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The metaphysical exposition of the concept of space in the Critique of Pure Reason Methodological aspects


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Ioan Buș
West University of Timișoara, Romania
e-mail: ioan.bus@e-uvt.ro


AGATHOS, Volume 15, Issue 2 (29): 61-72, DOI 10.5281/zenodo.13945821
© www.agathos-international-review.com CC BY NC 2024


Abstract: The Copernican revolution that Kant initiated in theoretical philosophy involves several types of transcendental arguments: expositions, deductions, and proofs. Among these, the expositions concern the concepts of space and time. Among the arguments put forth by the philosopher are those supporting the idea that space and time are not concepts, but intuitions. I shall briefly outline the main positions in Kant-Forschung, then present my own position. Space and time are, indeed, concepts, but not discursive ones; at the same time, they are intuitions because they directly relate to objects. 


Keywords: transcendental idealism, transcendental arguments, metaphysical exposition of space, a priori intuitions, discursive concepts


One of the most complex concepts (Begriff) in Kantian transcendental philosophy is that of space. Since the philosopher explicitly argues that space is not a discursive concept, but an intuition, in the very title of the chapter where he presents these arguments (two types), he uses the expression ’metaphysical exposition of the concept of space.’ This blatant contradiction naturally sparked many disputes in Kant-Forschung. Among the established exegesis, N. Kemp-Smith and H. Allison are the firmest in their positions. The former considers all four arguments of the metaphysical exposition to be weak, even circular, while the latter carefully attempts to prove the opposite. Building on the positions of these two scholars, I shall try to highlight a way which avoids the circularity of arguments and even provides an explanation for the possible pitfall in this direction of interpretation. I shall argue for the difference between concept and term, thereby implying a philosophy of language that Kant did not delve into, but which will resolve the announced contradiction.

 Kant presents his conception of space and time in his work Critique of Pure Reason, more precisely in the chapter entitled The Transcendental Aesthetic. The investigation of pure intuitions begins with metaphysical exposition. What is striking from the outset is the fact that the author, although arguing that space (and implicitly time) is not a concept, specifically a discursive concept, specifies in the title of paragraph §2 of the First Section that it is a metaphysical exposition of the concept of space. For the discussion of this issue, it is necessary to present the third argument, which makes the distinction between intuition and concept.

 The research method is quite clearly specified by the author, and I believe many exegetes would avoid some problems if they considered it at the level of importance it holds. “By exposition (expositio) I understand the clear representation (although not detailed) of what belongs to a concept; and this exposition is metaphysical if it encompasses what the concept represents as given a priori. (Kant 1999, B38) The significance of the expression “as given a priori” is well illustrated by J.G. Schulze (Prüfung der Kantischen Critik der reinen Vernunft, 1789 edition):

If I were to draw a line1 from one point to another, I must already have the space in which to draw it. And if I can continue drawing as much as I want, endlessly, then this space must be given to me as unlimited, that is, infinite. Conversely, I can successfully generate a cylinder or a body only in space, which means I can do so because space is already given to me, along with the qualities that allow me to assume that points exist everywhere, and which allow me to generate endlessly the three dimensions of extension.” (Kant 1999)

From this paragraph the meaning of the “condition of possibility” that the term “given a priori” carries can be inferred. The same meaning is preserved in the continuation of the transcendental process, in the chapters of The Transcendental Logic.

 Kant’s exposition of space (and, implicitly, of time) is divided into two directions, one concerning the apriority of the forms of sensibility, and the other concerning their intuitive nature. Although the arguments are similar for space and time, their expositions are nevertheless different. In the case of time, the third point is a transcendental exposition, whereas in the case of space, the transcendental exposition is given by the fifth point. Beyond these minor differences, it is considered that the metaphysical exposition of space presents arguments of apriority in points (1) and (2), with the same situation encountered in the metaphysical exposition of time, while arguments of intuitiveness are presented in the metaphysical exposition of space in points (3) and (4), and in that of time, in points (4) and (5). I shall present below the first arguments, those of the apriority of the forms of sensibility:

