General Reactivity Theory

Consider the simple reflex: the blink reflex or the patellar reflex, for example. There is a stimulus and a response: the stimulus is an impinging physical event and the response is a movement of the body. The stimulus elicits the response without any psychological intermediary; the reflex arc exists outside of consciousness and will, automatically, inexorably. It is a case of straight physical causation. But it is not quite as simple as it may appear, since more structure must be postulated than mere stimulus and response (plus linking pathways). First, the stimulus must be detected and recognized for what it is, if not by the person then at least by the person’s nervous system—there needs to be a stimulus receptor. Second, the response is not produced purely by the physical properties of the stimulus but by a suitable response generator—a mechanism for triggering an appropriate movement of the body. It would be no use if a tap on the knee caused the eyelid to close or if an incoming missile heading towards the eye caused the knee to shoot up! The generator must deliver a response that corresponds to the stimulus; nothing about the physics of the stimulus alone determines how the body will react. So the twofold stimulus-response structure is really a fourfold stimulus-receptor-generator-response structure. And note that the extra two ingredients are more internal to the organism than the stimulus and response as such, and they are more information involving. Furthermore, it would be wrong to characterize the stimulus-response nexus as merely a cause-effect nexus, as if there was nothing special about stimuli eliciting responses compared to physical causes bringing about physical effects. Lightning hitting a tree and scorching it is not an instance of stimulus and response, as falling to earth is not a response to the stimulus of gravity (the motion of the planets is not a response to the stimuli supplied by the sun). The stimulus-response relation is a special type of causal relation, if it is a causal relation at all. The obvious point is that it is purposive—a matter of design, adaptive and teleological. The response reflects the needs of the organism and contributes to its survival. We only call an event a stimulus if it affects organisms in certain ways not because of its physical parameters. And what counts as a stimulus for one type of organism may not count as a stimulus for another type, depending upon its receptivity and responsiveness (e.g. sounds that are too high for humans to hear or light that lies outside the humanly visible spectrum). The concepts of stimulus and response are proprietary to living systems and involve teleological notions. A stimulus is not just any old cause and a response is not just any old effect. The OED puts it nicely: a stimulus is defined as “a thing that evokes a specific functional reaction in an organ or tissue” (deriving from the Latin “goad, spur, incentive”). In short, it is a biological notion. The word “respond” is also defined by the OED in loaded terms: “to say or do something as a reply or as a reaction”. Correspondingly, a stimulus is said to elicit a response not merely to bring it about, as a response is a reaction to a stimulus not merely a consequence of it. These are all biologically loaded notions by no means equivalent to physical concepts. Living organisms are the proper subjects of these notions, and they purport to describe the specific nature of such entities. Even the simplest reflex is conceptually rich in the way outlined.[1]

The question I am concerned with is whether this network of notions has a wider application in describing the operations of mind. To put it with maximum bluntness: is the mind a stimulus-response system? I shall suggest that it is, so the simple reflex can act as a model for the general character of the mind. I intend this to sound outrageous, given the uses to which the notions of stimulus and response have been put, but on reflection we may have thrown the S-R baby out with the behaviorist bathwater. This may still be a useful and accurate way to talk, even though it has been multiply abused. The first point to note is that it has nothing essentially to do with any attraction to materialism or behaviorism: stimuli and responses may be psychological in nature, irreducibly so. Nor need they be observable or measurable or public or experimentally usable. For instance, we may reasonably say that pain is a response to a harmful stimulus, even if the pain is unobservable and non-physical–even if it is entirely immaterial. The point is that the sensation is automatically elicited by the stimulus—the two things stand in the S-R relationship. Likewise, a sensation can act as a stimulus eliciting a response, as when a pain elicits a cry or an itch elicits scratching. In fact, it is entirely appropriate to describe perception in general as a reflexive stimulus-response system: the impinging stimulus, say irradiation of the retina, elicits a sensory response, say seeing a red object. This is a “functional reaction” to an incoming stimulus—and the physical impingement acts as a stimulus for the organism in question. The perceptual response is an adaptive reaction to the organism’s environment, entirely analogous to the blink reflex or the perspiration reflex or the flinching reflex or the disgust reflex or the salivation reflex. Seeing an object is a stimulus-response linkage. And let it be noted that the extra layers of receptor and generator are present here too: the senses need receptors to register the stimulus and a mechanism to generate the percept that results. There is nothing behaviorist about this in the classic sense. It is unapologetically mentalist.

