March 2021 - Colin McGinn

Objects

March 27, 2021/5 Comments/in Uncategorized /by Colin McGinn

Objects

The word “object” occupies a prominent place in philosophy, but it is seldom scrutinized in any depth. What is an object exactly? On the face of it the word has two uses or meanings: it may be used as a descriptor of a certain type of entity in contrast to other types, as with the distinction between objects and properties; or it may be used to indicate a relation between a thinker and what she or he is thinking about, as in the phrase “object of thought”. In this latter sense we speak of someone as the “object of attention”, or of “objects of experience”, or of “my object in doing such and such” (goal, aim), or of the “direct object” of a verb, or of “nonexistent objects of hallucination”. [1]Objects in this sense need not exist: a mental state can have an object—it can be about something—even if that object doesn’t exist. Fictional objects are objects of thought that don’t exist. It is not always clear what sense is intended, or whether the duality of uses is even recognized. The OED gives this for “object”: “a material thing that can be seen and touched”, and “a thing external to the thinking mind or subject”. The confusion is evident here. Must an object be a material thing? Why make reference to what can be sensed? Why just sight and touch? Why must an object be external to the mind—aren’t there mental objects, and isn’t the self an object too? The philosopher seems to want to designate a very broad ontological category that exists independently of perceiving minds and makes no reference to mental acts (as with Frege’s and early Wittgenstein’s use of “object”), but also to speak of mental acts in which things are “posited” or “apprehended”. The word “object” shuttles between these uses rather indiscriminately, now meaning one, now the other. Linguistically, it’s a mess.

What should we say about these two ways of using “object”? One view would be that we have a straight ambiguity analogous to “bank”—the same sound or mark just happens to have two quite distinct meanings. But this is hardly plausible: surely the two meanings are connected in some way. It is natural to suppose that one use is primary and the other derived: “object” as a type of entity or “object” as a way of talking about mental acts. Suppose we take the first use as primary: then “object of thought” comes to mean something like, “object (first sense) that happens to be thought about”. This has the problem that not all objects of thought exist, but all objects in the first sense do: so “object of thought” can’t mean “existent thing that someone happens to be thinking about”. The whole point of the phrase “object of thought” is to make room for mental acts about nonexistent things. Also, objects of mental acts need not be objects in the first sense, since mental acts can be about properties, facts, moral values, etc.—these are their “objects”. More promising is the idea that the mental act sense is primary: an object is what is or can be an object of thought (experience, emotion, intention, etc.). This is supported by the etymology of the word: it derives from a Medieval Latin word objectum meaning “thing presented to the mind”. Thus whenever “object” appears in philosophical discourse it means, “object of thought”. There are two problems with this. The first is that not all objects are objects of thought, since some are not thought about—e.g. remote galaxies and their constituent parts. The second is that it is clear that not all uses of “object” by philosophers can be so paraphrased: for example, Wittgenstein’s use of “object” in the Tractatus. At 2.01 he says: “A state of affairs (a state of things) is a combination of objects (things)”; at 2.014 we have “Objects contain the possibility of all situations”; and at 2.02 we read “Objects are simple”. He clearly doesn’t mean the word “object” in the mental act sense, and indeed he slides between “object” and “thing” without giving any notice of a shift of sense. Similarly, when Frege announces that truth-values are objects he doesn’t mean that they are things that we think about; he means to be making an ontological remark. He is distinguishing between objects and concepts (functions, in his system)–as Wittgenstein is distinguishing between objects and facts. So it is wrong to suppose that this use of “object” can be paraphrased by invoking the other use. What is to be done?

One thing we can do is firmly mark the distinction and pay due attention to it. We could in principle simply ban one use so as to clean up the language and not be bamboozled by it: we could, say, reserve “thing” for objects in the first sense and continue to use “object” only in the second sense (thus respecting etymology). I am not against this idea, though it would be pretty impractical given the entrenchment of the first sense (but in an ideal language…). It has the advantage of preventing a certain kind of misguided objection to Meinong, namely the sneering riposte, “But nonexistent objects of thought are not objects”—as if Meinong is contradicting himself. Sure they aren’t, but the whole point of Meinong’s philosophy is to distinguish between what we think about and what really exists (the former having a special type of “being”). Let’s agree that objects of thought (“intentional objects”) are not objects in the sense in which Frege and Wittgenstein speak of objects—whoever said they were? We can continue to investigate the nature of objects of mental acts, observing (say) that such objects need have no mind-independent existence, or that they lack ontological depth, or that they violate the law of excluded middle. This verbal recommendation would certainly put paid to a lot pointless squabbling. I suspect myself that “object” in the ontological sense is an example of creeping semantic shift, whereby the original word (objectum) was extended to anything that exists whether thought about or not. This can lead to an unspoken idealism according to which everything that exists is really intrinsically a mental object—for everything is like an object of thought. We conceive of everything as if it were something thought about—an object of apprehension. But we need to make a firm distinction between an object of thought and a real existing object—though we do sometimes think about the latter. Clarity would be served by calling objects in the first sense “things” and reserving “object” for objects of thought. Thus we might ask how many things (of a certain kind) exist in a given room, and we might ask how many objects came before my mind in that room during a certain time interval: these are quite different kinds of question. I might have three cat-things in my room but have hallucinated a dozen cat-objects. It only invites confusion to report that there were three objects of a certain type at a given time in a particular place but a dozen objects of the same type at the same time (three actual cat objects but a dozen object-of-thought cats). In any case, we do well to be clear about the distinction and be constantly on guard against confusing the different uses of “object” that now infect our language.

It may be wondered whether we really have a notion of object in the ontological sense. Objects of thought are conceptualized things, unitary and well defined, but are things considered independently of the mind similarly unified and well defined? We might toy with the idea of a “natural object”—one that is unified by nature, as it were. Maybe there is such a thing—organisms provide plausible examples—but the principle of unification is not like that imposed by the mind. Nature is not as Gestalt as the mind is, and it obeys different rules of unification. I conceive of you as a unitary person, but nature might regard you as just an assemblage of parts. Is Mount Everest really the natural unity that it is represented as being in human thought? One can at least sympathize with those philosophers who have found in nature only undifferentiated stuff not individuated objects; they have an exaggerated response to the insight that the world is not as cleanly segregated objectively as human thought represents it as being. But objects of thought enjoy a kind of ideal unity, since they have no being beyond what the mind invests in them. They are the real objects not the amorphous and pointless stuff that populates the mind-independent universe. In other words, natural objects are not as clearly defined as intentional objects, which enjoy a kind of conferred unity. The latter are human objects, fitting human purposes; the former are just products of natural forces that lack conceptualized unity. If we project the unity of intentional objects onto nature, we endow nature with a mind-centeredness it doesn’t strictly deserve. We engage in a kind of unintended idealism. This is why I am not averse to restricting the word “object” to objects of mental acts and referring to everything else with the word “thing”, from which any suggestion of presentation to the mind is expunged. Thus the objective world is not strictly speaking composed of objects, though it is composed of things that bear a certain complex relation to objects of thought. [2]

I am struck by the fact that “object” in the mental act sense has so few synonyms or even metaphorical expressions (perhaps this is why Husserl had to introduce neologisms like “noema”). The closest word I can think of is “target”—what the mental act “aims” at. The mind targets its objects of thought. But even that is jejune and unhelpful: what kind of targeting is this, and with what weapon? We are stuck with the locution “object of” expressing a relation whose nature remains obscure. The word “object” here just seems to mean, “what is apprehended”—what is on the receiving end of thought, so to speak. Maybe the mind “grasps” this thing when it becomes an object of apprehension, but again this word lacks the limpidity one could wish for. At any rate, “object” in the intended sense should not be confused with designations of existing objects in space; it has a quite different grammar, as Wittgenstein would say. [3]

[1] In this use the word “object” functions like the word “referent”: both are descriptions that allude to a representational medium—mental acts or linguistic expressions. A referent is that which is referred to; an object (of thought) is that which is thought about. It is the same with “denotation” or “designatum” or “subject” (in the sense of “subject matter”).

