Hey, that's all good, but my question was about the kinds of thinking in Aristotle and whether Aristotle's philosophy allows for incomplete knowledge or if it's already always complete. I don't feel that there was an answer to these questions in your post. This is because...

a. The fact that Aristotle might also believed in gradations of knowledge does not mean that he believed in the exact same theory that Plato's analogy points to. Also, that particular question was about the kinds of thinking, not knowledge. There might be gradations of knowledge but Gerson distinguished between knowledge (as a kind of thinking) and other kinds of thinking. Which are these other kinds of thinking (which aren't necessarily kinds of knowledge)?

b. Again, the question was about Aristotle, not Plato, the Ancients in general or Aquinas. All these might share some doctrines but their theories are not necessarily the same top to bottom; unless this is what you're arguing for of course (but if this is so, let's first focus on what Aristotle says). Furthermore, the question wasn't really related to perception or to a possible apodictic nature of rational truths. It was about the possibility of incompleteness of our knowledge, whatever knowledge is. For example, is a geometer's knowledge of his science already complete from the get go or is this completeness achieved with time? The accuracy of the knowledge he has gained at anyone point is not the issue here, I'm just asking if he knows from the start all that there is to know. Also, taking a non-science example, do we, as regular people, know all there is to know from the start according to your understanding of Aristotle?

Aristotle, in De Anima, argued that thinking in general (which includes knowledge as one kind of thinking) cannot be a property of a body; it cannot, as he put it, 'be blended with a body'.

This then means that there are different kinds of thinking. Which do you think these are and how do they differ? Also, do you think that Aristotle draws any distinctions when it comes to knowledge? For example, is our knowledge always already complete or can there be incomplete knowledge?

It doesn't seem to be bookmarked, it starts from the beginning.

they're the 'intelligible forms' that the mind discerns in order to understand what a thing is. — Wayfarer

How would you say that the "mind" does this (as far as Aristotle is concerned)?

Depends on the specific branch of nominalism. The whole talk of nominalism is already steps away from Aristotle, it's parasitic to his work. I referred to it because I found it paradoxical that you want to argue against the idea that Aristotle was a "nominalist", yet what you ascribe to him (by way of "Aristotelianism" or "Platonism"), is closer to ancient "nominalists" like Lycophron. What's important is what Aristotle says about the way universals exist and nowhere does he say that universals exist "purely intellectually", as far as I know. That's one of the theses he argues against. I guess you're taking as a given that the matter in which we come to know, grasp or understand something, inevitably leads to how it's supposed to exist, i.e. if we know universals through the intellect, then universals exist in a purely intellectual manner. That's not what Aristotle says though. Neither the logic nor the conclusion makes justice to him. Even talk about knowing universals through the intellect can't be taken seriously as an interpretation of Aristotle, since it discounts numerous distinctions both regarding "universals" and the "intellect".

I skimmed through Feser's article. It's not about Aristotle's discussion of various ways of existing. It's entirely free of it. It's also free of any substantial discussion of various ways of existing simpliciter. For example, the part that you quoted only refers to various human faculties. There's no reference (let alone argument), to the various ways things exist. I'm somewhat familiar with Feser's work: I've read multiple blog articles in the past. Nothing scholarly in them, it's mostly cultural commentary (aka polemics). I would never recommend them to someone who wants to understand Aristotle. I've also read his introduction to scholastic metaphysics and his book on Aquinas. Better than his blog, still in no way a sound recommendation for someone who wants to understand Aristotle (or Aquinas for that matter).

In my first post I linked a few quotes from Stephen Menn's draft of "The Aim and the Argument of Aristotle's Metaphysics" - that's what I consider Aristotelian scholarship. Some related books and articles that I consider worth reading on this and related subjects (irrespective of the interpretation they provide):

Aristotle on the Many Senses of Being and The Question of Seperation -- Stephen Menn

Priority in Aristotle's Metaphysics -- Michail Peramatzis

The Priority in Being of Energeia -- Jonathan Beere

Ontological Priority and Grounding in Aristotle's Categories -- Riin Sirkel

Not object, but concept. Such a concept doesn’t exist anywhere but in a mind — Wayfarer

Not according to Aristotle. From the point of view of Aristotle, that's nominalism; closer to Lycophron's thesis than to his own.

But I think in Platonic philosophy generally, and in this context this includes Aristotelianism, there is an at least implicit conception of what is called the ‘intelligible object’, whose existence is purely intellectual, but which is real in own right — Wayfarer

Again, that's not what Aristotle says. Universals' existence is certainly not "purely intellectual" according to him. It might be true of "Aristotelianism" though, who knows.

I think that it should be kept in mind that mathematical principles are not the same kind of thing that mathematical objects (i.e. triangles or numbers) are. Same with logic. Whatever principles (or laws or axioms or posits) are, which is not at all clear as is usually the case with Aristotle, they do not seem to be treated or function similarly to "proper" abstract objects. For example, it is usually said that such axioms, laws or principles are intuitively or naturally grasped and they have to be grasped in order to be able to know anything. They are also said to be unprovable or indemonstrable, yet indubitable. Instead of "objects" or "things", these principles seem to be more like relations between such "objects" or "things". The debate around principles such as PNC seems to be whether Aristotle takes them to be metaphysical or just logical/mathematical.

When it comes to the way Aristotle thinks of universals I find it useful to think about it from the POV of "priority". It's usually accepted that Aristotle recognises different senses of priority. For example, priority in definition/account, priority in time, priority in nature and substance. A common view is that, according to Aristotle, universals have definitional priority compared to substances, but concrete objects are prior in nature and substance compared to universals. There's much literature around this and it gets really complicated really fast, but I think that the following quote from Stephen Menn's The Aim and the Argument of Aristotle's Metaphysics illustrates neatly the nuances between the platonic, the aristotelean and the nominalist approaches. The issue of priority is also discussed in terms of ways of existing, but it's also related to the issue of archai. Contra Plato and the the Pythagoreans, Aristotle argues that universals cannot be archai, that is to say, the cause of all being.