Immanently nitpicking Kant on Space

Jamais la nature ne nous trompe; c'est toujours nous qui nous trompons.

--- Jean-Jacques Rousseau, Émile, ou De l'éducation

Kant in his exhaustive categorization of the faculties for human cognition, in his search for the possibility of synthetic a priori judgements, mistaxonimized Space as an aprioric form of intuition, or a pure form of sensibility. Ultimately, the motivation behind this charge will be that Kant's transcendental idealism, if it holds to this aprioric spatiality as a form of pure sensibility, can never satisfactorily escape the domain of subjective idealism, wherein there is always, in the end, either too much determinative power placed within subjectivity or a concession to the realm of the inaccessible noumena to solve its necessary errors.

Kant erred in two specific ways: first, in abstracting down to mere space as the aprioric form of pure intuition and, second, that his transcendental idealism itself presupposes a transcendental object, but it cannot account at all for the relation of this object to the interiority of the sensibility and understanding. The most egregious example of this ambiguous relation is that Kant eventually obtains this transcendental object, or objects, or realm of noumena, by fraud, by abusing his own category of subjective causality, forcing it into a certain demureness before the realm of the intelligible, all the while deeming this real domain of exteriority as prima facie unknowable, unjudgeable. It should also be remarked Kant's confusing abstraction away from certain qualities of empirical perception, such as color, taste, texture, etc., in obtaining the transcendental conditions for the possibility of experience. These qualities of the exterior object wander, almost bastardly, around the Transcendental Aesthetic until finally being subsumed quite unsatisfactorily under the category of quality and legislated by the Anticipation of Subjective Perception. It is enough to say that as it stands solely within the first critique, Kant's taxonomy of Space as a pure formalism for exterior intuition is unnecessarily restricting. A proper transcendental idealism requires something of an invervention upon these errors. Such reformulation would be an inclusion instead of an a priori conception of activity, force, or perhaps individuated telos to explain satisfactorily the reality behind the phenomena and this reality's necessary relation to phenomena. (A remarkably fitting adjustment considering teleology's importance in his moral philosophy.)

This reformulation becomes necessary as the full exposition of the Aesthetic develops but it should be stated that this short text carries a certain limitation: I'm here dealing solely with Space as an aprioric form, and perhaps neglecting Time. I do not think this limitation renders these arguments impotent, for what will primarily be explored is, as Kant calls it, the domain of "outer sense"¹, or the reality within or necessarily synopsized as a manifold for inner understanding of exterior objects. In some sense, the givenness of sense impressions, and only how one relates appearances as they arise necessarily correspond to Kant's unthinkable a priori spatial, and solely spatial, determination. Time does a lot of bewildering things within this process, but its inclusion is not critical to simply explore the confusing process that develops even a present perception for Kant.

This exposition of Kant's position is motivated by a certain interpretative stance, one elegantly stated by Robert Pippin towards the end of his essay "Kant's Theory of Form" wherein he states "Kant's analysis of the forms of experience, however interpreted, commits him to some account of the relation between these pure forms and the 'material' of experience."² Kant's whole task could be said to be motivated by a desire to finally demarcate, with his transcendental idealism, the faculties of human knowledge into two 'types' that work codependently to produce judgement. His, as Pippin calls it, formal idealism was supposed to be separated from other idealistic systems by its reliance on the "material" of human knowledge that is given "from without". Pippin states, "If that formal idealism is to be successful, we must be able to understand its connection with this "material".³ To be clear, this search for clarification is not to dog Kant with demands for a more thorough explanation of how sensory impressions are gained empirically or how the faculties operate within experience; those questions, as Kant himself made clear, are for the natural sciences such as neuroscience or physics. But the critic of this transcendental system should instead seek clarification within the transcendental possibilities themselves regarding their ambiguities, particularly the bewildering "manifold of intuition".