[2] An enormous amount of philosophy (and science) is comprised in understanding the nature of this complex relation (Kant had a strong interest in it).

[3] This would be a good example of the way ordinary language can mislead us: we toggle lazily and confusedly between two uses of “object”.

Empty Materialism

March 25, 2021/8 Comments/in Uncategorized /by Colin McGinn

Empty Materialism

As everyone knows, Newton abandoned the materialism of his day by introducing the “occult” force of gravity. Clerk Maxwell expanded physics further into the immaterialist camp with his theory of electromagnetic fields of force. These developments cast the whole notion of materialism (or physicalism) into doubt. But was physics before Newton and Clerk Maxwell materialist? Was mechanism a materialist doctrine? To answer that question we need to know what “materialism” means, i.e. what matter is. We need a criterion of the physical: what is it for something to be physical (or material)? What are the necessary and sufficient conditions? This question is far from easy. The OED gives this for “matter”: “physical substance or material in general; (in physics) that which occupies space and possesses mass, especially as distinct from energy”. For “material” we read “the matter from which a thing is or can be made”, contrasted with “mind or spirit”. Under “physical” we have “relating to the body as opposed to the mind” and “relating to things perceived through the senses as opposed to the mind; tangible or concrete”. These definitions only take us so far and offer little to elucidate what is meant by the metaphysical doctrine known as “materialism”. Two points stand out: first, matter is to be distinguished from energy; second, matter is perceived through the senses. Energy is not material and what is not perceived by the senses is not material (what is so perceived is). This gives the result that energy is not subject to materialism and secondary qualities are material simply because they are perceived by the senses (and atoms are not material because they are not so perceived). This is far from what philosophers have intended by using the terms “materialism” and “physicalism”. We clearly need to go back to the drawing board.

One approach, much favored, is to invoke geometrical concepts like size and shape. Thus Descartes spoke of extension and modes of extension as characteristic of physical substance. It is necessary and sufficient to be physical that something has shape, shape being a physical attribute. More generally, the physical is to be defined as what possesses primary qualities. The view goes with the idea that space and matter are intimately connected: matter is what occupies space (as the OED states). There are many problems with this approach. First, as to sufficiency: don’t persons and sentient beings generally occupy space and have shape? Is it contradictory to suppose that God is spread out through space, as in pantheism, and has a tripartite form (the holy trinity and all that)? What if thoughts and sensations have shape of some sort—does that preclude them from being immaterial? Doesn’t it depend on what kind of stuff they are made of? Is extension logically sufficient to make something materially constituted? Descartes already had a problem with space in this regard, given that space is extended (his solution was to declare space a rarified form of matter). And is shape really a physical property? What if perceived shape is actually a secondary quality (as modern physics appears to suggest)? Then reducing everything to shape is not a form of materialism at all, since shape is projected from the perceiving subject, i.e. is mental. Maybe in objective physical reality nothing has shape, or at least determinate shape: does that imply that materialism must be false? But more fundamentally, is geometry physical? Is Euclid’s Elements a work of physics? There is certainly a strong tradition stemming from Plato and going back to Pythagoras that geometry is about the world of abstract geometrical forms, loosely proximate to the realm of the gods. If we are Platonists, we don’t regard geometrical forms as physical in the sense of being made of physical substance; and we don’t suppose that they are perceivable by the senses (the intellect must be employed). We might even adopt a kind of idealism about geometry, holding shapes to be ideas in the mind of God. In that context reducing everything to geometry is the furthest thing from materialism as traditionally conceived. So the prospects for a form of materialism based on primary qualities like shape depends upon your metaphysics of geometry: you have to think that geometry is about physical substances–whatever your account of that concept is going to be. Second, in regard to necessity: is it really a necessary condition of being physical that a thing has shape? Do electrons have shape just by being physical? What about fields? Could there be a physical universe with no shaped objects? So long as there is physical stuff we have a physical world; possessing shape is an added ingredient. The connection between matter and shape looks to be contingent and adventitious, not a matter of strict definition. The same goes for size and number: are these necessary and sufficient for being material? If size is relative, then nothing has size in a universe containing a single object; but surely there could be a physical universe with just one object. And how can number confer materiality on a thing, given the ontological standing of numbers? The basic point is just that these qualities are not intrinsically physical (whatever that means): they are, if anything, abstract, or possibly psychological. That is why Berkeley has no trouble including primary qualities like shape in his idealist universe. We still have no criterion of the physical that will confer content on the doctrine known as “materialism”.

You might think we could resort to the doctrine of mechanism: materialism is defined as the thesis that everything is subject to mechanism. This is certainly the form that materialism took before Newton and later Clerk Maxwell. The problem here is that mechanism is neither necessary nor sufficient for materialism. The OED defines mechanism as “the doctrine that all natural phenomena allow mechanical explanation by physics and chemistry”. Correct: but what is “mechanical explanation”? It is explanation by deterministic contact causation—the kind that is found in typical machines. But this is not a necessary condition of being material, since we can conceive of physical systems that don’t work by such causation: they are made of material particulars but their behavior is not to be explained in terms of deterministic proximate causes—maybe the entities concerned never actually touch each other, or act probabilistically. The nature of an object’s composition is not the same as the nature of the explanations that apply to it. And the applicability of mechanical explanation is not sufficient for materiality either, because non-physical things might interact by means of contact causation: immaterial minds might make contact and thereby influence each other, or a part of an immaterial mind might affect another part by immediate contact. The mode of interaction between things is not determinative of what composes them. So mechanism is not a good way to define materialism, conceptually speaking, though it was the form that materialism took in earlier times. Mechanism is a view of what constitutes an adequate scientific explanation not a view of the composition of basic reality: these are orthogonal questions. It isn’t as if planets ceased to be material once Newton’s non-mechanistic physics became established! So we still don’t know what it is for something to be material.

