Posts on: Identity
Here's an attractive picture. All there really is, at a fundamental
level, are fields in spacetime (or something like that). The world as we
know it, with its rocks and chairs and cats and people, somehow emerges
from this basis: all truths about rocks and chairs etc. are made true by
truths about fields in spacetime. But how? To explain this, it would
help if we could locate the familiar objects – rocks and chairs etc. –
in the physical description of reality. With the help of classical
mereology, which is plausibly analytic, this
seems possible: ordinary objects can be identified with aggregates of
spacetime points. They are regions in spacetime. With this, we can
explain how simple facts involving ordinary objects can emerge. For
example, what makes it true that my chair has steel legs is that its
region has a certain kind of subregion with high-amplitude excitations
of quark and electron fields in a certain arrangement.
In a nice little paper, "The Non-Transitivity of the
Contingent and Occasional Identity Relations", Ralf Bader argues
that if identity is relative to times or worlds, then it becomes
non-transitive and thus no longer qualifies as real identity.
Following Gallois, Bader assumes that a proponent of occasional
identity must insist that identity statements are always relativised
to a time. Now he considers a case where between times t1 and t2, two
objects B and D simultaneously undergo fission in such a way that one
fission product of B fuses with one fission product of D. Of the three
resulting objects A, C and E, one (C) is a fission product of both B
and D. Bader argues that at the initial time t1, it is then true that
A=C and C=E, but not that A=E. So identity at t1 is not
transitive.
In the (Northern) summer, I wrote a short survey article on
contingent identity. The word limit did not allow me to go into many
details. In particular, I ended up with only a brief paragraph on
Andre Gallois's theory of occasional identity, although I would have
liked to say a lot more. So here are some further thoughts and comments
on Gallois's account.
In his 1998 monograph Occasions
of Identity, Gallois defends the view that things can be identical at some
times and worlds and non-identical at others. For simplicity, I'll
focus only on the temporal dimension here. Gallois begins
with a long list of scenarios where it is intuitive to say that things
are identical at one time but not at others. For example, when an
amoeba A fissions into two amoebae B and C, it is tempting to say that
B and C were identical prior to the fission and non-identical
afterwards.
I have often encountered in articles, talks and classes the following argument for the necessity of true identity statements, always attributed to Kripke:
1) a = b (assumption)
2) ![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5CBox)
a = a
3) a = b (from 1, 2 by Leibniz' Law)
The argument is no good, and I think it is very doubtful that Kripke ever endorsed it.
Everything is identical to itself, and nothing is identical to
anything except itself. No two things are ever identical. If A and B
are identical then "they" are one, not two.
These are platitudes about identity, or rather about a
somewhat technical use of "identity" common in mathematics and
philosophy.
No doubt there are other uses. For instance, "identity" and its
cognates are often used to express sameness of kind, as in "this
record is the same Jones bought last week". Sometimes, "identity" is
used as a singular term for a thing's characteristc properties or
individual essence, as in "the festival has lost its identity". The conceptual platitudes
above do not apply to these other uses.
Yesterday, I said that it doesn't really matter whether we regard identity simpliciter as identity-at-our world -- individuationg referents extensionally -- or as identity-at-every-world -- individuating referents intensionally. Suppose we want to do the latter, so that the referent of "the amazon" determines a function from worlds to world-bound individuals, that is, an intension. So on the present account, we identify the amazon with something that completely determines the intension of "the amazon". The intension? What if, as two-dimensionalists argue, "the amazon" has two intensions? Which one is the one we want extensions to determine?
So there are several ways to make sense of restricted identities. Which is the right one? Maybe there is no fact of the matter.
The difference depends on which contexts are regarded as referentially transparent and which as opaque. And that in turn depends on how the referents are individuated. For instance, (de re) ascriptions of modal properties will be transparent iff the referents of singular terms are such that they determine the truth value of all such ascriptions, perhaps because they (the referents) are fusions of world-bound individuals with their counterparts, or because they are Carnapian individual concepts, or because they simply contain some hidden tag that determinately settles all their modal properties. At any rate, for de re modal contexts to be referentially transparent, the referents have to provide us with a function from worlds to world-bound individuals, as that's what we need to determine the the truth value of those ascriptions. Alternatively, if we hold that those contexts are referentially opaque, we decide that the referents do not contain that information. Instead, we put the information into another aspect of meaning, which we call the terms' intension. Is the difference really more than just a relabeling of semantic vocabulary?
Now restricted identities threaten to violate
Leibniz's Law: If R1 is identical with R2, then how can they differ in
their courses? If AD1 is AD2, how can they differ in their history?
If A1 is A2, how can they differ in their modal properties?
They can't. So either R1 and R2 (and AD1 and AD2, and A1 and A2) are
not really identical, or the don't really differ. Let's look at the
first option first. It says that R1 and R2 are not really
identical. Hence "R1 = R2" is false, even though
If you follow the Rhine upstream, you'll reach Reichenau in Switzerland, where its two tributaries, the Vorderrhein and the Hinterrhein, meet. As far as I know, it is undefined which of them, if any, is the Rhine. Obviously that's not a mystery but just a matter of stipulation. So let's stipulate that 'R1' is to denote the continuation of the Rhine through the Vorderrhein, and 'R2' its continuation through the Hinterrhein.