The Representation of Space as an A Priori Intuition in Kant’s Critique of Pure Reason

In the section of Immanuel Kant’s Critique of Pure Reason called the Transcendental Aesthetic, Kant argues that our representation of space “is not an empirical concept which has been derived from outer experiences” but is instead an a priori intuition (Kant A23/B38). In a section of the Transcendental Aesthetic called the Metaphysical Exposition, Kant provides four arguments for why this must be the case. His first two arguments contend that our representation of space cannot be empirical while third and fourth arguments contend that our representation of space is an intuition as opposed to a concept. Together, the four arguments constitute the reasons for Kant’s claim that our representation must be an a priori intuition.

In the first argument of the Metaphysical Exposition, Kant asserts that our representation of space cannot be empirical because our representation of objects presupposes the representation of space: “in order that certain sensations be referred to something outside me (that is, to something in another region of space from that in which I find myself), and similarly in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space must already underlie them” (Kant A23/B38). His argument is that when you experience anything as being outside of yourself or in a different place as something else, you are representing objects as in space. In order to represent objects as being in space, you must already have a representation of space itself which is prior to the experience of the objects. To Kant, a preexisting representation of space is required in order to make any kind of empirical observation about objects and therefore the representation of space itself cannot be based on one of these empirical observations. The representation of space must therefore come to us a priori. 

Kant’s second argument in the Metaphysical Exposition furthers his claim that our representation of space is not empirical in origin by pointing out that while we can represent the absence of objects in space, we cannot represent the absence of space itself: “One can never forge a representation of the absence of space, though one can quite well think that no things are to be met within it” (Kant A24/B38–9). If it is true that our representation of space comes from empirical observation, it doesn't make sense to Kant why we should be unable to conceive of its absence in the same way that we are able to conceive of the absence of objects. Because we cannot represent space’s absence, it cannot be the case that our representation of space is based on “outer appearances” like objects whose absence we are able to represent. To Kant, it must then be the case that our representation of space is “a condition of the possibility of appearances, and not as a determination dependent upon them” (Kant A24/B38–9). Therefore, Kant concludes that space “is an a priori representation that necessarily underlies outer appearances” (Kant A24/B38–9).

Kant’s first two arguments elucidate his idea that the representation of space is a priori and not empirical. However, according to Kant, both concepts and intuitions can be a priori representations. In the final two arguments of the Metaphysical Exposition, Kant provides his reasons for concluding that our representation of “space is not a discursive, or as one says, general concept of relations of things in general, but a pure intuition” ( Kant A24–5/B39–40). When Kant says that our representation of space is an intuition, he means that it is a singular and immediate representation that is objective. This is unlike a concept which is composed of many conceptual parts that makeup its intention. We are therefore able to describe a concept by naming its conceptual parts. 

Kant’s first argument in favor of the representation of space being an intuition is that we cannot break down space into parts in the same way we can a concept. He argues that a part of space would be any given place, but that this merely involves establishing a boundary around an area of the larger all-encompassing space itself: “one can represent only one space, and if one speaks of many spaces, one thereby understands only parts of one and the same unique space” (Kant A24–5/B39–40). Similarly to his first argument, here Kant is arguing that our representation of any one part of space or place presupposes the existence of space itself and therefore the parts of space cannot be conceptual parts that makeup a concept’s intention. In order for something to be a conceptual part of a concept, the representation of the part must exist independently of the representation of the concept. Kant argues that parts of space or places do not exist independently of the representation of space itself and therefore cannot be conceptual parts: “These parts cannot precede the one all-embracing space as being, as it were, constituents out of which it can be composed, but can only be thought as in it” (Kant A24–5/B39–40). Since the representation of space is not composed of conceptual parts and cannot be described by an intention, it cannot be a concept.

Kant’s fourth argument in the Metaphysical Deduction further contrasts the structure and content of a concept to that of our representation of space in order to support the claim that our representation of space is an intuition. Kant describes a concept as having subordinate concepts “under itself” that make-up its extension and representations “within itself” that makeup its intention. A concept can have infinite extension meaning that it can have an infinite number of representations that fall under it: “one must think every concept as a representation which is contained in an infinite number of different possible representations (as their common mark), and which therefore contains these under itself” (Kant B40). However, Kant argues that “no concept, as such, can be thought as if it contained an infinite number of representations within itself” meaning.a concept cannot have infinite intention because this would make the concept lack determinate content and make it undefinable (Kant B40). Kant argues that when we represent space, we conceive of it as having an infinite number of constituent parts or places. However, it is not possible for a concept to have infinite intention. In order to represent a concept, we must also be able to represent all of the conceptual parts that make-up its intention. Therefore, if our representation of space were a conceptual one, we would be required to represent all of its places in order to represent space itself. However, given that there are an infinite number of places that fall “within” space, we cannot represent all of space’s constituent parts: “all the parts of space are simultaneous in infinity” (Kant B40). If we were required to represent all places in order to represent space, we would be unable to represent space. Since we are able to represent space despite being unable to represent all of its constituent parts, our representation of space cannot be a concept and therefore must be an intuition.

While Kant’s third and fourth arguments are compelling, it is unclear why Kant chooses places as the constituent parts of space. In doing so, he appears to be drawing no distinction between space and its parts and the representation of space and its constituent parts. A counterargument to Kant’s third and fourth arguments is that this is a conflation and we might be able to construct a concept of space not out of the concept of places but of other concepts that appear to be constitutive and whose representations appear to be independent of a representation of space. Kant says that “space is represented as an infinite given magnitude,” so it would appear that the concept of infinity or of magnitude might constitute conceptual parts of our representation of space (Kant B40). Kant, however, does not consider other potential conceptual parts of our representation of space. He is instead committed to the view that places are the only constitutive parts of the representation of space and that their inability to fit into the whole-part relationship structure of a concept and its conceptual parts shows that our representation of space cannot be a concept.

In the Transcendental Aesthetic, Kant supports his claim that our representation of space must be an a priori intuition. In his first argument, Kant contends that our representation of space cannot be empirical in origin because it necessarily precedes any kind of empirical observation of objects in space. Furthermore, in Kant’s second argument, he points out that we are unable to represent the absence of space the way we are able to represent the absence of objects. His third argument is that our representation of space is not composed of conceptual parts that can be represented independently of the representation of space the way a concept is. Kant’s fourth and final argument is that since the representation of a concept requires the representation of a finite number of conceptual parts and we are still able to represent space despite being unable to represent the entirety of its infinite number of constituent parts, our representation of space cannot be conceptual and therefore must be an intuition. By contending in these four arguments that our representation of space cannot be empirical nor can it be conceptual, Kant supports the main claim of the Metaphysical Exposition that our representation of space must be an a priori intuition.