The interesting question is how far the S-R model can be extended, and here some controversy can be expected. Let’s consider belief, emotion, and intentional action. Belief can be viewed as a response to the stimulus afforded by perception: you see a red object and respond by forming the belief that there is a red object there. We need not suppose that forming a belief is an action—it is not—but we can suppose that it is a reaction to a percept; not all reactions are volitional. The cognitive system is set up in such a way that beliefs are triggered by perceptions: beliefs are “functional reactions” to the stimuli afforded by the perceptual apparatus. The seeing elicits the believing. In the case of beliefs that arise by inference we can say that the conclusion belief is a response to the premise beliefs: beliefs can function as stimuli that evoke other beliefs as response. Again, this is adaptive and functional—as is very evident for animals solving problems by reasoning. The premise beliefs don’t just cause the conclusion belief; they act as stimuli that elicit that belief—that is, they are part of a functional biological system. In some cases the inference pattern may be instinctual, in others learned, but it is an S-R arrangement in either case. In the case of emotions, the response is triggered by an external stimulus, say a threat; and the response may be rapid, automatic, and unavoidable (again think of animals). The emotion is an evoked response, also functional. Fight or flight responses are mediated by emotion, and the emotion is as much a response as the behavior that goes with it. We ask, “What was your reaction?” when hearing about some untoward experience of a friend, and expect to be told what emotions were evoked. This is just stimulus and response, though of a more complex and mediated nature than simpler cases. In the case intentional action we can introduce need and desire as stimuli: the organism is prodded to act (goaded or spurred) by its internal appetitive states, say hunger or amorous desire. The desires act as stimuli to the volitional (motor) system and they serve to elicit appropriate actions.[2] These stimuli can vary in intensity as perceptual stimuli can; the response evoked is thereby modified and enhanced. Logically, the case is just like other S-R linkages—biologically functional causal patterns. And again it will be necessary to postulate receptors and generators as well as the stimuli and responses themselves—all the machinery of response elicitation.

There is thus a recurring pattern in the functional architecture of the mind: stimulus-response relations elaborately organized, varying from simple to complex. There are chains of such patterns, as a response becomes a stimulus to a further response, which in turn becomes a stimulus.[3] We must purge ourselves of old associations of these notions deriving from an antiquated behaviorism. No doubt the early behaviorists were influenced by nineteenth-century biology, in which the idea of biological responsiveness played an important role—as in early studies of the nerve impulse. Neurons were discovered to work by means of stimulus and response, as one neuron abuts another and evokes action potentials in it. Tissue in general was described as “irritable”—reactive, alive, lively. The behaviorists then took this useful way of thinking and converted it into a positivistic picture of public bodily events. But the conceptual apparatus itself is quite independent of this move, merely recording the biological fact of one thing eliciting another in a functional manner. The whole organism is composed of reactive organs that respond in certain ways when stimulated in certain ways, the brain being no exception. It is then a short step to regarding the mind, itself a biological organ, as likewise an array of S-R linkages. This enables us to take the mind down from pre-Darwinian obscurity and religious obscurantism (the soul etc.) and locate it within the biological organism.[4] We thus obtain a healthy biologism about the mind not a doctrinaire behaviorism (unless we choose to liberate behaviorism from its materialist and positivist dogmas by opting for internalbehaviorism). It is true that the notions of stimulus and response must be extended considerably from the case of the simple reflex—in particular, in relation to the automatic character of such reflexes—but there is no logical bar to accepting that some S-R connections may be less fixed and invariable than others. There can be probabilistic response elicitation, even resistance to some types of potential stimuli (e.g. strong but unwelcome desires). We can allow that theory formation in the sciences counts as an advanced form of response elicitation by the stimuli offered by the evidence, odd as it may sound to talk this way. The S-R schema does not stop at the higher cognitive functions when suitably generalized. In addition, it should not be supposed that the mind admits of no other useful mode of description: we can certainly acknowledge that there are mental competences, mental faculties, and mental qualities. It is just that mental operations have a stimulus-response structure: mental transitions are always governed by S-R logic. Even the humble patellar reflex needs its underlying machinery—competence, if you like—and linguistic stimulus-and-response undeniably relies on an underlying structural competence. The same is true of organs of the body: each needs its specific architecture and cellular substrate in order to permit the stimulus-response connections in which it engages. But when we describe an organism as a situated living thing, acting and reacting in the world, transitioning from one state to another, we need the conceptual apparatus of stimulus and response. All I have done here is suggest applying it more widely than is customary. For it provides a nice unifying framework for thinking about the mind, shorn of all connection with behaviorism, conditioning learning theory, anti-nativist empiricism, and anti-cognitive bias. Cognitive science turns out to be S-R psychology after all, when properly understood.[5]

C

[1] The stimulus-response concept is not the same as the input-output concept. The latter concept is more general, applying to non-living systems as well as living ones, and it lacks the teleological connotations of the former concept. It derives more from computer technology than traditional biology.

