Kant's Account of Space
Kant’s account of space in the New Elucidation, Directions in Space, the Inaugural Dissertation, and the Transcental Aesthetic in Critique of Pure Reason. Submitted for PHIL 3903 on April 5, 2021.
Kant’s transcendental idealism, the notion that we can only ever cognize things as they appear under the conditions of our sensibility, never things as they are in and of themselves, paves a midway path between the rationalists and the empiricists accounts of knowledge and is undoubtedly a crucial narrative in metaphysics. Kant’s road to this conclusion, however, is not a perfectly straightforward chronicle. While he consistently maintains that we are in real interactions with objects of this world, Kant once defends the Newtonian idea of mind-independent, absolute space before reaching the conclusion of space as a mind-dependent, pure form of intuition which we apply to sensible objects. In this paper, I will outline chronologically Kant’s account of space, which is of particular importance to his solution to the transcendental problem of the possibility of a priori knowledge, as presented in the New Elucidation, Directions in Space, the Inaugural Dissertation, and finally, in the Critique of Pure Reason, primarily in the Transcendental Aesthetic section.
In New Elucidation, Kant posits that we are in real interaction with other substances, as opposed to the German rationalist precedent that we are only interacting with substances ideally. Kant’s argument in this 1755 essay is that if we were merely in ideal interaction with other substances, we could not receive “new determinations,” nor could our “inner states” be changed in any way (I:410).This is because if a change were to occur in a substance due to purely ideal interactions, this change of state must have resulted from the same internal grounds which have already determined the substance to be the opposite of that state; but this is not possible, for the same grounds cannot be both A and not A (I:411). Further, considering that “alterations,” which we observe through succession, do apparently take place in the universe, and considering that us “souls” do undergo “inner changes,” it must be the case that we are in real, not ideal, interactions with substances of this world (I:411-412).
Approximately a decade later, in his 1768 essay Directions in Space, Kant defends Newton’s claim that that space is absolute and also argues that it is mind-independent—that is, space has “a reality of its own” (2:378). In other words, at this point, Kant thinks that there are absolute directions, which cannot be defined by merely relative and conceptual terms under Leibniz’s account of space (2:377). Our understanding of any substance, Kant notes, does not only depend on the “relation and position of its part to each other,” but also on a reference to an “universal absolute space” (2:381). He offers the example of “incongruent counterparts” to support this claim (2:382). Specifically, Kant highlights that if we were to adopt the German philosophical idea of space as “a mere figment of our imagination” and something merely relational, then the left hand would occupy the same space as the right hand, because there is “no difference in the relation of the parts of the hand to each other” as to indicate to us that this is the left hand or that is the right hand (2:383). If this were true, then the left hand glove should be able to fit neatly into the right hand, and vice versa (2:382). Yet that is manifestly not the case. As we have seen, space as concepts and relations do not adequately explain the phenomenon of incongruent counterparts. But if we consider “true differences” in “absolute and original space,” then the phenomenon is compatible (2:383). Thus, directionality in space implies that space is absolute.
The Inaugural Dissertation published two years after Directions in Space marks a shift in Kant’s account of space in that although he still presents space as absolute and maintains that we are in real interaction with other substances, he no longer views space as mind-independent (2:389). That is, Kant now rejects the idea that space is objective and real, and instead proposes that space is “subjective and ideal”—it is a pure form of intuition, or a scheme, derived from the mind according to a “stable law” by which we coordinate and understand sensible things (2:403). This proposition is the result of Kant’s breaking away from the German rationalist tradition that views the distinction between sensibility and understanding as a distinction in degree only. Philosophers of this camp believe that what belongs to our faculty of sensibility, or what we feel, is simply “more confusedly cognised” than what belongs to our faculty of understanding, which has a “distinct cognition” (2:395).
