192 ARGUMENTS: MONOTHEISTIC CONCEPTIONS5 There is not 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.
The argument for premise 5 here is identical to the argument for premise 4
of the First Way, and hence has exactly the same problems. Further, coming
to exist is not a change in the thing which comes to exist; assuming the
definition of change offered above, it is not a change – non-existent things
have neither potentiality nor actuality. It is possible that X, which does not
exist at time T, comes to exist at time T1 does not entail X, which does not
exist, has the potentiality to exist; X has some potentiality or other entails
X exists. So the Second Way is not a proof.
The Third Way
Two simple definitions are helpful here.
Definition 11: X is generable if and only if X can be caused to come
to be.
Definition 12: X is corruptible if and only if X can be caused to
change and can be caused to cease to exist.
Aristotle and Aquinas seem to assume X can be caused to change entails X
can be caused to cease to exist, and conversely, so that necessarily anything
that meets one of the conditions of being generable also meets the other. It
is not at all obvious that this is so. In any case, the Third Way goes like this:
1 If X is generable and corruptible then X’s non-existence is possible.
2 There are corruptible and generable things. So:
3 There are things whose non-existence is possible (from 1 and 2).
4 Assume for the sake of showing it to be false that: For all X, X’s non-
existence is possible.^21
5 If for all X, X’s non-existence is possible, then there is some time T
such that nothing exists at T.
6 There is some time T such that nothing exists at T (from 4 and 5).
7 It is impossible that anything comes to exist without its being caused
to do so by something that already exists.
8 If there is some time T such that nothing exists at T, then for any time
T later than T, nothing exists at T.
9 Nothing exists at T* (from 5 through 8).
10 If there is some time T such that nothing exists at T, T has already
occurred. So: