Dear 125ers,

In lecture Thursday, I said a few things (some of which were new) about
"impure" properties.  This email serves to set out those ideas more
clearly.

First, in Black's (and Kant's) alleged counterexamples to the identity
of indiscernibles (II), we have spheres that (intuitively) are
apparently spatially separated, and this apparent spatial separation is
the reason we think there are 2 spheres, rather than 1, which "share all
the same properties".

In response to these examples, a bundle theorist (who accepts II) might
say "OK, in your example, the spheres don't really share ALL properties
in common -- they seem to differ in their spatial properties".  So, the
bundle theorist might then just try to include the spatial properties in
their bundles, and thus avoid the counterexamples and restore the truth
of the principle II.

At this stage in the dialectic, a substratum theorist (or an
Aristotelian) who rejects II usually says something like "Not so fast! 
Spatial properties are IMPURE -- they already presuppose the notion of a
substantive particular, or primitive thisness that transcends the II. 
So, you are not allowed to pack those properties into your bundles." 
So, "impure properties" are ones that are supposed to presuppose a
notion of particular (in some sense that transcends mere bundles of
properties).

There are various ways the bundle theorist can respond at this point,
some of which we discussed during the course.  But, it now seems to me
that there is another line of attack here -- to turn the tables back on
the substratum theorist or the Aristotelian.  Why can't the bundle
theorist just say at this point: "Well, you guys each claim to have a
THEORY of particulars that implies the falsity of II, right?  So, I ask
each of you, does your THEORY imply that spatial properties are impure? 
If so, how?"  To give a contrast here, think about Quine's or Lewis'
theory of particulars, which identifies them with spatial (or
spatiotemporal) regions.  On these theories, it is OBVIOUS why spatial
properties are impure.  The theories IMPLY straightaway that spatial
properties are essential to the notion of a particular.  But, it's not
at all obvious that substratum theory or Aristotelian theory has any
such implication.

Think about substratum theory first.  On this theory, a concrete
particular is whole constituted by (a) properties, and (b) a substratum.
 And, it is the substratum that provides the "thisness" which
distinguishes one particular from another. But, it seems pretty clear
that a substratum is not a concrete thing, since all of the physical or
material substance in a particular can be replaced, while it retains its
identity.  But, if a substratum is abstract, then why is it impossible
for two distinct substrata to occupy the same spatial region?  And, if
it's abstract, why can't one substratum be simultaneously "located" in
(or associated with) two spatial regions at once?  Maybe these things
are ruled-out, but it's certainly not obvious what the connection
between substrata and spatial properties is, and so it's not clear why
the substratum theorist -- BY THEIR OWN LIGHTS -- should view the Black
and Kant examples as reasons to reject the II.

The Aristotelian theory faces a similar worry.  On that theory, it is
the kind a particular instantiates that endows it with its
individuality.  But, what does THAT have to do with the spatial
properties of the particular?  Again, the connection -- IN THE THEORY --
is unclear.  And, so the OFFICIAL doctrine doesn't seem to place any
special emphasis on spatial properties.  Why, then, think there is
anything "impure" about them, or that they are "essential" to a thing's
being what it is (as opposed to some other thing)?

This is my current thinking on "impurity" as it relates to the theories
of particulars we studied in the course.  If you want to read a very
nice book on "spatiotemporal" approaches to particulars, have a look at
Ted Sider's "Four Dimensionalism".  That's a nice book to read after
taking this course.

Best of luck on the final, and beyond!

-Branden

P.S.  Remember, I have office hours next week: T (2-4) and W (4-6).
Also, Vanessa and Josh will have review sessions on Wednesday (and their
own office hours).  See the course homepage for details.