[2] There is nothing contrary to freedom in this fact, given a good analysis of freedom, but I won’t go into the question of free will now.

[3] In psychology it is customary to distinguish the proximal and the distal stimulus, e.g. the light proximally impinging on the retina and the distant object sending out that light. The same kind of distinction can be applied to the full range of S-R relations: the proximal stimulus to a belief might be a conscious perceptual state while the distal stimulus is a pattern of light on the retina. Also we can define the same kind of distinction for responses: the proximal response for a percept might be a belief while the distal response is an utterance expressing that belief. The same distinction can be applied to desires and emotions, where there can be closer and more remote stimuli and responses.

[4] I don’t mean to suggest that all mystery is removed thereby, only that the mind is set in its proper place as a natural attribute of organisms. We get a conceptual continuity between the various aspects of organisms.

[5] This enables us to inject a welcome dose of biology into cognitive science, which tends to view the mind as inherently divorced from the processes of life, like a computing machine. It is not as if theorists have adopted a computer model for the activities of the body. Cognitive science has in effect erected a new form of dualism, which the S-R schema helps us transcend.

Complex Minds

I wish to make a very general point about the complexity of the mind—not just the human mind but minds generally. There has been a tendency to think that the mind is relatively simple: it consists of simple ideas and principles of combination of these ideas; or it is a collection of reflexes, conditioned and unconditioned; or it is basically a blank slate; or it is composed of beliefs and desires; or it is made up of behavioral dispositions; or it consists of algorithms that are reducible to operations on ones and zeroes.[1] At a more immediate level, introspection doesn’t reveal a particularly complex entity: our consciousness may be puzzling theoretically, but it is not all that complex superficially. Compare it to the body and brain: everyone with any knowledge of the subject knows that the body and brain are amazingly complex entities, far more complex that casual inspection reveals. If you just look at a human body, you observe some complexity, yes, but not the enormous complexity that exists beneath the skin. This is why people were surprised to discover the degree of complexity hidden in the animal body: all those varying organs, the cellular structure, the interior of the cell, the packed intricacy of the brain. Commonsense does not anticipate the discoveries of anatomy and physiology, which reveal a complexity that goes far beyond what we might have imagined. No doubt all this complexity has a biological rationale; it is not to be supposed that evolution would equip the body with so much complexity for no reason. This is functional complexity not gratuitous ornamentation. But we don’t tend to adopt the same view of the mind: we don’t tend to think that the mind is vastly more complex than it appears. We tend to think that its complexity is limited to what we observe, give or take a bit. True, Freud supposed that there is a substantial hidden portion to the mind, viz. the unconscious; and modern proponents of an unconscious mind have likewise posited some underlying complexity. But I don’t think the magnitude of the mind’s hidden complexity has been compared to the magnitude of the body’s hidden complexity, as these have been conceived. Does the mind have the same degree of hidden complexity that the body has? Is it, in particular, as complex as the brain? I think it has been assumed that the answer to these questions is No—because it is not supposed that the mind requires so much hidden machinery.

Why is this? Evidently it’s because we don’t know as much about the hidden complexity of the mind. No doubt before anatomy and physiology developed (not to mention molecular biology) people underestimated the complexity of the body, supposing it to be not to be much more complex than it appears to the naked eye. But science disabused them of that impression: it revealed the body to be a lot more complex than it seemed. Similarly, we now don’t know that the mind has this kind of hidden complexity, so we don’t tend to acknowledge it—why postulate complexity when there is no empirical need to? Maybe the mind is actually fairly simple, just as it appears. The mind is just one organ possessed by the animal, it may be said, so its complexity might not be greater than that of other organs, say the kidneys. Maybe the mind only uses part of the complex brain, so it lacks the complexity of the full brain. There is no principled reason that the mind should be more complex than it has appeared to us hitherto—medium-level complex, one might say. Isn’t the mind of an insect a good deal less complex than its body—as complex as its digestive system perhaps? Insects have simple minds, reptiles less simple minds, and mammals have minds that are still relatively simple in comparison with their bodies. External observation does not contradict this idea, and introspection confirms it. Hence the relatively simple theories of mind offered by behaviorism and empiricism.

