244 NONMONOTHEISTIC CONCEPTIONSSubstance dualism, and its associated view of persons, has a highly
distinguished history. Plato, Augustine, Anselm, Descartes, Samuel Clarke,
and Thomas Reid all held it. It also has some distinguished contemporary
advocates.^5 Its popularity currently is at low tide, this arguably (if a pun be
allowed) being more a matter of fashion than of substance.
Identity
Symmetry and transitivity of identity
The proposition A is identical to B entails the proposition B is identical to
A. The proposition A is identical to B and B is identical to C entails the
proposition A is identical to C. These two simple facts about identity are
expressed by logicians by saying that identity is reflexive and transitive.
Whether A, B, and C are wombats, kumquats, tuxedos, numbers, angels, or
galaxies, identity among them is reflexive and transitory. To deny this is to
deny that there is any such thing as identity as applied to them, which is
the same as denying that there are any such things.
Numerical versus qualitative identity
In considering competing views of persons, and of personal identity, it is
crucial to keep firmly in mind the distinction between numerical identity
and the quite different matter of qualitative (so-called) identity or
resemblance. Suppose Tim has a penny in each hand, each minted in
Philadelphia in 1998, both bright and unscratched. He names the one in his
left hand “Cop” and the one in his right hand “Per.” Cupping his hands
together, he shakes the pennies and then again grasps one in one hand and
one in the other. Neither he nor we were able to keep track of either penny
during the shaking. In these simple circumstances, we know that Cop is still
in Tim’s left hand or else Cop is now in Tim’s right hand, and that either
Per is still in Tim’s right hand or else Per is now in Tim’s left hand. But we
do not know which.
This simple example illustrates various important concepts. Both Cop
and Per retain numerical identity over time. Since we do not know which
penny Cop is, Cop’s having numerical identity over time is a fact about it
independent of our knowledge of it. Cop and Per are qualitatively identical;
that is why we cannot, at the end of the shaking, tell which penny is which.
These basic notions can be formally characterized as follows: