General Reactivity Theory



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]



[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.


Action, Reaction, and Reflex



Action, Reaction, and Reflex



Analytical philosophy of action typically begins by distinguishing between mere reflexes and intentional actions. The blink reflex and the patellar reflex involve bodily movements with no psychological intermediaries, while bodily movements like directing traffic are prompted by beliefs and desires. The philosopher then declares that he or she is interested in the latter not the former—they are not really actions at all. The thought is that reflexes are elicited by external stimuli in a mechanical manner—no deliberation, no choice, and no freedom—while intentional actions are psychologically produced and do involve deliberation, choice, and freedom. Putting it in terms of causation, reflex behavior is caused by external non-mental stimuli while intentional action (action proper) is caused by internal mental states like belief and desire. The philosophy of action is then held to concern itself with the latter type of behavior. Maybe reflex behavior is grudgingly allowed to count as action in a colloquial sense (“reflex action” is not contradictory), but it is not deemed to be action in the proper philosophical sense—and so it does not belong to the philosophy of action.

But there is another category of behavior that fails to fit neatly into this dichotomy, which is seldom if ever discussed. I mean what we can call reactive behavior: reactions, in short. There are spontaneous actions that are performed without any prompting stimulus—stimulus-free actions in one terminology—and there are actions that result from an external occurrence.[1] For example, there are reactive acts of speech such as responding to a question or accepting an invitation, as there are reactions like rushing to help someone in distress, or flaring up at an insult, or holding up your hand to protect your face, or laughing at a joke, or slamming on the brakes when a car suddenly stops in front of you. The action would not have occurred but for the impinging stimulus, and it is appropriate to that stimulus; it is not spontaneous and stimulus-independent. Yet it is not a reflex: it has psychological antecedents, and is not a matter of a mere reflex arc. The agent perceives that something is happening and reacts to it, presumably motivated by some sort of desire; and it is possible to train oneself not to so react, unlike with genuine reflexes. People say, “I didn’t think, I just reacted”, thus distinguishing the case from fully voluntary free deliberative action; but they don’t suppose that the action was brought about purely from a mechanical external stimulus. The stimulus may have made the agent angry or fearful or amused, and this is what led to the reaction in question. So the external stimulus led to an internal mental state that was necessary for the reaction to occur. What we have here is something intermediate between the standard categories of intentional action and mere reflex, which has not been much explored. It fits into neither category; specifically, it doesn’t fit the paradigm of the spontaneous action prompted by belief and desire. An explanation of a reaction will not then mirror the explanation of a spontaneous action: it will refer not merely to internal belief and desire (if indeed it does this at all) but also to an eliciting external state of affairs. “Why did you raise your hand to your face?” “Because I was about to get hit in the face by a ball.” No doubt you desired not to get hit in the face, and no doubt you saw the ball coming; but it is also true that your action was a reaction to a stimulus. This was a stimulus-controlled non-reflex action: a hybrid, an intermediate case.[2]

As always the dictionary (OED) proves useful. For “action” we find: “the process of doing something to achieve an aim”. For “react” we find: “respond to something in particular way”; for “reaction” we have: “an instance of reacting to or against something”. For “reflex” we have: “an action performed without conscious thought as a response to a stimulus”. From these definitions we see how reactions sit between actions and reflexes, conceptually speaking. Note that reactions are not said to “achieve an aim”, presumably because they can be unwise and counterproductive: they may go against the agent’s interests and considered judgment. The agent may regret and lament their occurrence (“Sorry, m’ lord, I just lashed out when he insulted my mother”; compare, “I didn’t mean to kick the dog but someone tapped my knee with a hammer”). Note too that there is no hesitation in describing a reflex as an action, just an action performed without conscious thought. The reason this raises no eyebrows is that reflex behavior is purposive: it is precisely not like merely mechanical causation such as we find in the physical world. The eyelid blinks in order to protect the eye; the knee jerks upward because the tendon is designed so as to aid balance, the jerk being a side effect of that. By contrast, rivers don’t erode banks so as to widen rivers, and meteors don’t cause craters in order to pockmark the earth’s surface. The right thing to say, clearly, is that there are three types of action: reflex action, reactive action, and spontaneous action. All are unambiguously action, but there are three distinct types of action. The philosophy of action should concern itself with all three types, noting their similarities and differences; focusing exclusively on spontaneous action is a mistake. In particular, the case of reactive action needs to be brought to the fore. What should we say about crying or salivating? Are these reactions instances of action? They can be controlled to some degree, yet they seem close to involuntary reflex actions. What about biting and swallowing in response to food in the mouth? Is the response of turning down a Nobel Prize a case of reaction to a stimulus? Does all reaction involve desire—for example, screaming when hurt? How does belief feature in reactive action?

