Philosophy of the Modern Era

Kant

Kant's Theory of Space and Time

The most significant aspect of the "Critique of Pure Reason" is Kant's doctrine of space and time. In this section, I aim to undertake a critical examination of this doctrine.

Providing a clear explanation of Kant's theory of space and time proves challenging, as the theory itself is somewhat ambiguous. It is articulated in both the "Critique of Pure Reason" and the "Prolegomena." The exposition in the "Prolegomena" is more accessible but less comprehensive than that in the "Critique." Initially, I will endeavor to clarify the theory as clearly as possible. Only after this exposition will I attempt to critique it.

Kant posits that immediate objects of perception are partially conditioned by external things and partially by our own perceptual apparatus. Locke accustomed the world to the idea that secondary qualities—colors, sounds, smells, etc.—are subjective and do not belong to the object as it exists in itself. Kant, akin to Berkeley and Hume, though not in precisely the same manner, extends this view further by rendering primary qualities subjective as well. For the most part, Kant does not doubt that our sensations have causes, which he terms "things-in-themselves" or noumena. What appears to us in perception, which he calls a phenomenon, consists of two parts: that which is determined by the object, which he refers to as sensation, and that which is determined by our subjective apparatus, which he claims organizes the manifold into specific relations. He designates this latter part as the form of appearance. This form is not sensation itself and, therefore, does not depend on the contingencies of the environment; it is always the same since it is invariably present within us, and it is a priori in the sense that it does not rely on experience. The pure form of sensibility is termed "pure intuition" (Anschauung); there exist two such forms: one for external sensations and the other for internal.

To demonstrate that space and time are a priori forms, Kant advances arguments of two kinds: one set of arguments is metaphysical, and the other is epistemological, or, as he calls them, transcendental. The arguments of the first kind are derived directly from the nature of space and time, while the second kind is indirectly derived from the possibility of pure mathematics. Arguments regarding space are presented more thoroughly than those regarding time, as it is believed that the latter are fundamentally similar to the former.

Regarding space, four metaphysical arguments are posited:

1. Space is not an empirical concept abstracted from external experience, as space is presupposed in the relation of sensations to something external, and external experience is only possible through the representation of space.
2. Space is a necessary representation a priori that underlies all external perceptions, for we cannot conceive of the non-existence of space, while we can imagine that nothing exists in space.
3. Space is not a discursive or general concept of the relations of things in general, as there is only one space, and what we term "spaces" are parts of it, not examples.
4. Space is conceived as an infinitely given magnitude that encompasses all parts of space within itself. This relation differs from that of a concept to its examples; hence, space is not a concept, but rather an Anschauung.

The transcendental argument regarding space is derived from geometry. Kant asserts that Euclidean geometry is known a priori, although it is synthetic, meaning it is not derived solely from logic. Geometric proofs, he claims, depend on figures. We can see, for instance, that if two straight lines intersect at right angles, only one straight line can be drawn through their point of intersection at right angles to both lines. This knowledge, according to Kant, is not derived from experience. However, my intuition can anticipate what will be found in an object only if it contains merely the form of my sensibility, which predetermines within my subjectivity all actual impressions. Objects of sensation must conform to geometry because geometry pertains to our modes of perception; thus, we cannot perceive otherwise. This explains why geometry, despite being synthetic, is a priori and apodictic.

The arguments regarding time are fundamentally the same, except that arithmetic replaces geometry, as counting requires time.

Now, let us examine these arguments one by one.

The first of the metaphysical arguments regarding space states: "Space is not an empirical concept abstracted from external experience. Indeed, the representation of space must already underlie the ability to relate certain sensations to something outside of me (that is, to something in another location in space than where I am), as well as to represent them as existing outside [and in relation] to one another; thus, not only as different but also as being in different places." Consequently, external experience is only possible through the representation of space.

