Ignorance and Other Minds

Ignorance and Other Minds

What do we know better—material objects or other minds? In the ordinary course of things, there is a lot about material objects of which we are ignorant: their insides, their chemical composition, their unseen side, their atomic structure, the nature of matter itself. They are often too distant to see well, indistinct, occluded, seen through a haze, seen with poor eyesight. We are largely ignorant of them; we tend to know only their superficial properties and their existence (a black cat on a white mat). You would never say you had complete knowledge of them; we could say we have “incomplete knowledge”—partial, superficial. But in the case of knowledge of other minds none of that is true: we are not ignorant of their insides, their chemistry, their unseen side, their intrinsic nature. We think we know them as they are, more or less completely (I am putting aside the mind-body problem). We don’t think of them as having an unknown nature; we think we know all about them. In fact, we think we know their nature as well as we know our own mental states: we think of them as being the same kind of thing as what we know from our own case. We don’t think of them as having a different nature when possessed by other people—as if they grow an inside or a reverse face or an atomic structure. We don’t think they differ ontologically from our own mental states; they are the same but elsewhere. So, we have a kind of privileged knowledge of these objects—a comprehensive knowledge. If material objects are opaque objects, then mental objects are transparent objects—limpid not cloudy, given not hidden. If we are blind to much of what constitutes a material object, we are clear-sighted about the nature of a mental object: we know what a pain is quite thoroughly, while we have only incomplete knowledge of a cat.

This means that we have superior knowledge of other minds compared to our knowledge of material objects. We already know that there are no visual illusions concerning other minds[1], so that this source of skepticism does not apply to them; now we see that there is a deep asymmetry with respect to the extent of our knowledge of the two. I know the nature of someone else’s mind better than I know their body: I have superficial knowledge of their body and deep knowledge of their mind—as I do of my own mind. I have perspectival knowledge of physical things, but non-perspectival knowledge of mental things. The nature of other minds is more open to me than the nature of material objects, less confined. I may not know what it’s like to be a bat, but I do know what it’s like to be another human—e.g., what it’s like to see red. I know minds better than I know bodies—in the ordinary course of events. If I’m having an ordinary conversation with you, I know what kind of thing is passing through your mind, fully and transparently; it isn’t like trying to see a distant cat in the mist with invisible insides. I am not faced with acres of ignorance; I know the mental lie of the land. It’s easier to know the truth, the whole truth, and nothing but the truth about other minds than it is to have that kind of comprehensive knowledge of the physical world. And if I am uncertain, I can simply ask you for a self-report and you can tell me. I’m not dealing with some sort of alien subject matter that resists full disclosure. The mind is really an open book to me not a locked safe. Just think how long it took for human beings to find out the internal anatomy of the human body, let alone is chemical composition. We didn’t have to do any dissection at all to find out the anatomy of the mind—it was right there on the surface. The mind isn’t a sort of buried treasure, like the internal organs, but more like the play of light on water—a known not an unknown. It is good to remember these truisms when pondering the classic problem of other minds; we don’t usually worry that we know nothing about what other people think and feel. We take it for granted that our knowledge is in good shape; we are not languishing in the dark. I know what’s on your mind as well as I know anything (so long as you are not trying to deceive me). My mind is in tune with yours. It isn’t trying to step outside of itself into an epistemic abyss. There is no need to get all hysterical about other minds.  Does this solve the other minds problem? Not exactly, but it does take the sting out of it, the sense of panic. We are not epistemically bereft. [2]

[1] See my “Illusions of Mind”.

[2] There is a commonsense problem of other minds that arises from the possibility of deception, but the philosophical problem is greatly exaggerated: other minds don’t pose a uniquely serious skeptical problem. The absence of other mind illusions and the identity of mental items across knower and known make the problem less severe than in the external-world case. In that case, we have the prevalence of visual illusions and the ontological gap between the knowing mind and the thing known. In the other minds case, there is a tendency to focus on the body and its behavior and ask how we can construct the mind on this exiguous basis; but that is not the situation, since we have our own minds to provide the conceptual materials and we can be said to see the minds of others not just infer them. It really does seem to me that you have a mind; I see you as minded. Other minds are not like the deep sea or remote galaxies. They aren’t complete mysteries. Of course, the whole problem of other minds is tangled and difficult, but we are not wallowing in total ignorance. I actually know my cat’s mind better than I know its body.

