Mistakes are made. We are sometimes wrong about the time of the next train, the restaurant’s address, tomorrow’s weather. Grandly put, reality is not always as it appears. The good news is that all this false flotsam floats on a gigantic sea of truth. We might get the time of the train wrong, but we know that trains exist, that some of them arrive in Boston, that it snows in Boston, and that snow is cold and white.

Or do we? In a philosophical frame of mind, we might wonder whether mistakes are alarmingly more widespread. Perhaps all our beliefs derived ultimately from perception—trains exist, it snows in Boston, snow is white—are wrong.

According to Parmenides (who lived around the time of Socrates), such global error is indeed the human predicament. Careful attention to the verb “to be,” he thought, shows us that reality is a perfect indivisible eternal sphere. The appearance of change, motion, pluralities—grapes ripening, goats walking, and so on—is all illusion. As Parmenides put it, “There neither is nor will be anything else besides what is, since Fate fettered it to be whole and changeless. Therefore it has been named all the names which mortals have laid down believing them to be true—coming to be and perishing, being and not being, changing place and altering in bright color.” (Mortals themselves presumably do not exist, which makes Parmenides’ position somewhat paradoxical.)

Parmenides explicitly mentions color on his list of mortals’ many mistakes. And although few contemporary philosophers are as bold (or as crazy) as Parmenides, many agree with him on this point. Arguments that specifically target our ordinary beliefs about color—that snow is white and lemons are yellow—are philosophical staples. More impressively, the shocking conclusion that snow isn’t white and lemons aren’t yellow is also accepted by many color scientists. Open a recent textbook on perception and you may well read that colors are not “in objects,” but instead are “constructed by the brain.”

Let us say that color realism is the view that objects typically have the colors that they appear to have: lemons are yellow; blood is red; snow is white. The argument between color realists and their philosophical and scientific opponents is of interest in its own right, but it can also serve as an introduction to general philosophical questions about appearance and reality.

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If snow is white, we find out that it is by using specialized sense organs—our eyes. Aristotle thought that perception was a process by which one receives “perceptible forms without their matter, as wax receives the imprint of the ring without the iron or gold”; according to some commentators, Aristotle holds that when you see snow, your eye itself takes on the perceptible form of the snow—that is, the transparent jelly of the eye actually becomes white.

Serious progress was only made much later. Researchers in the 18th century knew that all colors could be produced by mixing together three “primary colored” lights in various proportions—color television takes advantage of this phenomenon. This “trichromacy” of color mixture was taken by some to indicate that there were three fundamentally different kinds of light. On the other hand, Newton’s famous experiments with prisms in the 1660s suggested that the varieties of light formed a continuum.

The great conceptual breakthrough came early in the 19th century, when Thomas Young realized that the data about color mixing could be explained by supposing that there are three different types of light receptors in the eye rather than three different kinds of light. As the psychologist J.D. Mollon has put it, Young’s predecessors made a “category error”: they mistook trichromacy for a property of light rather than a property of our visual system.

Color vision, we now know, operates roughly as follows. The human retina contains millions of photoreceptors of four types: rods, and three types of cones. The rods are sensitive to low light and are used mostly for night vision. The three types of cones are differently sensitive to different parts of the visible spectrum—light from about 400 to 700 nanometers (billionths of a meter). (The visible spectrum is a tiny fraction of the electromagnetic spectrum: FM radio waves, for example, have a wavelength of about 3 meters.) The L-cones are most sensitive to—that is, most likely to absorb—light of longer wavelengths (towards the yellow-red end of the spectrum); the M-cones are most sensitive to light of slightly shorter wavelengths, and the S-cones to light of much shorter wavelengths (the blue-violet end). (Hence, “L,” “M,” and “S,” for “long,” “middle,” and “short.”) The peak sensitivity of the L-cones, for example, is about 565 nm; light of this wavelength looks greenish yellow.

When a cone is stimulated by light, it produces the same response no matter what the wavelength composition of the light, though it is more likely to respond to wavelengths closer to the cone’s peak sensitivity. So if all you know is that a particular cone has responded to light, you know very little about the wavelength. But the visual system has much more to go on than that. The key to recovering wavelength information, and so to having color vision, is that the brain can compare the outputs from the different cone types. Orange light of 600 nm, for instance, will produce the greatest response in the L-cones, substantially less response in the M-cones, and essentially no response in the S-cones. Blue light of 475 nm will produce a very different pattern of response among the three cone types.

