“The things concerning intellect have certain perplexities. For, on one hand, intellect seems to be the most divine of all phenomenon, but on the other hand, if intellect is such a thing (ἔχων τοιοῦτος), [the fact of] how it would be (πῶς ἂν εἴη) [most divine] has some difficulties. For if it does not think, what would be the reverence [for a thing which is divine?] [If intellect does not think,] it is just like a sleeping man. If it intellect thinks, but something else controls intellect [i.e. process of thinking], since this is not [that thing] which is the essence of it [intellect] as a thought but as an ability [of thought], it would not be the best essence. For value [only] belongs to intellect through thinking. And yet, whether the essence of intellect is “intellect” or thinking, what does intellect think? Indeed, it either thinks of itself or thinks of something else. And if intellect thinks of something else, either it thinks the same thing always or different things. Does it matter somewhat or not at all whether it is thinking about the noble or [merely] something of happenstance? In fact, is [not] thinking about some things strange? Therefore it is obvious that intellect thinks about the most divine and most honorable thing, and it does not change [thinking about this.] For a change is for the worse, and such [an act] is already a kind of motion.” (Metaphysics 1074b15-26)

In this famous passage of Aristotle some of the difficulties of nous (intellect) are discussed. Aristotle’s method is to offer dichotomous choices, wherein one option is eliminated because the answer involves the necessary negation of the divinity/honor of nous. Because Aristotle begins this section of the metaphysics by assuming that the nous is the most divine thing (lit. is the most divine of phenomena), from his point of view any argument or notion that denies this basic fact about intellect must be abandoned.
Some have posited that this passage does not speak about God himself, in so far as he is pure intellect, but a type of universal intellect. It seems to me that the type of language used precludes such a reading. Immediately after Aristotle has introduced intellect as the most divine thing (theiotaton,) he raises the possibility of intellect not thinking, “What would be the holiness/reverence (semnon)?” The implication is that semnon is synonymous with theiotaton. That is, if intellect does not think, it would not be divine. This is absurd of course, and a contradiction, so it must be the case that the intellect thinks.

On the other hand, if intellect does think, but something else controls this thinking, then intellect is not an actual process native to intellect but only an ability to think, much like a calculator, which lies dormant until a person picks it up and decides to push its buttons. That is, it has only the capacity to think, i.e. “calculate”, but is not itself the source of the thinking, as that role is fulfilled by the human operating it. If nous is like that, a mere ability, then it is not the best essence (he ariste ousia eie). Not being the best essence (or existing thing) would also imply that nous is not a divine thing, but again, this is impossible; so nous cannot be a mere capacity for thinking, but must be actual thinking itself. As Aristotle adds that since the value we grant to nous is through its actual thinking, it must be that this thinking is the divine element in nous. Regardless of whether the thinking of the nous comes from itself or from outside itself, there is indisputably thinking occurring. It is to this concern that Aristotle turns next.

Nous, as we know, possesses the occurence of thinking in some sense. There are two questions Aristotle asks to clarify the “what is it” of the object of intellect’s thinking: (1) Does intellect think of itself or of something besides itself? (2) And if it thinks of something beside itself, does it matter whether it thinks of something great and noble, like love or justice, or whether it thinks of whatever pops into its head (so to speak!), such as lollipops and hair in the shower drain? Aristotle answers these two questions with another question. Wouldn’t it be crazy for there to be thinking about certain things? (ἢ καὶ ἄτοπον τὸ διανοεῖσθαι περὶ ἐνίων;) That is, it would be beneath the reverence (semnon) and divinity (theitaton) of intellect if it were to think about certain things, such as lollipops, or to take the illustration a step further, something as evil as murder or base as defecation. The conclusion of this line of reasoning, as Aristotle would lead us, is that intellect obviously does not think about something willy-nilly, but must think about the most divine and honorable thing, since intellect, in fact, is the most divine and honorable thing. Additionally since intellect is divine and the most honorable thing, it will not waver in its thinking about the divine and most honorable object, for that would involve a change for the worse, because thinking about anything else besides the best is a step down ipso facto. Such a demotion of state is necessarily impossible, by definition, for the most honorable thing. Furthermore this would involve a change in state, which in Aristotelian terms means a change in motion**, and necessitates physical existence. Physical existence however, as the precondition for motion, is an impossibility for something of the type that intellect is, a divine and non-physical thing.

* τὰ δὲ περὶ τὸν νοῦν ἔχει τινὰς ἀπορίας: δοκεῖ μὲν γὰρ εἶναι τῶν φαινομένων θειότατον, πῶς δ ̓ ἔχων τοιοῦτος ἂν εἴη, ἔχει τινὰς δυσκολίας. εἴτε γὰρ μηδὲν νοεῖ, τί ἂν εἴη τὸ σεμνόν, ἀλλ ̓ ἔχει ὥσπερ ἂν εἰ ὁ καθεύδων: εἴτε νοεῖ, τούτου δ ̓ ἄλλο κύριον, οὐ γάρ ἐστι τοῦτο ὅ ἐστιν αὐτοῦ ἡ [20] οὐσία νόησις, ἀλλὰ δύναμις, οὐκ ἂν ἡ ἀρίστη οὐσία εἴη: διὰ γὰρ τοῦ νοεῖν τὸ τίμιον αὐτῷ ὑπάρχει. ἔτι δὲ εἴτε νοῦς ἡ οὐσία αὐτοῦ εἴτε νόησίς ἐστι, τί νοεῖ; ἢ γὰρ αὐτὸς αὑτὸν ἢ ἕτερόν τι: καὶ εἰ ἕτερόν τι, ἢ τὸ αὐτὸ ἀεὶ ἢ ἄλλο. πότερον οὖν διαφέρει τι ἢ οὐδὲν τὸ νοεῖν τὸ καλὸν ἢ τὸ τυχόν; [25] ἢ καὶ ἄτοπον τὸ διανοεῖσθαι περὶ ἐνίων; δῆλον τοίνυν ὅτι τὸ θειότατον καὶ τιμιώτατον νοεῖ, καὶ οὐ μεταβάλλει: εἰς χεῖρον γὰρ ἡ μεταβολή, καὶ κίνησίς τις ἤδη τὸ τοιοῦτον.

**Motion for Aristotle was of four types: change of place (locomotion), increase, diminution, and change of quality/state. A change of the object of thinking would be an example of the last.