The double aspect theory discussed in chapter 6 is often confused with a much more powerful and very different theory known as neutral monism. The last well-known proponent of neutral monism was A. J. Ayer, writing in 1936. Earlier the view had been advanced by Bertrand Russell (between 1919 and 1927) and William James and the American new realists, but first and most powerfully by Ernst Mach. Mach’s fullest exposition is contained in The Analysis of Sensations, published in German in 1885 and then in English in 1897.
The view of the neutral monist is that neither mind nor matter is basic, and that both are composed of more basic neutral elements, elements that are in some ways very similar to qualia. Qualia-like things, or phenomenal properties, make up the world, rather than the world, or the brains of human beings, producing qualia. “Bodies do not produce sensations, but complexes of sensations (complexes of elements) make up bodies.”1
The view of the neutral monist is that neither mind nor matter is basic, and that both are composed of more basic neutral elements, elements that are in some ways very similar to qualia.
Recently there has been a revival of interest in this kind of view, as there has been in panpsychism and panprotopsychism. The revival of neutral views, including neutral monism, is in part due to the recalcitrant nonphysicality of phenomenal properties. They have resisted the best attempts of the twentieth century to analyze them away.2 Proponents of the neutral views, though, have recently been tending to interpret the phenomenal elements of neutral monism, such as colors and sounds, as concrete dynamical events in the world described by physics. Eric Banks, for example, writes that “qualities are simply the concrete manifestations of powers in events, observed or not, that occur around us all the time.”3 This is a view that differs hardly at all from Locke’s representational realism, the view that what we are aware of is not the real external world, but a representation, a mental image or sensation or perception. And this mental image, sensation, or perception is supposed by Banks to be a dynamic physical event in the brain.4
In fact, neutral monism takes as its basic elements genuinely neutral things such as “colours, sounds, temperatures, pressures, spaces, times, and so forth,”5 and takes both the self and the physical object as only more or less permanent collections of these elements. It is true that Mach sometimes rather misleadingly also calls his elements “sensations,” but he states quite clearly that he means not that they are psychological in nature, but that their nature is what turns up in sensation. They are psychological in nature when they are placed in a psychological causal sequence; otherwise, they are what we would ordinarily regard as the perceptual or qualitative content of sensations.
We cannot accept Russell’s own claim that he continued to be a neutral monist after 1927, and nor can we accept his claim that during this period he was not the kind of representative realist who took sensations to be part of the brain. In reality Russell gave up neutral monism in 1927, in favor of a view in which qualia are properties of events in the brain. But the brain is itself physical, or rather, the neutral brain elements—the images and qualia of the brain in all the perceptual modalities—are placed in the physical sequence and are, therefore, physical. Consequently, they cannot in any sense contain the neutral elements that are placed in a psychological sequence.
Banks writes, on Russell’s behalf and for himself, that “I now see that enhanced physicalist view of the world involving events and natural qualities comes first, before the mental in every sense. … Sensation qualities are just the higher-order qualities of very complexly configured events in our brains.”6 How is this neutral monism? It is a physicalist monism, “Russellian monism” as it is sometimes called now, though it is doubtful whether Russell himself ever held it, a view that ignores the qualitative in favor of the abstract and the physical. Russell’s view about the mind–body problem after 1927 was a form of central-state materialism, combined with representative realism.7 And in Banks’s description we also have a strong suggestion of a kind of emergentism. The qualia are “higher-order,” and the events are “very complexly configured,” which is somehow supposed to help in allowing the qualia to inhabit them.
The upshot of Mach’s view is that we should not conceive of perception as a transaction between things in the external world—things of which we are not directly aware—and a self, which then blossoms with sensations, of which we are directly aware: representative realism.
