Arg. for the Subjectivity of Space

2/27/04
Kant Journal 2

The Argument for the Subjectivity of Space

Kant believes that space, as we conceive of it, does not exist outside of our own minds. The shape of perceptions in the human mind are determined by the shape or constitution of that mind. Objects in the world appear to our minds as existing in the context of space simply because the human mind fixes on what is presented to it based on its own form, and one of the forms of human sensibility is space. This creates the 'illusion' of space existing externally in the objective world when really, according to Kant, it is an already-existing pure intuition of the mind which shapes our experience of sensory perception. Kant's most recognized argument for the subjectivity of space, the one that is most nearly acceptable to commentators, is the so-called argument from geometry. In the beginning of The Transcendental Aesthetic, he lays out the defining boundaries of the argument and explains the terms he will be using and exactly what space is and is not in his estimation of things. He then moves on to the structure of the argument itself.
Kant explains that 'space' is "to be regarded as the condition of the possibility of appearances, not as a determination dependent on them, and is an a priori representation that necessarily grounds outer appearances" (B 39, emphasis added). He focuses on geometric principles in particular, explaining that they would be impossible if they were not "grounded in this a priori necessity. For if this representation of space were a concept acquired a posteriori which was drawn out of general outer experience, the first principles of mathematical determination would be nothing but perceptions" (B39). Once this is clearly seen, it makes perfect sense that Kant wants to make "the possibility of geometry as a synthetic a priori cognition comprehensible" in this argument; doing so will have the very implications he wishes to prove for space itself (p.176 emphasis added).
Kant begins by positing geometry as an existing and valid science-- a move no one would dare dispute or even hold a hope of disproving. However in the same breath he describes it as "a science that determines the properties of space synthetically and yet a priori," and though most scholars of his day would have allowed that it did so a priori, most would have denied its synthetic nature (p.176, emphasis added). We can tell that geometrical propositions are gleaned a priori and therefore originate in intuition, Kant says, because they are all "apodictic, i.e. combined with consciousness of their necessity" (B41).
Geometry's synthetic nature is shown in that its principles go beyond the intitial, analytic concepts they begin with in a way that understanding simply cannot achieve singlehandedly (although it certainly plays a part in bringing together the manifold and exposing the relations geometry explores). This going beyond of geometrical judgments can only be achieved through the intuition of space as an infinite individual. Kant holds that space is apprehended through intuition and not through concepts. This is because in the formation of concepts we go from individual instances to universals; this is how we apprehend properties. In pure intuitions, however, we go from an immediate grasp of a universal whole to particular instances. This is how we apprehend individuals. We apprehend space in this way: as a huge, infinite, whole (or individual) of which we grasp only certain faces at any given time. In order to place any of these particular faces, a context must first be given, because without a context they could not exist in our minds at all. Therefore space is an infinite individual.
According to Kant then, geometrical propositions, or judgements, cannot be gained only through concepts. And because such propositions come a priori from out of intuition we see that-- necessarily-- our cognition of space must stem from pure intuition as well. This now more clearly synthetic yet a priori gathering of geometrical knowledge is therefore accomplished by drawing upon and combining both pure sensibility and understanding.
Space is, according to Kant, "merely the form of all appearances of outer sense, i.e., the subjective condition of sensibility, under which alone outer intuition is possible for us" (p.177). There are two parts to sensibility: matter and form. Form can be separated from experience because, although it relies upon experience in terms of original source (i.e. we can only imagine combinations of things which we have had some experience with before), "that within which the sensations can alone be ordered and placed in a certain form cannot itself be in turn sensation" (p. 173). Thus we see that matter is "only given to us a posteriori, but its form must all lie ready for it in the mind a priori, and can therefore be considered separately from all sensation" (p.173). The idea is that pure sensibility, stripped of its experiential trappings is pure intuition, and that it is through this intuition that (as our formal constitution dictates) we are affected by objects. Sensibility, as a part of this formal constitution, "is a necessary condition of all the relations within which objects can be intuited as outside us" (p.177). Sourced in sensibility, this outer intuition 'has its seat in the subject', 'inhabiting [its] mind' (p.176) and enabling it to bring an immediate representation to the subject's understanding of the form of the outer objects (p.177). Sensibility being a necessary condition of all relations simply refers to Kant's original thesis, that without sensibility (the existence of which rests in the human and its subjective standpoint), space would be meaningless. Objects in the world appear to our minds as existing in the context of space simply because the human mind fixes on what is presented to it based on its own form; the shape of perceptions in the human mind are determined by the shape or constitution of that mind. This creates the illusion of space existing externally in the objective world when Kant would say it is an already-existing pure intuition of the mind which shapes our experience of sensory perception. In other words, space is subjective.