The point I want to make is that this is unlikely to be true. It is more likely that the mind, like the body, harbors a vast inner complexity of which we have but a tiny inkling. That is, our impression of the mind’s lack of complexity results purely from our ignorance of its workings, rather as scientifically primitive people underestimated the body’s complexity for similar reasons. I don’t claim that this must be so, but it seems to me the more likely hypothesis. Why? The reason is that the mind, like the body, is the result of millions of years of assiduous evolution, constantly expanded, fine-tuned, minutely engineered, optimized, refined, and powered up. This is precisely why the brain is so complex—so as to cater to the needs of the mind. Of course, we don’t see all this on the surface—any more than we see the body’s complex machinery through the skin. Evolution has no need to show us its handiwork, but it does have a need to do that work—and it has been doing it for a very long time. It has been shaping, constructing, experimenting, honing, inventing, and advancing—just as it has with the bodies of animals. How could this not be so? The mind is bound to be complex—and just as bound not to be visibly so. Evolution is a relentless complexity-generator. We get a sense of this with recent work on vision in which the visual system emerges as much more complex than it seems to the average viewer (the complexity of visual constancy is notorious, despite its seeming simplicity). But much the same must be true of other mental phenomena, such as pain: pain is not some punctate atom with no inner complexity and an on-off etiology; it is a carefully calibrated biological system that has evolved over millions of years. In all likelihood the mind as a whole is an incredibly complex operation far exceeding what we currently imagine. It is just that so far we have received only hints of that complexity. And this is so for a rather obvious reason: we can’t open up the mind and have a peek inside, as we can the body. Dissection revealed the body’s hidden complexity (some of it), but dissection is no help in revealing the mind’s hidden complexity. For that we need theory, but psychology has not produced the kinds of deep theory that we might hope for; it hasn’t done for the mind what anatomy and physiology did for the body.

This perspective has an obvious consequence: an enormous proportion of the mind is not conscious. How much? Oh, let’s say 90% just to have a concrete figure. How much of the body’s complexity is hidden under the skin? I’d say roughly 90%, wouldn’t you? Most of the body is hidden from casual inspection: so isn’t it reasonable to expect that the same is true of the mind? Thus about 90% of the mind is unconscious. This estimate might be modified by advances in psychology, but it seems like a reasonable shot in the dark. If the mind has substantial hidden complexity, which general considerations about evolution suggest, then it follows that it has a substantial unconscious component. If the complexity were conscious, it wouldn’t be hidden to us; so given that it is hidden, it must be unconscious. We might picture this unconscious as analogous to the ceaseless operations of the cells of our body as they go about their life-sustaining business; likewise the machinery of mind hums away behind the scenes allowing us to function as we do and have the conscious minds we have. Language is a prime example here: there is good reason to believe that linguistic competence and performance are substantially organized unconsciously; and there may be deeper linguistic levels than any so far plumbed. The entire conscious mind is likely to be sitting on top of a mountain of unconscious machinery of unimaginable complexity, of which we are barely aware. We are like anatomists in the Stone Age, scarcely glimpsing the complexities of the human body. To be sure, our minds seem pretty simple to us now, but that may be an illusion born of ignorance.[2] On God’s complexity-meter the mind might be the most complex thing in existence, despite its relatively simple façade. Not more complex than the brain obviously, but close to it. The brain contains billions of neurons and even more billions of neural connections: how many parts and part connections does the mind have? Maybe a million times what it now appears to have?[3]

[1] I might also cite Wittgenstein as an apostle of psychological simplicity, given his doctrine that “nothing is hidden”. Granted he thinks that our language games can be quite complex, but the general tendency of his thought is to downplay any underlying complexity in our minds. It is true that he sometimes criticizes earlier philosophers and psychologists for oversimplifying the variety of mental phenomena, but he still keeps to a relatively simple view of the mind compared to the complexities of the body. (Note: this comment is subject to the usual caveats about interpreting Wittgenstein.)

[2] I should emphasize that judgments of simplicity are always relative, so when I say the mind seems pretty simple to us now I don’t mean simple simpliciter; I mean simple compared to things we regard as truly complex, like bodies and brains. Minds are certainly complex, according to common sense, compared to (say) leaves or electrons or grains of sand.

[3] The panpsychist will presumably concur, since he views the mind as a complex consisting of billions of mental elements corresponding to neurons (and their parts). For the panpsychist it is axiomatic that the mind is vastly more complex than it seems. Actually the same could be said of materialism, which might be used as an argument against materialism by an adherent of common sense: for how could the simple character of mental states consist in the kind of complex physical state present in the brain? Isn’t the feeling of pain a lot simpler than the physical state of C-fibers firing? The self indeed has been claimed to be simple simpliciter, whereas the body is extremely complex—so the former can’t be the latter. In any case, materialism confers the complexity of the body and brain squarely on the mind. The materialist is therefore committed to the idea that the mind has vastly more complexity than appears to us. I am suggesting the same picture but without the materialist assumption: the complexity of the mind is a mental complexity.