For us, therefore, the world does not consist of mysterious entities, which by their interaction with another equally mysterious entity, the ego, produce sensations, which alone are accessible. For us, colors, sounds, spaces, times … are provisionally the ultimate elements, whose given connection it is our business to investigate.8
Here as elsewhere I see only a phenomenalistic Mach, and my view is that the logical positivists who also interpreted Mach in this way were correct.9 It cannot seriously be doubted that Mach wanted the contents of unmediated experience (the things we see directly, hear directly, and so on, such as colors and sounds) to be his elements. It is easy to see how instances of colors and sounds can be taken neutrally, either physically or mentally. The same is not true of dynamical forces or Lockean powers to produce colored sensations in us, which are then to be identified with brain processes, especially since these brain processes are not in any literal sense colored or auditory or possessed of any of the other proper objects of the various sensory modalities.
For Mach and the Russell of 1919 to 1927, perception is, like everything else we know, a relation between the elements. Mach’s elements include, very significantly, “spaces,” and it follows that in themselves none of the elements is spatial. Space and position elements are associated according to Mach with the motor movement of the eye. Mach devotes two chapters, amounting to twenty percent of The Analysis of Sensations, to sensations of space, and to other closely related topics such as relative position and changes of shape with orientation.
I once heard the question seriously discussed, “How the perception of a large tree could find room in the little head of a man?” Now, although this “problem” is no problem, yet it renders us vividly sensible of the absurdity that can be committed by thinking sensations spatially into the brain. When I speak of the sensations of another person, those sensations are, of course, not exhibited in my optical or physical space; they are mentally added, and I conceive them causally, not spatially, attached to the brain observed, or rather functionally presented. When I speak of my own sensations, these sensations do not exist spatially in my head, but rather my “head” shares with them the same spatial field.10
There are, of course, sensations that are spatially as well as causally associated with our bodies, such as pain and hunger, but color and the other elements are experienced outside the body, if experience is to be our guide. I do not see the green of the tree’s leaves inside my hand or my eye. All the elements of the external world (the world external to our bodies), the elements of our bodies, and those we take to be nonphysical form a single mass, internally connected in various ways. “In this way, accordingly, we do not find the gap between bodies and sensations described above, between what is without and what is within, between the material world and the spiritual world”;11 for there is no gap.
Neutral Monism: The Theory
The most important tenet of neutral monism—what makes it genuinely neutral—is that a neutral element, considered in a physical sequence, is physical, but the very same element, considered in a mental sequence, is on that account to be regarded as mental:
The most important tenet of neutral monism … is that a neutral element, considered in a physical sequence, is physical, but the very same element, considered in a mental sequence, is on that account to be regarded as mental.
Thus the great gulf between physical and psychological research persists only when we acquiesce in our habitual stereotyped conceptions. A color is a physical object as soon as we consider its dependence, for instance, upon its luminous source, upon other colors, upon temperatures, upon spaces, and so forth. When we consider, however, its dependence on the retina [and other elements of the body], it is a psychological object, a sensation. Not the subject matter, but the direction of our investigation, is different in the two domains.12
Consider again Ryle’s simile of the University of Oxford and the colleges that make it up. Because the colleges and the university are different kinds of things, we cannot put them into one category and then proceed to count them. We cannot ask how many things there are in the following list of institutions: Exeter College, Trinity College, Balliol College, University College … (and all the other halls and colleges), and the University of Oxford. The list itself involves a category mistake. In just the same way, there is a mistaken categorization in the following list of gloves: a left-hand glove, a right-hand glove, a red glove, another red glove, a child’s glove, another child’s glove …, and three pairs of gloves. For neither a pair of gloves nor a number of pairs of gloves is a glove.
In just the same way, we can consider a sequence consisting of neutral illumination, a red surface, changes in electromagnetic potential, and so on. If we think of this very same red element in a sequence that includes blinking, human expectations, the color surround of the red element, the state of the retina, lack of damage to the area V2 in the visual cortex, and so on, then the red element is to be regarded as a psychological or perceptual event.
