In a recent post I outlined an argument against the possibility of an infinite regress in a *per se* ordered causal series. This post outlines two further such arguments.

The first I call the *sufficiency* argument:

- Every effect has its total sufficient cause.
- If a causal series ordered
*per se*did not have a*prima causa*(first cause), it would not have a sufficient, total cause. - Therefore every causal series ordered
*per se*has a*prima**causa*.

The first premise is evident. Whatever effect does not have its total sufficient cause would not have what is enough for its existence, and hence would not exist. In short, whatever effect lacks a total sufficient cause, does not exist.

By a *prima causa* I mean an ultimate source. Hence, without a *prima causa* there would be no ultimate source for the effect in question. What remains to be shown, then, is that the absence of an ultimate source is also the absence of a total sufficient cause. To show this, I will introduce the next argument, which I call the *addition* argument.

Here is the informal explanation of the addition argument. For every effect, it is necessary that the sufficient conditions for the existence of that effect are met in some number of causes at least equal to one. Suppose we add one cause C1 to effect E. C1 either meets the sufficient conditions for E or does not. If it does not, we must add at least one further cause C2. Either C1+C2 meet the sufficient conditions for E, or not. If not, we must again add a further cause to the series C3. For any number of causes Cn added to E, if Cn does not meet the sufficient conditions for E, we must add a further cause. Now, no instrumental cause added to E can meet the sufficient conditions for E, since an instrumental cause is by definition a *caused* cause. Hence every instrumental cause in itself presupposes the addition of some further cause. Note that this is true both for any *individual* instrumental cause, and for any *number* or *set* of instrumental causes. So for *any number* of instrumental causes added to E, the sufficient conditions of E are unmet and at least one further cause must be added. This means that even if an *infinite *number of instrumental causes are added to E, the sufficient conditions for E are still unmet, and we still must have a further cause. Hence an infinite regress of instrumental causes fails to meet the sufficient conditions for E. Only if there is a causal series which terminates in a *prima causa* can the sufficient conditions for E be satisfied. This shows that the second premise of the sufficiency argument is correct, as is the conclusion that every causal series ordered *per se* has a *prima causa*.

Therefore the sufficiency argument and the addition argument in conjunction provide very powerful overall support to Saint Thomas Aquinas’s premise that “it is not possible that in efficient causes it is proceeded into infinity,” which is used in a number of his arguments for the existence of God.

I endorse the cosmological argument from per se ordered causal series, but don’t think this particular way of defending it succeeds.

You write,

“Note that this is true both for any individual instrumental cause, and for any number or set of instrumental causes. So for any number of instrumental causes added to E, the sufficient conditions of E are unmet and at least one further cause must be added. This means that even if an infinite number of instrumental causes are added to E, the sufficient conditions for E are still unmet, and we still must have a further cause.”

I don’t think this follows. Here’s why: In your justification for ‘any number of instrumental causes added to E are insufficient’, you deal only with finite numbers: If I add instrumental causes C1 and C2 to E, it will be insufficient; if I add instrumental causes C1, C2, and C3, it will be insufficient; and so on. This correctly pumps our intuition that no *finite* addition of instrumental causes would be sufficient to generate the effect. But then you, without warrant, jump to the conclusion that any number *including an infinite number* of instrumental causes added will fail to be sufficient. Perhaps we should think this, but your brief defense of the principle doesn’t get us there. It leaves open the traditional Humean objection: ‘Once we have an infinite number, each individual instrumental cause is accounted for by its infinite priors, and so there is nothing left to explain.’

At any rate, I appreciate the exploration of the argument! If you’d like to check out my recent defense of it, you can find a paper I published on the subject here:

https://www.cambridge.org/core/journals/religious-studies/article/abs/powers-possibility-and-the-essential-cosmological-argument/AF21B3D7FEE42E9651B527F172A8A810

I’m curious to hear what you’d think.

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