It has often been pointed out that actions can be purely mental, as when you calculate in your head. Is the same true for reactions and reflexes? The answer is affirmative: you can react to an insult by plotting to get your revenge, or promise yourself not to visit places where temptation may lead you to act in ways you later regret; and surely the elicitation of pain or visual sensation is a matter of reflex (though these are not strictly actions). The mental analogue of reflex action would be automatically judging that something is so simply because you have seen it to be so: immediate and unthinking, yet active. Animals may be more prone to such purely mental reflexes than we are, what with our advanced rationality. So the subject of mental action needs to reckon with all three types of mental action not just the spontaneous kind. There are responsive mental actions as well as stimulus-free mental actions. Weakness of will too can apply to reactive actions as well as to the spontaneous kind: indeed, reactions more often involve doing things against our better judgment. And this can hold for mental as well as bodily actions. Linguistic actions can also fall into the three categories, whether bodily or mental. Much linguistic behavior is reactive—not like the standard case of making an assertion out of the blue. Conversation is precisely reactive verbal behavior: answering questions, responding relevantly, filling in silences. And verbal reaction can occur purely in the head: responding verbally to perceived events in one’s own mind, keeping on topic in one’s internal soliloquies. It is a question whether any verbal behavior may be aptly described as reflexive, whether internal or external: are speech acts ever mechanically elicited by a stimulus “without any conscious thought”? Perhaps infants do this for a while by uttering words at the mere sight of a stimulating object (“Dada!”), and some aphasics are prone to uncontrolled verbal output when a stimulus is presented. Are there words we can’t help saying inwardly when something agreeable or disagreeable happens? Verbal behavior is not generally of a reflexive nature, but there may be outlying examples of it where reflexes kick in. Could such reflexes be conditioned in subjects? In any case, verbal behavior is often reactive—in which case we should speak of “speech reactions” as well as “speech acts”.

Now an interesting question suggests itself: reactions are a type of action, but are actions a type of reaction? I don’t mean a reaction to an external stimulus, since that is clearly not true, but are those the only kind of stimuli there are? What about internal stimuli? Certainly we can react to states of our own body, as when we scratch an itch or moan in pain; and obviously you can respond to a medical problem by seeking professional help. But is there anything internal that actions in general might be construed as a response to? Indeed there is: desire. Organisms have needs, say for food and sex, and these get expressed as desires accompanied by sensations such as feelings of hunger. All this takes place outside of the organism’s volitional faculty, but it feeds into that faculty. We might speak of this as the internal environment, the desire landscape–and the animal can react to this environment. It can react by trying to modify the internal environment, by meeting the needs expressed therein. This is where action comes in: action responds to the stimulus provided by the internal environment of need and desire along with accompanying sensations (some highly disagreeable). Thus action is reaction to desire. It is a response to desire, an engagement with it, an interaction with it. In principle, an experimenter could intervene to modify the internal psychological environment in order to control the animal’s behavior, as the external environment can be so manipulated.[3] Theoretically, the cases are on a par: behavior is a response to environmental variables, both outer and inner. So spontaneous action (so-called) is really a type of reaction to a stimulus—the internal stimulus of desire. If so, the basic concept of action theory is reaction: all action is a response to something—there is no such thing as completely spontaneous action. It is true that actions can be stimulus-free with respect to external stimuli, but these actions are always stimulus-bound with respect to internal stimuli (so no support to behaviorism here). Or perhaps we should not use the word “bound” because there is some looseness in the stimulus-response connection (unlike the case of reflex); rather, the action is stimulus-directed (influenced, regulated). Just as I might decline to react in a certain way to an impinging contingency, so I might decline to act on a desire that is pressing its claim to expression; still, when I do act on such stimuli it is because of them that I do so. The action is always stimulus-triggered when it is triggered; it is not a reaction to nothing. Accordingly, the philosophy of action is the philosophy of reaction. To put it differently, the will is a reactive faculty.

If we follow this line of reasoning, we can see an element of truth in the behaviorist’s view of the mind: not indeed the doctrine that the mind is external behavior, nor yet the theory that all learning is conditioning, nor even the idea that there are predictive laws of behavior—but the thought that the mind is essentially a reactive being. The organism must react to its environment in order to survive, and that environment includes its own internal state—thus feeding behavior results from both internal hunger and the presence of external food material. The mind must orchestrate these interactions, reacting appropriately to the prevailing conditions: it must adapt itself tothem. Thus in a certain sense it is true to say that psychology is stimulus-response psychology: that granule of truth was then distorted and exaggerated by the behaviorist school. But that misguided school was at least partly grounded on an idea that it is not intuitively wide of the mark, viz. the mind is essentially a reactive organ (like other organs). The mind is a responsive thing, acting in relation to things, taking the measure of things (external or internal). If the essence of life is adaptive reaction, then the mind is one aspect of this biological principle. Action then is like a reply to a question.[4]



[1] Psychologists often speak of avoidance behavior and approach behavior, thus registering the reactive nature of much behavior; other forms of behavior make no reference to any object in relation to which the organism is acting in these ways, such as singing or playing football. Reactive behavior, which is stimulus-driven, is thus classified into two types, according as it involves attraction to the stimulus or avoidance of it. Not all reactive behavior falls into these two types, however, as with responding angrily to an insult.

[2] A good example from literature occurs in Melville’s Billy Budd. The evil Claggart falsely accuses Billy of mutiny in front of Captain Vere and the Captain asks Billy to respond to the accusation. However, Billy suffers from a speech impediment in situations of injustice like this and can say nothing in reply. Melville writes: “The next instant, quick as the flame from a discharged cannon at night, his right arm shot out, and Claggart dropped to the deck”. Clearly Billy’s action was reactive, but notice also that Melville compares it to an inanimate event and describes the action as if it were disengaged from Billy’s rational faculties—his arm “shot out”. This is precisely the kind of action I have in mind. (Despite the circumstances, Billy Budd pays for his arm’s reactive action with his life.)

[3] Compare increasing the intensity of an external stimulus with increasing the intensity of an internal stimulus: if the stimulus is unpleasant (as in those unethical experiments using electric shock or food deprivation), the animal’s behavior will be modified accordingly, as it reacts to the variation in the stimulus. The cases are entirely parallel.

