190 ARGUMENTS: MONOTHEISTIC CONCEPTIONSThe sort of dependence that T2 describes is non-reciprocal and consecutive.
The sort of dependence that T1 describes is reciprocal and concurrent. The
First Way requires that there be a sort of dependence that is non-reciprocal
and concurrent. Suppose that T1 and T2 are true and describe the only sorts
of dependence there are. Then the First Way fails. Nothing in the First Way
proves that T1 and T2 are not true and descriptive of the only sorts of
dependence that there are. So the First Way is not a proof that extends our
knowledge. Perhaps there is the sort of non-reciprocal dependence that
Aquinas requires, but we have no proof of it here.
Infinite series^19
It is not obvious why there cannot be an infinite series of changed and
changing things, whether we have chronological or concurrent cases of
causation in mind. We have seen why premise 4 – the rejection of an
infinite series of things changing one another regarding quality Q – is
needed. Aware of this, Aquinas offers a subsidiary argument for premise 4:
4a An infinite series has no first (earliest?) member.
4b If a series has no first (earlier?) members, it has no later or succeeding
members
4c If a series has neither earlier nor later members, it has no members.
4d No series can have no members. So:
4 Not-(a) – there is not an infinite series of changed and changing
beings (i.e., a series each member of which is both a changed and a
changing thing).
Aquinas^20 admits that there can be a temporally beginningless causal series;
so presumably it is concurrent, not chronological, causality that Aquinas
has in mind in this argument (and elsewhere in the Five Ways). The
argument for the fourth premise is puzzling. There were sharp disputes
among medieval philosophers as to whether an infinite series was possible.
Perhaps the sub-proof rests on the idea that, in constructing a series, one
has to begin somewhere, and if one does not start with a first thing one will
never construct even a two-member, let alone an infinitely membered,
series. Then the argument is correct but irrelevant, since those who contend
that there are series that are infinite does not contend that we have to
construct them. One can reply that any actual series must be one that could
in principle be constructed by someone, and an infinitely membered series
could not be. But then we need another argument that any infinite series
must be one that could in principle be constructed, and another to show