De Anima is probably the best source.

The short answer is kinda... like an amorphous "mind", or "reason" can exist independently of the body, but devoid of any particular features of any particular thinking subjects. No personality, no individual's soul that exists after death, basically.

What about respected secondary literature? Or is there enough in De Anima? I get the sense that Aristotle believed there would be no conscious awareness after death. So, a part of the human soul would live forever, but that part wouldn't even be conscious of its own existence.

I don't read much secondary literature, so I dunno.

It would probably be best to stick with Aristotle himself, if possible.

Aristotle was a traditionalist. He did not deny the existence of gods or fate in the afterlife and left the topic very much to religious faith rather than philosophy.

@ernestm
How would you defend that view? Sources?

Well, I think it is obvious from reading Aristotle. He admires the religious traditions in the poetics, for example, but has nothing to say on the Gods or fate in the afterlife. He leaves that to faith, not to rational debate.

"But, as a matter of fact, higher animals possess in
addition to the lowest form higher forms, e.g. man has the rational soul (410 b 16
24). These higher types of soul cannot, as above shown, be present in the air.
Therefore, if the soul is to be present uniformly in the air, it must itself be
homogeneous: and, if it is not homogeneous, it cannot be present uniformly
in the air. " - Aristotle De Anima.

That was a discussion of the alchemical idea that the world was made of atoms, with coarser atoms making matter and finer atoms making the soul. It was not a discussion of whether there is an afterlife. I should add, if you genuinely wish to understand what people believed in 500BC, the first step is to consider exactly what knowledge they had at the time. And the most important text to them, Homer, was handed down orally for 500 years. You cannot use modern methods of text analysis to understand them. You have to put yourselves in their shoes and see the world as they saw it: full of forces controlled by mostly indifferent Gods. Thats what everyone thought. Most people had no reason to challenge it.

You're just making shit up.

What? You are talking about a people whjo believed from childhood that there were Gods everywhere. There was a separate God for every single mountain and stream. Their world was run by Gods. Thats how they saw it. The real issue for faith, at that time, was not whether Gods existed, but how much Gods would ever care about humans, who were no different than ants as far as most Gods were concerned.