My Metaphysical Exposition of Space Cake
by Anaxagoras
1) “For in order for certain sensations to be related to something outside of me…the representation of space must already be their ground.”
[1] When I represent an object as being distinct from me, the concept of being distinct presupposes the idea of objects having diverse spatial location. Likewise, if objects are to be represented as distinct and next to one another, space must be a prerequisite for such a representation to even occur. Therefore, space must be a priori.
2) “Space is a necessary representation, a priori, that is the ground of all outer intuitions”
[2] Space is not a property that can be abstracted from an object like that of color, which can be considered merely by ignoring those other properties. Space is rather the presupposition that is necessary for one to consider or intuit any object at all. Consider the following argument:
All things must be in some place. But it is absurd that space should be in some place. Therefore space is not a thing but rather a condition for things to be intuited.
There is a logical distinction between the thing found in space and the space a thing is found in. For example, consider what proposition is prior, “a thing in space” or “the space the thing is to found in?” One can think of nothing in space, but the negation of the later proposition is impossible, i.e. no space for a thing to be found in. Hence, the space the thing is found in is prior. If space were an empirical concept that could be drawn from experience the thing in space would be prior and then space would be derived from the thing. Since space is prior to any empirical sensation and it is both universally valid and necessary for all things to be found in, it is therefore a priori.
A Critique of Argument (1): When the representation of being distinct is presupposed by a representation of space it does not necessarily follow that it is therefore derived from space and that space is a priori. The alternative may be that both representations are correlative and mutually dependent on each other. For example, a representation A could be presupposed by another representation B and not derived from it. In this case it would not follow that A is a priori. Maas argues that assuming the possibility of representations having a mutual dependence on one another, “the concept A could be obtained only by abstraction form the complete concept AB.”
[3]A Critique of Argument (2): It appears impossible to think of space with nothing in it. To represent space apart from the representation of a thing is merely an act of abstraction. An appeal to the Maass argument would suggest that although “we cannot represent the thing (B) without also representing their order of situation (A), we only arrive at the concept of the latter by an act of abstraction from the complete concept (AB).”
[4] If space is a priori, it should be possible to speak of space (a priori) without making recourse to empirical things (a posteriori). How can a priori concepts be dependent upon a posteriori representations? Since every argument that Kant makes for the a priori condition of space makes reference to objects of experience, it appears that space is not an a priori condition for things to be intuited, but rather it is mutually dependent on and correlative to empirical objects, thus making space a posteriori.
[1] Paul Guyer, trans. Critique of Pure Reason (Cambridge: 1997), B 38.
[2] Paul Guyer, trans. Critique of Pure Reason (Cambridge: 1997), A 24.
[3] Henry E. Allison’s, Kant’s Transcendental Idealism (New Haven: 1983), p. 84.
[4] Henry E. Allison, Kant’s Transcendental Idealism (New Haven: 1983), p. 84.
