"logical entities being nothing but intentions of the Real" suggests that the World, the Universe, is in some sense dualistic : While having overcome and denied the long cherished dualism in man (body-soul), we now seem still having to do with the dualism of the World consisting in logical entities on the one hand, and real entities on the other.
We must show that this is, like that of body and soul, not an ontological duality in the sense of two domains of fundamentally different ways of being, such that they can in principle exist independently of each other.
Well, the logical intention cannot exist apart from that what it intends (while that what is intended by a first intention can exist independently of this intention), because a certain formal content of it is a corresponding formal content of that what it intends, and what is intended is, ultimately, something which itself cannot intend anything else.
So the logical intention is in fact not a thing but a relation between things (that is, between parts of the brain [certain brain patterns that embody decoded formal contents] and parts of the things that are intended (resulting in signification and supposition). So the logical intention is reducible to just things, like any relation is.
Accordingly, in the contraposition of logical intentions on the one hand, and real things on the other, there is no ontological dualism involved. The (temporary) brain structure or neural pattern that is to be identified with one of the relata (fundaments of the relation) of the logical intention is without doubt a higher-level brain structure (a dynamic functional brain entity or wiring pattern), not detectable at the neuron level of the brain.
But although this relation, which is the logical intention, is a relation between real things, it is not a real relation, because it only exists in and through the knowing process.