What we cannot or should not do is create a sequence of physically interpreted elements containing a psychologically interpreted element, or a sequence of psychologically interpreted elements containing a physical element. The construction of the set of events that includes blinking, human expectation, the color surround, the state of the retina, lack of damage to V2, a perception of red, and the red physical surface makes a monumental category mistake, just as the construction of the set consisting of a neutral illumination, a red surface, changes in electromagnetic potential, and a perception of red makes a mistake of principle. Neither can be admitted as a legitimate causal sequence.
One of the more dramatic consequences of Mach’s monism is that such things as pains, taken in the physical sequence, are physical and not mental, as Descartes took them to be. I imagine that this view will be thoroughly unacceptable to almost everyone except for those of the medieval and earlier philosophers for whom sensations were physical, and of course Mach himself. It has the consequence that the distinction between the physical and the mental or psychological is not to be drawn where the study of physics and psychology placed it in Mach’s time, or where it is placed today. That is what Mach intended. Pains are physical things in the body that have spatial locations and can be associated with visual spatial locations, but they are not part of the physics of electricity and magnetism, of optics and acoustics and so on. Why should this disturb us?
Bertrand Russell describes neutral monism with the memorable image of an old-fashioned postal directory:
“Neutral monism”—as opposed to idealistic monism and materialistic monism—is the theory that the things commonly regarded as mental and the things commonly regarded as physical do not differ in respect of any intrinsic property possessed by the one and not by the other, but differ only in respect of arrangement and context. The theory may be illustrated by comparison with a postal directory, in which the same names appear twice over, once in alphabetical and once in geographical order; and we may compare the alphabetical order to the mental and the geographical order to the physical. The affinities of a given thing are quite different in the two orders, and its causes and effects obey different laws. Two objects may be connected in the mental world by the association of ideas, and in the physical world by the law of gravitation. The whole context of an object is so different in the mental order from what it is in the physical order that the object itself is thought to be duplicated, and in the mental order it is called an “idea,” namely the idea of the same object in the physical order. But this duplication is a mistake: “ideas” of chairs and tables are identical with chairs and tables, but are considered in their mental context, not in the context of physics.13
From the neutral monism of Mach and Russell we can take the idea of the two intersecting sequences of objects of inquiry, physical and psychological. From Ryle we can take the idea of the category mistake applied to these sequences. The mistake that produces the mind–body problem comes, just as Ayer and Ryle claimed, from concocting sequences of perceptual or psychological events ending in physical events, or vice versa, sequences that embody the category mistake at their inception. From Mach and the other neutral monists we can take the background understanding of what the two distinct sequences, mental and physical, must be, and why the category mistake is indeed a mistake, in the context of mind and body.
The real sticking point in the mind–body problem is to think simultaneously that the mind—all of it—is nonphysical and that the body—all of it—is physical. That would be like saying (i) that the left-hand glove and the right-hand glove are physical, and (ii) that the pair of gloves is nonphysical, because it is abstract. Either of these propositions can be asserted singly, but not at the same time as the other. To assert the two propositions simultaneously produces the paradox that when I have a pair of gloves I have three things, two physical and one nonphysical, which is absurd. Similarly, to assert that the mind is nonphysical and the body is physical produces a paradox: the mind–body problem. We should keep the two sets of accounts distinct, realizing that this does not prevent the mind and the body from interacting. As Moritz Schlick writes,
The so-called “psycho-physical problem” arises from the mixed employment of both modes of representation in one and the same sentence. Words are put side by side which, when correctly used, really belong to different languages. This gives rise to no difficulties in ordinary life, because there language isn’t pushed to the critical point. This occurs first in philosophical reflection on the propositions of science. Here the physicist must needs assure us that, for example, the sentence, “The leaf is green” merely means that a certain spatial object reflects rays of a certain frequency only: while the psychologist must needs insist that the sentence says something about the quality of a perceptual content. The different “mind–body theories” are only outgrowths of subsequent puzzled attempts to make these interpretations accord with one another. Such theories speak for the most part of a duality of percept and object, inner-world, outer-world, etc., where it is actually only a matter of two linguistic groupings of the events of the world. The circumstance that the physical language as a matter of experience seems to suffice for a complete description of the world has, as history teaches, not made easy the understanding of the true situation, but has favoured the growth of a materialistic metaphysics, which is as much a hindrance to the clarification of the problem as any other metaphysics.14
What should be said about the third proposition, which is that mind and body interact, from the point of view of Machian neutral monism? Here too “Mind and body interact” commits the same category mistake that we must be careful to avoid in conjoining the first two propositions. “The mind interacts with the body, and the body interacts with the mind” and “Mind and body interact” are sentences that embody the category mistake. “Words are put side by side which, when correctly used, really belong to different “languages.” This gives rise to no difficulties in ordinary life, because there language isn’t pushed to the critical point.” The recognition of the category mistake forces us to take language “to the critical point” and beyond, and it seems that we cannot say things such as “The wine made my mind feel tipsy,” without committing the category mistake.
