Metaphysics of Shape and Color

Metaphysics of Shape and Color

How many shapes are there in the universe, and how many colors? A standard answer is infinitely many in both cases. This answer is not incorrect, but it doesn’t go deep enough. Metaphysically, we want to know how many irreducible shapes and colors there are. As a matter of basic ontology, how many shapes and colors do we need to recognize? And is reductionism the right approach? How unified are the various shapes and colors—what kind of “ism” applies to them (monism, dualism, pluralism, etc.)? Is there a magic number or is it arbitrary? Is there an essence shared by all shapes, and ditto for colors? What is the metaphysics of shape and color?

First shape. We might begin with the idea that geometrical figures fall into a few basic kinds (natural geometrical kinds): triangles, quadrangles, polygons, circles, ellipses; then three-dimensional figures are derived from these. You can combine these to produce infinitely many possible shapes, but they are the basic building blocks; everything shaped is reducible to them. This would be quite an insight and it has shaped (!) human thought from Euclid on. But it doesn’t go far enough: can’t we reduce all possible shapes to variations on straight-sided figures and curved-sided figures? Triangles and squares (etc.) on one side, circles and ovals (etc.) on the other side. The rectilinear and the curvilinear. Once you have these core shapes you can derive the rest: for example, you can simply add a side to a triangle to get a rectangle, and you can squash a circle to get an ellipse; three-dimensional figures are got by analogous means. So, we might endorse a dualistic geometry—roughly, squares and circles. Then the claim would be that all the shapes of nature are reducible to these; and that claim is plausible enough. But have we gone far enough—couldn’t there be a more ambitious form of shape reductionism? Couldn’t geometrical monism be true? For consider: can’t we derive circles from squares by multiplying the sides of the square to infinity, using the concept of a limit? Isn’t there an intelligible procedure that will take you from squares to circles? And what about the idea of taking sections of the circumference of a circle, straightening them out, and putting them end to end? The gulf between squares and circles does not appear unbridgeable (it’s not like matter and mind or fact and value). The circle is a kind of modified square—we can imagine a square growing into a circle (or vice versa). We can always bend a straight line into a curved one and a curved line into a straight one—imagine performing this transformation with a piece of string. Circles and squares are topologically equivalent. Underlying the geometrical dualism, we have a geometrical monism. You can do a lot of work with a straight line (or a curved one). Metaphysically, we have variations on a theme. Ontologically, all shape is based on a single shape. A pre-Socratic might announce “All shape is One”: the many reduce to the one. A theologian might teach that God first created the square and then let nature take care of the rest. A philosopher may proudly call himself a “rectangle monist”. A modal philosopher might go a step further and say that necessarily all shapes reduce to the rectangle—in all possible worlds the only real shape is the rectangle. This might be called “shape minimalism” and Occam’s razor cited piously. And the doctrine is not wildly implausible; in fact, I might include myself under that label. The geometric jungle is analyzable into a single basic figure (I stop at reducing everything to the straight line). I might even be attracted by the idea of reducing every shape to the egg shape, on account of its poetic resonance: all geometry develops from an egg. This is certainly a debatable position in the metaphysics of shape.

But what about color? Here the situation looks very different: the colors are not all derivable from a single color, or even two colors. The basic colors are standardly said to be red, blue, yellow, green, black, and white. There could be other colors too, and some animals may see them, but they clearly form a plurality. You can’t deform blue to get yellow, or black to get white. These are color primitives, irreducibly different. They can combine to generate potentially infinitely many colors, but the procedure starts with a (finite) inventory of primitive colors. Color pluralism is the indicated metaphysical doctrine. Someone who claimed that all colors are one would be on shaky ground (“Everything is green” sounds like a non-starter). So, we know that the metaphysics of color differs in this respect from the metaphysics of shape. Shape is inherently unitary, but color isn’t. It is in the nature of color that there should be a variety of colors, actual or possible. There is no privileged color that reduces all the rest. So, when you look at an object and see the many shapes that compose it, you see variations on a single shape; but the many colors you see are not variations on a single color. There is geometrical unity but not chromatic unity. The two sorts of quality are intertwined, but their ontology is quite different. Colors form a family; shapes form a continuum. Colors are discrete; shapes are continuous. Colors are pluralistic; shapes are monistic. Visual perception is a mixture of both. And it knows it, tacitly anyway: it knows that shapes and colors are different in this way. We need different color receptors, but we don’t need different shape receptors (rods and cones and all that). The processing of shape is essentially simpler than the processing of color; shape perception no doubt preceded color perception in the evolutionary history of vision. The metaphysics of shape and color influences the cognitive science of human vision (and non-human types of vision). Shape is subjectively monistic, but color is subjectively pluralistic. This is a truth of phenomenology. The perceived world (the visual field) has a mixed metaphysics: partly monist, partly pluralist. We see things in both ways (seeing-as).

How does all this bear on the contents of platonic heaven? Interesting question. With color we would naturally say that it contains the usual six colors and no others—no shades or mixtures. These come from the mixing of colors that occurs in the empirical world. There is no need to stack up endless derivative colors in Plato’s heavenly storehouse. In the case of shape, one gets the impression that Plato favored a well-stocked geometrical heaven—triangles, rectangles, ellipses, circles, etc. But in the light of our reductive efforts, we could cut this down to the basics; and we appear to have a choice—the circle or the square. Circles seem the most appealing choice, in view of their reputed perfection; so, let’s go with that—the Form of Circularity only. Then we obtain the rest by sublunary operations and iterations. There is the Good, the Circular, and the Colors (neatly side by side). Geometry is commendably minimal (Occam-shaved) in its quota of basic Forms. It has a small but powerful cardinality. There is no need to wax extravagant in constructing Plato’s heaven, at least when it comes to shape. One shape will do the job.

Lastly, how do we explain these numbers—what do they signify? Or are they entirely arbitrary? Our mystical tendences favor special mystical numbers, but it is hard to see any meaning in the numbers we have arrived at. One is a nice round number for shapes, but six doesn’t sound very meaningful for colors—and anyway there may be other colors perceived by other perceivers. There is nothing Godlike about the number six (three maybe). Could there be worlds that have fewer colors, or completely different colors? That sounds strange, but it may be the result of our limited perception-driven imaginations. Surely, black and white will be universal, and it would be an impoverished world without red and blue. I will leave this question for further research into the mathematical metaphysics of color. The point I have wanted to make is that shape and color have different ontological profiles.[1]

[1] Isn’t it odd that this question has not been pursued in work on shape and color? To my knowledge, the questions I raise (and answer) in this paper have no traditional literature devoted to them, despite the interest in the two topics. The usual focus is on the distinction between primary and secondary qualities, not the question of intra-category reduction and inter-category divergences. Colors have no real essence in common, but shapes do. It is customary to construct geometry from points and lines in an atomistic style, but no such atomism will work for color science.