Is it the possession of mass? If we define mass as “quantity of matter”, we invoke the concept of matter in defining what matter is, which makes the definition circular. If instead we define mass as resistance to motion (inertia), then it doesn’t follow that the object in question is material: couldn’t immaterial entities vary in their degree of resistance to motion? And what about massless particles? Likewise, being subject to gravitational force (weight) is not logically sufficient for being material, since immaterial things might be subject to gravity too—this could be a basic law of a conceivable universe. What about limiting the concept of the material to the brain, which would still enable us to define a workable materialism for mental states? That is, we define “material” as “neural”, thus enabling us to claim that the mental is reducible to the neural—no need to attempt a general definition of the material. But are neurons material things? This takes us back to where we started: in virtue of what are they declared to be material or physical? Is it because they are objects of sense perception, or is it because they occupy space, or is it because they have shape? What if electricity is non-physical (as was once thought)? What if shape properties are non-physical in the manner of Plato? What if perceived shape is a mental projection, so that the shape of neurons is as subjective as their color? [1] What if in objective reality nothing really has determinate shape? We can certainly define a doctrine of “neuralism” that maintains that everything mental reduces to neural properties, but it doesn’t follow that materialistic metaphysics has been thereby vindicated. For that we would need a proper notion of what it is to be material; but the concept of materiality remains elusive. It is true that there is the popular sense of the word in which it connotes undue concern with worldly values (money, real estate, etc.), but that has nothing to do with materialism as a metaphysical thesis—though this thesis might derive spurious content by association with materialism understood as a life-style. Maybe the word “materialism” has always connoted that which is to be contrasted with the divine or supernatural, but clearly this notion is not specific enough to define the intended metaphysical doctrine (human and animal minds are not divine or supernatural). The notion is irredeemably hand waving and honorific, more a device of rhetoric than strict ontological taxonomy. It operates to define what side you are on in the wars of religion.

Is time material? Is space? What about numbers? And values? Are the four fundamental forces of nature material, or electric charge, or motion? We have the idea of chunks of stuff like rocks and furniture and bits of food, but this is not enough to give us a perfectly general notion of matter capable of making useful ontological divisions. This is why there have been such controversies, even within physics, about whether this or that qualifies as “physical” (gravity, light, fields of force, the ether, etc.). The concept of shape has been the last redoubt of the would-be materialist, but as indicated above that proves a frail reed too. Geometric form is really not a promising basis on which to define the putative concept of the material, because geometry itself is not a physical science in any intuitive sense; someone who believes that the world is a pure mathematical structure of abstract geometric forms is hardly a materialist. And space, the concrete reality in which geometry manifests itself, is a poor candidate for erecting a viable notion of the material, even if it is not defined by reference to human perception. We need some idea of space-occupying physical stuff, but what exactly is this elusive stuff supposed to be? It is no wonder that theorists, sensing the difficulty, have proposed that material stuff is really mental stuff: but then materialism turns out to be a form of idealism, i.e. the view that reality is ultimately mental. The panpsychist is no materialist.

We can imagine intelligent beings that revere matter for its supernatural associations, while finding mind quite far removed from the divine. They suppose that God miraculously created matter in the initial act of creation, while minds arose by mundane natural processes. These beings worship matter and extol its remarkable properties (they are very taken with light and love rainbows): they display big chunks of it in their temples and teach physics as a holy science. The soul excites them not at all—any more than the stomach does: for these happy beings are not much concerned with matters of moral conduct. For them there is nothing bravely hardheaded or thrillingly anti-religious about regarding matter as the basis of everything real (God, for them, is the Matter of all matters); for them it would be heretical to be an idealist, proclaiming the unreality of matter and asserting the sole dominion of the mind (that animalistic thing!). For us, however, materialism sounds anti-religious and we devoutly wish to distance ourselves from religious conceptions; while for them dwelling on the soul exclusively and repudiating matter is what excites religious opposition. Could it be that the historical enthusiasm among human freethinkers for something called “materialism” has its psychological roots in opposition to religion (no doubt well-founded opposition)? But once religion loses its cultural hold on us the rhetoric surrounding the term becomes obsolete: we no longer have any use for the concept of the material (beyond its quotidian practical uses). We can go on talking about the mind and the brain and wondering whether neurons are the ground of all mentality, but we can dispense with the general notion of the material. We need not concern ourselves with the pseudo-question of whether or not neurons are material things. We can ask whether they are mechanical things and expect to be talking sense (they are probably not), but insisting on an answer to the question of whether they are material or immaterial is outmoded gibberish—rather like forcing an answer to the question of whether gravity is material or immaterial, or energy, or radiation. We no longer think there is anything to the ancient contrast between the sublunary and the superlunary—this is a pointless bifurcation from a scientific point of view—so why cling to the obsolete and unhelpful contrast between the material and immaterial? Both belong to a worldview built around religion, but that worldview no longer commands scientific or philosophical interest. Materialism is accordingly an empty doctrine. [2]

Colin McGinn

[1] According to old-style biology, organic structures are imbued with vital spirits, and hence are not reducible to the inorganic materials dealt with by physics and chemistry. That would make neurons likewise imbued with vital spirits, this disqualifying them from being purely physical. So identifying mental phenomena with neurons would not vindicate materialism. And can such vitalism be ruled out a priori?

[2] Of course, immaterialism is empty to exactly the same degree. We might say that naturalism has rendered materialism null and void.

Qualia

March 22, 2021/1 Comment/in Uncategorized /by Colin McGinn

Qualia

When philosophers talk about qualia they are typically discussing the mind-body problem and the prospects for materialism. They are not interested in the general theory of qualia. They may cite some examples of qualia, but they don’t enquire into the general structure and function of qualia—as a linguist might study the structure and function of language. There is no “qualistics” analogous to linguistics. And indeed the subject is difficult and obscure, even more so than the nature of language. Here I will merely tickle the subject of qualia in the hope of eliciting a gurgle that might reveal the general nature of the beast. The analogy with linguistics provides a useful starting-point, because quite a bit about language has been discovered, particularly in the post-Chomsky period. The most basic fact about language is that it consists of a finite lexicon that is capable of infinite expansion by means of the rules of grammar. Language has an elements-and-rules structure with infinite potential. Grammars generate an infinite array of expressions by operating on a fixed and finite set of linguistic units. Is something similar true of qualia?

The plural form of the noun “qualia” suggests a stock of distinguishable discrete elements, and indeed introspection confirms that our sensory consciousness is constituted by a totality of just such elements—sensations of color, feelings of pain, tastes, smells, etc. These come in enormous profusion: it would be hard to put an upper limit on the number of qualia accessible to a typical human perceiver (or other animal). Just consider the number of distinct qualia you experience with a closed eyelid! I would suspect that qualia vastly outnumber words. So we may state the first law of qualia science: there exist a colossal number of qualia in the universe. The number is presumably finite, and is probably less than the number of stars, but it is truly massive. Moreover, qualia, unlike words, vary continuously, being more analogue than digital (just consider all the shades of blue): so the infinity of the continuum applies to them. The cardinality of the qualia lexicon is astronomically large. In addition to this the “grammar” of qualia is immensely productive: qualia can be combined ad libitum, both in space and time. Complex totalities can be formed that are completely novel and will never be repeated—as when you visually take in a new scene of any complexity. At any given moment the five senses are saturated with seething populations of qualia, which together yield an enormous array of variegated qualia ensembles. The brain in all its complexity must be responsible for this vast qualia universe, by virtue of mechanisms little understood. Consciousness is constitutionally capable of housing these gargantuan combinations of individual qualia. The brain is clearly an incredibly complex and intricate qualia-generating machine.

