3. It is impossible for the chain of actions to extend to infinity: there must then be something, in the getting of which the effort of the agent comes to rest. Therefore every agent acts to some end.
6. Actions are open to criticism only so far as they are taken to be done as means to some end. It is not imputed as a fault to any one, if he fails in effecting that for which his work is not intended. A physician is found fault with if he fails in healing, but not a builder or a grammarian. We find fault in points of art, as when a grammarian does not speak correctly; and also in points of nature, as in monstrous births. Therefore both the natural agent, and the agent who acts according to art and with a conscious purpose, acts for an end.
7. To an agent that did not tend to any definite effect, all effects would be indifferent. But what is indifferent to many things, does not do one of them rather than another: hence from an agent open to both sides of an alternative (a contingente ad utrumque) there does not follow any effect, unless by some means it comes to be determined to one above the rest: otherwise it could not act at all. Every agent therefore tends to some definite effect, and that is called its end.
Still there are actions that do not seem to be for any end, as things done for sport, and acts of contemplation, and things done without advertence, as the stroking of the beard and the like: from which instances one may suppose that there is such a thing as an agent acting not for any end. But we must observe that though acts of contempation are not for any other end, they are an end in themselves: as for things done in sport, sometimes they are their own end, as when one plays solely for the amusement that he finds in play; sometimes they are for an end, as when we play that afterwards we may resume work more vigorously: while things done without advertence may proceed not from the understanding, but from some phantasy or physical principle; yet even these acts tend to certain ends, though beyond the scope of the intellect of the agent.
Hereby is banished the error of certain ancient natural philosophers (Empedocles and Democritus, mentioned in Aristotle, Physics II, ii, 6) who supposed all things to happen by necessity of matter, and eliminated final causes from the universe.
3.1 : Preface to the Book that follows
3.3 : That every Agent acts to some Good