[4] The contrary view, which emphasizes the spontaneity of action, might be said to compare action in general to the speech act of assertion—a type of speech act that is not characteristically a response to anything. According to the reactive view, by contrast, perception poses questions to the motor system, to which it must reply appropriately; and desires pose questions too, along the lines of “Won’t you act on me, please?” Call this the “interrogative model” of action just to have a fancy name. Then the interrogative model proposes that all action consists of reaction—a response to a questioning stimulus. More literally, it views all action—spontaneous, reactive, and reflex—as having a stimulus-response structure (sans behaviorism, of course).


Complex Minds



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.







The word “agnostic” was coined by Thomas Huxley in 1869. I am concerned here with what state of mind is denoted by this word not with whether agnosticism is the correct position. I think it is commonly assumed that it denotes a state of mind that is neither belief nor disbelief: we can believe in God or disbelieve in God, and thus be either theists or atheists, but in addition we can be in a state of suspended belief on the question, and thus be agnostics. There is belief, disbelief, and a kind of neutral belief—undecided belief, null belief, belief that hovers but will not land. It is sometimes thought that agnosticism is vaguely disreputable or weak-minded, as if the agnostic is someone who hasn’t got the guts to form firm beliefs. He or she hasn’t the courage to form a belief, the stakes being quite high, so chooses to dwell in a twilight zone of non-commitment. This presupposes that there is such a thing as suspended belief—a state of mind in which no definite belief is formed. It seems to me that this is the wrong way to describe the agnostic’s state of mind: the agnostic has just as firm a belief as anyone else with respect to God’s existence, viz. that there are no rational grounds for preferring theism over atheism or vice versa. The agnostic may be quite certain that this is so, as committed as any ardent believer or disbeliever—she cannot be accused of being wishy-washy on the question. She has considered the question and formed the belief that no belief either way is rational. She has a meta-belief that is as committed as any: a belief about belief. So there is no third state of belief corresponding to agnosticism—no semi-belief or uncommitted belief or suspended belief. There is simply belief. In fact, there is really only one kind of belief, namely belief: the theist believes in God, the atheist believes there is no God, and the agnostic believes that no belief on the question is rational. That’s it—no subdivisions of belief exist of the kind commonly supposed. The state of mind of any of these three categories of person is simply a state of belief; nothing further needs to be added.[1]

The OED agrees, defining “agnostic” as follows: “a person who believes that nothing is known or can be known of the existence or nature of God”. That is, the agnostic has a belief about religious (or irreligious) belief, namely that it is not rationally warranted. There is no quasi belief or halfhearted belief or state of aporia. The definition, however, is lacking in another way: it is wrong. The agnostic need not believe that nothing is known of the nature of God, or even of God’s existence; he may accept that we know that if God exists he is omniscient, or even that God has possible existence (either in the epistemic or metaphysical sense of “possible”). What the agnostic contends is that such knowledge is not sufficient to tip the balance of argument in the direction of God’s actual existence. To think there are considerations on both sides of an argument, making it impossible to pick sides, is not to suppose that nothing can be reasonably asserted on either side. And clearly the agnostic can allow that the question of God’s existence might one day be decided; it is just that we don’t have the evidence now to justify either theism or atheism. The essence of the position is simply that nothing rationally justifies one belief over the other, not that we are condemned to complete ignorance of God’s existence or nature. Furthermore, the definition limits agnosticism to the religious sphere, but it is possible to be an agnostic about many things. You can be an agnostic about whether William Shakespeare wrote the plays customarily attributed to him, or whether Jupiter has five moons, or whether the earth is flat, or whether Roger Federer will retire within two years. You simply hold that the evidence you have doesn’t settle the matter one way or the other. There is nothing pusillanimous about holding this position, nor does it betoken a special state of mind of non-belief: it is a straightforward belief about what it is rational to believe in the circumstances. Perhaps this is why no special word existed for this state of mind before Huxley coined it—because there is no special state of mind involved (the “agnostic stance”). It is just one belief among others.

Here is an objection: what about someone who is just too lazy or poorly positioned to form beliefs on the matter at hand? If you ask his opinion on whether the Battle of Hastings was fought in 1066, he will throw up his hands and say he has no idea and doesn’t much care. He is, he tells you, agnostic on the question. It isn’t that he thinks that there is no evidence that favors one answer over another, or that the matter cannot be rationally decided. He just thinks that he, in his contingent ignorance, must remain agnostic. Two points can be made. First, he does believe that he has no evidence that would enable him to decide the matter, and this is what his professed agnosticism consists in. It is not that he is in a wavering and woolly state of mind; he will tell you that he is quite sure that he doesn’t know either way. He is not even inclined to favor one answer over the other. There are many questions like this, on which we feel ourselves uninformed and unable to offer an opinion, or we just haven’t thought about it. This is simple ignorance not considered judgment about the rational status of a debate. That is why (and this is the second point) we don’t normally call such a state “agnosticism”: it is not a considered opinion got by weighing all available evidence. It is just an admission of ignorance. The agnostic about religion is not saying that he has never considered the question of God’s existence and is hopelessly ill informed about it, as if the next thing you say might tip him in one direction or the other. So the case of the ignorant non-believer is not a counterexample to the general characterization of agnosticism being proposed. Agnosticism is always principled not casual.