The second law of qualia science states that qualia are extremely various. Each sense has its own proprietary range of qualia, and within each sense there is also considerable variety. There are a great many qualia universals. Qualia types are evidently more various than physical particle types (which are relatively few in number). Words differ in their types too, but qualia fall into far more categories. It would take a determined theorist to be a qualia monist (or an especially blind one). The qualia of different senses don’t mix, despite their freedom of combination within a given sense: you can’t see red and taste pineapple within the same sensory field. Qualia shun each other when they are too different, though they congregate happily when they share a basic phenomenology. Perhaps there could be olfactory eyes that respond to light and chemical impingement at the same time, thus producing a combined olfactory-visual field; but that is not the set-up on planet earth (so far as we know). So there is a definite limit to the combinability of qualia into unitary percepts, even though within a sense modality there is great plasticity (not to say promiscuity). Qualia are like members of a tribe that will hang out with any member of their own tribe but will not mix with members of other tribes.

But there are some strange borderline cases and apparent exceptions, which bring us to the heart of qualia darkness. For one thing, qualia enthusiasts never cite impressions of geometrical forms as instances of qualia: it’s always sensing colors not sensing shapes. Do we not have shape qualia? But surely we do perceive shapes, so there ought to be corresponding qualia. The reason for this omission, I suspect, is that we experience shape with more than one sense—with both touch and sight. So there is nothing qualitatively distinctive about sensing shape. Yet it does seem as if a single experiential type is involved in sensations of circularity (say). This is why it is tempting to give an affirmative answer to Molyneux’s question: yes, a blind man made to see would recognize circles based on his previous tactile experience with them. So here the quale seems to hover between sensory specificity and abstract generality. We don’t really know what to say about geometrical qualia—that is, qualia corresponding to the traditional category of primary qualities. This is why all the examples cited involve secondary qualities. But the question cannot be avoided: do we, or do we not, have qualia of what are called “common sensibles”? If we do, qualia can hop between the senses; but if we don’t, we are qualia blind to certain qualities of things. [1] The question remains infuriatingly obscure.

Obscurity mounts when we consider synesthesia. It is said that red resembles the sound of a trumpet, and some people experience letters of the alphabet as having certain hues. Is there, then, a type of experience that straddles the two—a type of quale that unites these disparate qualities? Are redness and trumpet sounds instances of a common qualia type for people who sense the resemblance? Are there such higher-order qualia? The idea seems not without merit. This suggests a hypothesis: that there are qualia that transcend specific concrete qualia but coexist with them. These unifying qualia hover in the background somehow, permeating our more immediately discernible qualia. [2] Maybe we have no words for them, but they are real nonetheless. Concrete instances may be variations on a phenomenological theme. Could it be that there is a single basic type of quale that gets specialized in the different senses, producing variety from uniformity? Can we imagine a sentient being whose entire qualia space arises from a subset of uniform qualia originating in a particular sense? Suppose that in this being vision evolves first and then the other senses piggyback on it by modifying the qualia associated with vision, thus producing qualia called by other names. The sensation of red is coopted by hearing to produce the sound of a trumpet, say. [3] Thus there are qualia universals that span the different senses—rather as there are linguistic universals that span different human languages. The variety we observe arises by a process of transformation amounting to metamorphosis. This seems like a strange idea, to be sure, given the qualitative differences between qualia across the senses, but can it be ruled out a priori? Might the variety of qualia be less than appears to casual inspection? Certainly we have repeatedly discovered deeper uniformities in nature than strike us at first sight. Concepts are not sense-specific—they don’t have a sense-modality written into them—so perhaps qualia are also more modality-neutral than we suppose. Could there be unconscious qualia that underlie the conscious kind available to introspection? Could the apparent heterogeneity disguise a more basic homogeneity? Might qualia admit of a distinction between surface structure and deep structure? We don’t know, but the question seems real enough. We are certainly familiar with the idea that the introspectively available part of the mind is only one part of it. Qualia might enjoy a substantial unconscious life in some form or other.

It may be said that the analogy with language is imperfect because the principles of qualia combination are nothing like grammar in the literal sense. I would agree with that—indeed, insist upon it—but this is a dispensable feature of the analogy. A better analogy would be bird song, which has the advantage of locating qualia at a lower evolutionary level: bird song is also built around a set of primitive elements and rules of combination, species-specific and quite intricate. Also, the notes of bird song vary continuously like qualia, thus producing enormous variety. Architecturally, then, individual qualia resemble the elements of bird song; we can readily imagine a mapping from one to the other. The basic brain mechanisms that allow one might allow the other (not that we know what these mechanisms are). From a computational point of view, both are functions from primitive elements to combinations of elements, possibly exhibiting hierarchical structure. Qualia do seem to cluster and embed, forming gestalts, dividing up the world into useful units for effective behavior (just consider your visual field right now). We have no idea how qualia evolved, singly or as combinable elements, but presumably mutations produced machinery capable of generating their distinctive form—a kind of program for qualia manipulation. And presumably this elaborate mental capacity has survival value: qualia help keep the organism around. The genes wouldn’t go to all that trouble for no reason. Qualia are psychologically real, cerebrally embodied, and functionally adaptive—they have to be. They must be as natural as bird song, and analogous to it (up to a point).

It should be noted that qualia are not confined to the senses. They also appear in the imagination: our mental imagery is qualia-laden. Here they combine in new and surprising ways, following the elastic rules of image formation. They take on fresh combinatorial possibilities, not being stimulus-bound. Thus we have the qualia-borne imagery found in dreams: boundless, bizarre, creative, and anarchic. Dreams are qualia heaven—the place where qualia go to do whatever they feel like doing. And they are so nimble, so mischievous, and so free. But even in daydreams qualia flex their creative power, fluidly combining and recombining, always resourceful, preternaturally agile. They form the inner speech of the senses. They also feed into the thought process, though they seem shy about actually entering that domain (we don’t “think in qualia”): what we think and believe is shaped by the qualia populating our sensory consciousness—colors, sounds, smells, tastes, feels. So qualia fit into the overall economy of the mind in characteristic ways; they aren’t just marginal. Again, they are like words in this respect—here, there, and everywhere.

I have tried to avoid the vexed question of the ontology of qualia. What are they exactly? Are they representations of external properties or are they qualities of consciousness itself? Are they non-physical? I will simply say that they are subjective-objective hybrids: episodes of seeming to apprehend qualities of things. The quale associated with seeing something red is a seeming to have a red thing before you: it is thus a synthesis of a subjective state and an objective quality (in one sense of “objective”). Not that any of this is easy to understand, but it is the right way to describe what is at issue. Accordingly, qualia are instances of such episodes of seeming—that is, states of consciousness in which a quality is apprehended. These are the things that exist in such profusion and that get combined so freely. If it is any consolation, it is also not at all clear what a word (lexical item) is: is it a sound wave, an act of speech, a mental entity, an abstract pattern, or a brain configuration? The ontology of words is also obscure (ontology often is: numbers, meanings, beliefs, even physical objects). But this obscurity shouldn’t prevent us from recognizing important truths about the subject matter in question, particularly its structural and functional features. As with so much about the mind, we are only at the beginning of understanding it, and may never achieve the understanding we seek. [4]

[1] People sometimes say we perceive visual shape and tactile shape, but never just shape: but this is an obvious cop-out—surely there is something in common between the two, something with phenomenological reality.