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Productivity

Productivity

I am perplexed by my own productivity. I don’t understand it. It seems like a bottomless well. As a psychologist, I’d like to have a theory about it. It’s something of a burden, truth be told, though not an annoyance. It seems out of my control. I wish I could bottle and sell it (I would make a million). The best I can say is that it is a combination of life-long persistence and a certain lightness of being (whatever that means). I observe that it is accompanied by other sorts of productivity, if that is the word; it isn’t just philosophy and matters of the intellect. My impression (corroborated by others) is that my tennis game improves whenever I step on the court—not by a lot, but perceptibly. This comes from simple repetition but also from an openness to trying new techniques and close observation of other players (there is no magic potion or “inspiration”). It’s not an accident. I find the same thing with my singing and guitar-playing: a steady, predictable improvement—though always surprising. Even my drumming, which I’ve been doing for 62 years. Knife throwing too. It feels like my brain and body are willing to keep developing. No doubt this will grind to a sickening halt one day—maybe next week, who knows? But not yet; not yet. My memory is not as good as it was, and the same for my hearing (vision is okay except for reading). I’m planning an athletic romance in the near future, and intellectual romances are still on the cards. Perhaps that’s what it is: different kinds of romance.

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Illusions of Mind

Illusions of Mind

Is it possible to maintain that we know other minds better than we know other bodies—or even our own body?  Can we be more skeptical about our knowledge of bodies than our knowledge of other minds? That sounds unlikely, given that we infer other minds from other bodies: we see other bodies and then conjecture what lies behind them mentally. We know external bodies better than we know external minds, don’t we? Isn’t that an axiom of epistemology? But there is a difference between the two sorts of knowledge that undermines this confidence: knowledge of other minds is not subject to visual illusion. There are no optical illusions of other people’s mental states, as there are no optical illusions of one’s own mental states. Our eyes never deceive us in this way. There are many optical illusions regarding physical objects, often quite striking: the visual brain is prone to these sorts of errors; there are glitches in the system. I needn’t give examples; they are a commonplace of psychology textbooks (the Muller-Lyer illusion will suffice to fix ideas). In addition, we have visual hallucinations in which whole scenes appear to us that don’t exist. You can’t believe your own eyes; they lie to your face. The visual system is inherently given to these illusions. The skeptic, then, can exploit them to undermine our knowledge of the external world—we might be under a giant sensory delusion. Perhaps my experience is not veridical but illusory; we can’t be certain this is not so, given the prevalence of illusion. It can even be argued that our impressions of color are visual illusions, since color does not really belong to objects. The visual system is set up for error, intrinsically fallible, a potent source of false belief. Knowledge based on it is shaky at best and non-existent at worst. It is an unreliable informant.

But the psychology textbooks record no examples of visual illusions of other minds. We don’t have visual impressions of other minds that mimic standard visual illusions: we don’t look at a bodily stimulus and seem to see a mental state that isn’t there. We may think a mental state is there that isn’t, but we don’t see such a state—we don’t have a visual experience as of a non-existent mental state. Our eyes don’t deceive us in this way. There is no Muller-Lyer illusion of the mind, or duck-rabbit drawing, or any other of the many illusions our eyes are prone to. Our perception doesn’t work this way. In fact, our perception of other minds is in this respect like our perception of our own mind: neither do we have illusions of non-existent mental states in ourselves. You never perceive a belief as a desire, say, or a belief that p as a belief that q, or an emotion as a thought. You are not capable of this kind of error: introspection is not prone to error through an analogue of optical illusion. There are no such glitches in the system; so, such error does not undermine claims to introspective knowledge. Skepticism cannot gain a foothold from this source. But nor can it gain a foothold from such a source in the case of knowledge of other minds. There is thus no argument from illusion in the case of knowledge of other minds: we never have a visual impression as of a non-existent mental state in someone else that is qualitatively just like a veridical visual impression of a real mental state—because we have no such visual impression to start with. We don’t seem to see a mental state as we can seem to see a physical state. You might see a body in an illusory way if (say) it had a Muller-Lyer figure etched on it, but you don’t (can’t) see a mind in such an illusory fashion; you can’t say “It really looked to me exactly as if he believes the sky is green, but I know he doesn’t actually believe that”. You don’t and can’t hallucinate another mind—as it might be a zombie that strikes you visually as replete with consciousness. You might believe a zombie has a mind, but you don’t see it that way: for what would a visual impression of a mind be like? There are no optical illusions of the mind, as there are no optical illusions of number (seeing 2 as 3, say). Your knowledge of other minds cannot therefore be undermined by their possibility or frequency; skepticism cannot be advanced on this basis. So, in this respect, knowledge of other minds is better off than knowledge of other bodies. I know your mind better than I know your body (or my own), as a matter of principle.