Interaction, with Perception as the Example
The details of the interactions between the mental and the physical are tricky to manage in neutral monism, yet they can be managed, and that is part of the real wonder of the mind–body problem. Apart from Mach, the neutral monists have not given any consideration at all to the details of how such interactions work. I want to consider three examples of the interaction, of three different types, to illustrate the way in which the neutral monist should understand the relationship of causation between mental and physical events.
To begin, let us imagine that we see some external object in the ordinary way. Let us imagine that we see our own hand in front of us. We have the hand, and we have the image of the hand; however, the concept of an image of something is yet to be understood. The hand is a member of a physical sequence; the image is a member of a psychological sequence. There is an intersection between the two sequences, and what can be placed in the psychological sequence can also be placed in the physical sequence. The neutral monist can assert that when the two sequences intersect, in the sense that there exists one element that can be placed in either sequence, we have the relation of causality between the physical and the psychological. We have causality beyond “the critical point” of language referred to by Schlick. When we do descend to the level of the individual elements, however, we can understand mind–body interaction. At the level of the elements, the two kinds of sequence intersect, in the sense that there are elements that can be placed in both sequences; and there we have interactions. For this to occur, however, the physical elements must be capable of being taken as nonspatial, or the psychological elements must be capable of being taken as spatial. At this level it is the conjunction of the first two propositions that is false in our original inconsistent tetrad. One of them is false. Dualism is false, and monism is true.
From the point of view of what we are aware of, we have the sequence: <light>, <hand>, <hand reflecting light>, <light striking retina>, <activation of the visual cortex>. These elements can be classified as instances of the processes and objects of optics, anatomy, opto-electronics, physiology, and physiology, in that order. That is a physical sequence. We also have the sequence of images of <table>, <hand>, <grandmother>, <spaghetti>, <hunger>. These elements can be classified as instances of perception, perception, memory, memory, and desire. The sequence is psychological. But the two sequences intersect.
The mind is to be taken as the sum of its parts, as Mach insisted; elements of desire, vision, memory, anticipation, and so on, and the relevant parts are capable of being “neutralized,” inserted into a physical sequence, and taken as physical. The body, too, or parts of it, can be stripped down to the neutral elements, which can then be inserted into a psychological sequence. What we are left with, then, is the fact that the third proposition (that mind and body interact) is true only if we are prepared to take a mental or physical event, position it as a neutral event, and thence as a physical event, and vice versa; and the fourth proposition is true simpliciter.
There are also other ways of creating sequences of the same type. We could also regard the element <hand> as psychological, because it is placed in the vertical sequence of elements formed of events relating to the physical body, such as <activation of the visual cortex>.