This analysis is confirmed by what would otherwise be puzzling: there is no analogue of agnosticism for desire or intention. We can desire something or desire its opposite, but we can’t be in a neutral state of desire agnosticism. We can believe that nothing favors one desire over another (a peach or a plum), but we can’t have some sort of intermediate desire analogous to suspended belief. What would that desire be? Similarly, I can intend to go to the movies or I can intend to stay home, but I can’t intend something mysteriously between the two—as if I have a kind of indeterminate intention. If belief were capable of this kind of indeterminacy, we would expect that desire and intention would be; but they aren’t, so we should question that account of agnosticism. The only kind of agnosticism there is consists simply in the belief that nothing decides the question—not some kind of non-committal belief or wavering desire or indeterminate intention. It is of course possible to suspend belief (or disbelief), as we like to say, but the agnostic is not someone who is suspending his belief in God or suspending his belief in the absence of God; he has no such belief to suspend. He simply believes that nothing favors one belief over the other. It is also true that someone could be quite neutral on a question simply because it has never entered his head to consider it, so that he doesn’t have the belief that the jury is still out; but again, that is not the position of the agnostic (or else animals and little children would be agnostics). The agnostic doesn’t lack a belief; he has a belief, which is what his agnosticism consists in. The agnostic is a believer, just as the theist is, or the atheist. He indeed takes himself to be a more rational believer than the other two, not to be someone with a problem about believing—a chronic hesitator or belief-a-phobe. The agnostic is a firm believer in belief.  He takes himself to knowthat belief in God is irrational, just as belief in the absence of God is also irrational. There is nothing peculiar about his belief system, as if he has trouble forming beliefs. To put it differently, the agnostic is a person who believes that faith is not the right way to form beliefs; and there is nothing more to it than that.[2]



[1] It would be wrong to model agnosticism on a reluctance to say whether one is a theist or an atheist: there is indeed a third way between saying that God exists and saying that God does not exist, i.e. saying nothing (perhaps for fear of courting unpopularity). But being an agnostic is not a reluctance to form a belief; it is just a type of belief, whether one is happy to express it or not.

[2] To put it in the usual analytic style, the meta-belief is necessary and sufficient to qualify someone as an agnostic. The sufficiency part is important: there is no more to agnosticism than holding such a belief—no more psychologically speaking. The necessity part tells us that agnosticism is always an explicit reflective position, never just a matter of ratiocinative indolence (a community of unreflective people who have never thought about God’ existence and have no opinions on the subject cannot be described as community of agnostics). The agnostic is someone who actively rejects both theism and atheism—he firmly and positively believes both positions to be irrational. (By the way, I am myself an atheist not an agnostic.)


Language and Music


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.


Problems with Panpsychism



Problems with Panpsychism


I will list as concisely as possible a number of problems that I see with panpsychism. Panpsychism comes in two forms, partial and total. Partial panpsychism says that all matter has a mental aspect as well as a physical aspect; total panpsychism says that all matter is wholly mental. I will focus on the total kind for ease of exposition, though the problems arise equally for both versions of the doctrine. In addition, panpsychism has been proposed to deal with two problems, which I will call the matter problem and the mind problem. The matter problem is the problem of what constitutes matter, and the claim is that the intrinsic nature of matter is consciousness. The mind problem is the problem of what makes mind possible, and the claim is that mind is possible because it arises from matter construed as consciousness.[1] These are separate claims: the first does not entail the second; nor does the second entail the first. I shall suggest that panpsychism cannot in principle solve the mind problem, though its prospects for solving the matter problem are brighter. That is, even if true as a theory of matter, panpsychism cannot explain how mind arises from matter, or how it is possible. The list runs as follows.


  1. The Incompleteness Problem. If there is any property of consciousness that is not explicable in terms of particle consciousness, then panpsychism cannot be the solution to the mind problem. The panpsychist position is that consciousness in animals can only arise from consciousness in the elementary components of matter, whatever they are (particles, strings, fields): so if there are facts of consciousness that cannot be explained in this way, then the theory fails. If there are such facts, then particle consciousness (as I shall say for convenience) is not needed to explain animal consciousness, so we may as well abandon it altogether. Even if there is just one consciousness property that cannot be explained in this way, then the theory is doomed—as it might be, one type of sensation that does not arise from more elementary consciousness. But clearly there are many properties of animal consciousness that are not mirrored in particle consciousness, whatever that may be like. For particles are few in type and cannot contain every form of consciousness that exists in the animal world: how can they harbor even the sensations found in the five human senses? The particles must contain only a subset of the consciousness properties that actually exist, but then their properties cannot explain the existence of those properties. It is no use saying that the latter arise by combination of the former, since it is not credible to suppose that sensation types are combinations of other sensation types—visual sensations of red are not combinations of auditory sensations, say. Animal consciousness contains many irreducible types of conscious state, far too many to be anticipated by particle consciousness, which must be quite limited given the physical facts. Electrons have one type of consciousness, protons another, and neutrons a third: that is a very meager basis for deriving the full panoply of animal consciousness. The explanatory basis is inevitably incomplete. The panpsychist might suggest that the brain fills the explanatory gap: it is the way the particles are arranged in the brain that generates the full variety that we see in the animal world. This is vague, but anyway it throws in the towel as a solution to the mind problem: for now we are admitting that the brain as a physical object plays an explanatory role in producing consciousness. Particle consciousness alone is not sufficient; we also need input from the brain’s structure if we are to account for animal consciousness–say, from the cellular structure of neurons. Neurons not neutrons are now doing the explaining. The explanatory basis in particles is just too exiguous to do the job. Of course, we don’t know how the brain does the job—that’s the basic problem–we just know that particles alone can’t do it.


