Assuming an isomorphy between the logical intending structure and the real, intended, structure, forces us again to think over what a logical intention in fact is. Already much earlier we stated that when the correspondence between the logical structure or instrument and the real structure to be known by it is no more than an isomorphy, the logical instrument is then not formal but only instrumental, and then the real is not actually reached or 'touched' by a knowing power, rendering knowledge in a sense subjective (subjective with repect to man, not with respect to the individual). What then precisely is the nature of 'intention' and that of 'isomorphy'?
This is a hard problem indeed, and we are not in a position to solve it now, but will add bits of explanation in the course of our further treatment of intentional Logic. To begin with we can, in this note, present some suggestions, that can later be worked out more fully or be amended.
It could be that genuine intention by some logical entity of something in reality, will only take place when that logical entity has finally become structurally such that it links up with that mentioned "something" in reality, that it hooks up with it, grabs it. And we can say that this linking-up will only take place when there is a sufficient degree of isomorphy between the intending (or pre-intending, i.e., not yet as such actually intending) logical entity and the intended (or pre-intended) aspect of reality. Only then genuine intention takes place, and knowledge acquired. The mentioned "degree of isomorphy" should not, however, be confused with 'degree of similarity', or 'degree of identity'. Isomorphy between patterns means them having some very general and abstract structure in common. This common structure can lie very deep, and be very inconspicuous. We assume that reaching the mentioned (degree of) isomorphy is equivalent to the discrete transition of the pre-intending structure into a truly intending structure, that is, the transition from a mere instrumental sign to a formal sign.