Kant’s Transcendental Aesthetic, Part 1: Space

Following upon the prior article on the a priori and the use Kant makes of it, let’s begin to examine what he does in the first chapter of the Critique of Pure Reason. The examination will proceed in Kantian fashion by setting out two questions that will structure the argument:

(1.) What does Kant mean by the phrase “transcendental aesthetic“? (2.) What does he try to accomplish in the Transcendental Aesthetic?.

What does Kant mean by the phrase “Transcendental aesthetic“?

In answer to the first question, I will break up the phrase “Transcendental Aesthetic” into its constitutive parts and consider the meaning of each word.

What does Kant mean by the term “Aesthetic”?

It may come as a surprise that the Transcendental Aesthetic (TA) attempts to establish how sythetic judgements in mathematics are possible. It may be surprising because the term “aesthetic” suggests that he intends to look into the way in which we experience the world, which doesn’t immediately suggest a connection with mathematics. But geometry is carried out through the use of visual aids and in the first part of the TA Kant takes up the notion of space as a precondition for any representation of objects of what he calls our “outer intuition” of the world as we experience it or imagine it. He is concerned to establish that the way in which we necessarily represent objects to ourselves–spatially–determines the way we formulate concepts about them, with geometry as the paradigmatic example.

A glance at the content of the section will illustrate the point. For example, Kant asks,

“How….can there exist in the mind an outer intuition which precedes the objects themselves, and in which the concept of these objects can be determined a priori?”

[B 41]

By “outer intuition” Kant means our immediate experience of reality, whether in sensation or imagination. It is immediate in the sense that it is not mediated by a prior discursive thought process. By “precedes” he indicates that “Space” is a precondition for our experience of objects in the world. Suppose that one were to take the contrapositive of following entailment:

(1) If any representation of an object in the world requires that it be represented spatiality, or R –> S, then,

(2) -S –> -R. Suppose there were no spatial element in the representation of an object. It follows that there could be no representation of that object.

Again, space or the spatial quality of objects is not something revealed to us by a discursive thought process, but something we experience as immediately present within ourselves that is also in a sense prior to our experience of the world as a precondition for it. Space is not a concept that we develop from our experience only to apply it back to our experience, but the very condition for our capacity to represent the world in sensation or imagination at all. It is always presupposed in any reasoning about the spatial properties of objects and so might be considered a condition necessary for the possibility of geometry and, by extension, of objects in the world in general. This is the “aesthetic” component of his argument.

What does Kant’s mean by the term “Transcendental”?

Next we come to the question of what is meant by the term “transcendental.” Consider what Kant writes at the beginning of Section 3 of the TA in relation to the remarks above about geometry:

“I understand by a transcendental exposition the explanation of a concept, as a principle from which the possibility of other a priori synthetic knowledge can be understood. For this purpose it is required (1) that such knowledge does really flow from the given concept, (2) that this knowledge is only possible only the assumption of a given mode of explaining the concept.”

[B 40]

What Kant is after here is some “concept” (e.g. space) that stands outside, in a certain sense, the discursive processes of a particular branch of knowledge and that grounds whatever a priori claims to knowledge it uses as the basis for further knowledge. For example, one might reason (as Kant does) that any two sides of a triangle must be greater than any third side. This can be taken to be a synthetic a priori truth of geometry. It expands our knowledge and reveals a necessary and universal truth, but not by the simple analysis of concepts. But its a priori truth is based upon a prior “transcendental” truth, the necessity of space as a determining factor of the way objects represent themselves to us. It is not a truth based upon an assumed definition that determines the basis for further deductions as is the case with Euclid’s axioms, but upon the way things must be for us, inasmuch as spatiality must be taken to be a precondition for the representation of an object in space. Although we might attempt to define it, as a precondition for any representation of an object, it stands outside the interplay of experience and conceptual refinement and so is a priori in a special sense. In this sense, “space” transcends the study of geometry.

As a confirmation of this reading, consider what Kant says in the sentences that immediately follow the quotation above:

“Geometry is a science which determines the properties of space synthetically, and yet a priori. What, then, must be our representation of space, in order that such knowledge of it may be possible? It must in its origin be intuition; for from a mere concept no propositions can be obtained which go beyond the concept–as happens in geometry….Further, this intuition must be a priori, that is, it must be found in us prior to any perception of an object, and must therefore be pure, not empirical, intuition. For geometrical propositions are one and all apodeictic, that is, are bound up with the consciousness of their necessity; for instance, that space has only three dimensions. ”

[B 40-41]

The final clause gives the most explicit sense of what Kant is after: our way of representing objects spatially is necessitated by the way in which we represent them to ourselves. That space (as opposed to time, an object of inner intuition for Kant) has only three dimensions is necessitated by the way in which we represent objects spatially, i.e., three dimensionally. This truth of our experience is not a concept developed out of our experience, so Kant argues, but a precondition for sensory experience itself and so can act as the basis for universal and necessary claims about the nature of experience in general. Furthermore, its transcendental aspect lies in its origin, our intuition of it as a basic reality, which precedes any attempt to define space itself axiomatically. Because of its immediate, nondiscursive intuitability, it has a claim to precede the science of geometry, which begins with axioms and definitions.

What does Kant Try to Accomplish in the TA?

We can now state in summary form what it is that Kant is after. He is trying to discover a foundation for synthetic a priori statements about the nature of our experience of objects in the world. Hopefully, this kind of statement can be read with greater clarity than at the beginning of the article. As the third quotation suggests, his reasoning is logical rather than psychological: from the fact that (1) synthetic a priori statements can be made in geometry there must (2) be something further that provides the basis for their necessity and universality, their intuitive truth. That something further, a transcendental concept not dependent upon the propositions of geometry themselves, is the way in which we are bound to represent objects, i.e., spatially, with its attendant necessary consequences.