As to “the mind is to be taken as the sum of its parts,” there is nothing inherently difficult about this “reductionist” view. The neutral monist sees no advantage in thinking of mental states coming together in one mental place, the so-called Cartesian theater. David Chalmers has described the approach this way: the neutral monist and those who split the self up into its various parts “deflate the subject, either by denying that experiences must have subjects at all, or at least denying that subjects are metaphysically and conceptually simple entities.”15 One may not have to go all the way to the first “no-self” view, because the sum of the mind’s parts can be regarded as the mind, but one does have to recognize that when the mind acts, or the body, it is not the whole mind or the whole body acting, as it were, concentrated at a point, but only one part of it. When I go to have lunch because of a feeling of hunger, it is the feeling of hunger, not the whole of my mental life, whether “deflated” or not, that takes me off to the diner.
Each of the first two propositions may be false, in the following way. Parts of the mind can be taken to be nonphysical, and parts can be taken to be physical, and the same is true of the body. When mind and body interact, one of two things happens. Either the relevant parts of the mind or events in the mind can be given spatial characteristics, and can then interact with the spatial body; or the relevant parts of the body and the events in the body can be stripped of their spatial characteristics and can then interact with the nonspatial mind.
Interaction, with Sensations as the Example
The relationship of the properly subjective sensations (e.g., pains, aches, seasickness, a feeling of a scratchy skin) to the body may seem harder to understand than the relationship of identity in the case of the part of the physical object by which we see it and the image, which can be thought of in a literal way as having a place within the totality of consciousness.
A stomachache, to take an example, seems to have little in common with the physical stomach. How then can there be an overlap between the two sequences, such as to allow us to say that what causes the ache is the stomach? For one thing, the stomach is to be found in physical visual space, but apparently the stomachache is not to be found in physical space. There appears to be no member common to the physical and psychological sequences; there is no member that can be interpreted both in a physical and in a psychological way.
This appearance, however, is delusive. The scientific orthodoxy today is that the stomachache is not in the stomach, but in the head, in the firing of some neurons perhaps. This view is a very peculiar one, even if the neurons are very well integrated informationally or whatever. The reality is that there is a pain space, an ordering of the pains in a definitely vague and dim spatial organization, which maps onto “physical” space, a combination of the visual and tactile spaces. In this mapping the earache is located in the ear, the toothache in the tooth, and the stomachache in the stomach. Some pains and aches are harder to place, and they seem to move around. Some pains have vague locations. Early manifestations of appendix pain can masquerade as stomach pains, for example. But the location of the pain is not so vague that it can manifest itself in the ear, for example, or a finger, and still count as the pain that it is.
However, if we are careful, we can establish a distinct and different phenomenology for each of the kinds of what is commonly called “stomachache.” We are not confronted with two blank and barely defined things: the otherwise undescribed mental pain, on the one hand, and the physical stomach, all of it, just sitting there, like a lump, on the other. The stomach is active, and there are numerous different kinds and causes of abdominal pain.
Among the causes of abdominal pain we have: ulcers; gallstones; pain from the appendix; menstrual cramps; indigestion; Crohn’s disease; infection of the urinary tract; and many others. The felt symptoms of all of these are different from one another. But so are the detailed internal signs, if we look for them, in the abdomen and in general physiology.
The pain from ulcers is a gnawing, searing, and burning kind of pain, with some resemblance to hunger. It is to be found quite high in the front of the body, reaching from the bottom of the stomach up to the breastbone. It can also be mixed with a feeling of nausea, and perhaps bloating, especially after meals. The position of the feeling of bloating will also correspond exactly to the dimensions of the distension of the abdomen.
Gall bladder pain, on the other hand, may extend toward the right shoulder, and can feel dull and cramp-like, though sometimes sharp, and increasing with breathing in. And so on. The phenomenology of the different pains is very different, though all, of course, are pains. If we attend to it carefully, however, it becomes increasingly obvious that the different kinds of abdominal pain overlap in a precise way with their physical causes.