Though this "manifold of intuition" is precisely what the Transcendental Aesthetic seeks to produce, or explain, this criticism cannot leave its clarification to a charitable demonstration of the Aesthetic alone, because it is precisely how it appears across both the Aesthetic and Analytic that engenders the problematic ambiguity, such that stems from what Pippin describes as a "dual characterization"⁴ Kant gives to the sensory manifold. On one hand, the sensory manifold, because of its being outside the discursive powers of the understanding, sits undifferentiated and indeterminate; on the other hand, there must be something within the manifold itself that engenders the discursive powers of the understanding to subsume objects necessarily beneath the categories in certain ways. Pippin produces a compelling question from this ambiguity, one that primarily motivated this present work. He states that "it has emerged that the basic claim in Kant's theory of sensation is that 'no unity comes to us through the senses.' But why not?"⁵

My critique turns this question perhaps on its head and states that, as will be demonstrated, Kant's aprioric form of Space could allow nothing of a unity of experience to exist in the realm of the intelligible because space as an aprioric formalism could never necessarily engender the manifold's synthesis within the understanding to produce all the qualities our empirical perception attributes to objects as they stand in exteriority, such as color or temperature. Aprioric space's inability to produce such a compelling manifold for synthesis is what is meant by space as unthinkable; it is not that a workable concept of mathematical space could not be obtained a posteriori or even that space could not be a discursive concept for the understanding, but rather that space could not be said to properly formalize intuition itself to produce sense impressions. Or if it does, we do not actually stray much from something like Berkleyan idealism where not much if anything is necessitated by that outside us except its indeterminate persistence as an inaccessible X. The attributes of things as they stand within experience would, with only spatiality as the formalism behind intuition, stand as arbitrary constructions of the understanding. Kant, however, obviously thought differently, or at least never faced fully this conclusion. But let us now move beyond posturing and positioning the argument, and finally delve into the Aesthetic and see firsthand how this aprioric space as a formal condition for the possibility of experience is obtained and defended.

The Transcendental Aesthetic does not start with an argument, but a flurry of definitions. Immediately, we are told an intuition is "whatever way and through whatever means a cognition may relate to objects, that through which it relates immediately to them, and at which all thought as a means is directed as an end..."⁶ This definition does not grant much, but it does strengthen Pippin's, and my own, positioning of Kant's idealism as formalistic. It is through the form of intuition that cognition renders objects. However, the confusing thing is that, just as the manifold carries a "dual-characteristic", Kant utilizes intuition in more than one way. "Kant uses the word 'intuition' in a way that deliberately exploits an ambiguity inherent in the notion."⁷ This ambiguity is in being able to argue for intuition as an act or object i.e., we can take intuition, as the definition above states, as that through which the material is given, the form, or, as Kant argues elsewhere, as the given itself, because Kant does argue that the aprioric forms of sensibility are also themselves pure intuitions. Consider: "Space is not a discursive or, as is said, general concept of relations of things in general, but a pure intuition"⁸ or, "This pure form of sensibility itself is also called pure intuition."⁹ This ambiguity between a subjective formality and actual givenness as something itself, here a background plane of spatiality, is what allows the 'intuition' to survive both the Aesthetic and Analytic. It is this ambiguity that weds the sensibility to the understanding in the sense that they both involve themselves with intuitions in differing respects. This wedding of the two faculties is represented by Kant in 'Axioms of Intuition' and stands as perhaps the core of transcendental idealism's involvement of both the "from-without" of the sensibility and the active determinations of the understanding as it thinks. Perhaps it's not a paradox, but it is certainly a malleability of usage, that we can both consider the intuition as the things or thing that we intuit or as a determinative "how we intuit objects as appearance." Regardless, before discriminating against either use of intuition, perhaps it would be fruitful to follow Kant's own development of space as a pure form of sensibility and see how it as a pure intuition arises. The third Metaphysical exposition, started above in its delineation between an intuition and a discursive concept, continues as such,

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 thought in it. It is essentially single; the manifold in it, thus also the general concept of spaces in general, rests merely on limitations.¹⁰

Essential here is the singularity of Space, argued by Kant, and singularity being a key delineating aspect of intuitions versus concepts, as Kant makes clear at the start of the Transcendental Dialectic, "the [intuition] is immediately related to the object and is singular."¹¹ This means that the differing spaces of experience, such as the different "extensions" of empirical objects, is not thought by Kant as representative of our discursive powers placing these objects, subsuming certain appearances, within specific instances of spatiality, but instead as limitations of a greater, homogeneous manifold. That this manifold is represented by sensibility as an "given infinite magnitude" is made clear by the fourth exposition, which states that, "a general concept of space (which is common to a foot as well as an ell) can determine nothing in respect to magnitude. If there were not boundlessness in the progress of intuition, no concept of relations could bring with it a principle of their infinity."¹² This is another argument against the potential discursivity of space, but keep in mind the necessity for Kant of the aprioric form of Space to be "boundless" in a sense, and only demarcated, in experience, by limitations of the manifold. It's intuitive rather than discursive because of its homogeneity and immediacy. But it is just this form of intuition, as a manifold, that needs to be problematized.

