In Aristotle's realist philosophy, a true thought is determined necessarily by the adequation of mind and the form of a thing. There is no gap between knower and thing known.
Your question, "how can one know that a discrete object in the brain corresponds to a discrete external object?" assumes something I do not believe is true. I believe there are events in the brain that roughly correspond to percepts of both internal and external, "objects," but the perceptions are hardly, "discrete." It is not events in the brain that I believe correspond to "external" objects, but percepts and concepts.
All of the old philosophers were never careful to identify and distinguish the difference between percepts (direct consciousness) and concepts (the identification of entities, events, and ideas, which, if done correctly, will be non-contradictory).
Since all concepts are about percepts (what we are directly conscious of) and what we are directly conscious of is what we mean by existence, both external and internal, it is not possible that concepts (ideas in our head) could not directly correspond to that existence.
There is, if you examine it, a mistaken notion in the Platonic mysticism Aristotle, and all those philosophers who follow him, have never extricated themselves from, that assumes we can know about "external" objects without first perceiving them. In fact, all that we know about we first had to be conscious of, that is, we had to perceive. All our knowledge is about and derived from those perceptions, and one of the first things we come to know is the difference between those perceptions of things external versus the internal (like our own feelings).
This distinction is not directly perceived, however. It is a concept about perception itself. Knowledge exists only at the conceptual level of consciousness. At the perceptual level we know nothing, we are simply conscious of things. All our knowledge is about that of which we are perceptually conscious. To suppose any other kind of knowledge requires some kind of mysticism.
Hank