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, Part 5, and Part 6. 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 fifth and sixth criticisms leveled against Aquinas.
A quantifier shift fallacy arises when an individual mistakenly swaps the existential and universal quantifiers. For example, merely from the fact that, for every student, there is a counselor, it does not follow that there is a single counselor for all students. With this in mind, though, consider premise 13: if it is not the case that chains of changes are infinitely long, then such chains terminate in one first member. Notice, though, that there seems to be an ambiguity here. Aquinas is either arguing (a) because each individual chain must terminate in a first member, there is one first member into which all chains terminate; or (b) because each individual chain must terminate in a first member, each individual chain has one first member that serves as this chain’s termination. Crucially, all Aquinas has demonstrated is (b), namely that since chains cannot be infinite, any individual chain must have at least one first member. But just as any individual student’s having a counselor does not entail there is a single counselor that all the students have, the fact that each individual chain has its own termination does not entail that there is one termination to which each and every chain traces back. If Aquinas is arguing for (a) but not (b), then P13 is simply false, since there being no infinitely long chains by itself tells us nothing as to whether or not all chains of changes terminate in one, single being. But if Aquinas is arguing for (b) but not (a), then P14 is false, since Aquinas holds that the unactualized actualizer is the monotheistic God, whereas (b) concludes to there being a whole host of unactualized actualizers standing at the termini of the host of series of causes/changes found in reality. And if Aquinas is trying to reason from (b) to (a), then he is committing a quantifier shift. In each case, though, Aquinas’s argument is unsuccessful.
Second, it is worth noting that even if a single chain cannot be infinite, it still does not follow that it has a single terminus. It may terminate in two beings, each of which imparts causal power to the rest of the chain. For instance, granted that a series of power strips (in order to charge my laptop, say) must terminate instead of being an infinitely long chain of derived power, it still does not follow that there must be one single power generator into which the “last” power strip in the series is plugged. Perhaps, instead, this last power strip has a cable that forks into three separate plugins, each of which is plugged into a power outlet on the wall, and each of which bestows the chain with power. In this case, we avoid an infinite per se chain of causes/changes, but it is still nevertheless not the case that there is a singular source or terminus of this particular chain.
Finally, even ignoring the above difficulties, there is a gap problem for premise fourteen. More specifically, there is a marked gap between being a mere “unactualized actualizer” and being “the God of classical theism”. Aquinas understands the God of classical theism as Pure Actuality, subsistent existence itself, a being whose essence and existence are identical. But merely being an “unactualized actualizer” does not entail “utterly lacking in all potentialities (i.e. being Pure Actuality)”, since any being which is an unactualized actualizer may have potentials which simply are not right now being actualized or are not required to be actualized for the being in question to serve as the terminus for a given per se chain of causes/changes. What’s more, the mere fact of being an unactualized actualizer speaks nothing to a being’s moral qualities, its degree of power, its intellectual and cognitive capacities, and so on. P14, then, seems to be afflicted by a gap problem, one consisting in the difficulty of bridging the gap between being an “unactualized actualizer” and being “the God of classical theism”.
I take it that the above considerations successfully rebut Aquinas’ argument from change for God’s existence. One somewhat plausible response on Aquinas’ behalf in relation to inferring one single terminus to which all chains of change trace is Occam’s Razor, the defeasible principle according to which simpler theories/hypotheses are, ceteris paribus, more probable. So, Aquinas may admit that, although we can only infer that each individual chain has its own terminus, the simplest hypothesis about how many such termini there are is that there is only one terminus rather than a large number of disparate termini to different chains of change.
An important but subtle thing to realize, though, is that Occam’s razor also cuts against Aquinas’ view. For consider that there are two types of simplicity: categorical simplicity and quantitative simplicity. It is preferable to maximize simplicity in both regards, but sometimes there is a conflict between the two. In this case, Aquinas would be reducing the quantity of different unactualized actualizers, but he is doing so at the cost of introducing categorical complexity. This is because he is introducing a new category into our ontology: a supernatural, immaterial being. So, although Aquinas reduces the number of different unactualized actualizers, the cost is an increase in categorical complexity. Occam’s razor, however, could lead us to reject this view. We could hold that there is a large number of different unactualized actualizers, but that they are all uniformly of one category which we already accept into our ontology: natural, material things. Perhaps the different unactualized actualizers are aspects of the fundamental layer (as it were) of natural reality (whether it be strings, quarks, quantum fields, energy, or what have you). In this case, although we pay the price of quantitative complexity in terms of the number of different unactualized actualizers, we maintain categorical simplicity in positing only natural, physical things as opposed to positing both natural and supernatural things.
I conclude, then, that even an appeal to Occam’s razor does not successfully address the criticisms raised in this section. At best, the appeal to Occam’s Razor is offset by Aquinas’ increase in categorical complexity. At worst, Occam’s Razor positively works against Aquinas’ view.