O aaruran

The Necessary Conditions of Containment


     In this paper, I will examine Kant’s claim that our representation of space is an inutition. Having established that space is a priori, Kant claims that its representation is not a “discursive or, as is said, general concept of relations of things in general, but a pure intuition” (Kant 175). Beginning with his conception of total space, I will elaborate on its implications regarding all other representations of space. After showing that our representation of total space is necessarily prior to all other representations of it, I will examine Kant’s deduction of space as an intuition. I will conclude with two potential objections.

     Kant’s argument begins with the claim that we can only represent a single space: total space. He argues that when we refer to many spaces, we are only speak of things contained in this total space. Consider a house and its comprising rooms. While each room occupies a specific individual space, all of these spaces are still contained in the space taken by the full house. If this is true, then it must follow that all non-total spaces are contained in total space.

     Now, if one could prove that the representations of non total spaces are prior to the representation of total space, then one could object to Kant’s argumentative thesis. One could claim that total space is a concept derived from the composition of non-total spaces, and thus must not be an intuition. Anticipating this, Kant adds that the representation of total space is necessarily prior to a representation of its contained parts, because its contained parts are “only thought in it” (Kant 175).

     Only total space is boundless; all non-total spaces are bounded. If a space is bounded, then it must have circumscribed limits that dictate the spatial locations that fall within that region of space. Because any bounded space is not total, there must then be spatial locations that do not fall within that region. Hence, by condition of being bounded, all non-total spaces must exclude some spatial locations.

     Yet, if something is not represented, it cannot be excluded. Thus, these excluded spatial locations must be represented. Hence, we must represent another spatial region that contains both the circumscribed region and the excluded spatial points. Now, we know that non-total spaces can be arbitrarily large – that is, anything but boundless – so, we must conclude that we represent total space.

     There must first be a container before anything can be contained in it. I believe this is self-evident; it is also nonsensical to suppose otherwise. Tea cannot be contained in a cup without there first being a cup which could contain the tea. If this is the case, then it follows that the representation of total space is necessarily prior to all other spatial representations. By all other representations of space, I mean all concepts that regard non-total spaces and the concept of total space.

     This is what Kant intends when he subsequently states that total space “is essentially single; the manifold in it, thus also the general concept of spaces in general, rests merely on limitations” (Kant 175) In reference to the earlier potential objection, Kant has shown that the representation of total space is not the composition of non-total spaces. Thus, by proving that the representation of total space – that is, the representation that is not the concept predicated on it – is necessarily prior to all other spatial representations, Kant concludes that all concepts of space must be grounded on an a priori intution of total space.

     In the introduction to the Transcendental Aesthetic, Kant writes, “in 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 is an intuition” (Kant 172). Thus, for Kant to have demonstrated that our representation of total space is an intuition, he has to have shown us that our representation of space fulfills 2 conditions: (1) singularity and (2) immediacy.

     To fulfill (1), Kant must have shown that the representation of total space presents particular object(s). As referenced by the earlier objection, Kant proved that the representation of total space cannot be derived from a group of things i.e. non-total spaces. Hence, the representation of total space does not bear a general feature that holds over a set of objects. If this is the case, then the representation of total space must not be general, and thus, is singular.

     To fulfill (2), Kant must have shown that the representation of total space is not related via another representation. He has proven that all other spatial representations must be mediate to the representation of total space. Yet, an objector can accept this, but still argue that this does not rule out the possibility that our representation of total space is still mediate to another representation. For such a claim to hold, (s)he must prove that the representation of total space derives from a representation that does not regard space. However, this is inconcievable. It is nonsensical to hold that one could derive a representation of total space from another representation that is independent of it. Hence, the representation of total space must be immediate.

     Not only does his argument meet the conditions of an inutition, but also I find his consideration of all non-total spaces as being thought in total space to be quite keen. Recall that the representation of any non-total spatial region necessitates the representation of a spatial region that contains it and its excluded points. I argued that since non-total spaces can be arbitrarily large, it must follow that the representation of total space contains any representation of a non-total space.

     An objector may claim that regardless of how arbitrarily large a non-total space W is, it is not represented in total space, but rather in a non-total space X that contains W and some spatial locations that W excludes. If this is so, then the representation of X can be thought in the representation of W. It would follow that the representation of total space is not necessarily prior to the representation of all non-total spaces. Rather, only the representation of a non-total space that contains the the non-total space we are considering as well as some of its excluded spatial locations is necessarily prior.

     Yet, we can turn the table and ask that if X is bounded – as it must be since it is non-total – then what circumscribes its limits? Dogmatic in his/her ways, (s)he will claim that it is only some non-total space Y that contains X and some of its excluded spatial locations. But then we can again ask: If Y is bounded – as it must be since it is non-total – then what circumscribes its limits? Like a true dogmatist, (s)he will claim – this time, hopefully a bit more hesitantly – that it is only some non-total space Z that contains Y and some of its excluded spatial locations. But then we can again ask that if Z is bounded…

     This will repeat ad infinitum until the dogmatic objector realizes that (s)he cannot legitimately circumscribe a non-total space unless it is represented in total space. Hence, we still arrive at Kant’s conclusion.

     Another objecter might model an argument off of the Cartesian plane. In the paradigmatic (x,y) coordinate system, we represent both axes with perpendicular lines and have a grid that corresponds to each pair of coordinates. At the poles of each axis, we draw arrows to illustrate that each axis extends infinitely. Both the dashes on the page and the area the coodinate plane takes up is all finite. Yet, the what is drawn on the page models infinite 2D space.

     This objector will agree that non-total spaces can only be represented within boundless space. Yet, (s)he will argue that this does not entail that our prior representation – the representation in which non-total spaces are thought in – must itself be boundless. Instead, this prior representation can model boundless in the same sense that the Cartesian plane models infinite 2D space, while also being bounded in the same sense the Cartesian plane is created in finitie space with finite scratches on the page. In this sense, we are not representing total space, but rather, a non-total space that can be extended.

     While an interesting effort, Kant would object to this for two reasons. First, in the way that we have been considering it, space cannot be extended. In our implicit definition, all spaces either contain a smaller space or are contained in a larger space. They cannot stretch; they cannot shrink. Also, Kant would argue that this mimics the earliest objector’s claim that total space is a concept derived from non-total spaces. Even though the Cartesian plane finitely models infinite 2D space, it is still predicated on the representation of the totality of 2D space. Therefore, regardless of whatever way one can think of mapping the coordinate plane to the representation of non-total spaces, it will still entail that total space is represented prior.

     In conclusion, I have elaborated on Kant’s argument that our representation of space is an intuition. After considering what he meant by total space, I have shown that it cannot be constructed through composition of non-total spaces. In doing so, I have shown that the representation of total space is necessarily prior to all other representations of space. To substantiate this claim, I considered singularity and immediacy, and showed that Kant’s argument does indeed satisfy these conditions. Already finding Kant’s argument to be sufficient, I then considered two possible objections and showed that Kant’s arguments still hold in light of their concerns.


Works Cited


     Kant, Immanuel. Critique of Pure Reason. Ed. Paul Guyer and Allen W. Wood. Cambridge: Cambridge UP, 1998. Print.