A well-known argument, due to Frank Jackson, goes as follows. (You can read the short version here.) The brilliant genius Mary has complete knowledge of physical reality. All the sciences, physics, chemistry, neuroscience, etc., have been completed—there is nothing more to add—so that the fundamental physical constituents and causes of all phenomena are known, together with everything that supervenes on them, and Mary has mastered all of this. But although Mary thus knows everything about the physical world there is to know, she does not know everything there is to know. For, a peculiarity about Mary is that she has lived her entire life in a black and white room and has never been permitted to view anything except in black and white. Thus, on the day when she finally leaves her room and sees, say, a red object, she will learn something she didn’t know before. She will say, “Ha! So that is what seeing red is like.” If this is correct, then, apparently, red, or the experience of seeing red, is not part of physical reality.
The “Mary” argument is just one of several ways to bring out what is really an old, classic problem with any sort of reductionistic physicalism. It is this. The fundamental elements of physics—the elementary entities and their properties, whatever they might be—do not include sensory qualities like colors, sounds, tastes, the feel of warm and cold, and so on. For example, say the elementary entities are subatomic particles like electrons and protons, with their properties of spin, charge, mass, and whatever else, and electromagnetic radiation with its properties of frequency and amplitude and whatever. Notice that these fundamental entities and properties don’t include qualities like red or sweet. And yet modern science is a reductionistic system: everything is supposed to be in effect constructed out of the fundamental entities and properties. For example, all the properties of a number 2 pencil are supposed to be explainable by its physical constitution: the arrangement of its atoms, their different internal structures, the forces binding them together into larger structures, and so forth. And for the properties of a pencil, you can see how this works. We really can explain all the structural and functional properties of a pencil in terms ultimately of its physical constitution.
But how are you going to explain the quality of being red (“what seeing red is like”) this way? What arrangement of particles or atoms brings red into existence? How can charge, mass, and spin (or whatever you like) be combined to construct red? To grasp the question seems to be to realize that one can’t begin to answer it. There seems to be no way to answer this question, even in principle.
This problem is as old as atomism itself. Democritus, one of the architects of the original Greek atomism, recognized the problem. In his ontology, nothing exists but atoms and the void. Atoms are the smallest units of matter, indestructible, impermeable, having shape, size, weight, and position, and that’s all. He recognized that although you can construct properties like hard and soft out of atoms and their interactions, you can’t do that with sweet, bitter, warm, cold, color, etc. Later, Galileo, in reviving atomism, encountered the same problem (in The Assayer). Newton likewise (in the Optics).
It is sometimes known as the problem of primary vs. secondary qualities. The primary properties are the ones of fundamental physics. Back in the day, that meant the properties of atoms: size, shape, weight, and position. Today we have a more sophisticated set, but the problem remains the same. The fundamental properties don’t include the “secondary qualities” (sweet, bitter, warm, cold, colors, etc.), and there seems to be no way even in principle to build secondary qualities out of the primary ones.
What people have typically said in response to the problem is that the secondary qualities are mental. Thus, Galileo: “I think that tastes, odors, colors, and so on are no more than mere names so far as the object in which we locate them are concerned, and that they reside in consciousness. Hence if the living creature were removed, all these qualities would be wiped away and annihilated.” And Newton: “For the rays, to speak properly, are not colored. In them there is nothing else than a certain power and disposition to stir up a sensation of this or that color.” But this is cheating, of course. For, what is the mind? Is it something outside the physical realm? Maybe that’s what these writers thought. But if you think the universe is completely physical, then you just recreate the problem all over again, this time in the brain rather than in the external objects. How do you build a “sensation of red” out of fundamental physical entities and their properties? If we couldn’t answer this question before, when it was about qualities of objects, we won’t be able to answer it now, when it is about sensations in brains. Putting sensory qualities in the mind just relocates the problem; it doesn’t solve it.
So this is why the problem can be taken to be an argument for dualism, and many philosophers today seriously advocate it as such. For instance, this was Jackson’s aim when he formulated the “Mary” argument.
However, my own take is that the problem does not force us to be dualists. I think the problem arises because the only properties we have scientific access to are (basically) causal. We know objects and their properties only through their effects. Ultimately, this means by their effects on our senses, but also by their effects on each other. Think of our knowledge of electromagnetic forces, or of particles like electrons. We know them only by what they do. They have certain systematic effects on certain objects, which we learn to formulate by mathematical equations in terms of constructs, such as “mass” and “charge,” which are ultimately defined functionally by their role in these very equations. (This is why fundamental physical entities can be defined by Ramsey sentences.) Thus, what anything is in itself we never observe or know; what we know about all things is what they do. Still, there must be some intrinsic properties. It can’t be relations or causes all the way down; there must be relata and things on which the causes operate. Our experience is in part of just such intrinsic properties, namely the sensory qualities such as colors. Experience has to include such intrinsic properties, because experience can’t be only of relations any more than reality can consist only of relations. There must be the things that are related.
Notice in this connection that the quality red doesn’t do anything. It has no effects (except by our psychological reaction to it; but that’s not something it does). The quality helps to constitute things that are related. It is not itself a relational or causal property; it is intrinsic.
So red may be physical after all, and it may exist in the world as well as in our experience. But though it may be physical, it will never be part of physics. The intrinsic character of physical reality is epistemically inaccessible to us.