Language and Music

What kind of phenomenon is language? I shall consider this question by comparing language with music—though I shall also be concerned with what kind of phenomenon music is, especially toward the end. Language occupies a curious no-man’s land, being neither purely external not purely internal.[1] We can talk to others out loud or we can talk to ourselves silently; and we can talk in a semi-whisper to no one in particular. It is sometimes hard to tell whether an act of speech is mental or physical: is your larynx moving slightly as you talk to yourself? You can make what feels like a smooth transition from inner to outer speech with no abrupt shift from inner to outer. You can also write words down as well as speak them, and this writing can take several forms. Audition need not be involved. It is hard to tell whether one’s inner speech is auditory or modality-neutral; for deaf people it is not likely to consist of auditory imagery. So language can manifest itself in many forms; it is not tied to a single medium or sensorimotor capacity. One might be tempted to call it a psychophysical phenomenon in an effort to capture its protean character, but that presupposes a kind of dualism better avoided (we don’t want to be procrustean about the protean). We could say multiform or variegated, though that doesn’t offer much in the way of illuminating description. What we can assert is that it would be quite wrong to assimilate language to a type of physical behavior, as it might be the sounds produced by the vocal apparatus; there is much more to language than that, and also much less.

Here music affords a helpful analogy: where does music exist? We can play an instrument or sing out loud, or we can quietly hum a tune to ourselves, or we can silently rehearse a melody in the mind. It may not be clear to us whether the music is purely within us or engages our motor faculties: were you minutely flexing your fingers to tap out that imagined rhythm, did your vocal cord contract slightly when you inwardly reached for a high note? The inner-outer dichotomy seems insufficient to capture the full range of musical expression: some music is more outer than other music, some more inner. And which is basic? Did music exist in our minds before we ever gave public expression to it? Music, like language, occurs in many forms, which we clumsily describe with words like “psychological” and “physical”; in reality it is fluid and various, seemingly indifferent to its contingent vehicle. It is possible to practice one’s singing without making a sound, just by inner note production aided by an active vocal cord. To identify music with external musical behavior would be hopelessly reductionist. Where does music exist? Everywhere and nowhere: it slips and slides from one domain to another, varying within the sensorimotor system and sometimes detaching itself from that system altogether. I would be inclined to say that it is primarily mental, as I would be inclined to say the same of language—though that too risks the procrustean. Music and language are creatures of many guises, many exemplifications.

This is partly because they are both essentially abstract, mathematical even. Language consists of a finite array of digital elements that can combine by rules to produce an infinite number of complex structures—a kind of computational system. As such it can take many forms without losing its identity: wherever the abstract system exists there is language–in the head, in the air, on paper, in neon. It is a form beneath a substance—a pattern not a stuff. Someone could be operating with language and be completely different from us mentally and physically, so long as they instantiate the abstract pattern of language: a combinatorial system equipped with syntax and semantics (a bit like a computer program, as is often said). But music is very similar, only it uses a different kind of abstract mathematical structure. Music is analogue not digital: it uses a continuous magnitude (pitch) and divides it into discrete units. Thus we obtain scales and keys by segmenting the sound medium in various ways: tones, semitones, named notes, octaves, etc. The major scale, say, is just a mathematical construct defined by using intervallic structure: it can be reproduced on any instrument permitting variations of pitch (which itself is just frequency of vibration). Rhythm is the same: intervals of time (not pitch intervals) punctuated by discrete sounds. Musical notation represents melody and rhythm by means of geometry: the placing of a mark in a higher or lower position on the stave, and the use of differently shaped marks for note lengths as well as distance along the stave. The abstract structure can exist in an instrument or in a voice or purely in the head. Without such a structure no music can exist (just noise), and where the structure exists so too does music.

Accordingly, when we hear language spoken we are hearing an abstract structure with certain formal properties (discrete infinity being central), and when we hear music being played we also hear an abstract structure with certain formal properties (a continuous infinity segmented according to recognizable rules). Breaking the rules destroys language and destroys music (unless another set of rules is set up): random order is the enemy of both language and music. Linguistic theory studies the form of these rules, as music theory studies the form of musical rules. In both cases it is an abstract structure that constitutes the phenomenon not its contingent vehicle: the same tune can be played on a piano or a trumpet or a human voice (outer or inner), as the same sentence can be spoken or written down or rehearsed inwardly. We hear sequences of elements in time that have been constructed according to certain rules and which admit of multiple realizations. We should not confuse the thing itself with its passing manifestations. The processing mind must be attuned to a formal structure as well as to a type of physical stimulus. The underlying psychology is mathematical.

