In Defense of Kant's View
of Space and Time

Kant, as I understand him, did not hold that space and time were not real properties of objective reality. It is controversial just what he meant in terms of the objectivity of space and time; but the idea that he meant to say that they are merely the mind's means of organizing experience, having no reality outside of the mind, I believe is untenable, given his twin assertion that the mind's activity produces objectivity itself. Of course, just what Kant meant to say is a matter of controversy, and I will attempt no exegesis here. But I will assume for my purposes in this essay that what Kant meant to say is that necessary logic applies not only internally to the mind's organizing of "relations of ideas" (in Hume's terminology); but that necessary logic is integral to the fundamental empirical forms in which experience is given us. That there is logical necessity bound up in the outer world of perception is the fundamental thesis of the rationalist; and I will give Kant the credit for holding that, in space and time--the fundamental structures of empirical experience--there is indeed logical (and not merely physical) necessity. Space and time are the fundamental dimensions that bring along with their very concepts logical necessity, necessity which applies to all experience insofar as it comes in the form of dimensions. This logical necessity in space is what allows Euclidean geometry to be logically necessary, while at the same time it is over and beyond the fundamental rule of logic that there be no contradictions.

But let us illustrate that logical necessity demands there be not only three dimensions (and a fourth, time); let us demonstrate that while we can never experience an object of two dimensions, a priori logic demands us to hold that, in the realm of experience, there are indeed planes of two dimensions, one dimension, and so on.

Take a music CD case. Obviously we experience it in three dimensions. In fact, it is impossible to imagine an object existing in the mind's eye, or even see one, of two dimensions (having surface area but zero depth or thickness). And yet, that three-dimensional CD case terminates at a certain point; it has limits.

Let us consider its "surface limit", then. The square of plastic has a thickness in our experience, that is, extends in three dimensions. But what about its absolute edge? What about the surface in which that CD case finds its termination?--for it obviously terminates at some point. Well, let us consider the area where it terminates. Either that area is of two dimensions, or three. Either the area where the CD case ceases and the air begins has a depth and thickness, or it does not. If it has a depth or thickness, then we have already supposed that it "goes beyond" its termination to some degree. If "the termination of the CD case" itself has thickness, that is, has three dimensions, it is by definition not where the CD case terminates; having thickness itself, the plane of termination must go beyond the termination to some degree. And so on forever; finally we must hold that there is, and must be, a terminating plane of the CD case that has zero thickness, is absolutely of two dimensions and not three. Otherwise, in a similar vein to a Zeno puzzle, we must constantly take the thickness of the "terminating plane" (if we always suppose it has a thickness), and consider how it goes yet farther than its termination, plane by plane, forever. We find that the terminating plane we consider must not have any thickness at all, or we shall go on forever supposing its termination goes just a tad beyond its termination.

Similar puzzles have been used to show that it is impossible to cogitate an "edge" to outer space or the universe; as soon as we suppose an edge, that edge must have thickness and go beyond itself a tad, and a tad more considering that tad; and so on forever. But if we just consider the limits of any empirical object (such as the square CD case), we end up with the same paradox that it goes on in space forever, so long as it has no terminating plane of absolutely zero thickness itself; that is, a two-dimensional plane.

So much for two dimensions: we have shown that, while it is impossible to perceive a thing in reality that has zero thickness but length and breadth, such two-dimensional planes must be assumed to exist for even three-dimensional experience to happen. Two-dimensional objects are never experienced by us, but they are necessitated to exist if we are to experience things like the CD case in three dimensions. Unless there is a termination of the CD case of zero depth--but which still is in fact part of the CD case--we could never experience that CD case as a limited thing at all.

A similar argument will do for one and zero dimensions. Take that two-dimensional plane which we must suppose is where the square of the CD case terminates; obviously this two-dimensional square it has a left edge, of zero (one-dimensional, this time) breadth--a line, of geometrical definition, where that edge terminates without "going beyond itself" to the left to any degree at all. For if it does stretch out to the left to any degree, we may consider in turn this "part that goes beyond". Without an absolute termination of one dimension, it will go beyond itself again and again, no matter how many "absolute edges" we consider, and thus never end.

Thus far we have dealt with two- and one-dimensional realities, and have come to the conclusion that a priori reason requires two- and one-dimensional realities for the three-dimensional world we indeed experience to be experienced by us. But we can never experience two- and one-dimension objects. We may look at a painting and suppose it is two-dimensional, but does anyone suppose it is possible to see a painting so thin it has height and breadth but zero depth? Of course, it is at least theoretically possible to see such an object; but, if we could see such an object, say, from the front, at least we can say that we'd have a hard time cogitating its nature.

But while two- and one-dimensional realities are impossible to be experienced, nonetheless they must be real, by the a priori reasoning above. So what of three dimensions? We have seen two- and one-dimensional realities are an a priori necessity; do we suppose, then, that the dimensions we actually experience are the only ones that have nothing logically necessary in their nature? If one- and two-dimensional realities have their being proven not by means of experience, but by a priori logic, then is a three- and four-dimensional spatial and temporal reality absolutely contingent, the only dimensions with no a priori necessity? Do they not have any logical necessity embedded in their nature as well as two and one dimensions?

Of course, I will stop short of proving my thesis, which is that three- and four-dimensional spatial-temporal reality bears an a priori logical (not just physical) necessity applicable to it, as soon as there is the notion of experience at all. The unfortunate thing about these dimensions is that they are the ones that happen to be experienced by us, such that one cannot demonstrate their existence as given a priori, for the very reason that they are in fact perceived. If we were five-dimensional creatures, we may not be able to comprehend what spatial and temporal experience would be like; in that case reason would demand three- and four-dimensional reality, but we could not experience them, while we would experience five-dimensional reality.

I have shown that two- and one-dimensional reality is an a priori precondition of any experience in three dimensions; showing that this is known a priori was made easier by the fact that we can never experience such dimensions. For if we could, it would be exceedingly difficult to show they come a priori. To show that a given body exists, and at the same time to see it there, may convince one it is real; but how can it convince one that this was known a priori, given that it was in fact experienced? If we lived in a world where we saw God with our eyes and verified him through experience, it would be the hardest thing in the world to prove, not that he exists, but that we knew he existed a priori. That two and one dimensions are known a priori is an easier point to make than three and four, since we in fact do not and cannot experience two- and one-dimensional objects; is there any question, then, that what we know about them comes from pure reason?

I would summarize and complete my argument with some rhetorical questions. If we know that two and one (and zero, by means of similar arguments to the above) dimensional realities exist and are a priori logically necessary components of higher-dimensional experience, do we then suppose that there is in fact no logical a priori necessity bound up in three- and four- dimensional reality (space and time)? Are not space and time, then, the fundamental rational, and not only empirical, forms of experience, issuing from the nature of reason and logic? Are space and time not radically more intimate with the human rational apparatus than any typical object of perception, such as a tree or a house? Do we see and hear and feel space and time because we exist in space and time purely contingently, or do we exist in space and time because that is the only logically intelligible way for us to see and hear and feel?

Angelhaunt.net: Because earth's madness is heaven's sense.