If I understand your point, realism is the position that the world as apprehended by the senses is real and can be understood by the intellect. If that is the case, how do we prove in the first place that our human senses can apprehend reality as it is. One of the main argument that the empiricists made was that all we can know is our experience of reality. In a sense, it is a form of subjectivism that makes it such that we have a hard having an objective hold on reality.
How do we jump out of our experience and experience reality as it is, with our senses?
Briefly:
Sense perception integrates sensations into a unified experience, such that the intellect is presented with all the sense data of a given thing that the senses receive.
The agent intellect “shines” its natural light upon this perception (illumination), and then abstracts the form from the thing perceived – which is “in” the perception via sense data. The thing’s abstracted form is impressed upon the possible intellect, creating the intentional existence of the thing within the actual intellect. From here, the intellect can gather new sense data about the thing, new forms, from which it can derive the “essence” of the thing, etc.
Basically, the intellect “divides” (i.e., sees two, reflects) the real thing, thus making the new “ideal” thing, all without changing/destroying the original reality.
The form of the thing is what is common to both reality and intentionality (i.e., the “inner world of the mind”); they only differ by their respective
modes of existence. The real thing has real matter and exists causally, independently, etc.; the intentional thing only has a sort of causally inert, mind-dependent “intellectual matter” (at best, or perhaps the “new matter” of the intention inheres in/consists of brain matter?). The possible intellect would be analogous to primary matter in that it’s inconceivable on its own w/out any form, as close to nothingness as you can get. The agent intellect actualizes the possible intellect by giving it form “from outside” (like man’s version of creation – letting there be light, making “new” forms, etc. –
creatio imago Dei, after all).
So the mind knows reality directly in the sense that it possesses the exact same form that’s in reality. In other words, the “two things” are in fact (formally) one, identical. Same form; different matter. One thing; two modes of being. (‘Thing’ is what exists and, strictly as such, is a potency, viz., the active potency or “substance”.)
Therefore, the things of your subjective world are the same things of the objective world. Of course, the perceiving subject is limited by a fallible nature/perspective and prone to sensory/interpretive errors. Still, the very first intention in the intellect, the “impress species” before further intellection – the illumination prior to abstraction – just is the form in reality.
[Hope that made sense. I get this mostly if not entirely from Aristotle/Aquinas, and I subscribe to it somewhat tentatively, w/details subject to clarification or revision. Note that there’s disagreement on this matter among schools of Thomism too.]