Does this mean there is no sense in which you can see another mind? That doesn’t follow, given the elasticity of the concept of seeing. And it sounds perfectly reasonable to describe our knowledge of other minds in this way: I can see that you are upset or happy or confused. Seeing is not restricted to a certain subsystem of our visual sense—the subsystem that produces visual illusions. So, there is a type of seeing that is not prone to visual illusions. Knowledge of another mind can be seeing it (or involve this), only not the kind of basic seeing that is subject to optical illusion. The case is not like theoretical inference in which no one would say seeing is involved (atoms and the like). This, too, provides a bulwark against skepticism about other minds; now we have knowledge backed by seeing that is not vulnerable to perceptual illusion. Things are looking up for our knowledge of other minds; it seems better off than many kinds of human knowledge traditionally thought superior to it. Might it be one of our best types of knowledge? That is certainly a pleasant thought (“You really know me!”) and it is not far from phenomenological reality: for it really does seem that I am (sometimes) perfectly well aware of what is going on in your mind—I can know, for example, that you are enjoying yourself while playing tennis or boiling an egg. I can see that it is so, and I know that no visual illusion can be getting in the way. What more could you ask for as a situation conducive to knowledge?[1] It isn’t like being surrounded by constant optical illusions or actual blindness: I am in the (or a) seeing relation to your mind, and I don’t have to worry about any malfunctioning in my visual system producing illusions. I am home free, epistemically. I can be quite smug about my knowledge of your inner life, not racked with epistemic anxiety. For I am using an illusion-proof visual faculty–unimprovable. Not so for physical objects; here I must contend with the vagaries of error-prone vision, the perpetual possibility of illusion and hallucination. I erroneously see objects as colored. LSD does a number on my sense of sight. I can’t even see when two short lines are the same length. No wonder the skeptic can attack my knowledge of physical reality, but he doesn’t have this resource in the case of my knowledge of other minds. I can therefore relax about this knowledge, secure in the knowledge that I will not be caught out by a processing error in my visual system. Nice![2]

[1] I am not ruling out other sources of skepticism such as lack of logical entailment—they are another story. But I do think the argument from illusions is one of the most potent and influential sources of skeptical doubt about our knowledge of the external world.

[2] Perceptual constancies provide a good illustration of the asymmetry I am drawing attention to. The brain must do a lot of work to cancel the effects of different sized retinal images in the perception of objects at varying distances, using various cues without which visual illusion would set in. But no such problem afflicts the perception of other minds: we don’t nurse a tendency to see minds as different sizes depending on their distance from our eyes, as we do in the case of heads. Nothing in the visual system is tugging us in the direction of falsely assigning different sizes to minds according to their distance. One might think that the human visual system is always on the brink of delivering false perceptions when it comes to physical objects, but not so for other minds.

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Romances

Romances

A romance is a love affair between two people. But this doesn’t specify what kind of love affair: it could be sexual love, but it need not be. It could be an intellectual romance; then it connotes shared passions and interests of an intellectual nature. The idea is of a cooperative, committed, passionate relationship between two people. I want to extend this idea to include what I will call athletic romance: two people sharing their common interest in athletic activity. This too should be cooperative, committed, and passionate—like a sexual romance. It is also bodily and may involve touching. It should be intense and consuming. It should form a higher unity consisting of the two persons—a kind of team or companionship. It may involve problems of infidelity, insecurity, jealousy, illness, separation, time, and rivalry. It is intimate and emotional, involving a type of love. It may not last forever. Learning will be a big part of it, as will respect. I see it as having a therapeutic component, as producing feelings of well-being and transcendence of the ordinary. It has a religious dimension. Overcoming obstacles is part of it. An athletic romance must be romantic.

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Mathematical Philosophy

Mathematical Philosophy

In 1919 Bertrand Russell published a book titled Introduction to Mathematical Philosophy, written while he was in jail; but the title is somewhat misleading, because the book isn’t about doing philosophy mathematically but about the philosophy of mathematics. Still, Russell did do a fair amount of mathematical philosophy: the theory of descriptions, existence as a propositional function, mathematical constructions of the external world, etc. So did Frege, Wittgenstein, Carnap, Quine, Tarski, Montague, Kripke, Davidson, and others. It was a movement, a meta-philosophy. We might call it formal philosophy or symbolic logic philosophy or technical philosophy or scientific philosophy—as opposed to informal philosophy or phenomenological philosophy or commonsense philosophy or ordinary language philosophy or humanistic philosophy. Its model is mathematical science not vernacular literature—arithmetic not art. It aligns itself with the mathematical member of the two cultures. I think we can add that analytic philosophy is by nature mathematical in that it employs conceptual analysis, which is a breakdown of the whole into its parts, isolated and enumerated. Concepts are composites of added parts. Such analysis results in equations—e.g., knowledge = true justified belief; it seeks conceptual equations. It also employs rigorous deduction like mathematics, hence the emphasis on logic: syllogisms, axioms and theorems, formalized arguments with premises and conclusions, logical variables. Thus, we have today formal epistemology, formal politics, formal ethics, formal semantics. The subject is steeped in formal methods and conceits. Twentieth century philosophy was awash in mathematics, for good or ill. The dispute between analytical philosophy and so-called continental philosophy might well be seen as a disagreement about the role of mathematical methods in philosophy—what do you prefer, aesthetics or arithmetic?

