The Aesthetic versus The Axioms, a Contradiction?

by Philip McPherson Rudisill

Written sometime before August 2, 2000
and slightly edited on January 24, 2017

In the Aesthetic of the Critique of Pure Reason Immanuel Kant asserts that time and space are pure envisagements,* and means with that (among other things) that our concept of each is based on a single and immediate sighting such that all parts of space and time are seen as mere limitations of, and contained in, these two “infinite givens.” For example and by looking in a slightly cross-eyed fashion, I spy the space of the entryway to my room when the door is open, i.e., an invisible and imaginary plane “hanging” between the inside edges of the door frame. That entryway plane is a determined space and I have to scan it to take it all in and “size it up” and see its shape and comprehend its boundaries. But when I pay attention to the context of this plane I see immediately that it is merely a portion or, as Kant likes to put it, a limitation of the all-embracing space which surrounds and permeates it and myself. Likewise any determined time, e.g., the time of a movement through that space, i.e., an entering into or exiting out of my room, is already and immediately seen merely as a division of infinite, given and all-encompassing time. In a word: space and time are each counted as infinite, and nevertheless also given, i.e., an infinite whole, and it is by virtue of these wholes that any part, i.e., any determined space and time, first becomes possible as a part or limitation; with respect to space and time the part is a function of, and follows upon, the whole and any determined space or time is seen as a division of the whole.**

* Anschauung, or at-look or on-look or viewing or take. In German the term suggests something which is very subjective, and yet which appears as a fact and non-imaginary to a viewer. A good example is the face in the cloud which one person may see very clearly and yet which may escape another completely. The face, we know, is a product of our imagination in configuring the textures and contours of the cloud, but the face that appears is quite pronounced and it is not merely imagination, i.e., we actually do see a face, albeit not a face of flesh, and indeed much as we see a face in an oil painting. One person looks at a tree lying down near a stream and says, “at first I thought that were an alligator”, and that would be his viewing/anschauung, i.e., his way of looking at that object. Now to say that space and time are viewings suggests that it is possible to look at things without the notion of space and time ever arising, for example: I might notice that things get larger and smaller (as a percentage of my visual field) without ever noticing that they are also getting closer and further away, respectively.

** In the first of his four points in his so-called Metaphysical Exposition of space,*** Kant notes that it is impossible to perceive that one thing is apart from and next to the viewer or another object, i.e., such information is not given through experience, but rather the representation of space must precede in order for such spatial relationships to be noticed, for it is not in the object that things are next to each other, but only in the looking at the objects, i.e., in the viewing. Hence if I am asked to discern a difference between two objects, e.g., the two letters, A and B, then the fact that A precedes B in this sentence is a way of looking at them, and not contained in them themselves or their relationship to each other on their own. Therefore I may examine them very closely and notice that one has more curves than the other or one a more narrow top, and yet I may very well not notice this spatial relationship of precedence in the sentence; however once this is called to my attention, then I see this relationship quite readily and realize that it was there all along, only I was not paying attention to it. Likewise, once it is pointed out to me, I could also tell that A is closer to the word “objects” in the sentence above, and that B is closer to the “d” of the word “and” which separates them, etc., all of which are ways of looking at A and B in their environment, and are not contained in A and B on their own. All of this is a long introduction to saying simply that I can spy a space, e.g., that occupied by a sofa, and not pay any attention to the context of this space, but once it is brought to my attention, then I see that this space, this sofa, is “drenched” in, and totally encapsulated by, space. It is like seeing a face in a cloud after trying for sometime; once sighted, it is clear that the face was "in" the cloud all along, only we were not looking right before (or so goes the common talk).

*** These are presented in a summary fashion in the appendix to this essay.

And yet in the Analytic of that same critique, in the section on Axioms of Viewings, Kant asserts what seems to be the diametric opposite of this thesis that he has expounded in the Aesthetic. For here in the Analytic he proclaims that all viewings (which would include time and space) are extensive magnitudes, and as such the parts must first be successively apprehended in order to arrive at any whole, i.e., the whole is a function of the part, as the following statement from the Axioms states very clearly:

“With respect to form, all appearances* contain an viewing in space and time which lies a priori to them all together as their foundation. Therefore they cannot be apprehended, i.e., taken up into an empirical consciousness, in any other way except through the synthesis of the manifold whereby representations of a determined space or time are generated.”**

* Erscheinung, that which "shines forth", the object of the empirical viewing, e.g., a face in a cloud or a face on the front of a human head.

