FOM: Kanovei's picture, Silver's comments

[A.P. Hazen]

   The Max Black paper Charles Silver refers to is "The Identity of
Indiscernibles," orig. pub. in "Mind" (English philosophical journal) in
1952, repr. in Black's "Problems of Analysis."
   Formulating the "Principle of Identity of Indiscernibles" is difficult.
Quine's proposal (in sections 24 and 47 of "Word and Object", ch. 5 of
"Philosophy of Logic," amusing logical complication in "Grades of
Discriminability" orig. pub. "Journal of Philosophy" 1976; repr. in Q's
"Theories and Things") is, essentially, to imagine a complete discription
of the universe in First Order Logic WITHOUT identity, and then define two
objects as identical if they satisfy exactly the same F.O. formulas (with
parameters).
   This, however, allows examples like Max Black's, in which the universe
is symmetrical, with objects on one side of an imaginary mirror being
indistinguishable from but still not identical to their mirror images on
the other side.  Let a and b be two mirror-image objects each five miles
from the mirror: a does but b does not satisfy the parametric formula "x is
ten miles from b."
    To get a version of the "P of I of I" with some metaphysical bite, you
have to do something more.  Randy Dipert, in a speculative article "The
mathematical structure of the world: the world as a graph" in "Journal of
Philosophy" 1997 proposes an interesting condition in terms of
automorphisms.  I'm not sure it's the principle we want (philosophical uses
of PII to argue for, eg, the "Mind-Body Identity Thesis" seem to require a
notion of property-identity, under which two different  predicates in an
initial description of the universe can be identified), but I recommend the
article as a starting place.
--
Allen Hazen
Philosophy Department
University of Melbourne