Aquinas (and other scholastics like Scotus) distinguish between at least two distinct types of causal series: per se and per accidens, or essentially and accidentally ordered series. A series of causes ordered per se is today often called a hierarchical causal series. Aquinas thinks that an accidentally ordered causal series could at least in principle have an infinite regress; but for an essentially ordered series such is absolutely impossible. Below is one possible argument for this conclusion.
Let an instrumental or mediate cause be any cause Y of effect Z which itself is caused in its very causal activity of Z by further cause X. I.e. Y is caused to cause Z by X; or Y’s causation of Z is caused by X. X can be either a first cause or another instrumental cause. Every instrumental cause is inherently dependent precisely qua cause, i.e. for its very causal activity. This causal activity is thus itself a dependent causal activity; it is insufficient in itself for its own activity.
For every causal series where there are members which are instrumental causes, the instrumental causes function altogether as a single instrumental cause. Suppose X and Y are both instrumental causes of Z. Z is dependent upon Y, but it is at least equally dependent upon X, since X causes Y’s causation of Z. X is itself an instrumental cause so it is further dependent upon cause W. W thus causes X’s causation of Y’s causation of Z. Hence Z is inherently dependent upon Y, X, and W as upon a single total cause. W, X, and Y are not actually a single cause; but in their causal activity they function as if a single cause. Their causal activity has a kind of essential unity, in that Z is inherently dependent upon the simultaneous, composite activity of all three acting in conjunction.
Hence, in a series of instrumental causes, the entire series, no matter how many individuals it contains, functions as a single instrumental cause. But every instrumental cause is dependent for its causal activity. Hence, in every series of instrumental causes, the entire series is dependent for its causal activity. Thus every series of instrumental causes is dependent for its causal activity. But the series obviously cannot be dependent upon another instrumental cause, because that instrumental cause would just be part of the series. So the series as a whole must be dependent upon a non-instrumental cause. A non-instrumental cause is a first cause. Therefore every series of instrumental causes is dependent upon a first, non-instrumental cause.
Technically, this argument makes no mention of an infinite regress at all. The infinite regress is impossible only if it rules out a first member; theoretically, as far as this argument is concerned, there could be an infinite regress as long as there is still a prima causa outside the whole series, outside of or transcending the regress.
A formalized summary of the argument:
- Every instrumental cause is a cause which is caused for its very causal activity.
- Every series of instrumental causes functions altogether as a single instrumental cause.
- So every series of instrumental causes is caused for its very causal activity.
- A series of instrumental causes can be caused either by another instrumental cause, or by a non-instrumental cause.
- A series of instrumental causes cannot be caused by another instrumental cause.
- Therefore every series of instrumental causes is caused by a non-instrumental cause.
- A non-instrumental cause is a first cause.
- Therefore every series of instrumental causes is caused by a first cause.