From Zeno to Complementarity: The Continuity of the Notion of Discontinuity

Article excerpt

Since I'm about to discuss a problem related to colors and surfaces, I would like to separate certain unwanted elements from my essential point of focus. Colors are characteristically said to be nonextensional entities in constitution, because they have an intensity and a frequency. Neither of which is a spatial property. A red so faint that it is but one step before total extinction can occupy the very same section of space that the brightest of reds can. Hence the brilliance or dimness of a color gains or loses nothing, whether it occupies a surface the width of Sahara or one the width of a postal stamp. Similarly with frequency. Whether something is red (a lower frequency) or blue (a higher frequency) can be fully decided by looking at something the size of a stamp without having to look at something the size of Sahara. Calling something blue rather than red is not to say anything about its size. Therefore the essence of colorhood has nothing spatial in its constitution.

This is a perfectly sound argument, provided it is not exaggerated to the point of divorcing colors from surfaces. At best, what it say s is that the notion of a surface is not a sufficient condition for the presence of a color. It does not say that it is not even a necessary one. Colors are things attributed to surfaces, if attributed to anything. That colors are not defined spatially is hardly like saying that colors are not exemplified spatially either. Pains are also entities of this kind. They too have a degree instead of an extension. But this is not to say that when I feel a pain I do not feel this pain somewhere (e.g., a toothache.) To instantiate a certain color is to instantiate a certain surface of which it is the color, and one cannot encounter the instantiation of a color that occupies no surface, intensity, frequency and all notwithstanding. A color has to be somewhere, to be a color, and something can be somewhere, if and only if it occupies the "somewhere," where it is. The link may be "extrinsic" but it is still unbreakable. This is all I require for the argument which follows.

Suppose I begin with a certain red surface and wonder how far I can proceed with its subdivision. I can certainly break it up into, say, four even (or uneven) smaller red surfaces. Its color will not be affected, precisely because of the other, nonspatial properties of red. (Which shows I'm on the right track.) Then I subdivide those latter and so on, until I will either conclude that the red surface is no longer divisible, whereupon I have reached its ultimate subdivision, or else conclude that no matter how far I subdivide, there will always be smaller red surfaces before me to do the very same thing with.

The former supposition is the atomistic one. There is an atom at the rock bottom of this surface and hence, since this (happened to) be a red surface, a red atom of the surface. The latter is the "plenum" supposition. There is no part of this surface which is the smallest one and hence, since this (happened to) be a red surface, no red part of which is the smallest. Both suppositions have their own problems. The plenum supposition is plagued by the problem of smallness before it is plagued by anything else. If the surface, red or what have you, is infinitely divisible, its smallest parts will accordingly be infinitesimal and then one would have a hard time reconstructing the initial surface back again. One cannot add literally dimensionless parts of (what used to be) an extension and get back to an extended anything. This is not a new problem with infinite divisibility, but it is a problem. Zeno was well aware of this problem and we will see that he has some things of unique importance to say about it.

However, the atomistic supposition has a different problem. Leibniz, Kant, and Bohr seem to be fully aware of this problem, each in his own way, though few others seem to be. And this problem, unlike the previous, does involve "red. …