We also have a competence-performance distinction in both cases: the competence can exist when performance is lacking through injury or fatigue. The competence has a heavy cognitive component, though it also contains motor instructions; by no means is it merely a matter of stimulus and response. Learning is involved in both cases, easier in childhood than adulthood, and no doubt there is an innate component (a gene for language, a gene for music). The two can sometimes converge as in song: the language faculty must mesh with the musical faculty to produce words with melody. Discrete digital infinity meets continuous analogue infinity. Speech rhythms interact with musical rhythms. Is this why song is so universally appreciated? It combines two of our most impressive attributes (sadly lacking in other animals that have no appetite for song). When you listen to a song your language faculty is fully engaged, with all its productive power, and in addition your musical faculty is fully engaged, with its capacity to resonate to melody and rhythm. Even a mediocre singer is operating at a very high cognitive and motor level; aliens might marvel at our routine ability to sing a song, thinking what superb mathematicians we must be in order to wield the abstract structures involved simultaneously. Also, language and music are regarded as expressive of thought and emotion. Music can use language this way, as in song, but language can use the resources of music too, as in variations of pitch and volume, or staccato utterance. The two faculties are not completely disjoined in practice, despite the distinction of modules. It would be wrong to say that language is a type of music or that music is a type of language—they embody quite different constitutive principles—but at a more general level the affinities are clear. Abstract mathematical structure with multiple realizations—a kind of fluid fixity, disciplined variety, creatively rule-governed. A twenty-six-letter alphabet, a twelve-tone scale—but all that coiled creativity! This is the power of combination applied to an economical base. In both cases, too, a lot happens behind the scenes: we don’t consciously apprehend what music theory and theoretical linguistics reveal—these belong to the unconscious mechanisms that enable us to hear the sound stimulus as exemplifying music and language. The brain computes and the mind enjoys, or at least understands. Teachers instruct you in the rules of grammar and musical composition, often bafflingly, but your unconscious was onto to this stuff long ago.

So we see an affinity between language and music, but there is one difference that stands out and threatens to undermine the analogy, viz. that there is no such thing as sign music. The deaf can use sign language, thus demonstrating the independence of language and the auditory medium, but no one “listens” to sign music, thus demonstrating the independence of music and the auditory medium.[2] Music seems more closely tied to sound than language is: sound strikes us as essential to music. How then can music consist in an abstract structure that is only contingently exemplified in an audible medium? So is music not like language after all? Is it a modality-specific phenomenon? These are good questions, but I think they have an answer—namely, that it is only contingent that non-auditory music doesn’t exist. Consider rhythm first: we usually register rhythm through our ears, but it is possible to register it through touch. We can feel pulses of rhythm in the air or by direct physical contact with the body, say by tapping; sometimes we feel our heart beating. It is imaginable that someone might develop this type of perception further and even come to enjoy the pleasures of touch that are involved. In the case of melody we need an analogue of pitch; here colors might do the trick, with blues for low notes and reds for high notes, along with degrees of saturation. We could map pitch differences onto color differences and produce sequences of colors with the same intervallic structure as pitches. Then an identical abstract structure would exist in the visual sense as now exists in the auditory sense. A composition could combine color presentations for melody with tactile stimuli for rhythm. Wouldn’t that be music? Suppose we came across an alien species that was constitutionally deaf yet musically inclined. They might have an elaborate musical culture built around vision and touch. We can suppose that the same emotional associations exist for them with respect to sights and feels as exist for us with respect to sounds. They have an advanced technology that enables them to combine visual and tactile stimuli into musical compositions that resemble our compositions—perhaps a body suit with a visual headset. They have never experienced or even heard of audible music and just assume that everyone consumes music as they do. They resonate to an abstract musical structure defined by an analogue of our pitch relations. A song is a series of visual and tactile stimuli that combine language and melody (defined by visual variations). Nearer to home, imagine that synesthesia is common, so that colors regularly evoke sound images in the mind: a musical performance consists of a sequence of visual stimuli that are known to evoke specific auditory images. The spectator gazes at the array of shapes and colors and experiences sounds inwardly, so that vision and sound blend together. Wouldn’t that be music? And not just because an auditory component is involved—the visual component would also be musical. Suppose the synesthesia faded away so that only the visual element was left: would that mean that these people no longer possess a musical sensibility? Music is certainly not tied to external auditory perception, since we can hear music inwardly, so why should it be tied to auditory phenomenology at all?[3] Poetry isn’t necessarily tied to hearing, given that there could be poetry in the form of sign language, so why should music be? It is true that we find it hard to imagine non-auditory music, but that tells us little about what is really possible; maybe we can’t fully grasp the musical phenomenology of the deaf aliens, but that doesn’t mean there isn’t one. Isn’t it just parochialism to suppose that music must exist for others in the form it exists for us? Maybe there is a Beethoven on another planet who composes purely in colors and whose symphonies are much prized; maybe even tastes and smells come into it! After all, music is based on intervallic structure, but that is not peculiar to sound. Or there might be music lovers possessed of another sense entirely, say one responsive to electrical fields: music is composed by means of varying electrical currents. Deep feelings might be aroused thereby. Just as language is a matter of patterns, so music is: and the patterns can exist in unlimited forms, i.e. types of sensory phenomenology. Imagine if there were a kind of inverted spectrum for sounds whereby a low frequency sound is heard by some people as a high note and by other people as a low note. Does that mean that music would be different for the different kinds of hearer? It’s the structure that counts not the absolute quality of the sound. Generalizing, we can move from this case to the synesthesia case to the alien case—all bona fide consumers of music. So it turns out that music and language are both inherently modality-neutral, contrary to initial expectations (it was difficult for hearing speakers to understand at first that deaf people speak a language just like theirs). For us music is inextricable from sound, but not so for all possible musical beings. On some planets they sing the blues using the color blue.[4]