  1. The Uniqueness Problem. The panpsychist typically agrees that not every physical object is a conscious being—brains are, but rocks are not. The components of rocks are conscious, but not the rocks themselves. But this raises a question: why is that so? There must be something about brains apart from the consciousness inherent in their particles that makes the difference. A brain and a rock may be identical in respect of their particle consciousness, since they may contain the same particles, so it must be something about the brain that accounts for the difference—and this something is not reducible to particle consciousness. But then the existence of consciousness in brains and not rocks must be explicable by something other than particle consciousness—say, by the organization of brains. But this implies that some other fact about matter is the explanation of consciousness in the one case but not the other. Brains uniquely produce (macro) consciousness and yet their quotient of particle consciousness does not differ from that of non-conscious objects: so the difference must trace back to a property of brains other than the consciousness of their constituents. Again, we don’t know what this is, but we know that it must be so—in which case panpsychism can’t explain the existence of (macro) consciousness. It can’t even explain why a brain is conscious and a rock isn’t! Even if all matter is agreed to be conscious, we still need something else to explain the facts about (macro) consciousness, specifically its distribution.


  1. The Overabundance Problem. This problem is connected to the previous one: how to explain why rocks are notconscious. Something must prevent a rock from possessing consciousness given that all of its parts are brimming with it. If there is so much consciousness within it—and nothing else if total panpsychism is true—how come it is devoid of consciousness itself? There is something it is like for every constituent of the rock but nothing it is like for the rock—odd! If we say that the constituents of the rock are not organized like the constituents of a brain, we are admitting that something other than particle consciousness plays an explanatory role—this becomes a brain organization theory of consciousness not a panpsychist theory. The difficulty is that to avoid the problem of why rocks are not conscious the panpsychist must invoke something other than particle consciousness to explain the facts about consciousness—in this case its absence from nearly all macroscopic objects. To get out of this difficulty the panpsychist may choose to say that rocks are conscious, so there is no problem about explaining why they are not given the panpsychist’s premises. But this is (a) massively implausible and (b) raises the question of why brains exist at all, given that they are not needed for full-blown consciousness. Why did evolution produce them if they are not needed to have the equivalent of an animal mind? This makes the brain’s complex machinery quite redundant in the business of engineering a conscious mind. And are we to suppose that rocks might have richer minds than ours, despite our large complex brains? Here the mounting absurdities are too much even for the staunchest panpsychist.


  1. The Specificity Problem. Animals have quite specific conscious states each clearly differentiated from the others, but how is that possible given that the raw materials afforded by particle consciousness are so limited? Shouldn’t animal minds be much less heterogeneous? Shouldn’t one type of conscious state blur into another? Let’s suppose that there are precisely three kinds of conscious state possessed by the basic constituents of matter, corresponding to electrons, protons, and neutrons—three types of what it’s like. How can many more types of conscious state arise from this slender basis? Shouldn’t animal minds be a lot simpler than they are? How can panpsychism explain the origin of the specific sensation of red, say, without something closer to that sensation? The panpsychist will not want to attribute such specific sensations to particles, hoping to work with something more capacious and pliable; but then how does that specific conscious state arise? How do conscious distinctions arise? Again, we cannot appeal to the brain’s organization, because that is to admit that we need another ingredient to explain the properties of consciousness. The more undefined we make the basic consciousness properties the harder it becomes to explain the specific character of the various conscious states we encounter. Something else will need to be invoked in order to reach consciousness as it actually exists.


  1. The Mind-Mind Problem. The claim is that the mini minds in particles explain the maxi minds in animals. One type of mind underlies another type of mind. Here the panpsychist faces a dilemma: either the mini minds are just like the maxi minds or they are not; the claim that they are thus alike is absurd, so it must be that they are not; but then how do they explain the maxi minds? Suppose someone was to say that human consciousness arises from insect consciousness: that would involve either attributing a lot to insect consciousness or supposing that a rather radical form of emergence is possible. We can dismiss the first alternative, but the second lands the panpsychist just where he started. For now the claim is that something quite unlike human consciousness can be the sole explanation of human consciousness—as if our consciousness can intelligibly arise from mosquito consciousness. What kind of consciousness is possessed by electrons? Presumably it is nothing like ours—maybe we can’t even know what it is like. But then how can it explain our consciousness? That is like supposing that bat minds are just extensions of human minds. You can’t get one type of mind from another of a radically different type. But how can particle consciousness fail to be radically different from animal consciousness? This is the mind-mind problem: how to get from one type of mind to another type without positing radical emergence—precisely the problem panpsychism was designed to solve. If electrons experience sensations of attraction and repulsion, how does that convert into the normal range of animal sensations? Some sort of magical transformation would need to be posited, just what panpsychism is supposed to avoid.


