Chapter 5: The Sensible Conditions of Human Knowledge
This was a long and dense chapter, though rewarding in its contents. I have separated the summary into sections to better organize and connect the arguments.
Summary:
Kant lists three exhaustive possibilities regarding the ontological status of space and time. They are the absolutistic, relational and critical positions, advocated by Newton, Leibniz and Kant, respectively. The chief concern of the Transcendental Aesthetic is to demonstrate the truth of the critical position (the transcendental ideality of space), and Kant goes about doing so by showing that space and time are a priori intuitions. Allison chooses to focus on Kant’s arguments for space, as they are generally in parallel with those of time.
The a priority of space
Kant says:
“Space is not an empirical concept which has been derived from outer experiences. For in order that certain sensations be referred to something outside me (that is, to something in another region of space from that in which I find myself), and similarly in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space must be presupposed. The representation of space cannot, therefore, be empirically obtained from the relations of outer experience. On the contrary, this outer experience is itself possible at all only through that representation. — Kant
Space is a necessary a priori representation, which underlies all outer intuitions. We can never represent to ourselves the absence of space, though we can quite well think it as empty of objects. It must therefore be regarded as the condition of the possibility of appearances, and not as a determination dependent upon them. It is an a priori representation, which necessarily underlies outer experience.”
Allison believes that these are two separate arguments that aim to establish the apriority of space, but that the second argument is much stronger than the first.
The first argument for the apriority of space: distinguishing objects from themselves and the self
Kant is arguing here that objects are only apprehensible by humans as distinct both from themselves and from the self if they are represented in space; this representation cannot be empirical (a posteriori, it cannot precede that which it makes possible), so it must be a priori.
This argument contains two presuppositions: that the representation of space is necessary in order for humans to refer to sensations external to themselves, and that it is also needed for humans to apprehend objects as external to each other. By the term “outer sense”, Kant means a sense through which one can become perceptually aware of objects as distinct from oneself; and by the term “inner sense”, he means a sense through which one can become perceptually aware of oneself and one’s states. Space as the condition of outer sense is not taken to be a logical necessity. Kant is not stating a tautology when he claims that space is the conditions for the possibility of outer sense, because space is not the only conceivable way of doing so - but it is this way for humans.
Similarly, when Kant says that space is the condition for the possibility of distinguishing objects from one another, he is not making a tautology. For humans to distinguish objects, these objects need to not only be qualitatively different but also numerically different; they need to reside in different places in space. But it need not be the case there are no other forms of distinguishing objects from one another that are nonspatial. Spatiality is the means in which humans distinguish objects from one another; these are not identical!
Some have objected by arguing that Kant ignores the possibility that space is an empirical representation which is mutually conditioned by other empirical representations; in other words, space could be derived as an abstraction from a complete concept of it and other empirical representations. But this misses the thrust of Kant’s argument: it is not merely that we cannot have representations of things without the representation of space, but that space operates as the underlying means in which these representations are apprehended. Furthermore, it is also the case that the awareness of the distinctness of objects from one another is a condition for the representation of space, for that is putting the cart before the horse. Space must not simply be concurrent, but also prior, to the representation of objects.
The second argument for the apriority of space: conceiving space as empty of objects
In the second argument, Kant says that since we can conceive of space as empty of objects, but that we cannot conceive of objects without space, it must be that space be considered as a condition for the appearances of these objects, and not simply a determination of them. Space is prior to the apprehension of distinct objects, and functions as a condition of doing so. And again, it is not a logical condition, nor is it a psychological condition (as in, it just happens to be the case that humans are unable to remove space from appearances); it is an epistemic condition for the possibility of representing distinct objects. It is through representing appearances as spatial that we represent them as “outer” - as distinct from ourselves (and also from each other). If space were to be removed, there would be no sensibility.
Space as an intuition
Kant’s arguments for the a priority of space have been covered. Allison then takes on Kant’s arguments for space as an intuition. There are two arguments, the second of which was completely re-done in another version. Allison focuses on the second of the second argument.
