Plato posited the Forms, the immaterial ideas of which the things we encounter in our terrestrial existence are mere instances. It is because of Forms that we are able to acquire true knowledge, for true knowledge is knowledge of the Forms. As perfectly separate and immaterial, the Forms are that which we define when we seek to give definition. No sensible object can fulfill this role because all material things are changing and imperfect. Our knowledge of things cannot be like this, so our knowledge cannot, properly speaking, be of such things.
St. Thomas sees this argument as reliant upon a premise which is not, in fact, true. The premise is this:
Something has the same mode of being as actually existing and as an object of knowledge.
What does this premise imply, logically speaking? Only this, that as we know, so things are. The intellect abstracts the universal from the particular and the mathematical from the sensible, therefore there are actual separate and abstract forms of particular things and actually existing mathematical entities which are independent from sensible reality.
St. Thomas does not think that this is a justified inference. Yes, the intellect knows by abstraction, but it is not necessary that this reflect reality as it is, meaning as it is apart from knowing beings. The way we know things does not correspond to the way in which they exist. The intellect understands universals and mathematical objects apart from singular and sensible things, but the separateness, universality, and immateriality that constitute this knowledge are modes of our understanding. They are not the modes under which the objects of our knowledge actually exist.
This argument is predicated upon a different assumption than Plato's:
Everything that exists in something else exists there according to the mode of the recipient.
St. Thomas Aquinas, ora pro nobis.