ARGUMENTS (1) 245Full Qualitative Identity: X is fully qualitatively identical to Y if and
only if for any quality Q, X has Q if and only if Y has Q
(here “Q” ranges over spatial and temporal qualities as
well as other qualities).
Nearly Full Qualitative Identity: X is nearly fully qualitatively
identical to Y if and only if for any quality Q, if Q is not
a spatial or a temporal quality, X has Q if and only if Y
has Q (here “Q” does not range over temporal or spatial
qualities).
The pennies Cop and Per are not fully qualitatively identical; they occupy
different places. But they are nearly fully qualitatively identical, hence our
inability to tell one from the other after they are shaken.^6
Any substance is self-identical, identical to itself at each moment of its
existence; identity in this sense is numerical identity. If substance X exists
at time T1 and continues to exist at the next moment T2, then the X that
exists at T2 is identical to the X that existed at T1; here, too, identity is
numerical identity.
Numerical identity, strictly speaking, is identity; qualitative identity is a
matter, not of identity, but of resemblance. For a dualist, personal identity
is numerical identity of a person – a self-conscious substance: identity to
itself at a time, and to its continuingly existing self over each of various
times.^7
Temporal endurance of a simple substance is sufficient for its continuing
numerical identity. For a simple substance X to endure from T through T
is for it to be the case that at each time from T through T, and for any
property Q such that Q is essential to X, X has Q at each moment from T
through T. The closest thing to^8 temporal endurance of a simple substance
X from T through T is for a certain sort of series of things to exist – a
series that contains X at T (and then X ceases to exist), and at each moment
from T1 through T one or another substance Y that is nearly fully
qualitatively identical to X at T exists. Such a series will exist if either (i) at
each moment from T through T, a different simple substance exists that is
nearly fully qualitatively identical to each other in the series, or (ii) at each
moment after T through T, there is one simple substance that is nearly
fully qualitatively identical to X, or (iii) something between (i) and (ii).^9
But that (i) be satisfied is not sufficient for there being a single simple
substance from T through T. The same holds for (ii) and (iii). If the closest
thing to temporal endurance of a simple substance enduring from T
through T is not sufficient for there being a single substance that exists
from T through T, then those conditions being satisfied is not the same as
there being a simple substance that endures from T through T*.