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I do not understand the notion of action in the following paragraph (Phys. 199a9–20):

As things are in action, so they are in nature; and as they are in nature, so they are in action, so long as nothing interferes. But action is for the sake of an end. So, natural things are also for the sake of something. For example, if a house were to come to be by nature, it would come to be as it in fact now comes to be by craft. And if things which come to be by nature came to be not only by nature but also by craft, then they would come to be just as they do by nature – one thing would come to be an account of another . . . If, then, things coming to be in accordance with a craft are for something, clearly so too are things coming to be in accordance with nature. For later stages are related to earlier among things coming to be in accordance with nature just as they are among things coming to be in accordance with a craft

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See Aristotle on Causality:

Each Aristotelian science consists in the causal investigation of a specific department of reality. If successful, such an investigation results in causal knowledge; that is, knowledge of the relevant or appropriate causes. The emphasis on the concept of cause explains why Aristotle developed a theory of causality which is commonly known as the doctrine of the four causes. For Aristotle, a firm grasp of what a cause is, and how many kinds of causes there are, is essential for a successful investigation of the world around us.

Causes "act" producing effects: changes.

There are four types of causes:

See 198a14-on:

It is clear then that there are causes, and that the number of them is what we have stated. The number is the same as that of the things comprehended under the question ‘why’. The ‘why’ is referred ultimately either, in things which do not involve motion, e.g. in mathematics, to the ‘what’ (to the definition of straight line or commensurable or the like); or to what initiated a motion, e.g. ‘why did they go to war?—because there had been a raid’; or we are inquiring ‘for the sake of what?’—’that they may rule’; or in the case of things that come into being, we are looking for the matter. The causes, therefore, are these and so many in number.

Now, the causes being four, it is the business of the student of nature to know about them all, and if he refers his problems back to all of them, he will assign the ‘why’ in the way proper to his science—the matter, the form, the mover, that for the sake of which. [...] The question ‘why’, then, is answered by reference to the matter, to the form, and to the primary moving cause.

And 198b10-198b16:

We must explain then first why nature belongs to the class of causes which act for the sake of something.

We can consider the paradigmatic example of the statue:

The material cause: the bronze of a statue.

The formal cause: “the form”, the shape of a statue.

The efficient cause: “the primary source of the change or rest”, e.g., the artisan, the art of bronze-casting the statue.

The final cause: “the end, that for the sake of which a thing is done”.

Thus, the efficient cause: the artisan, acts (i.e.produce) the statue, using the broze (the material cause) and shaping it [the formal cause] in order to manufacture the statue "for the sake of an end" : the final cause.

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There may be some subtleties lost in translation. Aristotle is suggesting that the natural world is monistic with regard to human action and natural action: that nothing which is seen as craft by human is distinct from an action of nature, such as a tree growing a branch. Therefore, human beings and their actions are natural actions. He does not address the idea of will: whether or not a tree wills a branch into existence or a human wills a house into existence, or whether causative action can be separated from effect.

For Aristotle, life probably seemed something like a nature documentary!

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