The first argument for space as an intuition: space is a totum analyticum; so it is not a concept
The first intuition argument assumes the exhaustive nature of the concept-intuition distinction, and goes about demonstrating that space cannot be a concept, and so consequently it must be an intuition. Kant claims that we can only ever represent to ourselves one space, which all places are parts of. However, space is not just a totality, or an aggregate of places. The parts of a totality are logically prior to the whole; this is the case in general for the marks of a concept. But the parts of space are only given in and through a single unified space. In other words, space is a totum analyticum. Since the parts do not precede the whole, as is the case with concepts, this means that space must be an intuition.
The second argument for space as an intuition: space has infinite intension; so it is not a concept
The second intuition argument assumes that space is represented as an infinite given magnitude and takes this to be conclusive that it is an intuition. In the process of explaining the second version of this argument (the first is quickly dismissed), Kant also further explains the differences between concepts and intuitions.
A concept has a complex logical form that involves both extension and intension. Extensionally, every concept has other concepts under it, arranged hierarchically in terms of generality, with each lower species of concept introducing new differences. Intensionally, every concept contains other concepts within it as component parts; this is the inverse as extension, as the lower species of concepts with greater differentia contain the higher concepts within themselves.
Compare this with an intuition, which is a representation of an individual. All parts of an intuition are contained within and presuppose the whole. Intuitions are divided by limitation, not differentia. Recall how this is also how a totum analyticum is structured.
The second argument uses these structures to illustrate how concepts and intuitions involve infinity. Concepts handle infinity with respect to its extension; there can be an indefinite number of concepts falling underneath it. Intuitions handle infinity with respect to intention; they can have an infinite number of parts within it, coexisting. Allison says that concepts cannot have infinite intension because such an infinite concept could not be grasped by the human mind. And space is given as an infinite collection of parts, just as an intuition is.
If this is the case though, does this contradict what Kant has to say in the Antinomies about the infinity of the world in space and time? Allison thinks there are different notions of infinity at play here. Space is always represented as being bounded by more of the same; there is a limitless progression of an all-encompassing space. This part of the text was a bit obscure, but if I am understanding correctly, the key point here is that space (and time) are tota analytica, but a world-totality is a totum syntheticum; space is divided into parts, while a world-totality is build up from its parts.
Given-ness, and the different species of intuition
Allison moves on to Kant’s notion of “given-ness”, as when Kant claims that “space is represented as an infinite given magnitude.” Kant uses the term “pure manifold” to describe the preconceptual framework that guides and limits human cognition. Space is never perceived as limitless, but rather spatial regions are perceived under the “pre-intuition” that they are parts of a limitless space. As an example, Allison quotes Schulze who illustrates how, in order to draw a line from one point to another, there must already be a space in which to draw it. It is this space that Kant calls a pure manifold.
In a very dense series of paragraphs, Allison explains how there are three different senses of the term “pure intuition”. There is a “formal intuition”, which is a determinate (conceptualized) pure intuition; there is also a “form of intuition”, which is an indeterminate (unconceptualized) pure intuition. The latter can either be the manner of intuiting, or it can be the essential structure (form) of that which is intuited.
So there is a form of the intuited, a form of intuiting and a formal intuition. A given, infinite, single and all-inclusive space which contains within it the manifold of spaces cannot be simply the capacity to intuit spatially, nor can it be a formal intuition (as it is not represented as an object); it must be the form of the intuited. Kant says:
“Space, represented as object (as we are required to do in geometry), contains more than mere form of intuition; it also contains [gives/supplies] combination of the manifold, given according to the form of sensibility, in an intuitive representation, so that the form of intuition gives only the manifold, the formal intuition gives the unity of representation.” — Kant
A crucial point raised by Allison is that a formal intuition (a determinate pure intuition of universal and necessary features of objects qua intuited) is a hybrid that requires both the form of intuition and a concept by means of which this form is determined.
