Proclus’s theistic argument is that every being proceeds from some first cause.
By “being” Proclus seems to mean more or less what we mean by “the universe”, i.e the totality of distinct things that one sees when he looks around.
He proceeds by elimination: either (a.) there is no cause of being at all (b.) all the causes of things revolve in a circle or (c.) the causes of being go ad infinitum.
But (a.) cannot be, says Proclus, for then there would be no science of being. There would, however, be a problem of self-reference here since, by this point in the book, he has been speaking about being as such for pages, and so any proof that the science was impossible would amount to a sound argument for the impossibility of logic. Sciences isolate some domain of experience and look, for among other things, for the extrinsic causes that gave rise to the things in that domain. Geology looks for the causes of planetary formation; astronomy for causes of stellar formation; biology for a clear account of abiogenesis.
True, we could respond to this that, while there is certainly a reason to look for causes in sub-universal domains, there need not be on in the whole universe. But this might be to miss the point: it is difficult to argue that the universe logically lacks any need of a cause, i.e. that we see a logical impossibility in it being caused, but the structure of any science is precisely from logical order.
Causality in a circle, however, either means that there is no causality or that something causes first. If a bunch of tow trucks are all hooked to each other, and moving around, then either they all have their motors running, or none do. If none, then they wouldn’t move at all, if all of them, then they aren’t towing each other, they are simply moving at the same time. But if one has its motor running, then this is the first cause of the motion, and it is no more being towed by something than a man is towed by pulling his own bootstraps. The remaining alternative is just a variant of the second option.
An infinite series of causes, however, has the same problem as was discussed in (a.), since a science is no more possible if the cause is placed at an infinite remove than if it is denied altogether.
And so Proclus’s proof – which seems clunky and thrown together, with all of its multiple options to be ruled out – seems structured in such a way as to point to the logical necessity of a being like God from the very possibility that the universe can be studied at all. Given that the universe could only be uncaused – if at all – as a fact and not by logical necessity, the very possibility of a science of the universe turns on there being some extrinsic cause of it.
An interesting corollary to this fact is that it might be possible for the universe to be a brute fact and caused by God. This is obviously not so if brute fact is taken as one for which no explanation is possible; but the usual account of brute facts is that they are such that no explanation is necessary. But if Proclus is right, the universe might be factually brute without being logically so.