, I think, should at least
impel us to a further examination of Putnam. I will
soon show that Putnam's argument is not pursuasive.
Too many postulates, too many assumptions, too much
razimataz to be a satisfying solution to the problem.
But it's not just logical "bulk" that concerns me;
it is the failure to match the analysis with a solution
to the problem as posed.
So give me a day or so to wade through Putnam's argument
and get back to yuz.
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