  1. The Species Problem. What kinds of conscious state should we attribute to matter? It is natural to be guided by our own case—particles have the kinds of conscious state that we have. They are like tiny mirrors of ourselves. But what about other species, here on earth or elsewhere, real or imaginary? Why not suppose that bats are the correct model for matter generally? Maybe electrons have sensations somewhat like a bat’s echolocation sensations, not like our visual sensations. Or maybe there is a species in another galaxy that is quite unlike any species on earth, and this species is the one that electrons most resemble. The question seems entirely arbitrary: why our species and not some other species? But species differ in their phenomenology, so which is it to be? The problem is that particles are uniform and must have uniform phenomenology; but animal minds are not, so the panpsychist is forced to choose arbitrarily. It’s all very well to say that all matter is conscious, but there is the question what kindof conscious—and this exposes a kind speciesism at work. We tend to think we are the model for matter in general, but that is anthropocentric and arbitrary. The only way out is to postulate some sort of species-neutral consciousness, but this is (a) not clearly intelligible and (b) lands us back with the Specificity Problem. Vagueness on the question of the precise character of electron consciousness is what enables the panpsychist to avoid confronting this problem. At bottom the problem arises from the variety of animal consciousness and the (relative) uniformity of matter.


  1. The Extension Problem. Are the mini minds extended in space? If they are, then presumably maxi minds are too: but that flies in the face of a strong intuition. If they are not, then how can they constitute matter, which is extended in space? The problem is that to solve the matter problem panpsychism exacerbates the mind problem: matter is extended, so whatever constitutes it must be too; but then it can’t constitute mind, if mind is not extended. To solve one problem disqualifies the theory from solving the other. Suppose that a particle has a certain size and shape; then its constituting mental entity must have that size and shape too. Very well, let it be so: but then we are committed to holding that the mental entities it composes also have size and shape. We might be willing to accept that, but we need to be aware that we are accepting it. Panpsychism either entails that the material word is non-spatial or that the mental world is spatial—which is it to be?


I am myself rather inclined to think that the stuff of the so-called material world and the stuff of the (also so-called) mental world are fundamentally the same stuff. I also think that panpsychism has at least the form of an adequate theory of the material world (though I have problems with the details). Perhaps the uniform stuff is most closely approximated by the simple minds of simple creatures, before complex minds like ours developed, so that reptiles (say) exist in a more unified way than mammals. Or maybe we need to descend further down the phylogenetic scale in order to find mind stuff in its purest form. The basic metaphysical picture promoted by the panpsychist seems to me not wide of the mark. But I am far more skeptical of the claim to solve the mind-body problem for the reasons stated above (and for other reasons too). It might conceivably offer a partial solution, but other ingredients would need to be added if we are ever to understand how consciousness came to exist.[2] It can’t be the wholeaccount of the origin of consciousness. So it looks like panpsychism has a better chance of solving the body problem than the mind problem, ironically enough.[3]



[1] For my reasons for calling it the mind problem, see my “The Mind Problem”.

[2] A hybrid position heaves into view: panpsychism plus mysterianism. The emergence of animal consciousness results from a combination of primitive consciousness at the basic level and an unknown factor at the level of the brain. The brain uses this unknown factor to convert primitive consciousness into the full-blown kind. How, is a mystery.

[3] A problem I have not mentioned because it is very recherché is this: why suppose that the basic mental properties apply to the objects identified by physics? Why should the soul of the universe be divided up according to the physicist’s carving knife? Why not suppose that mental reality exists in the interstices of the objects of physics? Perhaps space itself is permeated by consciousness, and electrons only derivatively upon that. True, this view prevents us from literally identifying electrons with packets of consciousness, but it still allows that consciousness is basic to reality. So the panpsychist needs to tell us why she insists that particles are the locus of consciousness and not the spatiotemporal manifold. In short: why isn’t space conscious but not particles in space? This shows how under-motivated the theory really is—and yet how attractive to the imagination.


Constructing a World



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.


Properties As Functions



Properties as Functions



I have always thought that there is something right in Frege’s idea that concepts are functions from objects to truth-values. Bear in mind that for Frege concepts are not psychological or subjective entities, nor are they senses, but rather belong at the level of reference, like objects. They are individuated extensionally and exist independently of the mind (or even of Fregean thoughts). His idea is that these objective entities act as—indeed are–functions with arguments and values, just like mathematical functions. The arguments are objects (but sometimes other concepts) and the function takes us to other objects as values, truth-values being objects for Frege. In other words, the semantic value of a predicate is a function from objects to truth-values—Frege’s main interest being semantics. But we can interpret the view so as to cut out language, holding simply that facts are composed of objects and functions, since concepts in Frege’s sense are the objective correlates of linguistic expressions. Frege never speaks of properties in the intuitive sense in his semantic theory, but there is nothing to stop us formulating his insight in terms of properties: properties are functions too, forming facts. What are they functions from and to? From objects evidently (except when second-order), but are their values truth-values? That seems stretched given that truth-values attach to thoughts or propositions or sentences and properties exist outside the realm of sense.[1] For example, the property white is a function that can take snow as an argument, but it can’t yield the True as a value unless there exists a proposition that says that snow is white—but that is not the same thing as snow simply being white. As a metaphysical claim, the function theory is a theory about the structure of non-linguistic facts, so we don’t want to define it by reference to language and truth-values. So how do we transpose Frege’s insight from the semantic level to the ontological level? What does a function theory of objective mind-independent non-linguistic properties look like?