[2] Sartre would say that every quale carries with it a sub-quale of nothingness, since nothingness is the essence of consciousness: in seeing something red, say, the subject apprehends the emptiness of consciousness itself. A referential theory of qualia would likewise imply that every quale embeds an awareness of an act of intentionality common to all qualia. In both cases we have cross-modal qualia of a rather abstract type.

[3] We can formulate a synesthetic version of Molyneux’s problem: would a person born deaf recognize the sound of a trumpet as similar to red if suddenly given the ability to hear? That is, is this similarity inherent in the red quale and capable of extrapolation? I myself sense a strong similarity between whiteness and silence, and also between hot peppers and hot objects (the use of “hot” for both is surely not an accident). Thus there might be a universal phenomenology (across the senses) analogous to universal grammar (across languages).

[4] It is an interesting historical fact that the word “qualia” and the associated concept have been around for over a hundred years (C.S. Peirce introduced “quale” in 1866 and C.I. Lewis introduced “qualia” in 1929), but the notion is still highly controversial even as a descriptive term. The subject is shrouded in obscurity, and hardly exists as part of scientific psychology. It awaits its Noam Chomsky to set it on a scientific footing. We barely have even a superficial taxonomy of qualia. Qualia theory is like the linguistics of the Stone Age.

An Identity Theory of Identity

March 18, 2021/2 Comments/in Uncategorized /by Colin McGinn

An Identity Theory of Identity

The identity theory I have in mind says simply this: identity is identical to indiscernibility. That is, the identity relation reduces to the indiscernibility relation. Why would anyone endorse this theory? First, there is a very clear connection between identity and indiscernibility, enshrined in Leibniz’s Law: x is identical to y if and only if x and yare indiscernible, i.e. have all properties in common. Second, if the two are not identical (identity and indiscernibility), then we cannot establish identity by ascertaining indiscernibility, since the identity relation transcends the indiscernibility relation. We could simply assert an entailment from the latter to the former, but this has the look of a stipulation absent any recognition of identity. Thus there is a danger that identities will turn out to be unknowable if not reducible to indiscernibility. Third, identity would be a sort of metaphysical dangler if not reducible to indiscernibility: it would stand apart from indiscernibility in a weird and gratuitous way—better then to trim it back to indiscernibility using Occam’s razor. Reality contains no identity relation over and above the indiscernibility relation. So there are reasons to hope that identity is in fact identical to indiscernibility.

But there is a well-known obstacle: while the indiscernibility of identical things seems self-evident, the identity of indiscernible things seems not to be. The classic example is qualitatively identical spheres at different points in a symmetrical universe. The example seems exceptional and contrived—we don’t normally encounter such potential counterexamples to Leibniz’s law—and not surprisingly there are counter-replies. First, we could simply stipulate that identity-with-x should be counted among the properties of x, in which case the qualitative counterpart y will not have this property (having instead the property of being identical-with-y). Second, we can include spatial location among the properties of each sphere, so that the two are not spatially indiscernible. Third, we could bite the bullet and declare the two identical, dismissing the thought experiment as fantasy: for if nothing distinguishes them they cannot be distinct. It is important here to denude the concept of discernibility of any epistemic connotation: the point is not that our inability to discern the difference between two objects establishes that they are identical; it is that the objective fact of indiscernibility, i.e. complete sharing of properties, entails identity (because it is identity, according to the identity theory of identity). Thus we can reply to the standard objection to the right-to-left reading of Leibniz’s Law: there is no proof that indiscernibility fails to entail identity.

The theory might be compared with a similar identity theory of numbers, viz. that numbers are sets. Once we have sets, it may be said, we don’t need a separate ontological realm of numbers—we can shave off the redundant ontology. Whether that is a good argument is not to the point; the point is that the analogous identity theory of identity can claim that there is no ground to distinguish identity from indiscernibility once we have a suitably relaxed notion of indiscernibility to work with. Identity just is complete objective indiscernibility, neither more nor less. It adds nothing to the basic fact of absolute and total coincidence of properties. It is possible to be an anti-reductionist about identity, holding it to be a separate relation altogether, but one can appreciate the position of someone who can’t stomach that kind of metaphysical multiplication. The reduction is not empirical, to be sure, and it qualifies as knowable a priori, and it may even be analytic: but it is informative in some way, and hence rationally disputable—it is not an empty tautology. It is piece of substantive metaphysics. An interesting feature of it is that it applies to itself: it says that identity is indiscernible from indiscernibility. For that is what identity is, according to the theory; therefore the identity of identity with indiscernibility is the same as the indiscernibility of identity and indiscernibility (and that “same” is also equivalent to indiscernibility). The word “identical” or “same” always expresses indiscernibility. Thus Leibniz’s Law is not just a stipulated biconditional in need of a rationale; it is tantamount to the proposition that identity is identical to indiscernibility. Leibniz has discovered a true identity statement connecting two expressions of the language: “identical” and “indiscernible” both denote the same relation, variously described as identity or indiscernibility. The case is no doubt special, but in broad outline it is an instance of a Fregean informative identity statement: one denotation with two names for it. Ontologically, the world contains indiscernibility facts, and these facts constitute identity facts. Logically, the case is just like the identity theory of mind and brain: the world contains brain facts, and these facts (allegedly) constitute mental facts. There is something pleasing in the result that identity itself might be subject to reduction via identity (i.e. indiscernibility).

A Day in the Life

March 17, 2021/6 Comments/in Uncategorized /by Colin McGinn

A Day in the Life

I began the day by putting the finishing touches to my essay “A Triple Aspect Theory”, on a subject I have been thinking about for over fifty years and still find inexhaustibly interesting. This was the usual intense intellectual effort in which the mind seems both to be struggling with its own limitations and soaring serenely over the landscape. I then posted the essay on my blog and sent it to my usual correspondents (Tom Nagel, Noam Chomsky, Steve Pinker, Rebecca Goldstein, Marie McGinn, Teddy St Aubyn, and my brother Keith). It was a perfectly satisfactory philosophical morning, if nothing out of the ordinary.

Then at noon I went to play tennis with my regular partner Eddie, having just played with him yesterday. It was the usual focused, intense, ballistic, brutal, and exhilarating hour and a half. I was using my new Wilson Clash racquet, which is both maneuverable and powerful, and I wanted to work on changing the direction of the ball. I have been practicing this against the wall for a while (over at the Biltmore club), particularly the down the line backhand drive. It’s not an easy shot to pull off but a very useful and satisfying one. I had the customary battle against Eddie, who is a fine player and never lets up (also a keen kite boarder). It was an all-out mental and physical effort.

I had an hour’s break before going to my voice lesson at 4pm with Nicole. Nicole and I have formed a group called the Duetones (she has been teaching me to sing for a year). We began by singing a new song “When Will I be Loved?” by Linda Ronstadt (written by Phil Everly), sung over the original record. Then we turned to “You Really Got a Hold on Me” by the Beatles (originally by the Miracles and written by Smokey Robinson). But then we did something different: we sang both songs without musical accompaniment. Now Nicole is a marvelous singer (me not so much) and I was fascinated to hear what we would sound like together singing a cappella. The Duetones have a philosophy, a mission even: we seek to unite opposites. She young, me old; she female, me male; she classical, me more rock and blues. I was hoping for what I was pleased to call the “magic sound”—what happens when two voices blend together perfectly (think Lennon and McCartney). And I believe it happened, especially with “Love Me Tender”, “Love Hurts”, “Funky Town” and “Give It Up” (by K.C. and the Sunshine Band). Again, this was an hour of intense effort, but deeply satisfying. There is nothing quite like singing together with another person, especially when it works. I recorded the lesson. When I got home I listened to the whole thing and relived the experience (not without the odd wince at myself). The Duetones are here, I thought.