[1] I could as well say speech, focusing on the performance aspect of language; in a deeper sense language might be identified with an underlying competence or cognitive structure. But speech itself exhibits the kind of variety I am alluding to before we even get round to examining the cognitive foundations.

[2] I am told that this is not entirely true—that there are musical compositions for the deaf that employ visual and tactile stimuli. Great: but they don’t seem to have much traction or scope, and are not appreciated by the hearing community. Still, this fact is grist to my mill, as will become apparent.

[3] Another kind of case to consider would be blindsight music, i.e. sound waves reach the ears but no conscious auditory response is produced yet there is a psychological effect on the hearer. We could describe these people as hearing music but not consciously. Evidence for this would be the occurrence of effects in these hearers like those experienced by ordinary hearers, e.g. improved mood or knowledge of the tune that was presented. People with this condition might well listen to music though their conscious mind shows no awareness of it: the musical response would occur in the non-conscious part of their mind.

[4] We can enquire whether other art forms are musical, at least partially. Dance is a good candidate: there is surely something musical about dance, which is why music and dance go so regularly together, and we might conjecture that it is because dance embodies in another medium some of the structure of music—rhythm certainly, but also something analogous to melody (segmented continuous movement in space). A machine might be hooked up to a dancer that converts movement into melodic sound, and musical performances produced thereby. Even pictorial art might be seen as having a musical aspect in the form of harmony and a fixed palette of “notes”. The mathematical forms of music can in principle be transposed to other artistic mediums. If so, music has already exceeded its conventional sonic bounds.

Constructing a World

Imagine yourself a deity idling away your days. It occurs to you to do something with your life (and the peer pressure has been mounting), so you decide to construct a world. The activity is new to you and you have never taken lessons, so you have to start from first principles. What is a world? It’s a way things are—or the way stuff is. It is something with definite being, the opposite of nothing. So far so good: but it’s not very far. How do you make one of those? You ponder the question and come up with the idea of objects: you have to create some objects. Okay, you can do that, but it quickly dawns on you that that is not going to be enough: the objects have to add up to a way things are, but mere objects can never do that—they need to be a certain way themselves. What is such a way? Here you feel stuck because you have been assuming that a world is a totality of objects—what else could it be? Eventually the solution occurs to you: you need to give the objects properties. These are things that confer a nature on objects—that give them definite being. Ways things are consist of properties objects have. It may seem ontologically excessive but there is no alternative: a whole new level of being must be invented or else your world will be indistinguishable from nothing. So you prepare to set a load of properties next to your bunch of objects. But then a problem strikes you: how are you going to connect the two? You can’t just have the objects and the properties; the objects must have the properties—they must (what’s the word?) instantiate the properties. Now this is going to require some serious world-engineering expertise! You wonder whether to consult the head god (old Grey Whiskers) but decide this would be embarrassing, so you set about solving the problem yourself—you too are a god after all. A clue comes to you in the form of the concept of a fact: you need to make facts from objects and properties, so there has to be a kind of glue that joins them to make facts. A fact is a type of combination, but combinations need methods of combination—combinatorial adhesive. Your objects and properties need to be formed into unities not just placed blindly next to each other.

Functions! These are things that apply to an object to yield another object: they are rules for mapping one object to another. Let the objects act as input to these rules and let the properties be the rules that yield facts as output. Properties must be so constructed that it is in their nature to generate facts from objects, and the notion of function is just what is needed. Design the properties as functions; then you will get the unity you need. So now the ingredients are all in place to make a nice shiny new world: objects, properties-as-functions, and facts. It’s a good thing you had the idea of functions or else your world might never have got off the ground. Functions are very useful in the business of world construction—functional, you might say.[1] Now you just have to decide what kinds of objects and properties to create, but the real brainwork has been accomplished—you have a workable blueprint for constructing a world. A world is now within your reach.

Some time later, with the world construction finished, you are feeling a bit bored so you decide it would be nice to create a way of describing the world you have constructed. You want to create—what to call it?—a language. But what is a language? It has to say things, surely: it has to say how things are in the world. The world divides up into facts, so the language needs to divide up too, and these items must say something. Let’s call them sentences, conceived as complete expressions that say something. But what is a sentence made of? You are the one constructing them, so this is a question you need to resolve. Clearly you are going to need sentence parts that correspond to objects—you call these names. But these are not enough because you also need sentence parts that correspond to properties—call these predicates. Then the sentences will correspond to facts, since objects combined with properties (via functions) yield facts. So now you have names and predicates strung together: but hold on, that is just a list—how do we get from a list to a unified complete sentence? Remembering your similar question about objects and properties, the solution is staring you in the face: functions! A predicate is a function from names to sentences: input the name; output the sentence. Predicates act as functions, creating unities from mere lists: the predicate isn’t just next to the name; it acts on the name. By acting on the name it forms a sentence that has an internal unity and says something—it describes a fact. So language is functional as the world is functional: function-argument structure runs through it, forming it, making it possible. Functions are not just central to mathematics; they are also central to worlds and languages. They are the binding glue.

One Sunday afternoon you hit on another plan: you decide to create some thinking creatures. You are going to need some creatures, clearly, and some thoughts for them to have. How to create a thought? Well, thoughts are about things, so they need parts to do that—parts that are about objects, evidently. The thoughts need to be about the world you so carefully constructed. Let’s call these parts individual concepts: they are a bit like names, but let’s not jump the gun, so we won’t just make up some more names for thoughts to use. These are psychological entities. But a thought can’t just be a concatenation of individual concepts; thoughts need general concepts too. So a thought is a combination of an individual concept and a general concept: but it is not just any old combination but one with a special sort of unity. You have been this way before so the problem is no great stretch: general concepts need to be functions from individual concepts to thoughts. The complete thought is the output of the function and the individual concept is the input to the function. The general concept is a function that acts on another concept as argument to give a thought as value. This enables the creatures you have created to have thoughts about the world you created. If you make these creatures in such a way that they can speak as well as think, then we can say that their sentences express their thoughts as well as describe reality. So world, language, and thought all line up: combinations of parts unified by functions. Note that the functions don’t cross boundaries: thought functions don’t take objects as arguments and give facts as values but individual concepts as arguments and complete thoughts as values. Nor do sentences step outside of the linguistic domain, keeping arguments and values within language. The way you set things up the arguments of the functions are confined to their proper domain—whether objects, names, or individual concepts. The trick has been to exploit the concept of a function to solve a problem in reality construction—facts, sentences, and thoughts.[2]

It is noteworthy that each step of your reasoning was substantive: there was no obvious move from the bare concept of a way things are to the apparatus of objects, properties and functions; and similarly for language and thought. The world as we have it conforms to these categories, but they are not part of the very idea of a world—the idea of definite being, or of a way things are. You made a conceptual choice; you worked with a theory. You imposed these concepts on a pretty blank slate: maybe you could have dispensed with the idea of objects and worked with an ontology of stuff, or just object-less instantiation (“feature-placing”). Once you made these decisions you faced certain challenges, notably the problem of joining properties to objects to generate facts, which luckily you solved. Senior gods may have shaken their heads over your decisions, preferring some other way to make a world (what about starting with undifferentiated substance and then carving it up?). The object-property scheme was bound to encounter the unity problem, which you solved by the skin of your teeth (or by dint of sheer brilliance, as you would prefer to put it). It might not have worked at all but for the concept of a function! What if there had been no mathematics to copy? You succeeded in constructing a world, but you might have failed at the early stages through lack of appropriate adhesive. Worlds don’t come easy.[3]

Colin McGinn

[1] See my “Properties As Functions”.

[2] Frege’s insight in semantics (which I have not considered here) was that if you want to develop a workable theory of meaning you need to invoke the apparatus of function and argument. That is, if you were constructing a meaningful language, you should (must) build into it the function-argument structure. He thus took what he called concepts, the denotation of predicates, to be functions from objects to truth-values. This basic approach can be adopted without accepting Frege’s specific stipulation about concepts. I have transposed this theoretical approach to semantic theory into a recommendation about how to construct a meaningful language ab initio (as well as worlds and thoughts).

[3] I have been discussing the construction of actual worlds, but even possible worlds need to be possible; the parts need to cohere too.