It is important to understand the background of the argument before undertaking an analysis of objections, so if you have not checked them out, I would suggest reading Part 1, Part 2, Part 3, Part 4, and Part 5. For each objection, I shall explicate the reasoning behind the objection, followed by an “assessment” section which evaluates the efficacy of the objection in question. Without further ado, let’s examine the fourth criticism leveled against Aquinas.
The justification behind Aquinas’ denial of infinite series of changes is captured in premise nine: if there were no first member in the series of changes, there would be no subsequent changes. The idea is that removing or taking away the first member, precisely because this member is causally responsible for subsequent members, would thereby remove the intermediate and subsequent members of the chain. Indeed, Aquinas makes this reasoning contra infinite chains even more explicit in his second way: “Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause.”16
This reasoning, however, is flawed and rests on a misunderstanding of infinite chains. In an infinite chain (of changes, causes, or what have you), there is no first member. But there being no first member is crucially different from removing or taking away a member from the series. To illustrate this, suppose we have a finite series of changers, where C changes C1, C1 changes C2, and C2 changes C3. Call this scenario Finite. But now suppose we take Finite and attach to it an infinite number of changers. This series (call it Infinite) now consists of C3 being changed by C2, C2 being changed by C1, C1 being changed by C, C being changed by C-1, C-1 being changed by C-2, and so on ad infinitum. Crucially, though, notice that considering Infinite in relation to Finite, we have not removed or taken away the first cause, C. Rather, we have merely demoted it, as it were, from its status as first cause. So, while removing or taking away a first cause or changer in finite chains of causes/changes thereby removes the chain itself, it is a mistake to presuppose that this also applies to infinite chains. Indeed, we even have reason to believe that we do not remove the first cause in infinite chains, but rather merely alter its status. Hence, Aquinas has not adequately justified his denial of infinite chains of changes.
The response to this objection is twofold. The first response is conciliatory, and it is that Aquinas does not adequately clarify or expound upon his denial of (certain kinds of) infinite chains. It will not do to merely point out that removing the first cause thereby removes the whole chain, since (a) we only have reason to think this applies to finite chains, (b) infinite chains do not involve the “removal” of a member but merely an alteration of its status, and (c) arguably it is simply question-begging to assert that removing or even altering one member of the chain would thereby collapse the whole chain, since this is precisely what the defender of infinite chains would deny and is precisely the issue at question. After all, the very thing needing to be shown is that removing or altering the first member would thereby remove the whole chain, since a defender of infinite chains would not grant this in the first place (thinking, as he or she does, that there are or can be infinite chains where the whole chain does not collapse in virtue of there being no first member). But it is precisely this claim Aquinas adduces in order to justify his denial of infinite chains. It seems, then, that Aquinas must already presuppose chains cannot be infinite in order to argue for that very result. In this respect, therefore, a concession needs to be made that, at least in the passage at hand, Aquinas has not justified his denial of infinite chains.
It should be clear from one of the foregoing discussions in this paper, though, that the Thomist does have the resources to justify the metaphysical impossibility of a certain kind of infinite chain (namely, infinite chains ordered per se). This is the second, non-conciliatory response to the objection in question. For consider that any member of a per se chain has no causal or actualizing power on its own, but wholly derives it from without. For instance, in a chain of power strips, no power strip has any power on its own to produce electricity. This means, though, that for any non-first member M of a per se chain, M only changes or moves in a wholly derivative manner, deriving its change/motion from all prior members of the series (since “wholly deriving x from y” is a transitive relation). But, if we suppose that no prior members of the series have causal or actualizing power on their own (i.e. they themselves only have wholly derivative causal or changing power), then it follows that M derives its causal power from without, yet there is nothing with causal power external to M from which M could derive its causal power (again, this is because we are supposing that all prior members have no causal power on their own, but yet M derives its causal power from all prior members. Hence, M derives causal power from without, but there is nothing from without that has causal power with which to supply M). But if there is nothing with causal power external to M from which M could derive its causal power, then M has no causal power. This is because M deriving x presupposes something from which M derives x, in which case there being nothing from which M derives x entails that M does not, after all, derive x. In that case, though, M either does not have x, or has x in a non-derivative manner. But since we are supposing M is a non-first member of per se chain, M does not have x in a non-derivative manner. Hence, M does not have x. But that is absurd, since we are supposing that M actually does have x (i.e. motion or change) since there are things in our experience which are in per se series of changes and are themselves undergoing change (like the staff in an earlier example). So, our original supposition is false, in which case it is false that no prior members of the series have causal or actualizing power on their own. Therefore, there is a member of the series with causal or actualizing power on its own. But, by definition, if the per se chain is infinite, then each member of the chain has previous members from which it derives its causal or actualizing power (i.e. no member has causal or actualizing power on its own). Therefore, per se chains cannot be infinite. Hence, for a given chain of per se changes, there is an unactualized actualizer or unmoved mover which is the ontologically most fundamental member of the chain in question.
This result, moreover, coheres with common sense. If we have a power strip and plug it into another power strip, we won’t get power at all. Nor will we get power if we add a third, or a fourth, or a fifth power strip. Indeed, even if we add infinitely many power strips, we will still never magically get power within the chain in question. There must be some non-derivative source of power which generates or provides power on its own but does not derive it from without. In effect, a per se chain that regresses infinitely is a vicious regress, not a benign one.
In conclusion, therefore, while a conciliatory point has been made that Aquinas’ passage alone does not sufficiently rule out infinitely regressing chains, the Thomist does have the resources to justify this premise by means of the distinction between per se and per accidens series.