But I think this story has history skewed: philosophy has been mathematical for much longer—indeed, it has never really been non-mathematical. I think philosophy is, and always at heart has been, a mathematical science, more or less successfully. That is what it aspires to be, though we must be liberal about the meaning of “mathematical” and “science”. It is about abstract and abstruse questions, aiming for precision and exactitude, obsessed with number, methodologically a priori, in love with logic, proudly technical and symbolic. It is a kind of geometry or geography of concepts or facts or realities. One of its most fundamental questions is numerical: is the world One or Many—and if many, how many? Hence, monism, dualism, and pluralism. Is the world finite or infinite, continuous or discrete, qualitative or quantitative? What kind of mathematics best captures its nature? Philosophy is all about distinctions, divisions, differences, relations. Identity is always a central concept. For example, Plato’s problem of the one universal and the many particulars: this is a quintessentially philosophical problem, and it is overtly numerical. We have the abstract form and the concrete particulars instantiating it: the form is a unity, but the particulars are a plurality. These are essentially different kinds of entity, yet they are intimately connected: many things are white, say. How can the One be Many, and how can Many be One? What is the relationship between them? It seems puzzling. More generally, is the whole world a unity or is it a plurality? How many types of entity are there? Is a person two things in one (mind plus body)? Are there values and facts or just facts? Is appearance the same as reality? How many kinds of good are there?  Are pleasures all of one kind? How many types of truth are there? Is necessity unitary? Are all words names? Polytheism or monism?  And so on. We want to know how many; we want to count our ontological commitments. We want to mathematically analyze the world. There are odd numbers and even numbers—are there universals and particulars, minds and bodies, values and facts? We look for unity but accept multiplicity. In arithmetic it all comes down to addition (subtraction is just the opposite of addition)—is that the way it is with the world generally? Metaphysics is a kind of mathematics of reality in its broadest outlines. We are applying mathematical conceptions, albeit elementary ones (but are any mathematical conceptions truly elementary?). This is not all we are doing, to be sure, but it is a large part of it; we are employing a diverse range of knowledge in conjunction with our mathematical knowledge.

So, the mathematical paradigm did not suddenly emerge in the twentieth century; it was alive and well for two thousand years or more. But it is so natural to us that we don’t notice it; we mathematize instinctively. Philosophy could hardly exist without it—or any science. It’s how we think scientifically, rigorously, systematically. The only question is how much we insist on it or extend it. I am not myself enamored of a sharp distinction between science and literature (I think literature is a type of science, mainly psychological). I think the human mind is essentially mathematical, here as elsewhere. It’s just a matter of admitting it, making it explicit as part of one’s meta-philosophy. We don’t have to mathematize philosophy because it is already mathematical. Even Sartre’s existentialism is mathematical, because it insists on the duality of the in-itself and the for-itself: Sartre is an ontological dualist—two things not one. The philosophy of language as it now exists is clearly a branch of mathematics—what with model theory and computational linguistics. Mathematical thinking is so entrenched in philosophy that we risk accusations of triviality just by drawing attention to it. It is an interesting question in the pre-history of ideas whether philosophy evolved in the human mind as an offshoot of an antecedent mathematical faculty. We are natural accountants, calculators, and bean counters; we brought these talents to bear on the most general questions of the cosmos. Mathematicians often have philosophical predilections. Mathematics and philosophy belong to the same intellectual natural kind.[1]

[1] Pretty much all science is mathematical to one degree or another; it would be strange if philosophical science were the exception. Inside each philosopher is a little mathematician struggling to strut his stuff.