We have two options, one of which is implicit in a theory Frege considers and rejects. This is the theory that sentences denote states of affairs or facts and not truth-values, which would enable us to say that properties are functions from objects to states of affairs or facts—as Frege could have said that concepts are functions from objects to states of affairs considered as the reference of sentences. The function theory is quite independent of Frege’s decision to make the values of concept functions truth-values, taken to be the reference of sentences. So let us say that properties are functions from objects to facts, to put it briefly: the property white is a function that gives the fact that snow is white as value for the object snow as argument. According to this theory, the values of property functions are specific to the objects and properties we are considering, not general entities like the True and the False. The second option, however, seeks to mimic Frege’s decision by introducing special entities to serve as values of property functions—I will call these the Real and the Unreal. Thus the value of white for snow is the Real, while the value of white for coal is the Unreal. Intuitively, snow is really white—this is part of Reality—while coal is not really white—not part of Reality. The Real is the ontological counterpart to the True, which applies properly to representational entities not to facts. There are real states of affairs and unreal ones, and the Real and the Unreal are the entities that encompass (somehow!) these. We thus preserve parity with Frege’s economical apparatus: properties are functions from objects to reality-values, either the Real or the Unreal. This is neat theoretically, though a bit jarring to normal sensibility, just like Frege’s parallel stipulation; I like it as a concise means of formulation, though it is good that we have the fact-based theory to fall back on. We can keep both options in mind, while preferring the second option on grounds of elegance. The important point is that both values are distinct from truth-values and that they exist at the level of reality not our representation of reality—they are metaphysically objective. Then we can say that a fact consists of a function applied to an object (or sequence of objects in the case of relations) that gives the Real as its value (or the fact in question if we prefer that formulation). The thrust of the theory is less the nature of the value of the function as the fact that properties act as—and are—functions defined over objects. That is, the concept of a mathematical function can be generalized to all properties, thus delivering a metaphysical theory of properties.

Mathematics came to be understood as a theory of functions with arithmetical operations taken as paradigms. Addition, say, is a function from pairs of numbers to another number: its nature is to map numbers to numbers. We speak of this as giving, yielding, delivering—as a type of abstract action. Functions do something. The structure of a mathematical fact is a functional structure—argument, function, and value. Frege proposed to extend this structure beyond mathematics, purporting to discover that non-mathematical entities were also function-like, such as the concept denoted by the predicate “is white”. Later theorists extended the notion of function in developing formal semantics, postulating that intensions are functions from possible worlds to extensions (including truth-values): that is, they suggested that meanings are functions taking worlds as arguments and extensions as values. This is already a significant enlargement, since it applies the concept of function beyond its original home in mathematics; the concept is allowed to be not strictly mathematical but to have wider application. Semantics accordingly becomes the study of a certain type of function, somewhat like mathematics. What I am proposing is that the concept be extended yet further to furnish us with a general metaphysics of properties, and hence of reality generally. Facts are function-argument structures, whether physical, mental, legal, ethical, or what have you. The world is the totality of function-argument structures.

This substantially affects the way we think of both properties and objects. Let’s switch terminology and speak of universals and particulars: then we can say that universals are essentially entities (what other word is there?) that contain a slot or gap for objects—the argument-place of the universal—and that particulars are essentially entities that occur as arguments in such functions. Addition is essentially an operation that takes us from numbers to numbers, and numbers are essentially things that are subject to such operations; similarly whiteness is essentially an operation that takes us from objects to objects (specific facts or binary reality-values), and objects are essentially things that are subject to such operations. Universals are intrinsically argument-directed and particulars are ripe for occurring as such arguments—each feeds into the other. No function without arguments, no argument without functions. Just as addition is for numbers and numbers are for addition (among other functions), so whiteness is for objects like snow and objects are for universals like whiteness. The two are made for each other; they link harmoniously together, forming a logical unity. A fact is not a list but an organic unity (such phrases are unavoidable): the fact of snow being white is the result of snow and whiteness standing in the argument-function relation. And let us take this very literally: it is not just that we can represent facts this way—this is what they are. Reality consists of functions applied to arguments: not just an object and a property but an object acting as an argument to a property acting as a function. Frege liked to say that applying a function to an argument “saturates” the function, conceived as an incomplete entity: it made the function complete. As it were, a function with only a variable in its argument place suffers lonely incompleteness, which a willing object could satisfactorily saturate; well, that applies to the whole of reality, given that properties are functions and objects are arguments. Objects saturate incomplete properties thereby acquiring them. To put it poetically: objects yearn for properties to slot into and properties yearn for objects to saturate them. Less poetically: objects act as arguments to properties and properties act as functions defined over objects. The function-argument nexus is the root of reality. The world is the totality of saturated functions. Plato tended to oppose universals and particulars, locating them in different places, elevating one over the other, but he should have realized that they are partners in crime, natural bedfellows, man and wife. A universal is defined as a function over certain particulars; a particular is an argument destined for certain functions.[2] And not just any argument or function will do: functions will not accept any old argument and become saturated, and arguments will not offer themselves to any function in order to perform the act of saturation. For example, we cannot add John to a carrot and get a certain number as value, and 2 and 5 will not serve to saturate the function of being to the left of. Properties and objects are selective in their partners, only accepting certain potential mates in the saturation relation. In other words, the function-argument structure is both intimate and exclusive. The vision of reality it promotes is that of interlocking elements designed to fit harmoniously together. No doubt this was Frege’s intuition in the case of predicates and names; I am extending the point to objects and properties generally. Thus we derive a metaphysical conception of reality as a whole, indeed of the very structure of any reality. For it is not to be doubted that any conceivable reality containing objects and properties will exhibit the function-argument form: this is a necessary truth about reality as such. To rephrase, properties are essentially entities that take something as input and give something as output, just as addition takes pairs of numbers as input and gives a number as output. There is something action-like about functions, almost as if they have a purpose. A theist might see in this metaphysical picture an argument for the existence of a Creator: the architect of the world made it so that objects and properties would be capable of joining together—a non-trivial problem in ab initio universe design—and the solution she hit upon was to impose the function-argument structure on reality (she already had extensive experience in mathematical design). Surely, our theist might insist, it cannot be an accident that the universe is so cunningly designed—properties must have been made that way. We can sympathize with the theist’s starting point, though we may demur from his conclusion: it is certainly a very fortunate fact that properties are functions or else the world would have had trouble fitting coherently together. As it is, objects and properties nestle tightly together in the nurturing womb of the function-argument structure.