Geometry and Incongruent Parts
Kant’s discussion of geometry is often taken to be the primary argument for the transcendental ideality of space, but Allison believes this is false. The discussion is brief, for nothing in Allison’s argument depends on this aspect of Kant’s thought. Geometry is taken to be a body of synthetic a priori propositions; from this, Kant concludes that this can only be explained if the representation of space is an a priori intuition, and therefore that space itself is transcendentally ideal and the form of outer sense.
Two points are raised by Allison. One, that the transcendental ideality of space is a necessary but not sufficient condition of geometry being a synthetic a priori science; in which case, if the latter is false, the former need not be; and two, the argument gets its to conclusion only by means of the a priori and intuitive nature of the representation of space; so if this can be established by other means (such as the arguments made earlier in this chapter), the argument from geometry can be bypassed. The most the geometry argument can prove is that the representation of space is an a priori intuition; that space itself is transcendentally ideal must be proven in other ways.
The “paradox of incongruent counterparts” is roughly that there are objects which are qualitatively identical but yet cannot be substituted for one another because they are different in their external relations, such as spherical triangles. I confess that I read this particular section no less than five times and I still don’t fully understand it. Regardless, Allison believes it is not a strong argument for Kant’s position.
Ontological conclusions
It is towards the end of the chapter that Allison moves to the overall argument Kant makes for the transcendental ideality of space. Before, it was focused on the nature of the representation of space (as an a priori intuition), but now it shifts to the ontological status of space itself (given that the representation of space is an a priori intuition). Kant draws two conclusions, and then claims that space is empirically real and transcendentally ideal.
The first ontological conclusion entailed from the representation of space as an a priori intuition: space is not a property of things in themselves
The first conclusion is that space does not represent any property of things in themselves (in the transcendental sense), nor in their relations to one another. This means that the representation of space, which was established to be an a priori intuition, does not contain any properties that can be predicated of things when they are considered apart from the subjective conditions of human intuition. Kant asserts (though without any justification) that no determination of an object can be intuited prior to the existence of this object and so therefore none can be intuited a priori.
The second ontological conclusion entailed from the representation of space as an a priori intuition: space is a condition of sensibility
Kant’s second conclusion is that space is nothing but the form of all appearances of outer sense; it is the subjective condition of sensibility under which outer intuition is possible for humans.
The transcendental ideality of space
From these two conclusions, Kant draws the third conclusion of the transcendental ideality of space:
“It is, therefore, solely from the human standpoint that we can speak of space, of extended things, etc. If we depart from the subjective condition under which alone we can have outer intuition, namely, liability to be affected by objects, the representation of space stands for nothing whatsoever. This predicate can be ascribed to things only insofar as they appear to us, that is, only to objects of sensibility.” — Kant
From this it can be garnered that Kant believes that spatial predicates are limited to appearances, the objects of sensibility, and cannot be applied to the things in themselves. The empirical reality of space comes from that notion that these predicates are applicable to these outer appearances, and so can be considered objectively real in the empirical sense. The empirical reality thesis is easy to make, but the transcendental ideality thesis is more difficult. Allison says that it is hard to find such an argument, but he endeavors to show that the transcendental ideality of space can be derived from the a priori and intuitive nature of its representation.
A priori intuitions are possible only if they are forms of sensibility and thus transcendentally ideal
To start, Allison points out that since concepts cannot be related immediately to objects, they can be formed independently of any experience of them. We can even think of concepts to which no object corresponds to, which is why we can think (but not know) the thing-in-itself. An intuition, on the other hand, is immediately related to the object in which it (re)presents to the mind. The problem of an a priori intuition is to explain how it is possible for an intuition to have nonempirical content, to not have content derived from the affections of an object? This would be impossible if the intuition presented things as they are in themselves, and not just for a priori intuitions but for empirical intuitions as well. But Kant is focused on a priori intuitions; by rejecting the aforementioned notion that a priori intuitions can have nonempirical content corresponding to things-in-themselves, it stands that these intuitions must contain nothing but the form of sensibility which predates all the actual empirical intuitions given from the affections of objects. An a priori intuition is possible if and only iff it presents to the mind a form of its own sensibility.
