Objection 1. It would seem that concupiscence is not infinite. For the object of concupiscence is good, which has the aspect of an end. But where there is infinity there is no end (Metaph. ii, 2). Therefore concupiscence cannot be infinite.
Objection 2. Further, concupiscence is of the fitting good, since it proceeds from love. But the infinite is without proportion, and therefore unfitting. Therefore concupiscence cannot be infinite.
Objection 3. Further, there is no passing through infinite things: and thus there is no reaching an ultimate term in them. But the subject of concupiscence is not delighted until he attain the ultimate term. Therefore, if concupiscence were infinite, no delight would ever ensue.
On the contrary, The Philosopher says (Polit. i, 3) that "since concupiscence is infinite, men desire an infinite number of things."
I answer that, As stated above (Article 3), concupiscence is twofold; one is natural, the other is not natural. Natural concupiscence cannot be actually infinite: because it is of that which nature requires; and nature ever tends to something finite and fixed. Hence man never desires infinite meat, or infinite drink. But just as in nature there is potential successive infinity, so can this kind of concupiscence be infinite successively; so that, for instance, after getting food, a man may desire food yet again; and so of anything else that nature requires: because these bodily goods, when obtained, do not last for ever, but fail. Hence Our Lord said to the woman of Samaria (John 4:13): "Whosever drinketh of this water, shall thirst again."
But non-natural concupiscence is altogether infinite. Because, as stated above (Article 3), it follows from the reason, and it belongs to the reason to proceed to infinity. Hence he that desires riches, may desire to be rich, not up to a certain limit, but to be simply as rich as possible.
Another reason may be assigned, according to the Philosopher (Polit. i, 3), why a certain concupiscence is finite, and another infinite. Because concupiscence of the end is always infinite: since the end is desired for its own sake, e.g. health: and thus greater health is more desired, and so on to infinity; just as, if a white thing of itself dilates the sight, that which is more white dilates yet more. On the other hand, concupiscence of the means is not infinite, because the concupiscence of the means is in suitable proportion to the end. Consequently those who place their end in riches have an infinite concupiscence of riches; whereas those who desire riches, on account of the necessities of life, desire a finite measure of riches, sufficient for the necessities of life, as the Philosopher says (Polit. i, 3). The same applies to the concupiscence of any other things.
Reply to Objection 1. Every object of concupiscence is taken as something finite: either because it is finite in reality, as being once actually desired; or because it is finite as apprehended. For it cannot be apprehended as infinite, since the infinite is that "from which, however much we may take, there always remains something to be taken" (Phys. iii, 6).
Reply to Objection 2. The reason is possessed of infinite power, in a certain sense, in so far as it can consider a thing infinitely, as appears in the addition of numbers and lines. Consequently, the infinite, taken in a certain way, is proportionate to reason. In fact the universal which the reason apprehends, is infinite in a sense, inasmuch as it contains potentially an infinite number of singulars.
Reply to Objection 3. In order that a man be delighted, there is no need for him to realize all that he desires: for he delights in the realization of each object of his concupiscence.
Source: Summa Theologica (New Advent)