ARGUMENTS FOR MONOTHEISM 191that an infinitely membered series does not fit this description. Plainly
nothing in the argument of the First Way, in either its main or its
subsidiary lines of reasoning, provides anything like this. Thus the First
Way seems not to be a proof of its conclusion.
The Second Way
Again we begin with a couple of definitions.
Definition 9: X is in motion per accidens if and only if X moves
only because X is part of or is located in Y and X
moves only because Y moves.
The car moves per se. A cup of coffee set in the cup holder of a moving
car moves per accidens.
Definition 10: X moves per se if and only if X moves and X does
not move per accidens.
The Second Way runs as follows; it takes coming to be or coming to
exist as a change.
1 If X comes to be at T then X’s coming to be at T is caused.
2 Nothing can cause its own coming to exist (it would have both to
exist to do the causing and not exist to be caused to come to be).
3 If X comes to be at T then X is caused to come to be at T by
something other than X.
4 Either (a) there is an infinite series of beings that come to be and
are caused to come to be by other beings that were caused to come
to be, or (b) there is a being that causes other things to come to be
but is not itself caused to come to be.
5 Not-(a). So:
6 (b)
Aquinas argues for premise 5 in this manner:
5a An infinite series has no first member.
5b If a series has no first member, then it has no later members.
5c A series having neither a first nor later members has no members;
a series without members cannot exist. So: