Maxwell’s Unique-Matching Theory

Philosopher of science Nicholas Maxwell offers a ‘Unique-Matching Theory’ of consciousness, positing a one-to-one, structure-preserving isomorphism between a multidimensional space of all possible sensations and a corresponding space of functionally described brain processes. This structural necessity accounts for specific correlations without requiring reductive explanation. The resulting theory, he claims, maintains explanatory power while preserving the phenomenological richness and privacy of experience (Maxwell, 2003).

Maxwell presents his theory in the context of his broader approach to a non-reductive account of consciousness, in which he addresses three fundamental philosophical problems about consciousness: its existence (“Why does it exist?”), intelligibility (“How do we explain and understand it?”), and the relationship between brain processes and mental functions (“How can we explain brain-consciousness correlations?”). He approaches these with a radically non-reductive, pluralistic framework that synthesizes philosophical insight, scientific realism, and imaginative metaphysics.

Philosophical Problems and Experiential Functionalism

Regarding the existence of consciousness, Maxwell argues that if cannot be explained in principle—the problem is inherently unanswerable, not due to the nature of consciousness itself, but due to the limits of explanation, because explanation requires reference to something else, which is absent in ultimate ontological questions. “We can, perhaps, explain the way the physical and the experiential are correlated; but it is inherent in the very concept of explanation that neither the existence of the realm of the physical, nor the existence of the realm of the experiential, is capable of being explained.” This is why Maxwell contends that the existence of consciousness is not mysterious but unexplainable in principle, paralleling the ultimate metaphysical mystery of why anything exists at all.

Regarding the intelligibility of consciousness, “What is so baffling and mysterious about consciousness is that each one of us knows it exists, and knows what it is, because we possess it, indeed we are it, in a certain sense; and yet, if we examine a conscious brain, we find such things as neurons and synaptic junctions, but nothing remotely like consciousness as we experience it.”

He claims that “(a) there is an explanation as to why science cannot explain consciousness, and (b) consciousness can be explained by a different kind of explanation, an empathic or ‘personalistic’ explanation, compatible with, but not reducible to, scientific explanation” (Maxwell, 2003).

While recognizing that functionalism, if correct, would solve all three fundamental problems, he sharply rejects functionalism as untenable. This is because, he says, “No set of physical statements, however comprehensive, can predict that a poppy is red, or that a person has the visual experience of redness,” such that “there are mental or experiential features which lie irredeemably beyond the scope of physical description and explanation,” including “the neurological processes going on in our brains.”

Maxwell’s argument goes as follows: “Physics, and that part of natural science in principle reducible to physics, cannot conceivably predict and explain fully the mental, or experiential, aspect of brain processes. Being blind from birth—or being deprived of ever having oneself experienced visual sensations—cannot in itself prevent one from understanding any part of physics. It cannot prevent one from understanding the physics of colour, light, physiology of colour perception and discrimination, just as well as any normally sighted person, In order to understand physical concepts, such as mass, force, wavelength, energy, spin, charge, it is not necessary to have had the experience of any particular kind of sensation, such as the visual sensation of colour. All predictions of physics must also have this feature In order to understand what it is for a poppy to be red, however, it is necessary to have experienced a special kind of sensation at some time in one's life, namely the visual sensation of redness.” (Maxwell notes, “I might mention in passing that this argument, usually attributed to Thomas Nagel [1974] and Frank Jackson [1982, 1986], was actually first put forward by me several years before Nagel and Jackson, in two papers published in 1966 and 1968.” Maxwell says that Nagel and Jackson later acknowledged this, each in a different way [Maxwell, 2003, footnote 7].)

With functionalism inadequate due to its inability to capture qualitative experience, Maxwell proposes a two-aspect theory—which he calls ‘experiential functionalism’—where consciousness is what it is like to have a brain process occur in one’s own brain. This form of awareness resists scientific explanation not because it is inherently mysterious, but because science only captures causally efficacious structures, excluding the subjective. Consciousness is instead intelligible through empathic or personalistic explanation, an anthropomorphic mode of understanding irreducible to science.

Here is what Maxwell means by describing ‘experiential functionalism’ as a two-aspect theory. “Sentience or consciousness, according to the two-aspect view I wish to defend, is that aspect or feature of a brain process that we can only get to know about as a result of having a sufficiently similar brain process occur in our own brain. It is what it is to have that kind of process occur in one's own brain. It is just that, and nothing more.” According to Maxwell, this makes consciousness private yet intelligible, explainable not by science but through ‘personalistic’ or ‘empathic’ explanation. Unlike scientific explanation, which is impersonal and objective, personalistic explanation requires relating the other to oneself. Moreover, it is essential for understanding the mental, which science must omit to preserve its explanatory power.

God-Like Being, Sensation Space, and Unique-Matching Theory

Regarding the brain-consciousness correlations, Maxwell relates that he had been stumped: “It seems that no amplification of personalistic explanation could do the trick either. Suppose there is a God-like brain that can experience all possible sensations; suppose further that He knows all there is to know about the way His brain processes and sensations are correlated. Despite this vast store of experience and knowledge, it would seem that the God-like being is in no better position to explain why brain processes and sensations are correlated as they are than we are" (Maxwell, 2003).

Then, Maxwell says, “it struck me that there is just one circumstance in which an explanation for brain-sensation correlations does exist. Suppose that a God-like brain is indeed possible; it is able to experience all possible sensations. Suppose, further, that our visual, auditory, tactile, olfactory, and other sensations form disjoint regions within the continent of sensations experienced by the God-like being. To us, the different modes of experience seem utterly distinct in kind. Visual sensations seem utterly different from auditory ones, which again seem utterly different from tactile and olfactory sensations. If one had only experienced visual sensations, one could never guess what auditory, olfactory or tactile sensations would be like. But let us suppose that the God-like being is able to experience endlessly many sorts of sensations that lie between our visual, auditory, olfactory, and tactile sensations. To Him, as he moves from the visual towards the auditory, there is a continuous, slight change in the quality of the sensations experienced, much as there is for us, within the auditory, when a tone goes continuously up in pitch. Moving, by means of continuous changes in the quality of sensations, from visual to auditory, the auditory comes as no surprise: it emerges as a result of smooth transitions, as in the case of the tone rising in pitch. And the same goes for transitions between other modes of sensations: the visual, the auditory, the olfactory, the tactile and so on” (Maxwell, 2003).

From this, Maxwell sets conditions for developing his Unique-Matching Theory. “For the God-like being, all possible sensations lie in a multi-dimensional ‘space’ of possible sensations, the experienced quality of sensations varying smoothly, continuously, indeed in a steady, linear way, as one moves around in the multi-dimensional ‘space’ (one kind of smooth variation in sensation, such as changes in pitch of a sound of specific timbre and loudness, corresponding to one dimension in the ‘space’ of sensations). To the God-like being, this vast realm of possible sensations has a kind of overall coherence, a unity, an overall structure, based on the fact that the quality of sensations varies smoothly, from sensation to sensation. There is, we may suppose, just one way in which all these possible sensations can be ordered and ‘placed’ in the multidimensional space, so that continuity is preserved throughout the space, so that the closer together any two sensations are in this space, then the more nearly alike they are experientially.”

Now Maxwell moves to formulate his Unique-Matching Theory by calling upon David Chalmers' ‘principle of structural coherence’ (Chalmers, 1996) in which the multi-dimensional ‘space’ of possible sensations “are mirrored in the ‘space’ of the functionally described brain processes that are the sensations.” In Maxwell’s telling, “As the God-like being moves smoothly from experiencing one sensation to experiencing a slightly different sensation in a neighbouring ‘place’ in the multidimensional space of all possible sensations, so the brain process, that is the first sensation, becomes the slightly different brain process that is the second sensation, slightly different, that is, when described in functional or control terms. The smooth coherence and unity of sensation space is matched by a corresponding smooth coherence and unity of brain process space, when brain processes are characterized in control terms. There is, as mathematicians would say, something like an isomorphism (a common structure) between the space of sensations and the space of brain processes. This matching of structure is, we are to suppose, unique. It can only be done in one way. Change the way sensations are matched up with (functionally described) brain processes, and the common structure between the realm of sensations and the realm of brain processes is lost… They have to be correlated in this way, because if they are not, the matching of structure, of unity, based on continuity, between sensations and brain processes, would be lost” (Maxwell, 2003).

Thus, Maxwell proposes his speculative but quasi-mathematically structured Unique-Matching Theory with three propositions:

• There is a kind of ‘space’ of all possible mental sensations, multi-dimensional and continuous.
• There is another kind of ‘space’ of all possible brain processes, corresponding and described functionally.
• There exists a unique one-to-one mapping between the two ‘spaces,’ such that, via this structural necessity, continuity and linearity are preserved.

According to Maxwell, a first reaction might be that his theory is “much too wild and crazy to be a serious candidate for truth (even possible truth).” Yet he argues that, although fantastical, his theory would be the only way to explain brain-consciousness correlation without reduction, because structural necessity would provide a deep isomorphic mapping between mental experience and brain function. Thus, Maxwell’s Unique-Matching Theory would integrate multiple modes of understanding—scientific, personalistic, and metaphysical—without collapsing them into a single paradigm (Maxwell, 2003).