Re: Coextensive properties?

From: Chris Menzel (cmenzel_at_remove-this.tamu.edu)
Date: 10/15/04 

Date: 15 Oct 2004 02:13:29 GMT

On Thu, 14 Oct 2004 20:55:48 -0400, Pierre-Normand Houle
<houlepn.nospam@attglobal.net> said:
>
> "patty" <pattyNO@SPAMicyberspace.net> wrote in message
>
>> But i still don't see Quine's real point. Again, suppose we collect our
>> measurements as {(C,(x,P)), ...} where C is the context of the
>> measurements including the particular instruments, the setting of the
>> measurements, and the agents doing the inquiry and their assumptions.
>> The the pairs (x,P) are certainly intensional to their Cs ... iow, they
>> are relative to them. Those same pairs do not become any more or less
>> intensional if we label them "x is member of class P" as opposed to "x
>> has property P".
>
> I gather from Francois Recanati, in his _Literal Meaning_, that Quine
> indeed once used a device that he calls a derelativization operator
> ("Der") which reduces by one the adicity of an n places predicate by
> existentially quantifying on one single argument. (Recanati cites
> Quine's Selected Logic Papers, p. 227, but I haven't looked it up)

This is from "Variables Explained Away". Der is one of a number of
predicate operators Quine introduced to develop a variable-free
"predicate functor calculus" equivalent to first-order logic.

> I suppose you could thus use Quine's "Der" operator to reduce a two
> place predicate such as ". is taken to have property P in particular
> (token) context ..." to the single place predicate (or "property")
> "There has occurred (or will occur) some particular context C such
> that the object ... was (or will be) taken to have property P in this
> context. This was how I understood your suggestion above. But I think
> it only seems to work because you really start with an extensional
> conception of properties.

While an analogous operator on intensions would of course affect their
extensions, there's no reason why one can't introduce one. Indeed,
George Bealer did exactly that for all of Quine's syntactic operators in
his book Quality and Concept (Oxford UP), wherein he develops a sound
and complete first-order logic of properties, relations and
propositions ("in intension", as they say). Ed Zalta did something
similar in his book Abstract Objects (Reidel).

Chris Menzel