That was a day worth living, it seemed to me. It makes you think what an amazing thing the human organism is, or can be. It also represented human cooperation at its finest. I felt it was worth memorializing here. I will refrain from analyzing it further, being content just to record the basic facts.

A Triple Aspect Theory

March 16, 2021/4 Comments/in Uncategorized /by Colin McGinn

A Triple Aspect Theory

Does pain have a nature that goes beyond the feeling of pain? Pain has a phenomenology, which we experience internally, but does it have any other properties? Apparently it does, since it has a functional role—a way it functions in the mind and in relation to the body. This functional role forms part of what pain is. It is the same with other mental states such as desire: desire has an introspective appearance but it also functions in the organism’s psychophysical life. This is fairly uncontroversial. Much the same could be said about water and other natural kinds: they have a phenomenological appearance but they also have a causal role in the world—a set of causal powers. But is that all—does pain have no further intrinsic nature? Well, what does it have its functional role in virtue of? We might say in virtue of its phenomenology: it functions as it does because of the way it feels. But this is not plausible for the following two reasons: (a) the functional role of pain includes its bodily causes and effects, which are not themselves phenomenological, but physical; and (b) states of the brain are the de facto causal basis of these bodily phenomena. It is hard to see how phenomenology alone could give rise to physical functional role, and anyway the brain already has that job covered. So the natural assumption is that brain states are the basis of the functional role of pain, not the phenomenology of pain. But given that functional role is partly constitutive of pain, it follows that the necessary conditions of functional role are too: that is, states of the brain are also part of the nature of pain. So pain has three aspects (as do other mental states): its phenomenology, its functional role, and its neural correlate. In fact its neural correlate is not a correlate at all, any more than phenomenology and functional role are correlates of pain; it is part of what pain is. Pain isn’t just correlated with the feeling of pain, and it isn’t just correlated with its neural basis either—any more than water is just correlated with H2O. Water comprises three sorts of property: appearance properties, underlying molecular properties, and causal properties. But so does pain: its appearance to introspection, its functional role, and its neural basis. It is thus more than its first-person appearance as a feeling; it has another type of reality altogether. Pain is partly made of brain stuff.

This is not some sort of generalized materialism (whatever that means); it is a point specifically about the nature of pain and other mental states. Because mental states have functional roles as part of their intrinsic nature they also have neural states as part of their nature, since the latter are the basis of the former. The best hypothesis is that the brain, as we now conceive it, forms part of the essence of the mind. Neurons are really part of the inner nature of mental states. This doesn’t mean for all conceivable types of mental states—Martians may not have neurons in their “brains” but some other type of unit. The point is just that terrestrial animals have minds whose nature includes the nature of their neural brains. The brain is not extrinsic to the mind, located somewhere outside of the mind. Brain states form the hidden machinery of the mind in much the way that molecular states form the hidden machinery of water, and for essentially the same reason, namely to ground the causal properties of the things in question. Mental natural kinds are partly constituted by neural natural kinds (here on earth)—but only partly because they also have a phenomenology. This is not some sort of reductionism about phenomenology, just the pedestrian (but important) point that the reality of the mind is not confined to its appearance to introspection—the brain is also an aspect of the mind (as molecules are an aspect of water). Maybe the phenomenological aspect is irreducible to anything else; maybe it is a complete mystery how anything can have both phenomenological and physical aspects; maybe the whole thing is pure magic: but still, mental states have a physical aspect existing in the brain. To repeat, not a correlate (as in traditional dualism) but an intrinsic dimension of their being: states of mind actually are partly composed of states of the brain physically described. There need be no necessary connection between phenomenology and a specific brain physiology; it is just that functioning mental states must needs be partly constituted by brain states of some sort. In the case of terrestrial animals brains have a certain sort of physiology, so the minds of these animals are partly constituted by that physiology. They don’t float above the brain, as “nomological danglers”, but are intimately enmeshed in the brain. Brain states don’t merely correlate with mental states; they constitute them. Just as H2O molecules are intrinsically involved when you wash your hands, so neurons are intrinsically involved when you think your thoughts or feel your pains (with the emphasis on “intrinsically”). They aren’t somehow removed, existing in another parallel place; they are right there in the thoughts or pains. They are as much in your mind as its phenomenology is. Perhaps we have a bias in favor of phenomenology because that is the way our minds strike us internally, but from a more objective perspective our minds are equally brain involving. The mind is just as steeped in the brain as it is steeped in its own subjectivity, i.e. its own introspective appearance. To put it bluntly, mental states have a neural architecture existing alongside their phenomenological character. [1]

I introduced the brain directly into pain via the functional role of pain, but once we have taken that step we can probably limit ourselves to just the brain combined with phenomenology; for the brain’s states can substitute for functional roles, given that they determine functional roles. It is not customary to say that water is H2O plus the causal role of H2O, since the former determines the latter; likewise we can say, not that pain is (partly) C-fiber firing plus the causal role of C-fiber firing, but just the C-fiber firing itself, since that determines causal role. Strictly speaking, we have a trio of aspects in both cases, but to all intents and purposes the physical basis makes mention of the causal-functional role redundant. So we could simplify and say that pain is constituted by the feeling of pain combined with the neural basis of pain, with causal role entailed by neural basis. The essential point is that the brain is just as integral to pain as its phenomenology is. This gives us a good deal of what the classic identity theory proposed (token or type), but not all. Mind and brain are inextricably intertwined, which is not to say identical.

[1] This doesn’t solve the mind-body problem, nor is it intended to; it simply tells us how the problem is shaped.

The Prudent Gene

March 13, 2021/9 Comments/in Uncategorized /by Colin McGinn

The Prudent Gene

Humans are capable of two types of selfishness, the prudent kind and the imprudent kind. Imprudent selfishness is quite common: a glutton grabs the cake from someone else and gorges himself on it, much to his future detriment. The genes, however, do not go in for this kind of imprudent selfishness; their selfishness is exclusively of the prudent kind. It is easy to see why: imprudent genes don’t stay in the gene pool, since they don’t maximize their own survival prospects. So we can say that genes have, in addition to the trait of selfishness, the trait of prudence: the genes that survive best are the ones that program their carriers to act prudently with respect to gene survival. That doesn’t mean with respect to individual survival: an organism can serve its genes by acting so as to benefit its offspring more than itself. What a gene will not do is produce organisms that act altruistically in an imprudent manner with respect to those genes. Genes work to produce organisms that protect the interests of their genetic descendants: that is, they act prudently with respect to their own future survival. They don’t do silly things like gamble their survival on the lottery, or construct organisms that laze around all day. The genes are not prudentially irrational. Genes operate by a principle of enlightened self-interest.

