Introduction to
Philosophy
05 March 2001
Identity
I. General problem for
identity: The Paradox of Identity
II. Paradox
A. Apparently-unacceptable conclusion, derived by
B. apparently-valid reasoning, from
C. apparently-acceptable premises.
III. Unacceptable conclusion: nothing
lasts
IV. Premise: indiscernibility of
identicals
A. If X is identical to Y, then for any property X has, Y has it too.
B. Alternative formulation: if there is some
property that X has and Y lacks (or vice versa), then X is not
identical to Y.
C. Different principle (identity of
indiscernibles): if for any property X has, Y has it too, then X is identical
to Y.
D. Alternative formulation of identity of
indiscernibles: if X is not identical to Y, then there is some property that X
has and Y lacks (or vice versa).
E. Leibniz’s Law: the indiscernibility of
identicals (not controversial) and the identity of indiscernibles
(controversial).
V. Reasoning
A. An object’s age is a property.
(assumption)
B. If X is identical to Y, then X and Y must have
the same age. (from indiscernibility of identicals)
C. Nothing can be identical to something that has
a different age. (from 2)
D. To persist is to come to have a different age.
(definition)
E. No one thing can persist. Nothing lasts. (from
3 and 4)
VI. No easy solution to the paradox.
Deep difficulty for basic beliefs about identity.
VII. Another problem example: the Ship of
Theseus
VIII. Special case of a problem about identity: Personal
Identity
B. What makes you you? Why is it that
no matter how much you change during your life, it’s still you?
C. “Conventionalist” answer
that’s attractive for Ship of Theseus example is no good here.