In the Thomist tradition that came out of John of St. Thomas (which includes the Maritain, the manual tradition and, for different reasons, the Laval school) “the intentional” is a distinct order of being, really divided from entitative being. To modify “being” with the adjective “entitative” is extremely bizarre – what sense is there to speaking of “a being that is a being entitatively”? This is the same as speaking of “a runner that is a running runner” or “a speaker that is a speaking speaker”, not in the sense of someone who can speak and who actually is speaking (though even then it is a useless repetition), but in the sense that one wanted to talk about a sort of speaker that was characterized by speaking. As opposed to what? What other kind of speaker could there be? This is the sort of consummate strangeness that one confronts in trying to understand the order of intentional being.
Leaving aside the Scholastic tradition, the strangeness of intentional being is still readily at hand: To use a word like “being” or “all things” requires that all things as a whole be taken as an object, and yet this object – all things – must somehow admit of an “other” which knows it. But how in the world can there be an other to all things? To be other than all things is to be nothing at all. One cannot wiggle out of this with Scholastic qualifications, since one must always admit some “other” to whatever is qualified.
[Note that we are completely avoiding the word "subject". We are only focusing on how knowledge requires that "all things" be other. To call this other "subject" is to go beyond what we actually know and to trap us in a labyrinth that we never needed to enter in the first place. No sooner do we invent this supposed "subject" than we must conclude that the object is nothing but a modification of it - in trying to explain the object we end up denying that it exists. Never mind the fact that in calling the other "subject" we are putting being outside of being.]
There are two useful approaches to this problem. The first is to approach being though the Nothing, as Heidegger does. Taken from this angle, the problem of the intentional (or of immaterial being) reveals itself through the analysis of Nothing. We cannot impatiently jump to an apophatic theology here- there is too much work to be done in just ironing out the immateriality of the person. For too long this immateriality was taken as a being among other beings, or even as part of a chain of being reaching from photons to God. But seeing it in this way led to inevitable contradictions and distortions in our view of the real. The person-so-far-as-being-is-an-object or question (what Heidegger calls Dasein) is put outside of being- even being itself is somehow outside of being. This was latent in the tradition from the beginning – to place the principle of contradiction at the foundation of thought means to understand being through its negation, i.e. Nothing.
The other useful approach is to stress that intentionality is being the other as that very other. We must make this total identification with the other for largely logical reasons – for unless we see knowledge as properly being the other as an other, then there will always be a contradiction in knowing being (and since contradiction itself involves the knowing of being, contradiction will be contradictory, that is, both a contradiction and not a contradiction simul)
These two approaches balance each other and develop each other in different ways. While the Heideggerian approach is a useful critique of the logical approach to being (“logical” could do with some clarification, but I get his sense), the second approach uses logic in a helpful way. This sort of critical development of the intentional order is long overdue – for too long we have been trapped in rather primitive problems arising from a rudimentary and dialectical understanding of the intentional order (I’m reminded of this when I read debates about free will and grace, or in general the relation between various orders of being and their interaction. Our homogeneous imagining of “being” tends to trap us in problems and mysteries that would be dispelled if we weren’t assuming a basically mechanical relation between orders of being.)