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God and Matter

God and Matter

Berkeley was convinced that matter and God are incompatible. If matter exists, God doesn’t; and if God exists, matter doesn’t.[1] I want to spell this out a bit, because Berkeley is onto something important here. His basic point is that if you postulate matter, you open the way for skepticism, mystery, and atheism; but this is theologically unsound, so matter must be rejected. Suppose God wants to create a world in which a certain moral drama is played out, leading to reward for the virtuous and punishment for the vicious (heaven and hell). One way to do that is to create immaterial spirits and present them with moral choices; to do this you need to create an experiential world in which things happen (or seem to). Moral choice certainly doesn’t depend on the existence of a material world; it just requires agents capable of moral decisions. The agents can be disembodied beings to whom things appear a certain way. To create such a world God can use his own mind to conjure up ideas of objects and then plant these ideas in the minds of his immaterial agents. Reality is thus constituted by God’s mind, which finite spirits perceive (God arranges things this way). In other words, God creates an idealist ontology. Then he sets to work to confront these finite spirits with objects as so constituted. He wants his creatures to know these objects exist and that he exists, and they can know these things given their mental nature. The objects are right there in the mind, and it is evident that God is behind their existence because he put them there; now he just waits to see how virtuously they handle the world thus constituted. God could easily have made the world this way, given his omnipotence; and there would be no reason to doubt his purposes and existence. He made an intelligible world in which we finite beings play our ordained part—no worries about the metaphysics or epistemology of the situation. And yet, according to materialist metaphysics, he did none of these sensible things; instead, he created a world of mysterious unintelligible matter that naturally leads to a general skepticism that takes in God himself. He creates a world in which the moral purpose is obscured by the wacky metaphysics and problematic epistemology. Absurd! Away with matter!

For consider: this supposed matter stuff is completely alien in its nature to the nature of God its creator; you cannot infer God from this stuff. It could in principle exist without God because there is nothing Godly in it. Moreover, we don’t know what it really is, unlike our own ideas and ideas in general: people say matter is extension, but extension of what? It is a complete mystery, an epistemological black hole. How can it even have causal powers, as spirits, finite and infinite, have causal powers? It is just an inert soulless enigma. Why would God create a world unknowable to the creatures that populate it? Wouldn’t that lead them to a generally skeptical cast of mind that includes God’s own existence—and this would undermine their commitment to the moral project that is the point of the whole exercise. How indeed could God create such a thing from his own nature, since he is immaterial himself—and why? It makes no sense given his overall intentions. What would be the point of creating matter that coexists with God in the absence of human souls, as the materialists suppose? First matter, then minds: but matter itself has no moral status without minds. And how could matter create minds? The whole idea makes God redundant: once you have got matter, nature can be left alone (allegedly) to produce life, mind, and morality. Matter usurps the role of God in the management of his creation. But God wants to keep his hand on the wheel, his foot on the gas; and this is no trouble given his omnipotence. Why would God create a rival to his own dominion—a kind of second material God (not that the idea makes any sense when you think about it). If God wants to alter the course of history, he must intervene in the actions of matter, producing what mortals call miracles. Better to create a world in which everything already obeys his will—no need to puzzle the mortals by having two conflicting sources of causation in the world. There are no miracles in God’s preferred world, only his continual beneficent presence. And there is an even more sinister implication of the matter theory: people will derive their concept of existence from the supposed material substance, and this will make God’s existence seem unintelligible to them. For God does not exist in that way—by being extended in space, or solid in substance, or perceptible by the senses. This will certainly give rise to atheism. Why put such an obstacle in the way of sound religious belief? To exist is to be a spiritual substance not this inert unintelligible something that only promotes skepticism and atheism. Religion (the Christian kind) cannot therefore coexist with materialist metaphysics; the two are in deep tension with each other. So, God doesn’t create a world made according to this plan; he creates an idealist world. If the external world of ordinary objects were material, we would be rightly skeptical of its existence; but that would be to be skeptical about God’s own creation and would inevitably lead to skepticism about God himself (his own creation, meant for us, becomes inaccessible and senseless). Instead, we should accept the idealist theory, in which objects are ideas in our mind and God’s mind—perfectly accessible intelligible items. It’s common sense: go for what you know not what you don’t know—mind, not matter. Materialism about the external world is clearly an anti-religious doctrine; it is inherently skepticism-producing and atheism-encouraging. If you try to combine materialism with religion, you get an insidious form of cognitive dissonance, which can only undermine religious belief. This, at any rate, is Berkeley’s credo.

I think he is right: the two are incompatible. God has no time for matter. But if so, the real existence of matter as a non-mental substance would undermine God. It’s one or the other; there’s no halfway house. A materialist account of creation, such as that produced by the mechanists of the seventeenth century, is incompatible with traditional Christian theology: rocks must be in the mind if Christianity is to be believed (and likeminded religions). We can prove metaphysical idealism from the claims of religion: if God exists, then this desk must be an idea in his mind, not a lump of matter. If matter were the root of all evil, then it would be clearly incompatible with a good God creating it—surely a beneficent God would not create such a world (though the devil would)! But even if it isn’t, it still violates sound theology. So, contraposing, if we remain wedded to matter, we cannot also believe in God. If you are looking for a disproof of God’s existence, you need look no further than the existence of matter. The bishop of Coyne was right about that. If God had accidentally created matter, he would be highly displeased with his creation and scrap it and start again.[2]

  [1] See my “Matter and God”.