1) Space is not an empirical concept that has been drawn from outer experiences. For in order for certain sensations to be related to something outside me (i.e., to something in another place in space from that in which I find myself), thus in order for me to represent them as outside <and next to> one another, thus not merely as different but as in different places, the representation of space must already be their ground. Thus the representation of space cannot be obtained from the relations of outer appearance through experience, but this outer experience is itself first possible only through this representation.
2) Space is a necessary representation, a priori, that is the ground of all outer intuitions. One can never represent that there is no space, though one can very well think that there are no objects to be encountered in it. It is therefore to be regarded as the condition of the possibility of appearances, not as a determination dependent on them, and is an a priori representation that necessarily grounds outer appearances. (Kant 1999, B38-39 / A23-24)

The exposition of the concept of time is similar2.

 What is striking from the outset is the tautological appearance: space is not derived from experiences, because space is necessary to have experiences. What is the actual argumentation? Of course, Kantian exegesis is divided (Allison 1983), not only regarding the tautology or circularity of the argument, but also regarding the relationship between the two points above. Are they two distinct arguments or just two steps of the same argumentation?3 On the one hand, Vaihinger (1922) argues that here we have a theorem supported by two proofs, the first being a direct proof, and the second an indirect one. In opposition to Vaihinger, Kemp Smith (Kemp-Smith 1918, 99-123) and Paton (1936) consider that the first argument is insufficient but that it is supplemented by the second. On the other hand, Allison (1983) considers that there are actually two distinct proofs here, each sufficient for the intended purpose.

 Allison considers that the first point invokes two presuppositions: the first one stating that space must be presupposed if one can claim to have sensations about something external, and the second stating that space must be presupposed if objects are to be represented as external to one another. Since “external” is a term with spatial implications, it is easy to admit that Kant’s expression is tautological. However, Allison argues that what is deceptive is not the argument itself but the way it has been constructed. What he considers to be the crucial point in the argumentation is the definition of “external sense” - that is, the sense through which someone becomes perceptually aware of the distinction between themselves (and their states) and objects. Analogously, internal sense is “the sense through which someone becomes perceptually aware of themselves and their states.” (Allison 1983, 83) Starting from these definitions, the exegete considers that the tautology disappears, “the representation of space functions as a condition through which we become aware of things as being external to us” (Ibid, 83). In his opinion, here we no longer have a tautology simply because other beings can now be conceived who can attain an awareness of things or their own states, but through means other than spatial and temporal ones. However, the argument does not seem to be valid. The reason why the possibility of other beings perceiving things without the conditions of space and time makes the consciousness of perception not contain spatial representation for a rational being (in the Kantian sense, i.e., a being endowed with the generic consciousness discussed in the Critique of Pure Reason) is not clear. The first statement of this argument, as interpreted by Allison, says that spatial representation must be presupposed where I have the consciousness of things external to me. The existence of other beings who have the consciousness of externality without spatial representation is, if not absurd, at least inconceivable for a rational being. The existence of these beings is not only a real impossibility (we have no guarantees that they can comply with the conditions of possibility of experience), but it is also a logical impossibility (the term “external” includes spatiality as a note of itself, so the term is completely lost if I abstract from this note, and it becomes contradictory in itself if I associate it with the contrary note, the lack of spatiality). Allison’s idea could be extended in the manner in which Rorty (1979) discusses schemes of rationality, but I do not think it will bring any benefit. It is possible to think, without any corresponding intuition, but only as a simple concept, of a scheme of rationality different from ours. However, to have consciousness of such a scheme, I must leave my own scheme, which is impossible. From the perspective of my own scheme of rationality, it is impossible to conclude that there is another scheme, different from mine, because even if I were faced with the signs of this different scheme, I could only interpret them through my own rationality, which would make those signs either absurd or meaningless. But even if, absurdly, Allison was right and beings could be conceived to have the consciousness of externality without the aid of spatiality, I do not see how this would make the tautology disappear, because Kant does not refer to a being in general, but explicitly relates to human rationality. Furthermore, if it were to refer to a being in general, then the statement would need an argumentation specific to the nature of human rationality, an argumentation that is missing.

