Objection 1. It would seem that there is no last end of human life, but that we proceed to infinity. For good is essentially diffusive, as Dionysius states (Div. Nom. iv). Consequently if that which proceeds from good is itself good, the latter must needs diffuse some other good: so that the diffusion of good goes on indefinitely. But good has the nature of an end. Therefore there is an indefinite series of ends.
Objection 2. Further, things pertaining to the reason can be multiplied to infinity: thus mathematical quantities have no limit. For the same reason the species of numbers are infinite, since, given any number, the reason can think of one yet greater. But desire of the end is consequent on the apprehension of the reason. Therefore it seems that there is also an infinite series of ends.
Objection 3. Further, the good and the end is the object of the will. But the will can react on itself an infinite number of times: for I can will something, and will to will it, and so on indefinitely. Therefore there is an infinite series of ends of the human will, and there is no last end of the human will.
On the contrary, The Philosopher says (Metaph. ii, 2) that "to suppose a thing to be indefinite is to deny that it is good." But the good is that which has the nature of an end. Therefore it is contrary to the nature of an end to proceed indefinitely. Therefore it is necessary to fix one last end.
I answer that, Absolutely speaking, it is not possible to proceed indefinitely in the matter of ends, from any point of view. For in whatsoever things there is an essential order of one to another, if the first be removed, those that are ordained to the first, must of necessity be removed also. Wherefore the Philosopher proves (Phys. viii, 5) that we cannot proceed to infinitude in causes of movement, because then there would be no first mover, without which neither can the others move, since they move only through being moved by the first mover. Now there is to be observed a twofold order in ends--the order of intention and the order of execution: and in either of these orders there must be something first. For that which is first in the order of intention, is the principle, as it were, moving the appetite; consequently, if you remove this principle, there will be nothing to move the appetite. On the other hand, the principle in execution is that wherein operation has its beginning; and if this principle be taken away, no one will begin to work. Now the principle in the intention is the last end; while the principle in execution is the first of the things which are ordained to the end. Consequently, on neither side is it possible to go to infinity since if there were no last end, nothing would be desired, nor would any action have its term, nor would the intention of the agent be at rest; while if there is no first thing among those that are ordained to the end, none would begin to work at anything, and counsel would have no term, but would continue indefinitely.
On the other hand, nothing hinders infinity from being in things that are ordained to one another not essentially but accidentally; for accidental causes are indeterminate. And in this way it happens that there is an accidental infinity of ends, and of things ordained to the end.
Reply to Objection 1. The very nature of good is that something flows from it, but not that it flows from something else. Since, therefore, good has the nature of end, and the first good is the last end, this argument does not prove that there is no last end; but that from the end, already supposed, we may proceed downwards indefinitely towards those things that are ordained to the end. And this would be true if we considered but the power of the First Good, which is infinite. But, since the First Good diffuses itself according to the intellect, to which it is proper to flow forth into its effects according to a certain fixed form; it follows that there is a certain measure to the flow of good things from the First Good from Which all other goods share the power of diffusion. Consequently the diffusion of goods does not proceed indefinitely but, as it is written (Wisdom 11:21), God disposes all things "in number, weight and measure."
Reply to Objection 2. In things which are of themselves, reason begins from principles that are known naturally, and advances to some term. Wherefore the Philosopher proves (Poster. i, 3) that there is no infinite process in demonstrations, because there we find a process of things having an essential, not an accidental, connection with one another. But in those things which are accidentally connected, nothing hinders the reason from proceeding indefinitely. Now it is accidental to a stated quantity or number, as such, that quantity or unity be added to it. Wherefore in such like things nothing hinders the reason from an indefinite process.
Reply to Objection 3. This multiplication of acts of the will reacting on itself, is accidental to the order of ends. This is clear from the fact that in regard to one and the same end, the will reacts on itself indifferently once or several times.
Source: Summa Theologica (New Advent)