Naturally this is only the beginning of an extremely complicated story. One obvious omission is an account of why the spectrum appears as it does. Why does it appear banded rather than continuous? Why do reddish colors appear at both ends? Why are there colors (many purples, for instance) that do not appear in the spectrum? And why is it a mistake to think that all yellow-looking objects (say) predominantly reflect light from the yellow part of the spectrum? These puzzling questions do have (lengthy) answers, but let us hasten instead to some arguments against color realism.

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George Berkeley, Anglican bishop of Cloyne, Ireland, in the early 18th century, believed that all material objects—snow, lemons, the hill of Golgotha, and so forth—were mental entities, collections of “ideas” that existed only when perceived. According to Berkeley, reality consists entirely of finite minds, the divine mind (of course), and their ideas. This view is called idealism.

Now, surely an idea of a lemon is a feeble substitute for a genuine lemon. So you might think that if reality is entirely mental, there are no lemons—in particular, no yellow lemons. Not Berkeley, though: he thought he could maintain, with common sense, that lemons exist and are yellow. In fact, Berkeley was anxious to defend the ordinary person against the “prejudices” of such luminaries as Galileo, Descartes, Newton, and John Locke. These philosophers and scientists all thought that science had shown that reality is frequently not as it appears—for example, snow is not white and lemons are not yellow.

But let us not worry about Berkeley’s official view—that lemons are yellow, albeit yellow ideas in our minds (or God’s). Instead, we can take some of the classic arguments in his Three Dialogues between Hylas and Philonous (1713) as attempting to show—in agreement with Galileo & co.—that objects do not have the colors they appear to have. Snow isn’t white, because whiteness is merely “in the mind.” Understood this way, Berkeley’s arguments are still repeated, in various forms and with various amendments, today.

The argument from variation. One of Berkeley’s arguments is the argument from variation. Berkeley’s spokesman Philonous (“lover of mind”) observes that something can appear to have different colors under different conditions, “without any manner of real alteration in the thing itself.” For example, “the same bodies appear differently coloured by candle-light from what they do in the open day,” and “the beautiful red and purple we see on yonder clouds . . . vanish upon a nearer approach.” Red and purple are not “really in” the clouds, so why think the clouds have any color at all? Hylas, Philonous’ opponent, replies by distinguishing the real color of a thing from its apparent color. True, sometimes an object can appear to have a color that it does not have: in the red light of a photographic darkroom, a cucumber will look black, not green. But that just shows that sometimes perception leads us astray—when the lighting conditions are bad, or when we are far away, for instance. It does not show that we never see objects in their true colors. Likewise, we are sometimes mistaken about the time of the train—when we read the timetable hastily, for instance. But that doesn’t show that we are always or mostly mistaken.

Indeed, Berkeley’s own example of the candle can be seen as supporting color realism. After all, it is hardly arbitrary to suppose that the colors of things are better revealed in sunlight than in the artificial light of a candle. Moreover, despite the enormous difference in spectral composition and intensity between candlelight and sunlight, the remarkable fact is that color appearances do not change all that much (lemons still look yellow, and so on), a phenomenon known as color constancy.

Much remains to be said about the argument from variation, which has returned in the contemporary color literature in a more potent form. But before getting there, let us first consider Berkeley’s other arguments.

The argument from microscopes. Berkeley asks us to consider how things look under the recently invented microscope. This wondrous device, Philonous says, affords us a “more close and accurate inspection” of objects than the naked eye. Also, “A microscope often discovers colours in an object different from those perceived by the unassisted sight.” (Imagine peering closely at a pointillist painting or a television screen, or looking through a magnifying glass at a color photograph in a magazine.) Furthermore, under high enough magnification some objects do not appear to have colors at all. If the argument from microscopes doesn’t quite get us the conclusion that everything is colorless, it gets us something almost as bad, namely that most of the time an object’s apparent color is not its real color. Lemons may be multicolored or colorless—at any rate, they are not yellow.