** The Axioms, first paragraph, first two sentences. The clear implication is that it is impossible to determine a space or time without this successive apprehension.

And so we have the Aesthetic telling us that with space and time the whole makes possible the part and that the part is always seen in the whole as a subdivision of that whole; and then in the Axioms we hear that any determined space and time must be accumulated gradually and thus that the part precedes and first makes possible the whole.

Now the reconciliation of this apparent conflict has to do with the notion of determination. A determined space or time (Axioms) is a time or space which is both finite and explored, i.e., its boundaries have been discovered and established. Any division of space and time is a space or a time. Space and time as objects themselves (Aesthetic) are infinite and their boundaries have not been established, nor can they be, for there are no boundaries to the infinite.

In the Axioms, the references regarding space and time are all to “determined times and spaces” or to the “determination of time and space in general.” Therefore all determined times and spaces are finite divisions of the all-embracing time and space which are the infinite givens, for infinite space and time cannot be determined. Kant puts this very clearly in the Aesthetic, namely:

“The infinitude of time means nothing more than all determined quantities of time are merely limitations of one time lying as their basis.”*

* The Aesthetic, Section 4, fifth paragraph, first sentence (CPR.4.5.1). Emphasis added. Although he does not say the exact same thing with regard to space, the general tenor of the Aesthetic indicates clearly that this holds also of space.

We can conclude therefore: there is no contradiction in Kant’s thinking with regard to space and time between the Aesthetic and the Axioms. In the Aesthetic Kant is speaking of space and time as single viewings and infinite givens, where the representation of the whole (of space and time) makes possible the representation of any part (of space and time), i.e., the part is seen by virtue of the whole as a limitation of that whole; and in the Axioms he is speaking of space and time as determinations and thus of finite objects, where the representation of the summation of the parts makes possible the representation of the whole (of a determined whole, whereof the boundaries are being established, but which [again per the Aesthetic] is still seen merely as a part and limitation of the infinite givens).

Turning now to a different section (B version of the Transcendental Deduction of the Categories, Section 26 and paragraph 3), but in a related matter Kant speaks to the unity of space and time and asserts that space and time are not only the forms of viewing/looking whereby (and indeed only whereby) a manifold is provided, but that they are viewings themselves which contain a manifold in themselves. Furthermore (and in a footnote to this paragraph) he explains that while space and time, as objects, require a synthesis, the unity of their respective representation is contained in the looking/viewing itself, with the understanding merely determining the sensitivity. In order to clarify this rather cryptic passage I will make use of an object that I will call an infinite line, namely: a straight line, each part of which is the second of three equal parts of a part of which. Now when I seek an image of this, I imagine a line of undetermined length, and I select any length of that line and call that Part B. Then, following the definition/rule, I let B be the second of three equal parts, namely A, B and C, and see that these together form a length which I will call Part B2.* At this point I don’t need to go further, for I see already that the synthesis cannot be completed in any time, but that in fact it is complete, for I see that Part B2 stands in the same relationship to the infinite line as Part B does, namely it is a part (and so in turn the second of two equal parts, etc.). Now it is in the constructed image that I spy this unity, and it is the understanding which tells me that I need go no further, and that nothing else would be added by continuing the construction, for I have grasped the pattern and have essentially completed the synthesis, or rather: I see that it is complete even if it cannot be completed in any length of time. If I were unable to picture this line (as would be the case with someone born and remaining blind), then the understanding would have no basis for any recognition of the infinitude of the pattern, for there is no end to the Bs, i.e., B, B2, B3, B4, etc., and so while I would be dealing with an increasing length, there would no end in sight which would call upon me to declare a completion in accordance with the category of total. And so it is in the viewing of the line itself (as constructed in my imagination) that I can see the pattern which then I can grasp to be such that the line is infinite.** ***

* This recognition of Part B is the recognition of a determined length and as such is a product of the procedure dictated by the Axioms of Viewing, namely the gradual apprehension of the parts reaching out to the entire length, which is seen then as complete by virtue of being finite. Hence we can say that the Axioms of Viewing serve for the determination of any finite expanse of time or space.

