Knowledge of Color
As colors have a metaphysics, so they have an epistemology. In addition to ordinary empirical truths about what colors objects have, there are also general truths stating a priori necessities: for example, “Orange is closer to red than to blue”, “There cannot be reddish green”, “Nothing can be white and transparent”, and “Nothing can be red and green all over”.  There is also knowledge of what colors in themselves are (“knowledge of things”): we know what red is, for example. We know quite a lot about colors before we even get to questions about the empirical distribution of colors among objects. Compare shapes: we also know a lot about shapes, both what they are and general truths about them, in addition to propositions about the shape of particular objects. This knowledge is also of a priori necessities. But there is a difference between shape and color: there is no analogue of geometry for color. There is no mathematical science of color comparable to the mathematical science of shape. There are no color theorems analogous to the theorems of Euclid’s Elements. There is barely a mathematics of color at all, though colors do form an abstract structure. Nor can we conceive of colors as derived from anything analogous to lines, as geometrical figures are so derived: you can form circles and rectangles with simple lines, but you can’t form red and green from a single basic chromatic primitive. Colors just don’t have the requisite degree of structure or quantitative character to allow a color geometry. Sounds are closer to shapes in this respect, as evidenced by musical theory: scales and keys are derived from mathematical relations of pitch (pitch being like line, constructively). But colors aren’t structured like closed many-sided figures, and there is nothing like angle in color space. So our knowledge of color doesn’t include anything comparable to geometrical knowledge, despite being a priori and necessary. Colors are not mathematizable in the way shapes are.
One might speculate that this is because colors are less objective than shapes. If colors are really experiential properties in disguise, then maybe it is the non-mathematical nature of experience that underlies the absence of a geometry of color. The same would not be true of shape, since we can separate objective shape from subjective shape: geometry is about objective shape not experienced shape; and maybe experience of shape is not susceptible to mathematical treatment either. But that kind of subjectivism doesn’t seem correct in the case of knowledge of color: such knowledge is not knowledge of experience as such—we are not thinking about experiences of color when we recognize general truths about color. Perhaps there are deep a priori connections between facts about color and facts about experiences of color, but it seems wrong to suppose that truths concerning color are simply analyzable as truths about experience—a color isn’t an experience! We have experiences of color, but the color of an object is not an experience in the perceiving subject. So the character of our knowledge of color is not immediately explicable in terms of our knowledge of color experience. Further, if we ask why experience of color is not mathematizable, the answer must surely advert to what such experiences are of, viz. colors: but this returns us to the non-mathematical character of colors themselves. There is much more hope of a mathematics of shape experience, given that such experiences are of shapes, which have a developed geometry to call their own. It appears, then, that it is colors as such that resist mathematical treatment: being red is not like being an equilateral triangle—the property itself lacks internal mathematical structure. This is just a basic ontological fact.
Here is another difference between color and shape: there is nothing analogous to space in the color case. What I mean by this has to be carefully stated: shape can be viewed as a mode of space, but color can’t be viewed as a mode anything analogous to space. Space, like matter, has extension (at least in commonsense physics), and shapes are modes of extension; but there is nothing analogous that has some chromatic property of which the several colors can be viewed as modes. A red object (isolated from other colored objects) is not surrounded by a sea of color, in the way a square object is surrounded by a sea of space. Shaped objects exist in a medium that shares their geometrical nature, but colored objects don’t exist in a chromatic medium: space isn’t colored! The color is simply in the object not borrowed from the medium in which it exists. Space and shape are natural partners, but space is not a progenitor (or twin) of color—and neither is there anything else that plays the role of space in relation to color. There is not some milky stuff, say, that houses the colors we observe in objects. Given space, shape is not a surprise; but space doesn’t prepare us for color, which appears as a radical addition. Color just seems plonked down in space with nothing comparable to support it. There is no chromatic ether.
Knowledge of color might be cited as a basic type of knowledge that could illuminate other types of knowledge. Puzzles raised by other types of knowledge might have precursors in our knowledge of color, in particular knowledge of what is necessary and a priori. Wittgenstein compares mathematical knowledge to color knowledge, hoping thereby to demystify it.  The comparison might help resist platonic conceptions of mathematical knowledge, given that colors are relatively “concrete”. Certainly we can use color knowledge to argue for the non-uniqueness of mathematical knowledge in its synthetic a priori character: mathematical knowledge doesn’t stand apart from all other types of knowledge in having that kind of status. Even perceived colors can give rise to synthetic a priori truths—not just abstract platonic universals. But the other area that might be compared to color knowledge is knowledge in ethics, which is often compared to mathematical knowledge. It is felt that ethical knowledge needs all the help it can get in securing its epistemic credentials, and mathematical knowledge is then wheeled in as a precursor or partner in crime. The idea certainly has strong appeal for a moral realist convinced that moral knowledge is a species of a priori knowledge. But the color case might be an even better model for ethics, because it is less rigorous than mathematical knowledge and, well, less mathematical. The critic will point to the asymmetry in respect of proofs and general formal sophistication, thus pooh-poohing the comparison to mathematics; but the color case mirrors ethics more closely in these respects. Ethical knowledge resembles our knowledge of color in being synthetic and a priori, and neither is at the level of mathematical science. This is not to downgrade them: it is merely the way they are given the properties and facts concerned. Colors are just not intrinsically susceptible to mathematical treatment (save very superficially), and there is no reason they should be; analogously, moral values are not susceptible to mathematical treatment, and there is no reason they should be. So color and morality belong together epistemologically (we could also bring in sounds and even tastes and smells). In both cases we have a faculty of knowledge that delivers insight into the subject matter in question, thus delivering types of knowledge traditionally described as synthetic a priori (i.e. not analytic and not derived for experience). Anyone seeking to question the status of moral propositions in these respects must explain why they decline to take the same line for propositions about color. It turns out that synthetic a priori knowledge is quite common (and indeed commonplace) and not confined to the supposedly elevated areas of mathematics and morality. Even the humble colors, perceived by human and beast alike, can give rise to such knowledge. Being right is not so far from being red, epistemologically speaking.