What within this homogenous, boundless space, would require for sensibility, or the understanding, to impose such limitations in experience? What in the formality of space would necessitate individual objects as bounded in their appearance? Because it seems, with only extensive magnitude, appearances as representations of a limitation upon extension, that the property of all things within their bound would fall away and what good does Kant's repeated assurance that transcendental idealism does not hit upon the existence of the "thing-in-itself", only the necessary form for their appearance for the subject, if he cannot explain the actual cause for the spatial representation in the first place, as an intuition or empirical concept? Perhaps Kant's delineation between these pure forms of sensibility and our empirical perceptions might elucidate, at least negatively, what is lost with only spatiality.

Immediately following the above explored expositions, Kant states flatly, "Besides space, however, there is no other subjective representation related to something external that could be called a priori objective." It's an odd demarcation and seems a bias towards the domain of vision. Is not the representation of an intuition of a hot stove, pure, in a sense that temperature seems something only representable as a homogeny that is limited, in the moment, within a specific object and is immediate and pre-reflective? Kant continues to state that,

The pleasant taste of a wine does not belong to the objective determinations of the wine, thus of an object even considered as an appearance, but rather to the particular constitution of sense in the subject that enjoys it. Colors are not objective qualities of the bodies to the intuition of which they are attached but are also only modifications of the sense of sight, which is affected by light in a certain way.¹³

This seems an odd and bewildering distinction and betrays transcendental idealism's supposed reliance on an exteriority to provide its material for the formal conditions for the possibility of experience. Kant states that one cannot think of space as an empirical concept, discursive, because it is necessary to have, in the background, a pure intuition of space for an object to appear for us as even spatial, but for Kant it is fine to not follow the mere sensations such as color, temperature, and smell, to their fundamental, transcendental explanation. These sensations, though differing as they appear to specific subjects, cannot be simply disavowed from the transcendental object. The activity that evokes them seems to be the main issue a transcendental exploration of this activity is required for explaining the necessity of the manifold to be synthesized in certain ways as well as the necessity for a correspondence between the appearance and the intelligible. In the Transcendental Aesthetic alone, Kant could speak without activity because he was explaining only the transcendental conditions for the possibility of a single manifold of sensibility. The Transcendental Logic, with its development of the understanding, is instead concerned with necessary connections between appearances and as such needs to explain, stated abruptly, not the homogenous but the heterogenous.

As Kant states, "Since every appearance contains a manifold, thus different perceptions by themselves are encountered dispersed and separate in the mind, a combination of them, which they cannot have in sense itself, is therefore necessary."¹⁴ What within sensibility alone, as a merely receptive faculty, however, could provide for the understanding appearances of outer objects which include disparate manifolds? How could a pure intuition of space, as it was demonstrated as a singular, infinitely extended manifold, produce for itself limitations and boundaries? It must be an inclusion of an a priori possibility for the receptivity of not just spatialality, but the activity within this spatiality. For it should be remarked, in the realm of appearance, that which appears as appearance would not represent to the understanding, in whatever form of perception tasked with representation, itself as having anything belonging to it not included in its intelligible activity. It is not that our perceived form of this force, matter as ideal, as argued by Kant, represents to us faithfully the reality behind such activity.

For example: that the apple drops to the Earth is not, as appearance, immediately representing to us the reality behind this activity and we are not privy to something like an immediate cognition the extent of the gravitational field's influence over the object (and whatever might potentially exist beyond gravity as engendering that activity, and so on and so on...) but such an appearance does always suggest to a necessary activity behind the appearance. This activity, as representative of a reformulation of a critical idealism's separation of the real from the ideal, could be criticized as having just as many positive conclusions as Kant's aprioric forms of Space and Time alone. But Activity has at least immanently going for it the possibility for a transcendental explanation for the possibility of individuated will and identity Consider that Kant himself, in the third Critique of Judgement, found it necessary to include an a aprioric conception of telos for the reflective judgement to define for Judgement its necessity as it corresponds particular purpose to individuated objects. Perhaps this points at least to a partial correctness of the above critique.