SCG III.i.2

[1] The first thing we need to show is: that in acting every agent intends an end.

[2] What is an end?

Some things obviously act for an end and others do not obviously act for an end.

Definition of an end: "that toward which the inclination of the agent tends."

If an agent attains this, the agent attains its end.

If an agent fails to attends this, it fails in regard to the end intended.

For example, the end of a physician is health and the end of a runner is "a set objective" (to win a race, to reach a destination, etc.).

This definition applies both to knowing beings and unknowing beings.

The end of an archer is the target; the end of the motion of an arrow is the target.

Does every inclination of an agent tends toward something definite?

Different kinds of actions stem from different kinds of powers.

The action of heating stems from the power of heat; the action of cooling stems from the power of cold.

Some actions terminate in something that is made:

For example, the action of building terminates in a house and the action of healing terminates in health.

Other actions do not terminate in something made:

For example, the action of understanding does not terminate in something made, nor does the action of sensing.

In the case of action that terminate in something made:

The inclination of a builder tends through the action of building toward a house and the inclination of a physician tends through the action of building toward healing.

In the case of actions that do not terminate in a product:

The inclination of the one who understands tends towards the action itself of understanding and the inclination of the one who senses tends towards the action itself of sensing.

What is the "something definite" that every inclination of an agent tends toward?

The "something definite" is the end toward which the inclination of the agent tends--and this can be either something that is made or, in some cases, an action.

[3] What is an ultimate end?

The ultimate end is that beyond which the agent seeks nothing else.

For example, the ultimate end of a physician is health.

The action of all agents has an ultimate end--something beyond which the agent seeks nothing further.

Nothing is moved toward what cannot be reached; so, whenever an agent is moved, he must be moved toward something that that can be reached.

The thing that can be reached that the agent is moved toward is "that toward which the inclination of the agent tends"--that is, the end.

Therefore, every agent acts for an end.

Note: Aristotle does not say in Posterior Analytics that it is impossible to proceed to infinity:

"Suppose it to be impossible to proceed to [50] infinity when starting from the last term and advancing upwards ...."

https://oll.libertyfund.org/title/bouchier-posterior-analytics#lf0248_label_081

[4] Actions cannot proceed to infinity.

If the action is directed toward producing something, the actions cannot go on to infinity. The reason is that the person would never get around to producing anything (he would never get to that point--because it would take an infinite number of steps to get there.

If the action is directed toward some kind of action--it would have to proceed through the active powers (such as sensing, imagining, understanding and willing) or through objects (such as body, soul, and God). But [for some reason I don't understand] it's not possible to go through an infinite number of steps to get an action either, so ...

There must be something that satisfies the agent's desire when it is attained--and that is the end. So every agent acts for an end.

[5] Sometimes the ultimate end (or effect) is the final effect of a series of causes and effects. (For example, a dish of beans is the final effect that started with preparing the soil and planting a  bean--with many intermediate stages in between.) So the harvesting of the beans is an end in relation to the planting, but an "active principle" in relation to the dish of beans. If the planter did not have the dish of beans (or some other end) in mind, but infinity, there would have to be an infinite number of infinite steps--which (for some reason) is impossible. So the planter and every other agent has a definite end in mind--"the agent's desire must be directed to some definite thing.

[6] When an intelligent person plants a garden to get a harvest and eat the food, they are thinking ahead of time in their intellects of what it is they want to produce in the end. They act from this preconception. So, the intellect is the principle of this kind of action. There is a likeness in the intellect of the thing to be produced.

In the same way, there is a likeness in a natural agent of the the thing that it will produce--for example, fire produces fire. An olive produces an olive. So, the action of a natural agent is determined to a definite result. 

So, this idea is just as much true of a natural agent as it is of an agent that acts with its intellect: every agent acts for an end.

[7] Another way to see this is by considering that we only find fault with an intelligent person or a natural agent if they fail to produce their appropriate end--such as when a physician fails to bring about healing or an animal brings forth deformed offspring. You wouldn't find fault with a builder if he fails to bring about healing, which shows that the physician and the builder each have his own particular end that he's aiming at.

[8] Also, if someone considered all possible results to be equally acceptable, he would never act--because you need to prefer one result over others before acting. Therefore, every agent tends toward a determinate effect--which is called an end.

[9] Even actions that don't seem at first to be directed to an end really are, if we think about it. We contemplate in order to contemplate--the end is an action, not a product. We play to obtain enjoyment or to be able to study more. We rub our beards because we have an itch (This last one is an example of acting or an end, but it is not an action based on achieving an end we preconceive in our intellect.)

[10] Ancient natural philosophers thought necessity was the cause of all things, but they were wrong. The failed to take into account that people and natural agents act for an end.

Bonus: Aristotle, Physics II,8

A thing's nature is a cause in the sense that it is a purpose.

Nature acts purposively and does things because they are better.

Take rain, for example. One might say that vapor rises and then cools and falls back to earth as rain. Why? Because heat causes it to rise and coldness causes it to fall back down. The fact that this phenomenon is essential to the growth of vegetation is a mere coincidence. It's just like when rain falls and ruins someone's grain. Is the purpose of rain to ruin grain? Of course not--it's just a coincidence.

The same thing can be said of teeth. Yes, front teeth are sharp and suitable for biting and back teeth are flat and suitable for grinding--but that's just a coincidence--the purpose of this arrangement is not to make it easier to chew, swallow, and digest food. The same goes for every other bodily function that appears to have a purpose--it's all just a coincidence.

A creature survives when all of its parts--spontaneously and by coincidence--all happen to be just as they would have been if they had a purpose--all happen to be put together in a useful way. But everything else is destroyed. 

But this can't be the way things are. For example, human being after human being is born, each one almost without except with all parts of its body (once it develops) functioning purposively. This doesn't happen with chance or spontaneous events.

Things can either happen spontaneously or purposively; since one cannot say that these things happen spontaneously, one must say that they happen purposively. So purposes are to be found in natural events and natural objects.