However—as pointed out in David Hilbert’s Color and Color Perception—a more close inspection of the argument from microscopes reveals a flaw. When we see tiny red dots in the bright yellowish-green areas of Seurat’s Sunday Afternoon on the Island of La Grande Jatte, we have not discovered that these apparently green areas are really red. Rather, we have discovered that the apparently green areas have red parts. This discovery may be surprising, but it doesn’t show that the large areas are not really green. In order to get the conclusion that the apparently green areas of La Grande Jatte are not really green, we need to assume something like the following principle: if a surface is green, then every part of the surface is green. And that principle is at the least not obvious.

A comparison with smoothness can reinforce the point. In The Problems of Philosophy Bertrand Russell applies the argument from microscopes to the case of texture. With the naked eye, he says, the table looks smooth. Yet, “if we look at it through a microscope, we should see roughnesses and hills and valleys, and all sorts of differences that are imperceptible to the naked eye. Which of these is the ‘real’ table?” The natural reply to Russell is that both are the real table. The deliverances of the microscope about the table are not in conflict with the deliverances of the naked eye. What we learn by close inspection of the table is that a smooth surface can be composed of parts that are not themselves smooth. The reply to Berkeley’s argument is exactly analogous.

The argument from other Species. Some nonhuman animals, as Philonous observes, see colors. “Is it not therefore highly probable,” he asks, “that those animals in whose eyes we discern a very different texture from that of ours, and whose bodies abound with different humors, do not see the same colours in every object that we do?” From this “highly probable” assumption he concludes that “all colours are equally apparent, and that none of those which we perceive are really inherent in any outward object.”

Philonous’ assumption is correct. Color vision is widely distributed among mammals, fish, birds, reptiles, and even insects. Plausibly many of these animals do not see the same colors that we do. Their chromatic photoreceptors are usually differently tuned and usually differ in number: birds are typically tetrachromats, with four receptors; most mammals are dichromats, with two. Many species—including the trichromatic honeybee—have a kind of photoreceptor sensitive to the near-ultraviolet, outside the visible spectrum.

But Philonous is wrong to think that the color vision of other animals creates troubles for color realism. Take the honeybee. Philonous’ first premise is his “highly probable” assumption: flowers (say) look different in color to bees than they do to humans. His second, implicit, premise is this: either bees and humans both perceive flowers in their true colors, or neither do. The second premise is surely plausible: it would be quite unmotivated to assume that humans see the true colors of objects and that all other species misperceive them.

But these two premises are not enough to give Philonous his desired conclusion, that “all colours are equally apparent” and that neither bees nor humans perceive flowers in their true colors. Maybe bees and humans both perceive the true colors of flowers. To exclude that possibility, Philonous needs the assumption that flowers can’t have both “bee colors” and “human colors.” Why not, though? Admittedly, we think that some colors exclude others: blue speedwell flowers are not also yellow. But that is presumably because we can see that some things are yellow: if speedwell flowers are yellow as well as blue, why don’t they look that way? However, we cannot see bee colors at all. Hence there is no clear reason for denying that blue speedwell flowers have other colors visible only to bees.

Now the idea of “colors invisible to human beings” might be slightly discomfiting. Suppose we arrange all the (human) colors by similarity into one of the familiar color solids—for instance, two cones pressed base to base, with the hues red, yellow, green, and blue going round the middle, white at the top apex, and black at the bottom. How could an extra color be squeezed in? And if a so-called “bee color” is not related by similarity to the human colors—if it does not have a home on the color solid—why think it is a color at all?

These are good questions, but asking them won’t help Philonous. If bees don’t see colors but rather detect some other sort of floral feature, then the argument from other species doesn’t even get started.

Berkeley’s last two arguments have some major problems, then. Before returning to his first argument, the argument from variation, let us look at another argument against color realism—the one that was historically the most influential.

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Again, Berkeley saw himself as defending common sense: his official position was that snow is white and lemons are yellow. Galileo, Descartes, Newton, and John Locke all thought otherwise: modern science, they argued, has shown that snow is not white and lemons are not yellow. According to Locke, whiteness is no more in snow than “Sickness or Pain is in Manna [a 17th-century laxative].”

