See Geach on the Real Distinction I for some background on the distinctio realis. This post lays out the argument from intentionality to the real distinction.
A theory of intentionality ought to explain how the objective reference or object-directedness of our thoughts and perceptions is possible. Suppose I am thinking about a cat, a particular cat of my acquaintance whom I have named 'Max Black.' How are we to understand the relation between the mental act of my thinking, which is a transient datable event in my mental life, and its object, namely the cat I am thinking of? What makes my thinking of Max a thinking of Max? Or perhaps Max is in front of me and I am seeing him. What makes my seeing a seeing of him?
Here is what Peter Geach has to say, glossing Aquinas:
What makes a sensation or thought of an X to be of an X is that it is an individual occurrence of that very form or nature which occurs in X -- it is thus that our mind 'reaches right up to the reality'; what makes it to be a sensation or thought of an X rather than an actual X or an actual X-ness is that X-ness here occurs in the special way called esse intentionale and not in the 'ordinary' way called esse naturale. This solution resolves the difficulty. It shows how being of an X is not a relation in which the thought or sensation stands, but is simply what the thought or sensation is . . . .(Three Philosophers, Cornell UP, 1961, p. 95)
But what the devil does that mean? Allow me to explain. The main point here is that ofness or aboutness is not a relation between a mental act and its object. Thus intentionality is not a relation that relates my thinking of Max and Max. My thinking of Max just is the mental occurrence of the very same form or nature -- felinity -- which occurs physically in Max. Max is a hylomorphic compound, a compound of form and (signate) matter. Old Max himself, fleas and all, is of course not in my mind. It is his form that is in my mind. But if felinity informs my mind, why isn't my mind a cat? Here is where the distinction between esse intentionale and esse naturale comes in. One and the same form -- felinity -- exists in two different modes. Its mode of being in my mind is esse intentionale while its mode of being in Max is esse naturale.
Because my thought of Max just is the intentional occurrence of the same form or nature that occurs naturally in Max, there is no problem about how my thought reaches Max. One could call this an identity theory of intentionality.
What if Max were, unbeknownst to me, to cease to exist while I was thinking about him? My thinking would be unaffected: it would still be about Max in exactly the way it was about him before. The Thomist theory would account for this by saying that while the form occurs with esse intentionale in my mind, it does not occur outside my mind with esse reale.
That in a nutshell is the Thomist theory of intentionality. If you can see your way clear to accepting it as the only adequate account of intentionality, then it supplies a reason for the real distinction. For the account requires that there be two distinct modes of esse, an immaterial mode, esse intentionale, and a material mode, esse naturale. Now if F-ness can exist in two different modes, then it cannot be identical to either and must be really distinct from both. (Cf. "Form and Existence" in God and the Soul, pp. 62-64.)
This argument for the real dstinction is only as good as the Thomist theory of intentionality which in turn rests on the notion of a common nature, felinity, say, which is indifferent to existence inasmuch as it can exist with esse naturale in Max and with esse intentionale in a Max-thinker, but taken in itself and absolutely is neither material nor mental, neither many nor one.
The aporetics of common natures will be taken up in subsequent posts.