ARGUMENTS FOR MONOTHEISM 185If Tim is Tom’s father, then Tom is not Tim’s father; being a father, being a
mother, being a parent are irrefiexive relations.
It will be useful to have two further ways of talking about relations. Let
us say that if X has R to Y then X has R forwardly to Y, and that Y has R
backwardly to X. Reflexive relations between X and Y are had both
forwardly and backwardly by both X and Y. Irrefiexive relations between X
and Y are had only forwardly by X and only backwardly by Y.
General structure
The general structure – the logical skeleton, as it were – of Aquinas’s
arguments, typically called the “Five Ways,” as we will see, can be
expressed either as:
1 There is an X and a Y such that X bears relation R to Y.
2 Either (a) there is an infinite series of items such that each member
has R both forwardly to something and backwardly to something, or
(b) there is some item that has R only forwardly.
3 Not-(a). So:
4 (b).
or as
1 There is an X and a Y such that X has R to Y.
2 Either (a) there is an infinite series of items such that each member
has R both forwardly to something and backwardly to something, or
(b) there is some item that has Y only forwardly.
3 If (a) then (b).
4 If not-(a) then (b). So:
5 (b).
Chronological versus concurrent causes
If we are to understand Aquinas, it is important to distinguish between
what we will call chronological versus concurrent causes.
Definition 3: X is a chronological cause of Y if and only if X’s doing
something or having some quality at some time before T
is necessary for Y at T.