 The second statement is addressed by Allison in a similar manner. The statement that spatial representation is necessary to realize things as being external to one another is not tautological in the exegete's opinion if the distinction is made between numerical diversity, quantitative diversity, and qualitative diversity. Thus, Kant’s argument is reconstructed: “(...) Kant can be interpreted as arguing that, in order to be conscious of things as numerically distinct from one another, it is necessary not only to be conscious of their qualitative differences but also of the fact that they are located in different spaces. In other words, the representation of place, and therefore of space, functions for human experience as a necessary condition of the possibility of distinguishing objects from each other. Furthermore, as in the previous case, it is not a logically necessary condition” (Allison 1983, 83). Not only are the arguments of the second statement similar to those of the first, but the objections that can be raised to the exegete are similar to those mentioned above. What Allison argues seems rather not a defense of Kant’s ideas, as declared in the title of the work, but a contradiction of them. The conclusion that spatial representation is not necessary for the possibility of distinguishing external things, or of distinguishing them from the knowing subject, is contrary to the Kantian text: “Space is a necessary a priori representation (Kant 1999, B38/A24) ...”, “Time is a necessary representation, which underlies all intuitions” (Ibid, B46/A30). Of course, the tautology of the statement, or the vicious circle of argumentation, do not disappear, but I will try to argue towards the end of the paper that it should not disappear either; on the contrary, the fact that it does not disappear is a consequence of Kant’s theory of space and time. Given these considerations, I shall not present other viewpoints that attempt to avoid the tautology expressed in points (1) and (2) of the metaphysical exposition of space and time.

 An interesting observation is made by Dryer (2017): “To recognize things as being red, someone must already have the concept of red. But this does not establish that this concept is not empirical. To observe certain things about ourselves, we must represent them in space. However, how can this fact prove that space is not an empirical concept?”. This objection can be easily dismissed: the concept of “red” is not a priori because it precedes a certain experience, but because it does not precede any experience, as in the case of space and time, which precede any experience. Furthermore, the precedence in question here is a logical one, not a temporal one.

 It is evident that Kant’s intention here contradicts Leibniz; things depend on space and time, not space and time depend on things. In other words, the pure forms of sensibility are universal forms of all things.

 The second argument for apriority is considered by the same exegete to be much stronger than the first, but essentially it supports the same thing, albeit in a positive formulation. The second proposition in the argument is actually the premise: “we cannot represent the absence of space, but we can represent space devoid of objects.” Allison reformulates the argument so that its structure is more visible: “if X can exist (or can be represented) without A, B, C or their reciprocal relations, but A, B, and C cannot exist (or cannot be represented) without X, then X must be considered as a condition of possibility for A, B, C, and their reciprocal relations.” (Allison 1983, 86)

 Kemp Smith rejects this argument on the grounds that it relies on a psychological impossibility to represent things without space. Other exegetes argue that here Kant asserts the impossibility of conceiving the non-existence of space. Of course, Allison, as mentioned above, considers that space is not logically necessary. Another example can be brought forth in favor of the necessity of space as a representation of things. The judgment “Every body has extension” is an analytic judgment (Kant 1999, XX, §IV). If it is analytic, it means that the concept of body includes the note of extension, and since all things (Gegenstand) are bodies, it means that they have an extension. Therefore, all things necessarily depend on their representation on the forms of sensibility (in this case, on spatial ones, but it can be easily shown that they also necessarily depend on temporal representation).

 Allison considers that the psychological impossibility mentioned by Kemp Smith is actually an epistemic one, because space and time are conditions of possibility for phenomena. It is not possible to eliminate space and time while maintaining intuitive content in representations at the same time. “Like the first argument, this one establishes the a prioristatus of space and time representations by indicating their unique and foundational role for human experience.” (Allison 1983, 89). But, unlike the first argument, the latter also highlights the fact that space and time (if we also refer to the corresponding argument for time) have their own content that remains when abstraction is made from anything empirical, i.e., from sensation in intuition.