** Although it is beyond the scope of this discussion, Kant utilizes the respective unity of space and time to assert (TDB.26.3) that a manifold given in space and/or time is seen as an “overlay” of this unity of the space and time through which the manifold is given as such, and it is by virtue of this unity that the category comes into play as the prompt to a discovery of the connection which gives this manifold a unity to correspond to the merely spatial and temporal unity contained in the viewing. The spatial and temporal unity might be called a provisional unity or a potential unity, for it is only through the connection by means of the category of the understanding of the manifold sighted and apprehended in the precedingly unified space and time that an actual unity arises which entails necessity. For example (and using Kant’s own example in TDB.26.4) I notice the manifold of a house in a spatial viewing as a singularity (albeit only provisionally), and then, in order to transform this empirical viewing/looking into a perception, I peruse and apprehend the manifold in this viewing, e.g., the siding, the windows, the roof, etc., and reach a completion at the boundaries of the appearance (the viewed house), and this apprehension is driven and hence made possible by the category of quantity or total. And so in this wise Kant will prove that the category is necessary in order for any perception to arise, a perception being a careful apprehension of an empirical manifold for the sake of determining that manifold.

*** In a like manner it is only possible through sight to recognize the infinitude to the pattern of the Arabic numerals, e.g., 1 2 3 . . . 8 9 10 11 12 13 . . . 18 19 20 21 22 23 . . . 99 100 101, etc., for it would be impossible for this to occur in listening merely to the spoken names, e.g., ten eleven twelve.

Summary

As a summary we can say with Kant that

1. any determined space or time requires a synthesis from part to part such that the whole arises through the accumulation of these parts and with an expression of the completion of that accumulation being made possible by the category,* e.g., in the recognition of a determined part of a line which is itself as of yet of undetermined length (which is the thesis of the Axioms of Viewing); and

* And indeed the accumulation itself is prompted and made possible by the category, but, again, which is incidental to our subject at hand.

2. any determined space or time is already seen as a division and mere limitation of an all-embracing and all-encompassing space and time as infinite givens, even as the determined part of the line is seen as a mere section of the line which is always (visually) of greater length than any determined part; and

3. infinite time and space, as infinite givens, call for a synthesis, but not such that a category is needed, but rather one whereof the infinitude and the unity is sighted immediately in a pure viewing which is exemplified by the imaginary infinite line pictured in mind and which is grasped by the understanding in a recognition of a determined pattern arising from the definition which serves as a rule for construction.

And we can now conclude more generally from this that Kant has in mind a unified theory of space and time which is not marred by a contradiction. The distinction is a space or a time, as a determined space or time, as compared with space and time as infinite givens.

Appendix

Summary Presentation of the Four Arguments of the Metaphysical Exposition of the Concept of Space
from the Aesthetic of the Critique of Pure Reason

Kant's purpose in the Metaphysical Exposition is to prove that the terms of space cannot have arisen from any experience, and so would have to be considered as entirely a priori. Only the exposition with regard to space is presented here, although there is another exposition to accomplish the same thing with regard to time, and which parallels that of space very closely.

1. The spatial terms would be utterly meaningless if we tried to derive them from empirical exposure, for the fact that something is apart from me or from other things is not contained in any way in the vision of that something, but only in the way that I look at that vision.

2. All empirically conditioned objects are such that I can negate them in my imagination; but I cannot do this with space, i.e., I cannot imagine the absence of space; and so therefore, etc.

3. Empirical concepts are developed by comparing two or three things and attending to what is common and dismissing what is different. Thus I see this thing called Tree and that thing called Tree and am puzzled because they are different, and then I look more closely and see that they both have trunks and branches and leaves and so take the term Tree, which heretofore I had been treating as a proper noun, and reducing it to merely tree which is now a concept, i.e., a rule for the synthesis of a manifold into a determined appearance. But space is not developed in this way at all; we don't see this space and that space and notice that they are different and then look more closely to see the roominess as their common element. Indeed what we call different spaces are really seen merely as partitions or limitations of one and the same all-embracing space. Thus space is not arrived at logically but rather is an immediate and singular representation, and so is a pure viewing.

4. space is seen as an infinite given, which is impossible empirically, for no empirical synthesis can continue to infinity. Now it is true that with empirical concepts we can imagine an infinite count of objects corresponding to, and thus covered by, the concepts, e.g., table, but with space we think quite differently, for there we think of an infinitude of objects as contained within that concept, for all parts of space are merely limitations of this one, all-encompassing space.

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