Identity is unity or union; either because the things which are said to be the same are plural in their being, and yet are called the same insofar as they agree in some one factor; or because they are one in their being, but the intellect treats them as though they are plural in order to think a relation. For a relation can only be thought to obtain between two extremes, as when something is said to be the same as itself; for then the intellect treats what is one in reality as though it were two; otherwise it could not designate a relation of something to itself. Wherefore it is clear that if a relation always requires two extremes, and in relations of this sort there are not two extremes in reality but only in the mind, the relation of identity is not a real relation but only a relation of reason . . . for if the relation of identity were some thing besides that which is called the same, that thing which is a relation, since it is the same as itself, for the same reason would have another relation which would be identical with itself, and on to infinity. But it is impossible to go to infinity in things. But in matters of the intellect nothing prohibits it. For when the intellect reflects on its acts it understands that it understands, and it can understand this as well, and so on to infinity.
--St Thomas Aquinas, Commentary on the Metaphysics, Lib.V, lectio XI, par.912, my translation
A couple of thoughts about this passage. First, it's a good example of the fact that some of the "problems" that modern philosophy finds the most challenging and fascinating, such as the nature of self-identity, are for the classical and scholastic mind non-starters (the converse is also true, of course). In fact this disconnect between what modern thinkers find interesting or worth spilling gallons of ink on and what I find interesting and worth reading and thinking about is part of what makes reading much modern philosophy so difficult for me (it's rather like my reluctance to read contemporary fiction rather than classical and medieval poetry). Not only are modern philosophers frequently preoccupied with issues that to the classical mind seem rooted in silly misunderstandings, but those - to us - misunderstandings also seem to breed contempt for the kinds of thinking that I and the scholastics do find worthwhile. In any case, Aquinas is not alone here in finding nothing mysterious or profound about identity, since it's a mere relation of reason: what's difficult is understanding the being and the essence of a thing, not how that being is the same as itself. But, as I've claimed on this blog before, it seems to me that a lot of the absurdities of modern philosophers stem ultimately from an inability to tell the difference between real being and beings of reason.
A second, related, thought is that Thomas' point here not only makes use of an infinite regress argument, but is important for understanding infinite regress arguments in general. Anyone who's read much of the modern literature on arguments for the existence of God will know that the denial of the impossibility of an infinite regress is a favorite way for moderns to wiggle out of them. St Thomas' comments suggest that the reason an infinite regress, so obviously absurd to the scholastics, is unproblematic to the moderns, is (again) because moderns are not used to carefully distinguishing between real relations and relations of reason. And this is unsurprising, given that so much modern philosophy (and "science"), being born of Cartesian mathematicism, has been accustomed to axiomatically assuming that mathematical techniques are paradigmatic for philosophical (and "scientific") knowledge. But mathematical objects are indifferently divided between purified (i.e. denuded of what the Thomists always call material conditions) formal abstractions from experience and mere relations of reason, which happily sit on the number line together. Mathematics itself doesn't care about the distinction, but metaphysics must.
I believe this thought is suggested by Thomas here but it jumped out at me because it reminded me of a passage in John Deely's recent Medieval Philosophy Redefined, which I read a couple of months ago (the following is from page 268):
This contrast between relations in the physical order which depend upon actual characteristics of actual individuals (upon "subjective accidents of substances" in Aristotle's terms) and relations in the objective order which are not tied to actual subjective characteristics but may be founded upon whatever other relations happen to exist within a given cognition was the reason why Aristotle, and the Latin logicians after him, rejected arguments which led to an infinite regress. An infinite regress is actually possible only in the mind, because only in the mind can relations be founded upon relations. So any argument that involves an actual infinite regress, to the extent that it involves one, is an argument that has lost touch with the order of physical being as something to be explained through proper causes. For proper causes are found only within the physical interactions of finite substances, and these, as finite, are always determinate within the order of moved movers. . . .
Deely gives a further reference to his book The Human Use of Signs, which I have not read. In any case it's interesting to note that modern thinkers so often take the rejection of infinite regress as an arbitrary ad hoc principle whose only purpose is to force one to accept a First Cause, when the scholastics themselves not only see it as completely necessary and self-evident but also use it constantly in a host of nontheological contexts.