An ens rationis or 'being of reason' is the traditional name for what is conceived on the model of a being but cannot actually exist as such. An obvious example of such a being of reason is a hole. Holes are things we conceived on the model of beings -- we count them as if they were beings, we can talk about them interacting as if they were beings -- but a hole, as such, is not an actually existing thing. The example of a hole gives us an important aspect of the concept that often throws people off. To say that something is a being of reason is not to say that it is illusory or simply nonexistent; quite the contrary, we treat beings of reason as existing, and we need to do so. Whether or not there is a hole in your roof is not entirely in the mind, nor is the hole an illusion, nor can it be dismissed as just nonexistent at all. You can point to holes. You can use holes. You can manipulate holes. They change the way actually existing things work. But you can also understand me entirely if I say that the hole in your roof is real but that a hole is not an actually existing thing.
Another example would be a crack. You can point to cracks, you can manipulate cracks, you can use cracks to perform some activity. There is even a branch of physics that studies the dynamics of cracks; as it happens, the physics of the motion of the leading edge of a crack in a substance is very similar to the physics of the motion of particles through a medium. But you can also make perfect sense of saying that a crack just doesn't and can't exist in the same way that the medium in which it is found exists.
Since beings of reason are conceived on the model of beings, some kind of being has to be the start of any conception of being of reason we might have. What makes these conceptions different from conceptions of the beings themselves is that beings of reason are organized by negations and rational relations. If I say, "There is a hole in the wall," I conceive the hole on the model of a section of wall, but instead of simply doing so (which would be incorrect, since a hole in a wall is not the substance of the wall), I conceived it under a negation: a section of the wall is not there, the hole is the not-section. In addition, we can think of the hole by relation to both the surrounding wall and to things that can pass through it -- it's not a bare lack-of-section-of-wall, but a lack-of-section-of-wall-such-that-through-it-something-can-pass. The wall really can have a hole in it, but the hole itself is identifiable only by negation of something (part of the wall) and by relation to other things (like the rest of the wall and moving objects).
Shadows are another example of how this works. A shadow is conceived as a shadow by relation to something -- a shadow is a shadow of something -- and by negation -- of the surrounding light. Actually, a shadow is conceived in relation to three different things -- a light source, a light-blocker, and a surface to which the shadow is attributed. A shadow is thus a negation on a surface of light from a light source due to something that intervenes between the light source and the surface. But we can point to shadows, and we can use them (as when find shade), and we can manipulate them (as when we do shadow-puppets). They are in some sense real, and you cannot develop an accurate understanding of the world without understanding them to be in some sense real. But they are beings of reason, things conceived with negations and relations on the model of beings that nonetheless cannot be actual things existing in their own right.
This easily missed because as a matter of technical terms, the opposite of 'being of reason' is 'real being'; but the 'real' here means 'as a thing in its own right', and not real in a more expansive thing. Beings of reason are broadly real, but they are not things in their own right -- indeed, they couldn't be, because they always inherently involve negations of and relations to other things. At the level of objects of understanding, however, there is no fundamental difference between beings of reason and real beings. As noted above, we can do a physics of particle trajectories or a physics of crack movements in much the same way; that particles are real beings and leading edges of cracks are beings of reason doesn't actually affect much, beyond the fact that a leading edge of a crack can only ever be understood in terms of negations and relations. A hole or a center of gravity is a being of reason, but it has objective reality.
In fact, beings of reason end up being quite important because a vast portion of our understanding of the world is based on them. Indeed, I think one can argue that physicists, for instance, almost exclusively study beings of reason. This does not imply idealism or anything like it; it mostly just indicates that physicists spend a lot of their investigations studying things wholly insofar as they are related to other things. And physicists are not particularly shy about use of beings of reasons; they will explain behavior of actual systems by idealized models that can't exist as such in the actual world, for instance. The ideal structures that are doing the explaining are beings of reason. But physics is in no way unique here. Objective reality is not as straightforward as one might have thought.