Kant, on the other hand, discerns such a distinction to be a distinction in kind. Understanding, or noumenon, he writes, is our faculty to present to us things that cannot “by their own quality” come before our senses (2:392). Objects of understanding thus contain nothing but what is knowable, not sensible (2:392). Kant states that sensibility, or phenomenon, is receptive and, in a way, passive (2:392). In essence, in order to be affected by the “presence of some object,” the subject’s sensibility must be capable of that modification in the first place, because objects are not simply sensible “in virtue of their form or aspect” (2:392-393). In other words, substances do not “light up” in our brain just because they are substances, they do so because we understand them as substances according to an “internal principle” (2:393). As a result, things which are sensible are “representations of things as they appear,” and our consequent mental state reflects both the contribution of the object and of our own nature (2:393). Our contribution, or “the schema and conditions of everything sensitive in human cognition,” Kant identifies, are the “absolutely primary and universal” pure forms of intuition of space and time (2:398). Therefore, no matter how “universal” or logical our understanding of some objects becomes, we only ever know them as appearances, never things in themselves (2:394).
In his magnum opus, Critique of Pure Reason, Kant builds upon his current view of space as absolute as well as mind-dependent, and he argues in detail why our intuition of space as the form of our outer sensibility is pure, not empirical. Central to this task is establishing the possibility of synthetic a priori judgments, included in them are pure mathematical judgments (B14). Math is a priori because mathematical propositions are necessary truths and “cannot be derived from experience” (B14). However, it is surely easy to think that because math is a priori, it must be analytic (B15). That is, the concept of sum is an outcome of the analytical principle of contradiction alone, not of synthesis of any kind (B15). Kant provides the concept of summation as a counterexample to this claim. If we say the mathematical judgment 7 + 5 = 12 is analytic, Kant proffers, we are saying that the concept of 7 + 5 contains in itself the concept of 12 (B15). But when we think of 7 + 5, we are only thinking of the concept of the addition of two numbers, and the answer 12 was not contained in 7 + 5—we can never find a sum by mere analysis, we always need help from intuition to do so (B15-16). It is thus shown that math is always synthetic (B16).
Pure geometry is also synthetic. The concept of the shortest path between two points, which is the predicate, is not contained in the subject of a straight line, and therefore cannot be drawn by mere analysis (B16). This is because the concept of a straight line contains a quality, not a quantity that measures whether something is the shortest (B16). It is only when we elicit help from intuition that we synthetically form the “concept of the shortest” (B16). In both arithmetic and geometric judgments, then, intuition is what makes the “synthetic” in synthetic a priori possible. The intuition here so emphasized is that of the pure forms of intuition of space and time (B36).
Kant specifies in the Transcendental Aesthetic that our intuition of space is not a posteriori, or derived from empirical experiences, because in order for us to position appearances of substances as outside of me, I must, first and foremost, already think of them as existing in space (B38). Space is the a priori, necessary ground of all “outer experiences” (B39). Space is the precondition to our sensations of any appearances in space, not a “determination dependent on them” (B39). Then, Kant argues that because mathematical judgments are a priori, the intuition of space upon which math is grounded must also be a priori, otherwise mathematical judgments would be “nothing but perceptions”—math would be contingent on experience, not necessary truths, but we know this to be false (B39). Furthermore, space is not a “discursive or … general concept of relations,” or a general representation of what is possible to a multitude of things. Instead, space is a singular, “pure intuition” that is given “infinite magnitude” (B39). This is due to the fact that we cannot identify space as an instance of an universal space, nor can we establish anything in terms of its magnitude if we were to think of space as a general concept of relations (B39). All these amounts to the conclusion that while space is empirically real, as it is a necessary precondition for our empirical experience that we subjectively impose on the representation of things, it is at the same time transcendentally ideal, as it is not a representation of any things in themselves (B44). Thus, what we intuit in space can never be things in themselves, but mere “representations of our sensibility,” or appearances of objects (B45). The “transcendental object,” so long as we still operate within the constraint of space and time, is ever unknown to us (B63).
In this manner, he clearly diverges from the German rationalist thought that sensibility is just a part of understanding that is more logically confused. Kant has argued that sensibility, the “receptivity of our mind to receive representations,” is distinct in kind from understanding, which is the faculty we use to think about these representations (B75). Consequently, if we wish to apply our faculty of understanding to learn something beyond what is contained in the subject itself, we do so through our intuition of space and time, which prevents any judgment coming from it to “extend beyond the objects of the senses” (B73). Whatever a priori judgments that results, thereby, can only hold for objects as they appear to us. The culmination of Kant’s account of space illuminates what Kant terms the “transcendental idealism,” namely, that we never come to know things subsisting in themselves, independent of our intuition.