0.) Descartes has the strange position of being almost universally critiqued by those who end up basing their thought in one way or another on some Cartesian claim.
1.) Descartes is the last great anti-Dominican or, put positively, the last great developer of Franciscan and Jesuit later scholasticism. If you read the Meditations with any awareness of the debates on omnipotence, intuitions of existence, the Ontological Argument, God’s role in human knowledge, etc. this all becomes clear as day. Descartes is rebooting scholasticism in an attempt to retrieve its original project of compressing knowledge: where the 12th and 13th Century Scholastics were trying to compress the sprawling, prolix patristic literature down to a clear and minimal coherent system, Descartes tries to do the same thing with late Scholasticism. One can present this either as an advance of Scholasticism or a destruction of it, but it certainly crushed the Dominican tradition.
2.) The critiques of Descartes theory of knowledge as dualist, human-centric, and unable to overcome his skepticism are relatively superficial and leave the deep features of the system untouched in a way that guarantees we will never escape the Cartesian problem. At the same time, it gives rise to the modern conception of what knowledge is, and so shifts the meaning of “science” to the one more familiar to us.
3.) The deep features of the Cartesian system (and it’s not clear the extent to which even Descartes was aware of these features) are (a) a denial of the reality of relations (b) the denial that the concrete participates in the abstract and (c) a belief in the essential subjectivity of knowledge.
4.) The consequence of (a) is that all things are absolute entities in themselves if they exist at all, so if ideas exist they are things in themselves with no co-existent or correlative being beyond themselves. The problem of how ideas relate to the world now becomes unavoidable. For that matter, the problem of how ideas relate to a self becomes unavoidable. They are now understood as strange “absolute knowns”, without reference either to self or world, and can now only be imposed on the world by will.
5.) The teaching of (b) is something that was perhaps less-than-clear in both the Aristotelian and Dominican traditions, and the denial of (b) was more a result of the Franciscans pushing for a clarity on the nature of abstract ideas or natures that lead to what we now call nominalism. as we’ve known for at least the last 50 years, it’s not always easy to pin this label on the Franciscans in a way that divides them from Dominicans since the difference seems to be that the D’s were content to leave things a bit more blurry than the F’s were. But it seems pretty clear that the D’s allowed some way in which what is called the abstract was an ontological principle of the concrete whereas the F’s refused this. The clearest illustration of this is Ockham’s refusal and continual refutation of the idea that things are, say, round by roundness or hot by heat while STA develops a theory of participation that demands to allow for just this sort of causality.
But since ideas are abstract, the Franciscan teaching introduces an ontological division between ideas even as representations and things in the world. Even if one allowed that ideas relate to the world (already a problematic claim from [a]) they are not reflections of the world but models of it. The aristotelian axiom that the mode of knowing is not the mode of being gets a new interpretation. For the D’s, this axiom meant that the form in things was considered apart from individuated matter but was still a principle of the real existence of the thing. For the F’s, this form was of itself individuated and so could not be related to the thing in the world, even as a principle.
6.) Descartes most long-lasting success was to re-define knowledge as subjective or in-the-person. This is both a corollary to (a) and (b) and its own independent claim. If all forms are absolute, then knowledge must be simply an absolute accident, like a quality; if the concrete does not participate in the abstract, then the idea cannot be anything beyond the mind of the knower (say, something that all knowers are sharing in). But the main difference is that the Dominican’s followed Aristotle in defining powers though objects, and subjects through powers. Defining knowledge thus begins with the reality of the object and defines the known as that which is apt to be in another, in the same way that defining fishing either begins with assuming the reality of fish or takes the whole activity as in vain. In STA’s account, for example, realism about the material world is either attainable or cognitive activity is pointless, but in the Jesuit-Franciscan account of cognitive action we get a third possibility. Even if the world did not exist there are still necessary truths and therefore bona fide human knowledge – in Descartes’s scheme we still have mathematics, ideas, the cogito, and a proof for the existence of God.
7.) When we put all of these things together we get a Cartesian account of knowledge that is still specifying the modern project: knowledge and thought is a kind of entity. One of the hardest things to explain about the Dominican tradition is that it divided the way knowledge exists from the way entities exist: starting with the object and bolstered by claim (b), they argued that entitative existence was when forms gave reality to things and intentional existence was when the very same form gave reality to knowledge. Form either informed matter making a material thing, or informed a cognitive power, making consciousness (i.e. a sense awareness or an idea). By rejecting (b) and asserting (c), the lynchpin of the Dominican theory was pulled out and knowledge became just another accidental form like redness or warmth. But on the Dominican theory one can’t hope to give a scientific account of knowledge as an entity among other entities or activity among other activities since it must be divided from this sort of existence in order to be understood at all.
One gets garbled, telephone-game accounts of this Dominican idea in Descartes’s division between the mental and physical, or in the claim that there can be no “objective” accounts of “subjective” experience, or in the claim that intentional existence is not physical, etc. It’s hard, however, to flesh out these garbled accounts without falling into some Cartesian paradox like the interaction problem or absolute skepticism, and much of the contemporary puzzles about intentionality are really just puzzles about the reality of relations – admit that relations are real, and the puzzle of how anything can be “about” something is no more pressing than the puzzle of how it can be “above” something or “hotter than” something. Relations are real, and one relation to another is to be about it. Done.