 The following presentations are classified as arguments in favor of the intuitive nature of space:

3) Space is not a discursive or, as is said, general concept of relations of things in general, but a pure intuition. For, first, one can only represent a single space, and if one speaks of many spaces, one understands by that only parts of one and the same unique space. And these parts cannot as it were precede the single all-encompassing space as its components (from which its composition would be possible), but rather are only thought in it. It is essentially single; the manifold in it, thus also the general concept of spaces in general, rests merely on limitations. From this it follows that in respect to it an a priori intuition (which is not empirical) grounds all concepts of it. Thus also all geometrical principles, e.g., that in a triangle two sides together are always greater than the third, are never derived from general concepts of line and triangle, but rather are derived from intuition and indeed derived a priori with apodictic certainty.
4) Space is represented as an infinite4 given magnitude. Now one must, to be sure, think of every concept as a representation that is contained in an infinite set of different possible representations (as their common mark), which thus contains these under itself; but no concept, as such, can be thought as if it contained an infinite set of representations within itself. Nevertheless space is so thought (for all the parts of space, even to infinity, are simultaneous). Therefore the original representation of space is an a priori intuition, not a concept. (Kant 1999, B39-40 / A23-25)

In these expositions, Kant speaks of space (and time5) as intuitions, meaning that they refer directly to objects. If space were a discursive concept, then there would be something real that corresponds to it, and furthermore, what corresponds to it in reality should be such that space represents the common note of those entities. It is evident that in reality, something with the character of infinity cannot be known, which means that space itself cannot be perceived. However, since it is not perceived and yet we have knowledge about it, it must belong to our cognitive forms. At this point, two possibilities arise: in a Kantian manner, space may belong, as a form, either to sensibility or to the intellect (or even to reason, as a faculty of knowledge). By elimination, it is attributed to sensibility because if it belonged to reason, it would be an idea, and it would not be at the basis of experience but rather at the other end of its systematization. If it belonged to the intellect, it would mean that it is a pure concept, which would not be possible since it is not found in any function of the intellect in judgments. The only possibility left is for space to be a form of sensibility. However, if space and time are intuitions and not discursive concepts, then the question arises: what sense does a metaphysical exposition of the “concept” of space (or time) have? In what sense is space (or time) a concept? It has been shown that it is not a discursive concept, and from this, it has been deduced, by opposition, that it is an intuition, but neither the categories are discursive concepts. They are pure concepts, but they are not intuitions. Are there other types of concepts to which Kant could refer? The distinction between representation and intuition must first be clarified. As an original representation, space is not a concept but an intuition. Could it be a concept as another kind of representation? If we also consider the theory of intellect and especially the relationships established between sensibility and intellect, new perspectives on this problem can be brought up. As far as I understand, we can speak of representations of things only when the intellect participates in the synthesis of the diverse. Moreover, the first step of synthesis, the apprehension in intuition, can be interpreted as the result of the action of categories on the diversity of sensibility. Along this path, spatial (or temporal) representation is necessary to be aware of things as being external to each other, or external to us, or successive, or simultaneous because they primarily relate to things. I believe that only after the transcendental object intervenes in the synthesis of diversity does sensation place the object as exterior to consciousness. A simple example is provided by “the judgments of perception”- improperly called so, as Kant himself considers (Kant 2002). In a judgment where the categories of the intellect do not produce the synthesis of diversity, we are not dealing with objects, meaning sensations do not rise to the level of concepts. Thus, the question arises whether in this situation the forms of sensibility still organize the matter of the phenomenon. I believe the answer is negative. For example, when we hold a stone in our hands, if we do not reach the synthesis of diversity through categories, all we can say is that we feel a weight, unlike the objective judgment about an external existence: “This stone is heavy.” In judgment, more precisely in the representation of weight, isolated from its object, the reference to something external disappears, meaning no specific location in space corresponding to that felt weight is specified. However, I still feel that weight, so I am aware of my own state, meaning I am aware of a succession of my internal states. This observation must imply the contribution of temporal intuition in the judgment of perception. However, I believe that this implication occurs only if it is accompanied by transcendental apperception, namely the possibility of the judgment “I think” being associated with those states. But the contribution of apperception is not necessary, because when I feel the weight, I do not have to affirm (and this is the case in judgments of perception) that that state belongs to me. Of course, this argumentation is possible only by considering the order of the synthesis of diversity, because otherwise, to say that in a previous state I felt a weight, I must be conscious that I felt that weight, meaning I must be aware of my own internal states, in other words, I must be given in apperception. To summarize, judgments of perception do not presuppose any synthesis of diversity produced by the intellect, but their analysis can only be done indirectly. However, when Kant speaks of time and space, he constantly refers to these forms as representations. Since they are representations, it means they are accompanied by the self-awareness of the knowing subject. This is also the argument that allows Kant in the chapter “Refutation of Idealism” and in the note from the 1787 Preface to the Critique of Pure Reason, which supports the ideas from the mentioned chapter, to consider that an awareness of internal states presupposes spatial representation. What the intellect gives to pure diversity is unity. Space and time as representations have this unity from the intellect.