[2] It was the devout Descartes who laid the groundwork for atheism, contrary to his intentions. He wasn’t mistaken (Berkeley would say) in postulating an immaterial mind; his mistake was to postulate a material body. For that is not consistent with a belief in God as the creator of the universe. Nor does it help to follow Hobbes and postulate a material God, since this still leaves us with a theology inconsistent with materialism about anything. There is a further question here about whether an ontology of immaterial substances is also incompatible with traditional theology, given how little we know about them (how do we even know they exist?); I have not discussed this question here, but the question is real. We might be forced into an even more extreme idealism of free-floating ideas.

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The Selfless Gene

The Selfless Gene

The logic of selfish gene theory is impeccable, but its usual formulation leaves something to be desired in point of strict and literal accuracy. I propose to remedy that. No harm will be done to the theory thereby; we will merely clarify its exact import. First, some terminology: by “gene” I will mean a particular piece of matter that exists on an individual strand of DNA—a specific localized chemical lump. I will not mean the type of gene of which this is a particular instance: this is a general form that can be instantiated in many individual instances; it might be viewed as the information contained in the chemical instance or the general type of which there are many instances (my genes, your genes, etc.—construed as local particular lumps of matter in individual bodies). We might call these gene tokens as opposed to gene types. This distinction is vital to the point I want to make, because we might mean the token gene is selfish or the type gene is selfish. Is the gene token (that particular lump) selfish?

To answer this let’s consider an ordinary case of selfishness: a person who cares only for himself and no one else—he always comes first. Such a person might coexist with copies of himself—replicas, twins. Perhaps they have been created by cloning him; they are exactly like him, but they are not him (that individual). Let’s suppose he doesn’t give a damn about these copies; he cares only for himself. He would happily let them die if it suited his own selfish purposes. Now contrast this selfish person with another person who also has many copies, but he does care about them; he goes out of his way to help them out, share with them, even sacrifice himself for them. This person is selfless not selfish; he is an altruist not an egoist. But suppose he is indifferent to anyone who is not a copy of himself; he is selectively selfless. It would be wrong to call him selfish, but his selflessness is sharply limited to his doubles, duplicates, twins. His altruism is confined to a certain select group of individuals: these he promotes and supports, feeds and protects—though anyone else gets the cold shoulder. It is this individual who best represents the concept of the selfish gene not the outright selfish person. The gene token seeks the welfare and survival of its copies not itself alone; it will go when the body it is in disintegrates, and it knows it. But its replicas will live on—and that is its mission in life. It may even sacrifice itself for the sake of its copies—as when a mother gives food to its babies even at a considerable cost to herself. It produces as many copies as possible, so that its type survives, possibly immortally; but it itself will perish with the bodily vehicle in which it exists. The copies will exist even when the individual gene that made them has gone. This gene is not selfish in any reasonable sense—though we might say the gene type is selfish because it sees to it that this type will survive into the future.

We really have two questions: are gene tokens selfish and are gene types selfish. No to the former, and yes to the latter. It depends on what we are referring to. I rather think people generally mean the former, in which case they misspeak, because the tokens are selfless not selfish. The token is selfless in the way the individual animal is selfless: the mother is concerned to protect her offspring copies even when this goes against her own individual interests (she might die as they suckle at her teats). It would be strange to say she was selfish because her type is trying to protect that type; she is protecting her copies not herself, as opposed to being a type that is protecting itself. So, the so-called selfish gene is not really selfish but selfless—altruistic, other-interested. Our genes (individual tokens) are actually generous and other-directed, but only within the class of recipients limited to type-identity with them. They are like a person only altruistic within his tribe or family, only more strictly. The Selfish Gene could have been called The Selfless Gene and said essentially all the same things, reserving for a footnote the observation that gene types can be said to be selfish in an extended sense of “selfish” (we don’t say person types are selfish but only person tokens). Still less is the information inside a person itself selfish. It is really a lot simpler simply to say that genes (those bits of matter) are selfless, adding that their sole focus of altruistic interest is their own copies. They don’t survive bodily destruction, though their replicas do. They are not physically passed on, though physical entities just like them survive in future bodies. It is certainly not true that my token set of genes is literally made up of the same material entities that existed in my ancestors; what survives are just the old types, or the information they contain. As I say, this doesn’t detract from the correctness of selfish gene theory, though it does recommend changing the rhetoric slightly. And I think the book would have attracted a lot less misunderstanding if it had been called The Unselfish but Selective Gene.[1]

[1] For philosophers steeped in the type-token distinction in application to the mind-body problem this paper will be pretty straightforward, but that distinction is not always apparent to people less prone to logic-chopping. I have tried to make it as clear as possible, based on past experience. The logical point is simply that “x is a replica of y” doesn’t entail “x is (numerically) identical to y”—in fact the opposite is true.