But this raises a question about imprudent animal behavior: why do animals sometimes act so as to not maximize genetic survival? Why are they imprudent with respect to their genes? Mostly they are prudent in this way, by storing food for later consumption, or not fighting bigger animals, or building nests and other dwellings. They plan for the future, ensuring their own survival and that of their genes. That’s how the genes built them. Then why isn’t this a universal law? Consider masturbation, not just in humans, but also in a wide range of other species (elephants, walruses, squirrels, turtles, etc.): isn’t this imprudent with respect to gene survival? Isn’t it a waste of good genes? Even if there is no ejaculation, it is sexual behavior not spent on reproductive success. The chronic masturbator is not much of a reproducer. A gene for masturbation would not stick around for long, unlike a gene for copulation. Yet masturbation is common and normal in many species. Genes for masturbation don’t seem very prudent—even if they form part of what makes an organism happy. Thus masturbation presents a problem for prudent gene theory.

The only possible solution to this problem is to regard masturbation as an unwanted side effect of a trait that is prudent from the genes’ point of view. But it is hard to see how such a side effect could withstand the test of natural selection: how could natural selection favor, or even tolerate, a trait that could lead to gene termination? Think of an animal that does nothing but, leaving copulation to others—its genes will not get passed onto future generations. I am led to conclude that the existing arrangement is a compromise solution to a difficult engineering problem. The genes need to motivate animals to reproduce, and pleasure is a powerful motivator; but then the loci of pleasure can be stimulated in other ways, thus producing non-reproductive sexual activity. But how can the genes prevent animals from abusing the system they have created? They agree that masturbation is genetically imprudent, and they are paragons of prudence, but they can’t think of a way around the problem: if you reduce sexual desire in order to discourage masturbation, you end up discouraging copulation. If masturbation in turtles became too common, reducing copulation significantly, then turtles would be in reproductive trouble; but as things are the balance just about allows for the coexistence of prudent copulation and imprudent masturbation (with respect to gene survival). The problem is a little like the problem of pain: it is so important to give organisms the sensation of pain for ensuring survival that the genes tolerate a downside to pain that serves no survival purpose. Masturbation looks like a waste of resources and energy that could be devoted to surviving and reproducing, and it is just that; but the genes tolerate it because otherwise animals would not be equipped with the motivational apparatus that propels them towards reproductive copulation. The genes are scrupulously prudent, but even they know when they are beaten: they can’t put a stop to masturbation without undermining reproductive motivation. Either that or masturbation is a complete mystery and a blot on the genes’ reputation for prudence. [1]

[1] It is generally easy to see why imprudent behavior, such as overeating and sugar consumption, is an offshoot of adaptive traits, but the existence of masturbation in many (but not all!) species is far more puzzling. They do it a lot and it is quite contrary to the genes’ interests. There ought to be a gene for not masturbating.

Addition and the Origin of the Human Mind

March 11, 2021/2 Comments/in Uncategorized /by Colin McGinn

Addition and the Origin of the Human Mind

How did language and arithmetic evolve? [1] It is natural to ask about both in the same breath because of certain broad similarities between the two, particularly regarding discrete infinity, recursive rules, and computation. It would be nice if a common feature could be revealed allowing both to have the same origin. This would also provide an identical explanation for the learnability of arithmetic and language: the same basic cognitive mechanism is responsible for acquiring both sorts of competence, suitably specialized. The idea is that a single mutation, occurring around 200,000 years ago, provided the human brain with the cognitive machinery to grasp both the syntactic structure of language and the structure of arithmetic. No doubt this basic machinery got supplemented and shaped by the demands of externalization and other factors, but the core principle evolved in a single genetic mutation encoding an instruction for the construction of human brains. A new brain circuit implementing a cognitive trick or trait sufficed to permit the arrival of arithmetic and language. Thus the specifically human mind evolved as an upshot of this remarkable mutation; and the rest is history. The question is what this magical mutation might be. It needs to be both simple enough to evolve in the standard manner and yet rich enough to encompass the essence of the competences it permits. This is no doubt a daunting question, but presumably it has an answer—and we might as well set about trying to answer it. So: what structural, operational principle lies behind both arithmetic and language?

The answer I will propose is: addition. We should first rid our minds of the usual connotations of that word, namely school sums written with the plus sign. The OED gives this for “add”: “join to or put with something else”. Notice this does not even mention numbers specifically; it is a very general operation of joining or combining different things. The mathematical sense of “add”, as we now understand it, is given by the OED as “put together (two or more numbers or amounts) to calculate their total value”. Roughly, then, addition is an operation of joining different things to form a whole—as in joining 3 and 5 to get 8. What is the analogue in the case of language? Conjunction, of course—in the narrow logician’s sense and in the wider grammatical sense. In the logician’s sense the word “and” works to conjoin two sentences to deliver a certain truth table: one sentence is added to another to produce a larger sentence true if and only of both conjoined sentences are true. The truth-value of the whole may be said to incorporate the truth-values of the conjoined sentences, rather as 8 incorporates 5 and 3. In the grammarian’s sense conjunction is not limited to “and” and its synonyms: the OED gives “a word used to connect clauses or sentences or to coordinate words in the same clause (e.g. and, if)”. So disjunction is a type of conjunction: it is a way to add sentences to other sentences. In fact, the concatenation operation is itself just another type of addition: in a sentence or phrase words are joined together by an operation of addition (“concatenate”: “link together in a chain or series”, OED). This operation has infinite potential. It is clearly part of our linguistic competence, even though it may be unconscious and automatic. But the same is true of arithmetical addition: our mathematical competence is likewise predicated on a grasp of numerical addition, which may also be unconscious and automatic. So there is a factor in common here: a principle of addition that takes us from one set of elements to another—a joining together of parts into wholes. The hypothesis, then, is that mastery of this operation lies behind the origins of our human mastery of language and arithmetic. In short, there was a mutation for addition (the cognitive competence) and this is what allowed arithmetic and language to get off the ground. It was like the development of an aerodynamic wing (in both biological evolution and aircraft technology).

There cannot be much doubt that addition is fundamental to arithmetic. As the mathematics textbooks say, subtraction is just the inverse operation to addition (it “undoes” addition), and any subtraction formula can be rewritten as an addition formula. Multiplication and division calculations likewise involve addition. When someone grasps the concept of addition he or she grasps the concept of subtraction: what can be added can also be taken away. If you can add 3 to 5 to get 8, you can also subtract 3 from 8 to get 5: the two concepts are intertwined. Also, each number can be viewed as the continued addition of 1 to 1, or some other type of addition of integers. Isn’t arithmetic really the systematic study of addition? The natural number series is just one long addition; the successor function simply adds 1 to the preceding number taken as argument. There is no need to labor the point: addition is the lifeblood of arithmetic. In the case of language, we are not adding numbers, but we are adding another type of unit—what we call a word, a unit of meaning. This is not just a matter of uttering words in temporal sequence; it is a more abstract mental operation, often carried out entirely inside the mind. It is a compositional process analogous to numerical addition (which may involve adding amounts of stuff not merely numbers). The suggestion, then, is that this additive compositional process might be the foundation on which mature language and arithmetic are based. In order to evaluate this proposal I will now list the defining features of addition in the intended sense; it will emerge that addition has specific formal features that suit it to performing such a role. It is a more refined and structured operation that might at first appear: it is both rich and yet primordial—exactly what we need to solve the problem of origins for language and arithmetic.

