 Two remarks on this last version are in order. First, it opens the door to thinking that besides abstract and concrete entities (assuming that physical objects, in a broad sense, are concrete), there are mental entities that are neither concrete nor abstract. As mentioned above (section 1.2), there is no need to insist that the distinction is an exhaustive one. Second, while the approach may well draw an important line, it inherits one familiar problem, namely, that of saying what it is for a thing to be a physical object (Crane and Mellor 1990; for discussion, see the entry on  physicalism).  In one sense, a physical entity is an entity in which physics might take an interest. But physics is saturated with mathematics, so in this sense a great many paradigmatically abstract objects—e.g. \(\pi\)—will count as physical. The intended point is that abstract objects are to be distinguished, not from all of the objects posited by physics, but from the concrete objects posited by the physics. But if that is the point, it is unilluminating in the present context to say that abstract objects are non-physical.