186 ARGUMENTS: MONOTHEISTIC CONCEPTIONSPutting the water over the fire, causing it to boil; turning the key in the
ignition, causing the car to start; throwing the ball, causing the window to
break, are chronological causes.
Definition 4: X is a concurrent cause of Y if and only if X doing
something or having some quality at T is a necessary
condition of Y at T.
Holding a door to keep it open; holding one’s breath to keep one’s lungs full;
pushing the bell to keep the bell ringing are cases of concurrent causation. It is
typically cases of concurrent, not chronological, causation that Aquinas has in
mind in offering his arguments. Thus criticisms based on the assumption that
he has chronological causation in mind will be off target.
Each of Aquinas’s five arguments concerns a different relationship as
follows.
Argument 1: something moving/changing something else.
Argument 2: something causing something to come to exist.
Argument 3: X can cease to exist by becoming Y.
Argument 4: things having different degrees of worth.
Argument 5: something behaving at least as if it were seeking a goal.
Domains, forwardness, and backwardness
A finite domain is a collection having a finite number of members; a pile of
forty rocks, a flock of seventy geese, a galaxy of a million stars are finite
domains. Suppose that we have a domain of three things – Al, Bob, and Carl.
Suppose that an irreflexive relationship – say, being a father – relates Al and
Bob, and Bob and Carl. Within this domain, Al stands in the relation being a
father only forwardly, Carl stands in the relation being a father only
backwardly, and Bob stands in the relation being a father forwardly toward
Carl and backwardly toward Al. If this domain is all there is, Al has no father
and Carl has no children. This domain is ordered by an irreflexive relationship.
Each member of the domain is related to every other by an instance of the
same irreflexive relationship – in the case just described, by being a father.
Consider a different domain – a domain denned in terms of its members
being ordered by a particular sort of dependence relationship. The sort of
dependence in question is non-reciprocal dependence where B non-
reciprocally depends for existence on A if and only if B depends for its
existence on A and A does not depend for its existence on B. Suppose, then,
that there exists a domain of things each of which stands in a non-reciprocal