In the field of philosophy Kant was the first to take the next decisive step towards the point of view that not only the qualities revealed by the senses, but also space and spatial characteristics have no objective significance in the absolute sense; in other words, that space, too, is only a form of our perception.

What is meant by "the representation of space"? What distinguishes one representation from another? Does this mean "how does one see that one thing is not another thing?" What constitutes a change of focus?.. .What about "another way of establishing (?) "thingness"? "Something" can be either one thing or another (without turning the rabbit on its side)..

Some forms of Kantianism put great weight on “what we can imagine” holding that this can be a source of insight into necessary connections. Thus various of Kant’s arguments about space and time depend on the purported fact that it is impossible for us to imagine certain things: we can know, Kant claims, a priori that space has only three dimensions because we cannot imagine it as having more than three dimensions. History in the form of non-Euclidean geometry and modern physics has put paid to that particular line of argument, but in general we should beware of depending too much on “What we can imagine?,” especially in politics. As Nietzsche puts it somewhere, sometimes the fact that you can’t imagine a situation in which things are very different from the way they are now is not an especially good argument for the claim that they must be as they now are, but, rather, represents a failure of your powers about which you should feel mildly apologetic.

All characteristics of material things as they are presented to us in the acts of external perception (e.g. colour) are endowed with the separateness of spatial extension, but it is only when we build up a single connected real world out of all our experiences that the spatial extension, which is a constituent of every perception, becomes a part of one and the same all-inclusive space. … every material thing can, without changing content, equally well occupy a position in Space different from its present one. This immediately gives us the property of the homogeneity of space which is the root of the conception, Congruence.

Space, subjectively, is the coexistence of perceptions — perceiving two objects at once.

Space is only the form of external intuition, and not a real object that could be perceived externally, nor is it a correlate of phenomena, but the form of phenomena themselves. Space, therefore, cannot exist absolutely (by itself) as something determining the existence of things, because it is no object, but only the form of possible objects. Things, therefore, as phenomenal, may indeed determine space, that is, impart reality to one or other of its predicates (quality and relation); but space, on the other side, as something existing by itself, cannot determine the reality of things in regard to quantity or form, because it is nothing real in itself.

Kant's distinction between things in themselves and things as they appear to us has both epistemological and metaphysical components. He is committed to a genuine idealism about things as they appear to us, but this is not a phenomenalist idealism. He is committed to the claim that there is an aspect of reality that grounds mind-dependent spatio-temporal objects, and which we cannot cognize, but he does not assert the existence of distinct non-spatio-temporal objects.

Because we do not have a sensory organ dedicated to space, the representation of space is a quintessentially cognitive sensibility: it is the binding problem writ large.

Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i.e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature. ...A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space.

Up to now sculptors have preferred the mass and neglected or paid little attention to such an important component of mass as space.. ..we consider it as an absolute sculptural element. I do not hesitate to affirm that the perception of space is a primary natural sense which belongs to the basic senses of our psychology

Unlike vision, touch, or smell, which are prewired and based on Kantian a priori knowledge, the spatial map presents us with a new type of representation, one based on a combination of a priori knowledge and learning. The general capability for forming spatial maps is built into the mind, but the particular map is not. Unlike neurons in a sensory system, place cells are not switched on by sensory stimulation. Their collective activity represents the location where the animal thinks it is.

The concept of space, therefore, is a pure intuition, being a singular concept, not made up by sensations, but itself the fundamental form of all external sensation.

There is no pure visualization in the sense of a priori philosophies; every visualization is determined by previous sense perceptions, and any separation into perceptual space and space of visualization is not permissible, since the specifically visual elements of the imagination are derived from perceptual space. What led to the mistaken conception of pure visualization was rather an improper interpretation of the normative function... an essential element of all visual representations. Indeed, all arguments which have been introduced for the distinction of perceptual space and space of visualization are base on this normative component of the imagination.

[W]e saw that mental representation is about percepts, mental simulations, conceptual representations... [C]onceptual representations give us concept spaces, and... these concept spaces... give us an interface for our mental representations we can use to address and manipulate them, and we can share them in cultures. [T]hese concepts are compositional. We can put them together to create new concepts. ...[T]hey can be described using higher dimensional vector spaces. They [vectors] don't do mental simulation and prediction, and so on, but we can capture regularity in our concepts with them.