And science was supposed to impugn more than color. “The fundamental principle of the modern philosophy,” David Hume reported in his Treatise of Human Nature (written 26 years after Berkeley’s Dialogues), “is the opinion concerning colours, tastes, smells, heat and cold; which it asserts to be nothing but impressions in the mind.”

How was this conclusion reached? Snow and lemons, according to Hume’s “modern philosophy,” are made of small, differently shaped, solid particles, or corpuscles, moving around and interacting by contact. Only such “primary qualities” of bodies are needed to explain the interaction of snow and lemons with light, and why snowballs, but not lemons, cause “ideas of whiteness” in us. That is, science can explain why lemons look yellow without supposing that they are yellow. The hypothesis that lemons are yellow is entirely gratuitous.

Of course, the 17th-century mechanistic theory was wrong—Newton’s discovery of gravity, which operates at a distance and not by local pushes and pulls, had already shown the theory’s limitations. But the demise of mechanism does nothing to weaken the argument from science. It actually makes it stronger, because contemporary science is considerably better placed to explain why lemons look yellow than the science of Galileo or Newton. The properties of lemons and the like that are responsible for their looking colored are now very well understood. So we can be quite confident that an adequate explanation of why lemons look yellow can be given in terms of their physical properties, with no explicit mention of their color.

Colors as powers. The argument from science tacitly assumes that yellowness is an addition to the scientific inventory of the properties of lemons. That is why the hypothesis that lemons are yellow is supposed to be gratuitous. But perhaps the assumption is wrong: can we find some scientifically certified feature of lemons that is a plausible candidate for being yellowness itself?

If we reexamine the features that science has shown lemons to possess, we notice that they do not just have what Locke called “primary qualities”—such as solidity and shape. They also have the capacity to affect human beings in certain ways; in particular, lemons cause experiences of yellow in human beings. Lemons, in other words, have a power or disposition to look yellow—an example of a secondary quality. Just as a fragile glass is disposed to break when struck, a lemon is disposed to look yellow to normal humans in daylight. What’s more, just as a glass can be fragile even if it is never struck,a lemon can be disposed to look yellow even if no one ever looks at it. So why not say that yelllowness simply is that secondary quality—the power to produce experiences of yellow in daylight? Although this secondary-quality theory of color ties the colors of things to human experiences, it is still a form of color realism: it says that lemons are yellow, and remain yellow even when the refrigerator door is closed.

This view, in one form or another, has proved extremely popular among philosophers. But there are many objections to it. Imagine, for example, the mythical animal invented by the philosopher Mark Johnston: a shy but intuitive chameleon that is usually green but that instantly blushes bright red when anyone is about to look at it. If this chameleon were before us now, it would simply look red. Even when no one is looking at it, the chameleon is disposed to look red to humans in daylight. Therefore the secondary-quality theory predicts that the shy chameleon is red when no one is looking at it, which is incorrect.

Colors as ways of changing the light. Suppose that the secondary-quality version of color realism succumbs to some such objection. Still, with a little more imagination we can come up with another response to the argument from science. Recall that we arrived at the secondary-quality view by the bold move of saying that the yellowness of the lemon was already on the scientist’s list of its features. We picked the lemon’s disposition to look yellow, but perhaps yellowness is another item on the scientist’s list—say, the chemical composition of the lemon’s surface, or the distinctive way it selectively reflects and absorbs light. Could one of these properties be yellowness?

In the 1960s, the Australian philosopher J.J.C. Smart suggested that the answer was yes, and this view has subsequently been developed by others. Arguably the most natural physical candidate to be yellowness is not the chemical composition of the lemon (which it does not share with many other things that appear yellow) but its capacity to reflect light of some wavelengths while absorbing others—the “characteristic way the object changes the light,” as the philosopher Jonathan Westphal has put it. At an appropriately general level of description, lemons, bananas, and other yellow objects change the incident light in the same way. This conception of colors fits nicely with the basic facts about how color vision works; it is clear in outline how the visual system can recover such information about distal objects, and what the ecological advantages of such information might be. The shy but intuitive chameleon turns out to be green, as desired. Further, the view implies that many colors are invisible to humans, thus making room for bee colors, because there are innumerable ways of changing the light to which humans are not at all sensitive.

