Let us posit the distinction between those objects that are susceptible to the faculties of sense and the ones that are grasped by the intellect. The concepts of shape, weight, height, ratio, likeness, difference etc. are in and of themselves not perceived by the senses. They indeed are realisable in objects of sense, yet their presence qua concepts is purely intelligible. By “realisable” I mean that this very keyboard I’m typing on has a certain shape, weight, height. All such instantiations are measurable. Whereas the noetic objects as such are not commensurate with quantification—they are absolute.
This metaphysical bifurcation enables us to make mental divisions of objects or phenomena that are otherwise continuous and organically whole. Think of how we may speak of our very own person in its various social roles or functions: the friend, the sport enthusiast, the political activist and so on. It is not the case that we exhibit a polymorphism of sorts, whether by changing shape or personality, or by becoming a multitude of persons. This array of selves, which all refer to a single human being, has a strictly intelligible presence.
Imaginary objects also are “in our mind”. The qualitative, epistemological distinction between them and the intelligible objects is that they do not necessarily correspond to objects of sense. Kafka presents us with the story of Gregor Samsa, a human who woke up one day to discover he had transmogrified into a vermin. While this is a striking tale, it is well established that human beings do not arbitrarily transfigure into insects. The ‘fact’ that Gregor underwent a metamorphosis is true only within the confines of Kafka’s sublime novel. For all other purposes, the setting and events taking place within it are imaginary.
As concerns intelligible objects, we can, at least potentially and by approximation, establish their substance in a manner that is objective, consistent with experience and reason. By “objective”, we may suggest that regardless of actual notation, terminology or other superficialities, intelligible magnitudes can be recognised (or is it discovered?) by several people of different cultures and epochs, all operating independently. In contradistinction and notwithstanding the aspects that are grounded in reality, the objectivity of imaginary presences can only be conventional; an agreed upon canon that is upheld by intersubjective sanction.
Provided the intelligible object names an abstract pattern, it can be assumed to represent a universal. The aforementioned notions of height, weight, shape etc. encompass all possible instances of objects with such features whose realisable quantities are susceptible to our experience irrespective of whatever we may think of them. We just can’t proceed to cancel their corresponding thought in an effort to annul them.
That something may be “in our mind” does not necessarily render it arbitrary and whimsical. Such assertion would amount to a crass misunderstanding. Avoiding sloppy thinking requires attention to detail and to the sort of nuance that underlies distinctions like the one outlined herein.