 As a general note on the metaphysical exposition, it is observed that each argument takes for granted what needs to be proven. This interpretation views the argumentation in a syllogistic sense, or at least as an inference leading to a conclusion. From here arise several problems, noted by Kantian exegetes. Firstly, if we are dealing with an argument, as mentioned earlier, then it does not achieve its goal, being circular. Moreover, these four arguments are part of the metaphysical exposition of the concept of space, in the situation where the third and fourth arguments explicitly state, “space is not a concept.” How is it then possible to expose the concept of space if space is not a concept?

 The solutions are multiple. They can be grouped into two categories: positive, which attempt various interpretations of the arguments so that they are not circular, or negative, which emphasize their circular nature and conclude their futility. I believe another interpretation can be supported as well. Taking Kant’s expression of “metaphysical exposition” as a premise, several conclusions can be drawn. Kant understands by this expression “the clear (though not detailed) representation of what belongs to a concept; and this exposition is metaphysical if it includes what the concept represents as given a priori” (Kant 1999, B38). In other words, the four arguments are not strictly inferences leading to a conclusion, but rather an analysis or explanation of a concept.

 But the question still remains unanswered. Space is an intuition, yet Kant provides an exposition of the concept of space. This issue, I believe, encompasses two aspects:

 1. What kind of concept is space?

 2. Why didn’t Kant provide an exposition of space as intuition?

It can be argued that space is indeed a concept, but not a discursive one encompassing common features of multiple objects. As a concept, it must belong to the intellect. However, its content is provided by sensibility, i.e., by intuition. Other concepts also have content provided by intuition, but they do not have intuition as their object, meaning that the entire spatial representation is not their content. Thus, the concept of space has intuition as its sole object. Therefore, clarifying the concept of space means representing its content, i.e., intuition. Clarifying the features of the concept is equivalent to specifying the features of spatial intuition. Thus, a pure concept of space is possible, which has spatial intuition as its sole object. This concept is expounded in the Transcendental Aesthetic. The same applies to the concept of time.

 In this situation, another problem arises: why did Kant prefer an exposition of a concept, since the original representation is much more suited to intuition? The answer may be simple: since intuition is a direct relation to objects, and in the Transcendental Aesthetic sensibility is isolated from everything empirical or belonging to other faculties, an exposition of space could not be done as intuition, because intuition has no features and therefore there would be nothing to expose, only the concept about that intuition has features. An intuition cannot be expressed in language except through a concept. I believe that now we can also respond to the issue of the tautology of the argumentation. In fact, in the metaphysical exposition, we do not have deductive, foundational argumentation, but rather an analysis of a concept. Since the concept of space and that of time are based on corresponding intuitions, any argument that seeks to prove the resulting attributes can only be circular. All the properties of space, whether considered as a concept or an original representation, are derived from the corresponding intuition. If the arguments were not apparently circular, this would mean that they are synthetic, i.e., they assert more about space and time than is contained in their intuitions, which is impossible, since the concepts were constructed based on intuitions. All four expositions would lose any meaning if they were to abstract from their corresponding intuitions. Furthermore, these points could not be expressed if intuitions did not have corresponding concepts. I believe this interpretation manages to reconcile the positions initially presented while consistently describing Kant’s argumentation.