Frege’s motivations for his theory that concepts are functions were partly theoretical and partly intuitive. Theoretically, this idea might help with the problem of the unity of the thought or sentence; and it promises an enormous simplification in the semantic apparatus, as well as extending the reach of mathematical concepts (agreeable to a mathematician like Frege). Intuitively, a predicate joins with a singular term to form a sentence that is true or false, so its job is to ascend from one kind of expression to another concerned with truth. Likewise, the extension of this theory to properties is motivated both by theoretical and intuitive considerations. Theoretically, it might help with the problem of the unity of the fact; and it promises a striking uniformity in our metaphysical apparatus, as well as extending mathematical concepts still further. Intuitively, it seems natural to suppose that properties create facts from objects: facts are combinations of objects and properties, and the function theory enables to grasp the nature of this mode of combination. Frege’s overall theory strikes one at first as quite bold and counterintuitive in some ways, but it grows on one and one starts to see language through its theoretical lens (everyone should go through a dedicated Frege phase). Likewise, the theory I am proposing may seem startling and counterintuitive at first, but after a while one starts to see the world through its eyes—one looks at objects and their properties and sees them as function-argument structures. Certainly the theory affords an enormous simplification as well as other theoretical benefits, so any intuitive resistance it encounters should be regarded with suspicion. It is a nice theory, combining a sense of real discovery with an intuitively comprehensible foundation (viz. properties generate facts from objects).

Once we have absorbed the theory we can apply it further. Frege took logical connectives to denote truth functions construed as mappings from truth-values to truth-values (taken as objects). We can follow his path and understand conjunctive facts (say) as involving reality functions: conjoining two simple facts as arguments gives as value a further complex fact, or the reality-value the Real. Negation takes us from a fact to its opposite, or from the Real to the Unreal (or vice versa). So we can apply the theory to complex (“molecular”) facts not just to simple (“atomic”) facts.[3] For second-order functions we simply mimic the standard story: existence, say, is a function from properties to properties: the fact that dogs exist is analyzed as consisting in the first-order property-function dog as argument yielding the fact that that function is instantiated, where instantiation is a second-order function from functions to existential facts or reality-values. The instantiation function as applied to the dog function gives as value the fact that dogs exist, or simply the contrived theoretical entity the Real. Reality is composed of functions all the way up the hierarchy of properties, which is to say it is also composed of arguments to functions. All facts consist of arguments and functions locking together. If mathematical facts consist of function-argument combinations, the same is true of empirical reality. Thus in a certain sense all of reality is mathematical, since it has a structure characteristic of mathematics. The form of an empirical fact is the same as the form of a mathematical fact.

The value of a function is uniquely determined by its arguments, so that it depends on those arguments: the value of the addition function is fixed by the arguments inserted into it—if the arguments are 2 and 3, then the value must be 5. But the same is true of facts and properties: the fact is uniquely determined by the objects that occur as arguments and the identity of the function. Given that we are considering John and Mary and the marriage function, say, it is determined that the fact is that John and Mary are married (assuming they are): it could not be that the value of this function for those arguments is the fact that Paris is in France—the fact is a function of the function and its arguments. Intuitively, once you have the objects and properties the fact (state of affairs) is fixed; you can’t get a fact involving other objects and properties. So again facts, objects and properties relate just as mathematical functions and their arguments and values relate: the value of the property function for those arguments is uniquely such and such a fact, just as the value of the addition function for those arguments is uniquely a certain number. The dependency we observe in the mathematical case is mirrored in the non-mathematical case–one more reason to trust the analogy.

Finally, the humble variable achieves metaphysical significance: for it marks the place at which arguments are inserted into functions, and this operation is the key to constructing worlds.[4]



[1] This difficulty applies to Frege’s own theory, since concepts and truth-values are supposed to lie on the side of reference not sense, and yet truth-values are the reference of thoughts. We can suppose that Fregean concepts could exist without senses (they are close to sets of objects), but could truth-values? Aren’t truth-values precisely what thoughts stand for? I suppose Frege could maintain that truth-values, being objects, could exist in the absence of thoughts, and hence be the values of concept functions applied to objects; but that is certainly a very odd view and not one that we find Frege enunciating. Here we have the True and the False but with no thoughts to denote them! Note that if Frege had chosen states of affairs as the reference of sentences, instead of truth-values, he would not have faced this problem.

[2] We might see in this conception reconciliation between Plato’s view of universals and Aristotle’s view: by all means bring particulars into our account of universals (Aristotle), but don’t assimilate the two (Plato). Functions and arguments form a natural pair, but we need not deny that functions have being of their own.

[3] We thus obtain Russell-style logical atomism along with an injection of Frege-style function-argument theory.

[4] Allow me to add that the perspective developed here came to me as something of a revelation: the empirical world has more in common with mathematics than I had supposed (the same thing could be said about meaning understood in terms of functions). The abstract structure of the empirical world mirrors the abstract structure of arithmetic—how Pythagorean!