Allison says there are two steps to the overall argument: that an a priori intuition is possible if it contains a form of sensibility, and that such an intuition is possible only if it does this.
The first component of the argument for the transcendental ideality of space: an a priori intuition is possible if it contains a form of sensibility
To analyze the first component, Allison defines a few terms, as what Kant means by “form of sensibility” is not straightforward. “Appearance” is an ontologically neutral term, which refers to an object that is given in experience (contrasted with those that are merely conceived). “Form” means condition”, and “matter” means that which is conditioned by a form. A “form of appearance” is a feature of an appearance in virtue of which its elements are related to one another; the representation of space functions as a form in this sense.
Recall that “form of intuition” can refer to either the formal structure of intuited objects, or the mode in which these objects are intuited. The former sense is equivalent to a form of appearance, but the latter is inherently subjective and related to the mind’s receptive capacity.
“Form of sensibility” can also be taken in two ways, both having references to mind. It can either be a form of sensibly intuiting (sometimes called a form of receptivity), or a form of objects qua sensibly intuited. Allison refers to these as forms of sensibility(1) and forms of sensibility(2). In claiming that a form of appearances (intuited objects) is a form of sensibility(2), Kant is also claiming that it pertains to these objects in virtue of the mind’s form of sensibility(1). Thus the first step in Kant’s overall argument here is saying that, if an intuition is a form of sensibility(2), then this is due to the form of sensibility(1), which in turn entails that the intuition must be both a priori (as it is necessary and universal for all subjects with the same form of sensibility(1)) and pure (as its source is not in any sensible data). Therefore, if we assume that the representation of space is a form of sensibility(2), then it is a pure a priori intuition.
The second component of the argument for the transcendental ideality of space: an a priori intuition is possible only if it contains a form of sensibility
The second step is more complicated than the first. Broadly construed, the only other alternatives for the possibility of an a priori intuition are the Newtonian and Leibnizian positions. Kant’s argument seems actually mostly compatible with the Newtonian absolutist view of space. Indeed, why can’t space (and time) be transcendentally real and the form of experience of transcendentally real things rather than just mere appearance? Yet Kant explicitly rejects the Newtonian view when he says that “space does not represent any property of things in themselves,” and any a priori intuition of a thing in itself.
Kant believes that the Newtonian theory is incapable of accounting for the possibility that the representation of space functions as a form of human experience; in other words, taking space to be an ontological condition of objects is incompatible with it being an epistemic condition of them. Excluding the Kantian position that space is a form of sensibility, there are two alternatives: that we have an innate idea of space that exists in a “pre-established harmony” with the real space, or that the idea of space is derived from the experience of real space. The first alternative is ad hoc, while the second denies that space can function as a condition of the possibility of the experience of objects. There is a contradiction involved with the notion that the representation of a condition can have its source in that which is conditioned.
Ultimately, the question of how an a priori intuition is possible is actually equivalent to the question of how the representation of space can function as a condition of sensibility. Therefore, everything rests on Kant’s claim that the representation of space functions as a form of human experience.
The “neglected alternative”: could space be both a form of sensibility and a thing-in-itself?
But might it be the case that space is a form of human sensibility but that it is also a corresponding feature of things-in-themselves? How can Kant hold that things-in-themselves are unknowable, but simultaneously hold that they are not spatial? This is known as the “neglected alternative”, which has been assumed to have been ignored by Kant. Of course, the Antinomies could be used to justify Kant’s position, though as we have seen they are not very strong.
Allison notes, however, that while space as a form of sensibility(2) is inherently subjective and so thus the numerical identity of this form with a real space is impossible, qualitative similarity is also empty of any meaning. It is not as the “colored spectacles” analogy claims it to be, where space is akin to pink-colored glasses in a world that happens to also be pink in-itself. If Kant is correct when he says that space is a form of sensibility, then spatiality simply is not a predicate that one can meaningfully apply to things-in-themselves.