Re: Coextensive properties?

From: Pierre-Normand Houle (houlepn.nospam_at_attglobal.net)
Date: 10/15/04 

Date: Thu, 14 Oct 2004 20:55:48 -0400

"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) 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.

The problem is that your definition of "property P" or "class P" clearly
Does not deliver the extension of property P as understood by a property
realist. It rather looks equivalent to ". has once been judged to be P by
somebody once performing the appropriate measurement (or observation)"
And, obviously, many such things do not have property P. And also, of course,
many things having property P have not been and never will be judged
or measured by anybody to be P.

Maybe I can go a bit further along your suggestion and propose another
"relativized intensional" definition of the "... has property P" predicate.
This would be in the spirit of Putnam's (Pierce inspired) internal realism,
which I do not endorse, but which might do as an illustration. And then
let's see if your trick can remove intensions.

The modified definition (D1) is : "... would be judged to have property
P by an observer who, were he to have had access to that object, would
have used observation methods in conformity with the norms that ought
to be established at the end of the scientific enquiry regarding property P."

But we must now explicitly relativize this before we can apply the "Der"
operator to get a proper extensional definition. And it will be a bit
complicated to apply "Der" repeatedly on this definition to "de-intensionalize"
it, so lets abbreviate it to (D2) "... would be judged to have property
P by an ideal observer who would conform to all clauses of D1." (And then
you can even vary D1 to conform to whatever strictures you believe
property realists ought rather to insist on.) Properly relativized, D2 would
become something like D2R : "... would be judged, in possible particular
context ..., to have property P by ideal observer ... who would happen to
conform to all clauses of D1." And now apply "Der" twice to get
D2Ext : "There exists a possible observer O and possible context C such that
O in C would judge . to be P while conforming to D1." Now, even supposing
that the "conforming to D1 clause" is well behaved (i.e. not intensional,)
we have clearly failed. The "property" (one place predicate) D2Ext is
intensional through and through because of the double occurrence of
the "possibility" operator. But this is required and ineliminable,
I think, because of the double normativity constraint of the rationality
of the observer and normalcy of the observational context (including the
"well" functioning of instruments).

> In your other post you say:
>
> > It makes differences in modal contexts. You can say : This car might
> > not have been red (it might have been painted blue instead.) That is
> > to say : that *very* car might not have had the *very* property red.
> > But you can not say : This car (which belongs in the "red" class)
> > might not have belonged to it. That is, you can not say : This *very*
> > car might not have belonged to that *very* class. That is a logical
> > contradiction. A definite class could not have had different members.
> > That would necessarily have been a different class.
>
> When you talk of these cars as a class you leave unspecified how they
> came to be put in their class;

Yes, that's the whole point if classes are not individuated by intensions.
The class of all free nonionized atoms having atomic number 1 might be the
same as the class of all free nonionized atoms possessing one electron.
But those two intensions correspond to two distinct properties.

> but when you talk of their property
> redness you specify that they could have been painted red or not. You
> have changed the context of the example and thereby have come up with a
> difference. But it is the change of context that made the difference.
>
> Can you keep the modal context constant between using "class" as opposed
> to using "property" and still make a difference ?

No, I can't keep the modal context constant. But the context is not
external to the evaluation of the concepts (classes and properties.)
Rather, is just comes with them! "Property" is an irrreductively modal notion
and "class" is not. An object that has a property could have been deprived
of it. (Unless the property is essential to this object: a gold atom could not
have had an atomic number different than the one it has. But this does not
affect the point about extensions. Some bearers might not have existed) So,
the extension of the predicate ". has property P" could have been different
than it in fact is. But a class could not have had different members than the
ones it in fact has.

> > But we hold (not
> > Quine, but realists about properties) that a definite objects might
> > have had definite properties contrary to the ones it in fact has.
>
> Well i think i am a realist about properties, and i think you are too.
> (Are you?)

Yes.

> But i do not "hold that a definite object might have had a
> definite property contrary to the ones it in fact has".

Do you mean that your car could not have been painted another color? That
it would then have been another car? What then if you do paint it another
color. Does it eo ipso become a different car?

> I do, however,
> hold that a object might have had a property that i did not measure
> correctly, or that i did not infer correctly. Iow - i do not hold my
> senses, or my assumptions, or my logic to be infallible. Does Quine say
> i must ?

I am unsure what Quine would say. Maybe he would say that you sometimes
revise your assumptions to better accommodate new data. This would be a case
of your changing your dispositions to use certain sentences (observation
sentences, theoretical hypothesis, etc.) in reasoning--a matter of
(covert verbal) behavior modification. (Again, I am not with Quine
on this, but I am just trying my best to get him right.) But there
would be no objective properties which good (scientific) behavior tracks.
Rather, good predictive behavior group observational data in useful
classes--nothing objective here apart from better of worse predictive
success.

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