ARGUMENTS FOR MONOTHEISM 187dependence relation to something, and that this domain is finite. Then it
follows that some member of this domain stands in the relationship of non-
reciprocal dependence only forwardly. The only alternatives are that the
domain is infinite (which we have stipulated is not so) or that there is a circle
of non-reciprocal dependence, which is impossible. If B non-reciprocally
depends on A, and C non-reciprocally depends on B, and A non-reciprocally
depends on C, then the relationship between A and B is reciprocal dependence,
not non-reciprocal. A circle of non-reciprocal relationships is logically
impossible. So some member of the domain must stand in the relationship of
non-reciprocal dependence only forwardly^14 – i.e., must exist independently of
the other members of the domain ordered by the irreflexive relationship of
non-reciprocal dependence.
Aquinas takes this relationship of non-reciprocal dependence to be one
involving concurrent causation – if the existence of A fully explains the
existence of B, then so long as B exists it must be the case that A is causing it to
exist.
It is not obvious that the world of physical things and nondivine minds is a
finitely large domain of things ordered by the relationship of non-reflexive
dependence. But that it is such a domain is something that at least the first
three of Aquinas’s arguments require.
Change, potentiality, actuality^15
Aquinas defines change in a way reminiscent of Aristotle’s philosophy.
Definition 5: X is in actuality with respect to some property Q if and
only if X has Q.
Definition 6: X is in potentiality with respect to some property Q if and
only if (i) X does not have Q, but (ii) X is the sort of thing
capable of having Q.
Elk cannot be prime numbers, eggs cannot run faster than hares, and pigs
cannot fly; so these things are not in potentiality with regard to these
properties. Elk can be dyed pink, eggs can be swallowed whole, and pigs can be
dressed in tuxedos, so they are in potentiality with respect to these properties.
Elk have legs, eggs have shells, and pigs have ears, so they are in actuality with
regard to these properties.
Definition 7: X changes with respect to property Q if and only if X
moves from potentiality to actuality, or from actuality to
potentiality, with respect to Q.^16