The phrase "outside of me (that is, in another place than I am)" is challenging to comprehend. As a thing-in-itself, I do not exist anywhere, and nothing spatially exists outside of me. What can be understood beneath my body is only the phenomenon. Thus, all that is genuinely implied is expressed in the second part of the statement, namely that I perceive different objects as objects in different locations. The image that may arise in someone's mind here is that of a coat check attendant hanging different coats on different hooks; the hooks must already exist, but the subjectivity of the attendant organizes the coats.

There exists, as in every aspect of Kant's theory of the subjectivity of space and time, a difficulty that he seems never to have felt. What compels me to arrange objects of perception as I do rather than otherwise? Why, for instance, do I always see people's eyes above their mouths and not below them? According to Kant, eyes and mouths exist as things-in-themselves and provoke my separate perceptions, yet nothing within them corresponds to the spatial arrangement that exists in my perception. This contradicts the physical theory of colors. We do not assume that colors exist in matter in the sense that our perceptions have color, but we believe that various colors correspond to waves of different lengths. Since waves, however, encompass space and time, they cannot, according to Kant, be the causes of our perceptions. If, on the other hand, the space and time of our perceptions have counterparts in the world of matter, as physics suggests, then geometry is applicable to these counterparts, rendering Kant's argument false. Kant believed that the understanding organizes the raw material of sensations, yet he never considered the necessity of explaining why the understanding organizes this material in one way rather than another.

Regarding time, this difficulty is even greater, as one must account for causality when considering time. I perceive lightning before I perceive thunder. Thing-in-itself A causes my perception of lightning, while another thing-in-itself B causes my perception of thunder, yet A does not precede B, since time exists only in the relations of perceptions. Why, then, do these two timeless things A and B produce effects at different times? If Kant is correct, this must be entirely arbitrary, and thus there should be no relationship between A and B corresponding to the fact that the perception caused by A occurs before that caused by B.

The second metaphysical argument asserts that one can conceive of the absence of things in space, but one cannot conceive of the absence of space itself. It seems to me that a serious argument cannot be based on what can or cannot be imagined. However, I emphasize that I deny the possibility of imagining empty space. You may imagine yourself gazing at a dark, cloudy sky, but in doing so, you are still located in space, and you are representing clouds that you cannot see. As Weininger pointed out, Kant's space is absolute, akin to Newton's space, rather than merely a system of relations. Yet, I do not see how one can imagine absolutely empty space.

The third metaphysical argument states: "Space is not a discursive, or as it is often called, a general concept of the relations of things in general, but a purely intuitive representation. Indeed, one can only conceive of a single space, and when multiple spaces are spoken of, they merely refer to parts of that same singular space. Moreover, these parts cannot precede the one all-encompassing space as its constituent elements (from which it might be constructed); they can only be thought of as existing within it. Space is essentially one; the diversity within it, and thus the general concept of spaces, is based solely on limitations." From this, Kant concludes that space is an a priori intuition.

The essence of this argument lies in the denial of multiplicity within space itself. What we call "spaces" are neither examples of the general concept of "space" nor parts of a whole. I cannot precisely determine their logical status according to Kant, but in any case, they logically follow from space. For those who accept, as nearly everyone does in our time, a relativistic view of space, this argument loses its force, as neither "space" nor "spaces" can be regarded as substances.

The fourth metaphysical argument primarily concerns the proof that space is an intuition rather than a concept. Its premise is that "space is imagined (or represented) as infinitely given." This is the perspective of a person living in a flat region, like that where Königsberg is located. I cannot see how an inhabitant of alpine valleys could accept it. It is difficult to comprehend how something infinite can be "given." I must consider it obvious that the part of space that is given is that which is filled with objects of perception, and that for other parts we have only a sense of the possibility of movement. If I may employ such a vulgar argument, modern astronomers assert that space is not actually infinite, but curves, akin to the surface of a sphere.