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Mathematical Knowledge

Mathematical Knowledge

We can all agree that human beings have mathematical knowledge. We understand mathematical concepts. But how extensive is mathematical knowledge—what subjects are mathematical? The OED defines mathematics as “the branch of science concerned with number, quantity, and space, either as abstract concepts or as applied to physics, engineering, and other subjects”. But the question is which other subjects—psychology, sociology, geology, geography, history, ethics? It is tempting to divide all learning (academic and non-academic) into two groups, mathematical and non-mathematical; but is this right? One subject you study in math class, the other subjects in other classes (music, literature, Spanish). I am going to argue that this distinction is artificial, misguided, and simple-minded; mathematics is everywhere. All (or nearly all) knowledge is mathematical to one degree or another. In fact, mathematical knowledge is cognitively fundamental. Elsewhere[1] I have argued that logic and ethics are (partly) mathematical; now I will extend that thesis more broadly. It turns out that this is not that difficult to do once we have shed certain prejudices and curricular conventions. I will quickly survey the whole field of knowledge to establish this claim; then I will turn to theoretical conclusions.

Psychology has a mathematical side; mathematics is applied in it. Psychophysics, statistical methods, computational models, laws of memory (recency and frequency laws), theories of learning, IQ tests, and so on. You can’t be a psychologist and be mathematically illiterate. Sociology is much the same. Geology is concerned with questions of depth, hardness, age, weight, and molecular composition. Geography deals with land masses, distance, size, height, and so on. Biology involves morphology, genetic structure, population dynamics, cellular forms, and energy consumption. History records dates and times, movements of populations, rates of social change, distribution of political power. Economics states laws of supply and demand, discusses money, tracks financial markets. Poetry is concerned with meter. Literature may include word counts. Music is mathematical. Space and time are mathematically described and they condition everything. Both in class and in the street the knowing mind is working mathematically. The case of language is of special interest, because it has taken recent linguistics to recognize the mathematical character of linguistic competence: a natural language is a combinatorial capacity to operate on discrete symbols to produce infinitely many sentences; Chomsky’s Merge operation is set-theoretic and recursive. Grammar is basically mathematical (“computational”). There isn’t much that doesn’t have a mathematical side, whether salient or submerged. It isn’t just math proper along with physics and engineering; mathematics seeps into everything (astronomy, botany, cookery, art). Mathematical knowledge is ubiquitous.

This has a bearing on certain philosophical questions. First, mathematical and non-mathematical knowledge are not discrete states of mind but interwoven. The a posteriori is infected by the a priori—what we call applied math. Second, the problem of mathematical knowledge is not limited to pure math, or school math; it applies to all knowledge, give or take a bit. The farmer has this problem as much as the professional mathematician. Third, Quine’s indispensability thesis applies not just to physics but to every branch of science and beyond. Fourth, philosophy of mind (including cognitive science) must take account of the prevalence of mathematics in the human (and animal) mind. The mind is not just computational but also numerical. The brain too—neuroscientists must reckon with the mathematical brain. The mind-brain not only processes information; it calculates, does sums. This doesn’t fit classic empiricism in which perceiving is the fundamental operation of mind, unsullied by such rational faculties as mathematics. If mathematics in innately known, then all knowledge has elements of the innate in it. Epistemology also must acknowledge that the foundations of so-called empirical knowledge cannot be innocent of non-sensory contents. Math is foundational too. Empirical knowledge is a mixture of the purely sensory and the abstractly mathematical. Such knowledge is a fusion of the qualitative and the quantitative. Even colors need numbers (they have extent and intensity).