In 17th-century terminology (harmlessly distorted), this view identifies colors with primary qualities. It will come as no surprise that, despite its many attractions, the primary-quality view of color faces some serious problems. One is posed by a reinvigorated version of Berkeley’s argument from variation.

The argument from variation revisited. The reinvigorated version of the argument from variation appeared in C.L. Hardin’s Color for Philosophers—a book that helped revive philosophical theorizing about color, in part by introducing philosophers to the basics of color science.

Hardin’s version of Berkeley’s argument from variation appealed to an important feature of the colors that we have not yet mentioned. We all know that orange paint results from mixing together yellow paint and red paint; likewise green paint results from mixing together yellow paint and blue paint. However, these facts about pigment mixing are not exactly reflected in how the colors look. Orange looks like a mixture of yellow and red: every shade of orange is either a shade of yellowish red, or of reddish yellow. But green does not look in the same way like a mixture of yellow and blue: shades of green are not shades of bluish yellow or yellowish blue. (Indeed, nothing is bluish yellow or yellowish blue.) Rather, every shade of green is either yellowish green or bluish green—with one interesting exception. There is a shade of green that is not at all yellowish and not at all bluish—this shade is called unique green, and green is called a unique hue. In contrast, there is no shade of orange that is not yellowish or reddish—orange is a binary hue. Whether something looks unique green to someone is relatively easy to measure, and Hardin’s argument takes advantage of this fact.

It turns out that different human beings with normal color vision classify different stimuli as unique green, and the extent of this variation is surprisingly wide. Some of it is due to differences in pigments in the optical media of the eye, and some of it to differences in the light-sensitive pigments inside the cones. Imagine, Hardin says, that you and a colleague are looking at an arrangement of chips, which appear to be varying shades of green: “One of them would be your considered choice for unique green. Your colleague might make a different choice. If so, which of the chips is unique green?” Presumably they can’t both be. But there seems to be no non-arbitrary basis for saying that you are right and your colleague is wrong, or vice versa. (And it is precisely here that Hardin improves on Berkeley’s version of the argument from variation.) Since at most one of the chips is unique green, and the situation is symmetrical, we must say that none is unique green. And once that small entering wedge is secured, it is hard to stop the slide to the conclusion that nothing whatever is colored. Lemons produce experiences of yellow in us, but that is all—the lemon itself is entirely colorless.

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Let us leave the souped-up argument from variation without trying to resolve it. Contemporary philosophy contains a lively specialist literature on color realism, and consensus on the matter is not exactly imminent.

Lack of agreement in philosophy is not in itself particularly disturbing; it may simply reflect the peculiar difficulty of the subject matter. But it might be a symptom of a deeper malaise. Perhaps resolution is elusive because the participants are talking past each other, like a New Yorker arguing with a Londoner about whether a certain bitter vegetable “really is” endive. If so, seemingly profound disputes about appearance and reality turn out to be harmless tiffs about words. Fortunately for philosophy, this view is not very credible. If we argue about whether the train leaves at 5 p.m., this is a genuine disagreement about a (modest) portion of reality; why should the dispute about whether objects are colored be so different?

Another reaction is that the debate can be settled on the side of the color realist without fussing too much about the empirical details. Perhaps it would somehow be violating rules of our language to deny that lemons are yellow—a view associated with Wittgenstein. Alternatively, perhaps the proponent of a colorless world has to believe that objects are colored in order to state her position, which would make it self-undermining—a view recently defended by Barry Stroud in The Quest for Reality.

Finally, perhaps the case against color realism is a little too strong. As briefly alluded to earlier, the position that snow and lemons are not colored is naturally paired with the position that they are not cold and sour either. And—as Berkeley pointed out—arguably the modern philosophy cannot stop there. A properly worked out version of the argument from science might show that all the apparent properties of snow and lemons, including their apparent shapes and motions, are, in Berkeley’s phrase, “a false imaginary glare.” Taking the argument to Parmenidean extremes, there are no snowballs or lemons, or even people, only a vast 11-dimensional blob of superstrings. And no trains.