I think that the argument Kant makes here for the subjectivity of space is very good, as far as such an argument goes. Yet there are several particularly weak points-- for example, his assumption of Euclidean geometry and his position regarding the necessity of intuition. They seem to sort of sneak in, unproven, taken for granted. I don't believe these weak points are simply weak arguments: I think they are pure assumption. I do, however, feel very daunted by the task of trying to explain something which I found lacking (me!) in the amazing work of such a great mind. Since you ask it, I will attempt it-- and also try to construct possible solutions, given the pieces Kant has provided, to the holes I percieve in my reading of the text. But... please don't expect too much! I am truly embarrassed by this part of the assignment...
I was left rather unsatisfied with his use of geometry as an example of mathematics. The secondary text by Ottfried Höffe helped me incredibly with its explanation about the difference between pure mathematics and applied mathematics. Kant seemed to waver between these though, not making consistent use of them even within the structure of his argument. The distinction proposed by Höffe (62) between the three levels of spatiality (transcendental spatiality, mathematical space, and physical space) was also quite useful in understanding the level where Kant felt himself to be working. "Each of the succeeding levels depends upon the preceding without being derivable from it," Höffe says, further stating that in any case, "mere spatiality is not yet the object of geometry.
This object comes to be only by means of the objectification of spatiality; through imagination and by declaration the mathematician conceives the mere form of intuition as an obejct in its own right with certain structural characteristics, which he studies free from experience in the context of pure geometry. An unbridgeable difference exists between space as a transcendental condition and space as an object of geometry... Mathematical and physical propositions do not have transcendental significance, but only-- on a deeper level-- their conditions, which according to the Copernican revolution lie in the "constitution" of the knowing subject free of all experience" (p.61)
I don't know. I need to think about this more to really have an idea about it. I don't know how to talk about it. But that passage really helped me sort some things out, at least.
Kant's terse proof left me wondering as to other things as well, such as what the reason was for his seeming ignorance of non-Euclidean geometry. It had been discovered already by the time he wrote The Critique of Pure Reason, and I cannot believe that he didn't know about it. In fact Höffe states that he acknowledged it in his treatise Thoughts on the True Estimation of Living Forces (Höffe, 61). So why did he purposively limit his work in this way? It would seem (on sixth or seventh glance, if one tries to reconcile it with his philosophy as a whole), that Kant believes the human mind to have the form of Euclidean geometry and to be unable, therefore, to comprehend in full or make use of any other kind of geometry. If our minds are 'shaped' like Euclidean geometry, so to speak, then we can only pick up, synthesize, and understand that which fits the mold. This sounds somewhat like wishful thinking, but at least it makes the limitation cohere with the rest of his thought.
We theorize a lot about non-Euclidean geometries; mathematicians have explored the idea for years that perhaps we are not limited to Euclid's geometry. I don't know much about the higher levels of mathematics (though they have always fascinated me), but aren't we finding that non-Euclidean geometries do, in fact, have physical applications? This would be a problem, since Kant made no allowances for this in his philosophy. There's no room for it. He admitted that he was not ignorant of the idea, he simply felt that the human mind held the form of Euclidean geometry only, and that it dictated what we were capable of seeing as real. Kant was sort of gnostic about what was 'out there' apart and away from the human standpoint, stating that "since we cannot make the special conditions of sensibility into conditions of the possibility of things, but only of their appearances, we can well say that space comprehends all things that may appear to us externally, but not all things in themselves" (p.177). The only relevant thing to him was what we experience, or intuit directly. But the question now is whether we can really say any longer that the only perceived space is Euclidean space? .... (concl. cut)