With ulcers, we have only to look at the sores in the stomach lining to understand more about the kind of pain that is suffered, and inspection of the sores might lead one to an understanding of the imbalance of stomach acids that can be a cause of ulcers. It is the sores or perforations that cause the pain, and the pain is in the sores. They certainly look sore, which is why they are called “sores.” This is more than a learned association. It is a piece of phenomenology.
The element with ulcers at which a physical and psychological sequence cross is a searing located between the stomach and the breastbone. “Searing” means both the visible and felt fiery aspect of the sores, and the scorching that is caused by the stomach acids. For Descartes it was essential to override the ordinary language with which we describe the psychological pain and the physically painful condition, by means of arguments to the effect that we can conceive the psychological element without the physical element. But this kind of argument is in the end unrealistic. It is perhaps logically possible to have the pain of ulcers without ulcers, but what does this tell us? If such a strange condition were to occur, things would not be as they seem, and we would have no right to apply the ordinary psychological and physical criteria for identifying the pains. Are they really scorching pains? Are they properly localized? Is there the gnawing feeling present? And if the answers are still all affirmative, we should I think look for a physically interesting stomach condition that mimics ulcers, rather than concluding that the mind and the body do not interact. Nor should we conclude that they interact dualistically, in the sense that there is no logical, structural, or phenomenological overlap between the physical and the psychological.
Some recent research is going in this direction in the most interesting way. Martyn Goulding and his team at the Salk Institute have described the surprising discovery that the spinal neurons implicated in the tingling of a light touch are not the same neurons as those that relate to the pain (“chemical”) itch, such as one due to a mosquito bite. The hope is to provide insight into the treatment of the chronic itch, because there is a neural pathway devoted to the pain itch.16 Astoundingly, itching has its own complex physiology that is not the same as the physiology of the light touch. It is to be hoped that science will advance to a more and more specific understanding of the physiology of sensation in this sort of way, and I believe that the physiology and the psychology will move closer and closer and eventually converge, as they already do in the case of ulcers and many other examples in the other sensory modalities.
One might wonder how it can be that two such supposedly different things as sores and sorenesses can interact, or even be the same thing, or how the same thing can be represented by two senses, or by one sense and by thought. To answer this, we should consider what Leibniz says about Molyneux’s problem. The problem is whether a man born blind, who has handled a cube and a sphere, would on regaining his sight, be able to tell by sight alone which was the cube and which was the sphere. Leibniz’s answer is that the newly sighted man would be able to tell which was which:
I am not talking about what he might actually do on the spot, when he is dazzled and confused by the strangeness—or, one should add, unaccustomed to making inferences. My view rests on the fact that in the case of the sphere there are no distinguished points on the surface of the sphere taken in itself, since everything there is uniform and without angles, whereas in the case of the cube there are eight points which are distinguished from all the others. … These two geometries, the blind man’s and the paralytic’s [to whom touch is denied] must come together, and agree, and indeed ultimately rest on the same ideas, even though they have no images in common.17
It is the same with the geometry of pains and the geometry of the physical body. They “rest on the same ideas [concepts], even though they may have no images in common.”
Interaction between Thought and Action
Finally, even in the most extreme examples of pure thought in the mind, we can find an overlap between the psychological sequence of thoughts, and the physical sequence that includes the resulting action. Suppose I raise my right arm high, doing so because I believe that I have the right answer, and because I want the teacher to call on me. As a schoolboy, my arm has been trained over the years to rise, to shoot up, in the right way, palm forward. The thought that I have the right answer enters my conative and action-oriented consciousness, and here I am phenomenologically aware of it flowing into my “arm consciousness.” The hardness and the strong pressure on my elbow on my desk seem to vanish. I have fingertip feelings above my hand, a sort of dancing toward the ceiling, and also a feeling that I know the right answer, and the answer is located in the palm of my hand! This is certainly very strange, and other people may have completely different but equally strange sensations, or none at all. I also have a strong awareness of my teacher’s face, especially his eyes. Up goes my arm, with my fingers wiggling toward the ceiling. Will I be called on to give the wonderful right answer, the answer that is mine?