References:

  1. Allison, Henry E. 1983. Kant’s Transcendental Idealism. An Interpretation and Defense. New Haven and London: Yale University Press.

  2. Dryer, D. P. 2017. Kant’s Solution for Verification in Metaphysics. Routledge.

  3. Freidman, Michael. 1985. Kant’s Theory of Geometry. The Philosophical Review, 94 (4): 455-506. doi:10.2307/2185244.

  4. Freidman, Michael. 1998. Kant and the Exact Sciences. Reissue edition. Harvard University Press.

  5. Fullerton, George Stuart. 1901. The doctrine of space and time: I. The Kantian doctrine of space. Philosophical Review: 113-123. doi:10.2307/2176506.

  6. Kant, Immanuel. 1999. Critique of Pure Reason . The Cambridge Edition of the Works of Immanuel Kant. Translated and edited by Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press.

  7. Kant, Immanuel. 2002. Prolegomena to Any Future Metaphysics that Will Be Able to Come Forward as Science. In Theoretical Philosophy after 1781, pp. 20-170. Edited by Henry Allison and Peter Heath. Translated by Gary Hatfield and Michael Friedman. Cambridge University Press.

  8. Kemp-Smith, Norton. 1918. A Commentary to Kant’s ‘Critique of Pure Reason’. London: Macmillan and Co.

  9. Paton, Herbert James. 1936. Kant’’ Metaphysics of Experience. London: Macmillan and Co.

  10. Rorty, Richard. 1979. Transcendental Arguments, Self-Reference, and Pragmatism. Vol. Transcendental Arguments and Science. In Transcendental Arguments and Science, by Rorty Richard. Edited by P. Horstmann, RP. Krüger, L. Bieri. Dordrecht: D. Reidel Publishing Company.

  11. Vaihinger, Hans. 1922. Kommentar zu Kants Kritik der reinen Vernunft. Stuttgart: Union Deutsche Verlagsgesellschaft.

1 “For Kant, as well as for Newton, spatial quantities were not composed of points, but generated by the motion of points” (Freidman. 1998. Kant and the Exact Sciences, p. 83). This idea was also presented in an older article (Freidman. 1985. “Kant’s Theory of Geometry”).

2 “Time is <1> not an empirical concept that is somehow drawn from an experience. For simultaneity or succession would not themselves come into perception if the representation of time did not ground them a priori. Only under its presupposition can one represent that several things exist at one and the same time (simultaneously) or in different times (successively).

2) Time is a necessary representation that grounds all intuitions. In regard to appearances in general one cannot remove time, though one can very well take the appearances away from time. Time is therefore given a priori. In it alone is all actuality of appearances possible. The latter could all disappear, but time itself (as the universal condition of their possibility) cannot be removed.” (Kant 1999, B46 / A30-31)

3 The idea of arguing in two steps is not foreign to Kantian exegesis, even regarding The Deduction of the Categories from 1787, where once again a division of the argumentation is considered.

4 In Fullerton’s conception, space, as form, is coextensive with the matter that gives it content - in this sense, it is limited. (Fullerton 1901)

5 “4) Time is no discursive or, as one calls it, general concept, but a pure form of sensible intuition. Different times are only parts of one and the same time. That representation, however, which can only be given through a single object, is an intuition. Further, the proposition that different times cannot be simultaneous cannot be derived from a general concept. The proposition is synthetic, and cannot arise from concepts alone. It is therefore immediately contained in the intuition and representation of time.

5) The infinitude of time signifies nothing more than that every determinate magnitude of time is only possible through limitations of a single time grounding it. The original representation time must therefore be given as unlimited. But where the parts themselves and every magnitude of an object can be determinately represented only through limitation, there the entire representation cannot be given through concepts, «for they contain only partial representations», but immediate intuition must ground them.” (Kant 1999, A31-32/B47-48)