First, addition is infinitely productive: you can keep on doing it ad infinitum. You can keep on adding numbers to numbers to get further numbers, and you can keep on adding words to words to get more words. The word “and” by itself has infinite productivity: you can conjoin sentences and predicates to infinity, but you can also conjoin singular terms, as in “gin and tonic” or “strawberries and cream”. The concatenation function likewise has infinite range, as does our grasp of it (logically it is just like the function expressed by “plus” in arithmetic). In both cases addition operates over discrete entities, thus generating discrete infinities (as opposed to continuous magnitudes). It is no small matter to acquire a capacity to handle such an infinitely productive operation. Connectedly, addition is generative: it generates one thing from another. It isn’t passive or static but active and dynamic. Thus we have generative grammar and generative arithmetic—rules that produce something from something else. Third, addition is combinatorial in the sense that it brings things together to produce something new: it isn’t just a brute process of sequencing but the production of a new entity considered as a whole. Adding 5 and 3 produces the number 8, which is not just a sequence (ordered pair) consisting of 5 and 3. Likewise a sentence is a new whole derived by combining parts; it is not just a list of words but a new type of linguistic unit. So the agent of such construction must be able to grasp the whole that results from the operation of combination as a whole. It isn’t just setting elements side by side but combining them. Fourth, and consequently, addition is ampliative (Kant’s word) in the sense that it generates something not already present in what is added together; it produces not just arbitrary strings but organic unities (to use the old-fashioned term). New phrases and sentences are unities in their own right, just as numbers are: addition has the power to confer such unity on its outputs. Fifth, this ability is reflected in the creativity of addition: that is, mathematical and linguistic competences consist in a capacity to create brand new wholes, new unities. Even a simple conjunction (“grass is green and the sky is blue”) exhibits this kind of creativity—rather like the production of a number no one has ever thought of before. Addition is not merely “mechanical”: it involves breaking new ground, going where no man has gone before. It might even intersect with creation in the usual sense of exceptional human production—as in writing poetry or discovering a new type of number. Without the ability to “put things together” mentally human creativity in the usual sense would not be possible. It is actually quite a feat to add 5 and 3, and likewise a feat to produce even a simple sentence like “the sky is blue” (adding one word to another till we get the desired result). Sixth, and important, addition is hierarchical: you can add what has previously been added. You can add 3 to 5 and then add the resulting number to another number. The addition operation can be applied cyclically and recursively: this would include adding to the result of a subtraction in order to get a further number. Bracketing becomes necessary for depicting such computations. In the same way language allows for hierarchical structure: we can, for example, conjoin conjunctions (as well as disjunctions etc.). In this respect addition is like Chomsky’s Merge operation, which also applies to its own outputs in a hierarchical manner. [2] Indeed Merge may be seen to incorporate Add, since it involves joining or combining elements to produce a new element: merging X and Y into Z is adding X and Y to get Z. In both operations we have the ability to apply the operation to its own outputs generated at a lower level. Seventh, addition has scope in the logical sense: there is always a question as to what the scope of the addition operation is supposed to be. It is like the scope of quantifiers: not every variable to the right of a quantifier is bound by it, just as not every number following a given one is automatically included within the addition operation. We have conventions, generally expressed by brackets, for indicating scope, and addition needs such conventions in order to avoid ambiguities. Addition is thus selective in its intended scope, not all-inclusive. Eighth, and worth emphasizing, addition is notably liberal in its domain of operation: you can add quite disparate things to each other; similarity is not required. Any number can be added to any number (not just even numbers to even numbers, say), just as any sentences can be conjoined regardless of subject matter. This enables us to transcend natural associations between things: things don’t have to be conjoined in nature to be conjoined in thought. That is how set formation works: a set may contain the Eiffel tower and your favorite aunt and that dog over there. There is a certain freedom to the addition operation: it is not too choosy about what it will combine. This gives it enormous creative power; it liberates thought from the tyranny of nature. A mind possessing it thereby possesses considerable freedom of expression. We should not underestimate the power to put things together ad libitum (as well as ad infinitum). Finally, addition has an inverse: what can be added can be taken away. Addition is a reversible operation. You can add 3 to 5 but you can also subtract it from 8; you can conjoin two sentences but you can also de-conjoin them (as in conjunction elimination in logic). This gives addition flexibility—it isn’t stuck with the wholes it has produced. You can form ever more complex sentences, but you can also simplify sentences by removing parts of them; indeed, this is just the other side of what addition is. Adding and subtracting are parts of the same package.

Putting all these properties together, we can see that addition is by no means a simple matter of setting things side by side like marbles in a drawer. It has subtlety and structure, a rich cognitive profile. Yet it is conceivable that it arose by a relatively localized mutation, producing a distinctive piece of neural rewiring. It might have arisen much like the cornea or the eyelash. But it also has the power to carry us a long way in the manufacture (the engineering) of arithmetic and language (i.e. syntax). A great deal of these two cognitive faculties can be fitted into the framework of addition—that mental operation has considerable power to produce what is characteristic of arithmetic and language. Perhaps not all—other factors no doubt joined with his basic factor—but as a fundamental cognitive principle it is capable of a lot of work. Certainly other animals are lacking in its productive power: they may have primitive communication systems and an elementary grasp of counting, but they don’t have the full structure generated by addition in its abstract form. They have not yet reached the stage of unlimited mental conjunction. What the human mind is particularly good at is forming new wholes by means of addition (composition, conjunction, putting together)—where this is to be understood by reference to the ensemble of features enumerated above. Once this operation evolved in the human brain it was available for use in various worthwhile endeavors such as calculating, thinking, and talking. It arose by chance but it was soon exploited and promoted by natural selection. Thus we became the adding species, the dedicated conjoiners, the arithmeticians and grammarians. Now we add up all the time, constantly using our capacity to put things together, always creating sums. This theory seems like the optimal combination of simplicity and fecundity necessary in any proposal for explaining the evolution and learning of arithmetic and language, with the bonus that both areas fall under the same theoretical framework. Both are offshoots of a primordial ability, arriving a couple of hundred thousand years ago, to perform acts of addition. Arithmetic is the application of addition to numbers, and language (syntax) is the application of addition to words. [3]

[1] This paper was stimulated by things Chomsky has said in various places. It presupposes a lot and is very compressed.

[2] See Why Only Us by Robert Berwick and Noam Chomsky (2016), especially 72-4. My suggestion might be viewed as complementary to this but with a different emphasis.

[3] We should note that the theory is not intended to explain the origin of words (lexical elements) or concepts of numbers. It doesn’t even explain the existence of standard grammatical categories. It is solely concerned to explain the most abstract features of language and arithmetic (as the Merge operation is supposed to). It tells us how certain structural properties of the two domains may have come into existence. It is basically a theory of the origins of the human combinatorial capacity. Much would need to be added to it to reach arithmetic and language as they now exist in the human species. Still, we do need a theory of the basic cognitive architecture of these two domains that is consistent with their having evolved in the usual way. We need a theory of the basic form of the innate program for acquiring these capacities.