The transcendental (or epistemological) argument, best articulated in the "Prolegomena," is clearer than the metaphysical arguments and is also more readily refuted. "Geometry," as we now know, is a term that encompasses two distinct scientific disciplines. On one hand, there is pure geometry, which deduces consequences from axioms without questioning the truth of these axioms. It contains nothing that does not follow from logic and is not "synthetic," nor does it require figures such as those used in geometry textbooks. On the other hand, there is geometry as a branch of physics, as it appears in general relativity; this is an empirical science in which axioms are derived from measurements and differ from the axioms of Euclidean geometry. Thus, there are two types of geometry: one a priori but not synthetic, the other synthetic but not a priori. This distinction alleviates the need for the transcendental argument.

Let us now attempt to examine the questions Kant raises when he considers space in a broader sense. If we adopt the view accepted in physics, which requires no proof, that our perceptions have external causes that are (in a certain sense) material, we arrive at the conclusion that all actual qualities in perceptions differ from the qualities in their imperceptible causes, yet there is a certain structural similarity between the system of perceptions and the system of their causes. For example, there exists a correspondence between colors (as perceived) and waves of specific lengths (as derived by physicists). Similarly, there must exist a correspondence between space as an ingredient of perceptions and space as an ingredient in the system of imperceptible causes of those perceptions. All of this is based on the principle of "the same cause, the same effect," juxtaposed with its opposite principle: "different effects, different causes." Thus, for instance, when visual representation A appears to the left of visual representation B, we will assume that there is some corresponding relation between cause A and cause B.

According to this view, we have two spaces—one subjective and the other objective, one known through experience, and the other merely inferred. However, there is no distinction in this regard between space and other aspects of perception, such as colors and sounds. All of them, in their subjective forms, are known empirically. All of them, in their objective forms, are derived through the principle of causality. There is no basis for considering our knowledge of space in any way distinct from our knowledge of color, sound, and smell.

With respect to time, the situation is different, since, if we maintain faith in the imperceptible causes of perceptions, objective time must be identical to subjective time. If it is not, we encounter difficulties already discussed concerning lightning and thunder. Or take this case: you hear a speaking person, you respond to him, and he hears you. His speech and his perception of your response, both to the extent that you touch them, exist in the imperceptible world. And in this world, the former precedes the latter. Furthermore, his speech precedes your perception of the sound in the objective world of physics. Your perception of the sound precedes your response in the subjective world of perceptions. And your response precedes his perception of the sound in the objective world of physics. It is clear that the relation of "precedes" must be the same in all these assertions. While, therefore, there exists an important sense in which perceptual space is subjective, there is no sense in which perceptual time is subjective.

The arguments presented above assume, as Kant believed, that perceptions are caused by things-in-themselves, or, as we must say, events in the physical world. This assumption, however, is not logically necessary in any way. If it is rejected, perceptions cease to be "subjective" in any substantial sense, since there is nothing to oppose them.

The "thing-in-itself" proved to be a very inconvenient element in Kant's philosophy, and it was rejected by his immediate successors, who consequently fell into something very akin to solipsism. The contradictions within Kant's philosophy inevitably led those philosophers who were influenced by him to quickly develop either in an empiricist or in an absolutist direction. In fact, it was in the latter direction that German philosophy evolved until the period following Hegel's death.

Kant's immediate successor, Fichte (1762—1814), rejected the "thing-in-itself" and pushed subjectivism to a degree that seemingly bordered on madness. He posited that the I is the sole finite reality and that it exists because it asserts itself. But the I, which possesses subordinate reality, also exists only because the I acknowledges it. Fichte is significant not as a pure philosopher but as the theoretical founder of German nationalism in his "Addresses to the German Nation" (1807—1808), in which he sought to inspire the Germans to resist Napoleon after the Battle of Jena. The I, as a metaphysical concept, easily blended with Fichte's empirical view; since the I was German, it followed that Germans surpassed all other nations. "To have character and to be a German," Fichte declares, "undoubtedly means the same." On this basis, he developed an entire philosophy of nationalist totalitarianism that exerted considerable influence in Germany.

His immediate successor, Schelling (1775—1854), was more appealing but no less a subjectivist. He was closely linked to German Romanticism. Philosophically, he is insignificant, although he enjoyed a certain renown in his time. An important outcome of the development of Kant's philosophy was the philosophy of Hegel.