We are edging towards the doctrine that all knowledge is mathematical, necessarily so. This is a strong doctrine, but it has its appeal. Consider intentionality: all mental states are directed at some object or other—some discrete, distinguishable, countable object. Typically, we have multiple intentional objects before our minds simultaneously, each comparable with the others—larger, smaller, heavier, lighter, louder, quieter, closer, further away. These are all quantifiable relations. The visual field alone is replete with mathematical content (mainly geometry). Some of this mathematical complexity is imposed by the mind, which is mathematically pre-established. Thus, where there is intentionality there is mathematical content (quantity, number); and all knowledge presupposes intentionality. The idea of a spatiotemporal world consisting of discrete particulars builds in mathematical structure, and it is omnipresent. Plus, the very notion of plurality is implicitly mathematical: it is the idea of a set. Not for nothing did Frege liken predication to the function-argument structure in mathematics; it involves the idea of one thing being a member of a set of things. Set-theoretic thinking is basic to human cognition (perhaps all cognition). We are beginning to seem like natural-born mathematicians, at home with abstractions. Born to be mathematical (and wild). Baby, I was born this way (and in other ways too).

This prompts two further thoughts: is it the same with other animals, and does it also apply to perception. I think yes in both cases, though human knowledge no doubt has additional properties. Animals size each other up, travel great distances, compute the time from the position of the sun, estimate the reproductive fitness of potential mates, and so on. In these activities they demonstrate basic mathematical skills, make quantitative comparisons, count objects (up to a point).  They are not mathematical ignoramuses. I suspect bees are pretty math-savvy. Survival depends on getting your numbers right. Even worms need to estimate how deeply to bury themselves (see Darwin on worms). Number is part of Life on Earth, part of our biological heritage, embedded in our genes (the mathematical gene). The lioness must count the number of her cubs and estimate how much food they need. In the case of perception, it is eminently plausible to suppose that the eyes perform calculations to gauge distance and produce impressions of depth. People write books called things like “The Intelligent Eye”; someone could write one called “The Mathematical Eye”. The senses are calculating prodigies in the production of perceptual constancies, computing size (say) from perceived distance. So, mathematics is biologically primitive and no doubt ancient; number sense may first have evolved with the most primitive of organisms—but then went on to perform spectacular feats of mathematical cognition, culminating in Isaac Newton and the great mathematicians of history. Mathematics (the faculty) evolves. It has a natural history.

Philosophers are fond of the question of what is ontologically basic and universal. Some say sense-data, others material objects in space and time. You don’t have to be Plato or Pythagoras to see the universality of number: everything real is countable and hence subject to arithmetic. Kant located material objects in space and time, and these are quantifiable things; mathematics is part of the spatiotemporal manifold. And sense impressions can also be counted and measured (e.g., for vividness). Yet people seem reluctant to make numbers ontologically basic (the opposite in fact), probably because they are not “concrete”. In our conceptual scheme mathematics occupies a unique place as a kind of universal language or framework or background. It needs more respect; more room at the epistemological table. In any “descriptive metaphysics” it should be accorded a central place, because it is all-pervasive, an aspect of the lens through which we perceive reality. Sense, reference, and number: for reference depends on singling out one thing from other things, and that involves the deployment of concepts of identity, difference, and plurality—the very basis of number science. We refer to what we can count. If you imagine a mind transitioning from a blurred world to a differentiated world, thus achieving individuated reference, then you will see that mathematical concepts come into play when reference comes on the scene. We might speak of the “mathematical theory” of reference—the embedding of reference in a matrix of mathematical ideas. A space of points, a plurality of particulars. Referential competence presupposes mathematical competence (as linguistic competence in general does). Not school arithmetic, to be sure, but its cognitive underpinnings (quantifiers, sortal concepts, etc.).

It strikes me as not surprising that mathematics was the first science to develop: it is the most salient characteristic of the scientific mind, and the most rigorous. A species bad at arithmetic will not last long. It’s a pity, then, that in its modern academic incarnation it is so forbidding and inaccessible as a field of study (it should be easy!). We are born to be mathematical, as we are born to be linguistic, but the knowledge is not easily articulated or systematized. It is more of a practical skill than conscious theoretical knowledge. Yet everything mathematical seems to be in us from the start (as Plato taught). Of course, this knowledge is philosophically puzzling, even mysterious, but there it is, bubbling beneath the surface. Moreover, it is good knowledge to have (as Plato also taught); it isn’t epistemic junk (a type of gossip). You can be proud of your mathematical knowledge. Fortunately, the human mind has evolved to be in tune with mathematics. Evolution has produced something both useful and admirable. If God existed, he would be a mathematician. In the beginning was the number.[2]

[1] See my “Mathematical Ethics” and “Mathematical Logic”.

[2] Not the deed, not the sense-datum, not the material object, not the process, not the thought—but the number. For all the above are numerable. We have the finite and the infinite, the natural, the negative, the prime, the real, the imaginary, the number zero. You can’t get away from them. You can’t eliminate them from your conceptual scheme. Counting is part of human nature.

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