Now if we filter from all this phenomenology what is physically relevant, which is to say what can be located in space, we find the Machian element of the arm shooting up, with sudden considerable acceleration, a snap in the elbow, and the fingers twitching at the ceiling. What do we find on physical observation of my arm? The arm shooting up, with considerable acceleration, a snap in the elbow, and the fingers twitching at the ceiling. Our two Machian elements coincide. Of course, we have to screen out much in the physical elements to see the match, and the same goes for the psychological elements; but the match is there. And when it is made, we know that we have the causation of the physical action by the psychological event: mind–body interaction. Such interaction can occur, because mental events can “become” or rather be taken to be physical elements, via their corresponding neutral elements. Which they are taken to be is a matter of which causal sequence they enter into. The first proposition in the inconsistent tetrad forming the mind–body problem is false, in the case under consideration. Here the mental is physical.
Mental events can “become” or rather be taken to be physical elements, via their corresponding neutral elements.
None of this means, however, that there are not elements “which obey only physical laws (unperceived material things, for example), some which obey only psychological laws (namely images, at least), or ‘wild particulars,’ as Russell called them, and some which obey both (namely sensations). Thus sensations will be both physical and mental, while images will be purely mental.”18 There could certainly be disagreement about which the “purely mental” elements are, but all we need in order to solve the mind–body problem is that the interacting elements, whichever they are, can be assigned to the physical or to the mental sequence, not that all elements have this character. There are images, in Russell’s example, that simply refuse a placement in a spatial scheme, and there are others that do not. There are also other images that can be placed at will in both sequences—for example, “floaters,” the distorting wormlike images caused by condensations of the vitreous humor in the eye.
A Model for the Mind–Body Problem
To close, I want to develop a model of the inconsistent tetrad with which we started. This model will allow us to formulate the solution that neutral monism gives to the mind–body problem.19 Imagine six refrigerator magnets, each with the shape of a numeral from “1” to “6,” with all six numerals represented, and each having one of six colors, red (R), orange (O), yellow (Y), green (G), blue (B), and violet (V), with all of the familiar six colors represented.20 Thus the elements of the array in the “refrigerator world” are colored numerals. The front of the refrigerator looks like this:
Let these elements be the only things the refrigerator world contains. It contains only colored numerals. The colors and the numerals themselves are secondary. The primary things are the elements: colored numerals, not colors and numbers in the abstract.
However, we can arrange our elements in two very different sorts of sequence: mathematical and nonmathematical. The most familiar mathematical one goes 1, 2, 3, 4, 5, 6, and the most familiar nonmathematical one, the spectrum, goes R, O, Y, G, B, V. Now we can ask about our model world, in the quaint idiom of the scientists, “How does the nonmathematical element in a nonmathematical sequence ‘arise’ from the mathematical one?” How can we get colors out of numerals? Well, the short answer is that we don’t, because we can’t.
Suppose we find a sequence 1, 2, 3, 4, 5, V, for example. This is obviously impossible, as 1, 2, 3, 4, 5, V is not any sort of sequence, and we have the “numeral-color problem.” But it is also a category mistake to place a color in a sequence of numerals. If you want the next term of a sequence represented by 1, 2, 3, 4, 5 …, it may not be 6, but it cannot be V.
We can now create an inconsistent tetrad in our refrigerator world, numbered (1r) (the “r” for “refrigerator”) to (4r), with the first and second propositions expressed as plurals. Mach was right to see the importance of not regarding the mind as a substance, uniformly physical or nonphysical. When the mind or its analogue in the r-tetrad is split up into its Machian elements, we can consider them separately, as in (1r), (2r), and (3r), below. It is important to develop this tetrad, as the neutral monists for the most part have contented themselves with vaguely thinking that the mind–body problem would go away merely if we were to think of all the elements as neutral. (Russell, writing in “On Propositions,” is an honorable exception.) Here is the new tetrad.
