Coextensive properties?

From: Bill Modlin (modlin1_at_metrocast.net)
Date: 10/11/04 

Date: Mon, 11 Oct 2004 13:26:51 -0400

This Quine quote often cited by Longley cropped up once again in a note
by Patty...

> 'If it makes sense to speak of properties, it should
> make clear sense to speak of sameness and differences of
> properties; but it does not. If a thing has this
> property and not that, then certainly this property and
> that are different properties. But what if everything
> that has this property has that one as well, and vice
> versa? Should we say that they are the same property? If
> so, well and good; no problem. But people do not take
> that line. I am told that every creature with a heart
> has kidneys, and vice versa; but who will say that the
> property of having a heart is the same as that of having
> kidneys?
>
> In short, coextensiveness of properties is not seen as
> sufficient for their identity. What then is? If an
> answer is given, it is apt to be that they are identical
> if they do not just happen to be coextensive, but are
> necessarily coextensive. But NECESSITY, q.v., is too
> hazy a notion to rest with.
>
> We have been able to go on blithely all these years
> without making sense of identity between properties,
> simply because the utility of the notion of property
> does not hinge on identifying or distinguishing them.
> That being the case, why not clean up our act by just
> declaring coextensive properties identical? Only because
> it would be a disturbing breach of usage, as seen in the
> case of the heart and kidneys. To ease that shock, we
> change the word; we speak no longer of properties, but
> of CLASSES......
>
> We must acquiesce in ordinary language for ordinary
> purposes, and the word 'property' is of a piece with it.
> But also the notion of property or its reasonable
> facsimile that takes over, since these contexts never
> hinge on distinguishing coextensive properties. One
> instance among many of the use of classes in mathematics
> is seen under DEFINITION, in the definition of number.
>
> For science it is classes SI, properties NO.'
>
> W. V. O. Quine (1987)
> Classes versus Properties
> QUIDDITIES:

Since Quine is no longer around to ask, perhaps David will help me to
understand this better.

The example chosen by Quine to illustrate a problem with "properties"
seems silly. We say that an organism has a heart because we dissect it
and find a muscular lump of tissue suited for pumping blood. We say
that it has a liver because we find a different lump of tissue, in a
different location, suited among other things for filtering harmful
chemicals from the blood.

Because each is involved with blood, it is not surprising that they tend
to be found in the same organisms, that their occurrences are highly
correlated. But I don't see how such a correlation, even if perfect,
among clearly distinguishable properties should lead one to want to
consider them the same property.

Quine seems to be saying that we should take "having a liver" and
"having a heart" as defining the same property, and says that the only
reason we don't take this step is that it would be a breach of common
usage. He then suggests that we switch to using the word "class" as
though this will somehow make it reasonable to ignore the differences
between hearts and livers....

Which is absurd. The criteria for determining whether or not an
individual is a member of a class of liver-possessing entities is still
quite distinct from the criteria for membership in a class of
heart-possessing entities. If those two distinct criteria are
empircally determined to lead to identical classes, that is useful
information. It suggests that there may be a connection between the two
criteria, a relationship between the properties, which is worth
following up and may lead to more information about things like
circulatory systems and blood flow. But it in no way suggests an
identity between hearts and livers, or between classes of things having
them or between the properties of having them.

I can imagine cases where different labels may be applied to vaguely
defined properties, cases in which one might discover that one was
making a distinction without a difference, and clarity might be better
served by recognizing the equivalence of properties previously
considered different.

But this is not such a case, and the class of things with livers remains
distinct from the class of things with hearts, regardless of the
empirical coextensiveness of those classes.

I don't think science requires us to ignore relevant distinctions just
to allow silly wordplay at this level.

However. My impression is that Quine was pretty smart. Which suggests
he might not be making the silly mistake this seems to me to be. So
I'm open to further explanation, if someone can show me where I missed
the point. Just please don't direct me to more of Quine's words... I've
read them, many times, and I don't think I'll get any more from reading
them again at this time.

Bill Modlin

Relevant Pages

  • Re: Coextensive properties?
    ... > This Quine quote often cited by Longley cropped up once again in a note ... Than he uses 2 criteria or properties to farther differentiate this ... first the heart and second the kidney. ... coextensiveness of properties is not seen as ...
    (sci.logic)
  • Re: Coextensive properties?
    ... for kidneys, using criteria as singular, and various typos... ... I am told that every creature with a heart ... > identity between hearts and livers, ... > empirical coextensiveness of those classes. ...
    (sci.logic)
  • Re: Coextensive properties?
    ... I am told that every creature with a heart ... >and find a muscular lump of tissue suited for pumping blood. ... The criteria for determining whether or not an ... >empirical coextensiveness of those classes. ...
    (sci.logic)