(1r) The color violet [an analogue for a part of the mind] is a nonmathematical [nonphysical] thing.
(2r) The numeral 6 [an analogue for a part of the body] is a mathematical [physical] thing.
(3r) Violet [a part of the mind] and the number 6 [a part of the body] follow [an analogue for causation] one another.
(4r) Mathematical [physical] and nonmathematical [nonphysical] things cannot follow one another.21
It is important that in this analogy, the tetrad (1r)–(4r) refers to individual elements, in the plural (the colors, such as 6, and the numbers, such as violet), and not to two things representing “the mind” and “the body.” (These analogues would be “color” and “number,” both, as we say, “in the abstract.”) For Mach and most neutral monists the right approach to the mind is the deflationary one. It is reductionist, in the sense that it reduces the mind to its elements.
If we substitute “the violet number (or numeral)” for “the color violet,” it becomes immediately apparent that we can assign the neutral element (the violet number or numeral 6) to the mathematical sequence (1R, 2O, 3Y, 4G, 5B, 6V), in which case (1r) is false, or we can assign the colored numeral 6 to the nonmathematical sequence (R1, O2, Y3, G4, B5, V6), because it is violet, and (2r) is false. In both cases, the “color–numeral problem” has been solved. If we apply the lesson learned to the original tetrad about the mind–body problem, then the mind–body problem has been solved as well. The desire for coffee is usually placed in the psychological series. If it is, it makes no sense to also place at it the end of a physical causal chain, any more than it makes sense to put V at the end of the sequence 1, 2, 3, 4, 5 … . But if we regard the desire as a physical one, and place it in the appropriate place in a physical sequence, we have mind–body interaction, for the desire is now to be regarded as a physical one, given a rough location in the body, and then given its appropriate causes and effects, including my reaching out for the cup of coffee.
We can even represent the different standard philosophical positions about the mind–body problem within the refrigerator world as attempts to make the tetrad consistent by rejecting one of its constituent propositions. For example, behaviorism states that a color is to be analyzed in terms of the disposition of a numeral to fall in a specified group of numerals; central-state materialism states that a color is identical with a numeral; functionalism states that a color is a functional or computational state of a machine, a machine that computes colors from numerals; eliminative materialism states that a perfected science will eliminate color descriptions in favor of the mathematically superior numerical descriptions; dualism states that colors and numerals are distinct entities. The last position is of course true in the real world, but false in the refrigerator world. With some ingenuity, the main existing scientific accounts of consciousness can be represented in a similar manner.
We do well to remember that the mind–body problem really is a paradox. Its solution is to be found in the intricate arguments for the four propositions in the inconsistent tetrad, and in the concepts embedded in these propositions. Neutral monism allows us to see this point very clearly indeed. We are used to thinking of the tetrad and the mind–body problem in fixed concepts, of the mental and the physical, and of the mind and the body. Then there is nothing for it; something has to give. Yet it is no good trying to wriggle out by assimilating one set of concepts to another, so that everything mental is declared to be really, incomprehensibly, physical, for example. The beauty of neutral monism is that it allows us to shift our given elements from one category into another, in a way that is legitimated by the phenomenology and does nothing to undermine the integrity of the given categories. Everybody knows that somehow the mind–body problem calls for a very fundamental shift in our understanding, and this is it. Our concepts must change gear, and neutral monism shows us how to do it. The pain of an ulcer is mental, in the sense that it can be scaled in entirely in psychological terms, and without a spatial reference, by its intensity, duration, quality, and felt location; but if we wish to understand the pain in relation to the body, we must learn to see how the psychological body schema can be aligned with the body, and how the pain can then be pointed to at a genuine location within the body and the wider physical world.
