Tranquility Ethics

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Tranquility Ethics

What constitutes the good life? According to ethical hedonism, the good life is the life of pleasure. But what is it about pleasure that makes it conducive to the good life? Is it pleasure’s inherent phenomenology or is it something to which pleasure gives rise? Is it the way pleasure feels or is it the kind of effect that pleasure produces? What might that effect be? Consider the following case: you are setting out to write something important to you so that you require undisturbed time alone; however, a good friend of yours of hedonistic persuasion decides to give you a lot of pleasure by arranging all manner of delightful diversions. You do not welcome these intrusions despite their undeniable pleasurableness. Or consider the pleasure machine that ensures non-stop enjoyment but gives you no time to do anything else: again, this will detract from other values you hold dear. Too much pleasure seems to upset the balance. Nevertheless, pleasure does achieve one kind of outcome for which you have reason to be grateful: it spares you the discontent that comes from having unsatisfied desires. You don’t have to worry about desires you can’t satisfy, needs that go unmet. So you want the amount of pleasure that accompanies satisfaction, contentment, but you don’t want so much pleasure that you feel deluged with the stuff. The good life, then, is not so much the maximum amount of pleasure as the right amount of pleasure. But what is the right amount?

            I suggest it is the amount that ensures tranquility.[1] The qualitative feel of pleasure may be part of what gives it value, but that is not the whole story—there is also its connection with what might be called peace of mind. For example, the pleasure of eating is associated with the knowledge that one is not going to go hungry in the near future, and it is incompatible with hunger pangs felt in the moment. Present and future hunger pangs are not consistent with a tranquil, contented, peaceful state of mind. If (per impossibile) pleasure invariably led to a troubled and distracted state of mind, then it would not have the value it now has; indeed, one might wonder if it has any value. So some of the value of pleasure derives from its instrumental value as a way of achieving tranquility—though it can lead to the opposite of tranquility in certain (unusual) circumstances. Perhaps this link to tranquility explains at least part of the attraction of ethical (and prudential) hedonism. The pleasurable life is the tranquil life—calm, peaceful, composed, restful, and agreeable. It is the opposite of chaotic, anxious, vexatious, and annoying. And tranquility is a value to which we can readily assent: we all want to live a tranquil life; we all subscribe to what might be called “tranquility ethics”. One of the things we ought to do (morally and prudentially) is bring about a state of tranquility. Tranquility is a good thing.

            Now consider virtue ethics: the good life is the virtuous life. This looks like a very different conception of the good life from that of the hedonist: instead of pursuing pleasure we should act as we morally ought to act. Then and only then will we be living a good life. Obedience to God is one version of this general position. A reason often given for following this precept is that we will not have to suffer the pangs of conscience: we will be contented with ourselves and not tormented by perception of our moral failures (and prudential blindness). The virtuous life is a life untroubled by a guilty conscience. But notice the affinity between this rationale and that presented by the reflective hedonist: the virtuous life is similarly the tranquil life. We will not be distracted by the pricks of conscience; we will be free to pursue whatever occupations appeal to us. We will not lie awake at night berating ourselves for our bad deeds—as the hungry person lies awake wondering where his next meal is coming from. So tranquility is part of the appeal of virtue ethics too. It turns out, then, that hedonism and moralism (as we might call it) share a common feature, namely that both rest upon an underlying commitment to the value of tranquility. We can imagine a moral theorist beginning with tranquility and moving on from there to advocate (limited) hedonism and (moderate) moralism. Thus: tranquility is clearly central to the good life (morally and prudentially); hedonism and moralism serve the cause of tranquility; therefore we should adopt hedonism and moralism. But we only accept them in a form that respects tranquility: not excessive injunctions to maximize pleasure, and not extreme forms of moral self-abnegation, but sensible precepts that don’t upset the delicate balance that ensures peace of mind. Then we will be living the best possible life for a human being. Given the nature of human existence, we know that tranquility is difficult to achieve, but it should be our focus, our ideal; it should form the core of the good life.[2] A life with much pleasure in it will be a tranquil life (as long as the pleasure is not too distracting), and a life of virtue will also be a tranquil life (if not pushed to absurd extremes): so we should find room for both things. Thus tranquility ethics unites hedonistic ethics and virtue ethics, as well as highlighting a central value often neglected. The happy person is seen not as someone overflowing with pleasure, or as sternly following the moral law, but as someone internally at peace, untroubled, cool, calm and collected.

No doubt many characters from literature could be cited as fitting this description, but James Bond provides a simple and familiar example of the type (if somewhat cartoonish): always in pursuit of pleasure but heedful of the demands of duty, never flustered, inwardly calm (even when delivering necessary violence), utterly imperturbable. He faces situations of utmost stress but he never loses his quietness of mind, his composure, his sangfroid. Even his name suggests firmness of purpose, an internal unity. No wonder people envy James Bond his life-style, his easy way with the world. Despite his superficial difference from another famous spy, George Smiley, both men have a kind of inner constancy, a preternatural calmness under pressure. You feel they would remain tranquil in the most perilous of situations (likewise Mr. Spock for different reasons). By contrast, Shakespeare’s characters (Hamlet, Othello, Lear, Macbeth) are hardly ever tranquil, always worked up about something. As to ordinary humans, their life is full of anxiety, disquiet, inner conflict, turmoil, uncertainty, fear, and want—the very opposite of tranquility. This is why it makes sense to urge its importance, and its difficulty. This is also why we envy trees their tranquil lives. It is strange that the Western tradition in philosophy places so little weight on tranquility.

Colin McGinn

[1] Eastern traditions emphasize tranquility as essential to the good life, but I won’t talk about this here except to say that detachment from emotions and from other people does not seem to me a good way to achieve the right kind of tranquility. Tranquility comes in degrees, and perfect tranquility strikes me as unachievable given human nature.

[2] The concept of tranquility is not the same as the Aristotelian concept of flourishing: the latter concept connotes realizing one’s potential in forms of excellence, while the former concept is more negative in that it suggests an absenceof turmoil as part of the good life. Tranquility is not feeling certain things like anxiety or self-hatred or anger. Rocks are tranquil.

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Perceiving

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Perceiving

Two positions have dominated the philosophy of perception: naïve realism and the sense-datum theory. Either we see material objects “directly” or we see only sense-data. I will describe a hybrid theory according to which the objects of perception are indeed material particulars located at some distance away in space but the properties we see these objects as having are not the objective physical properties actually possessed by such particulars. Instead the properties in question are projected by the mind and have no objective counterparts in the physical world. Thus we should be, to use the standard terminology, naïve realists about the objects perceived but sense-datum theorists about the properties these objects are perceived as possessing. We see physical particulars existing in the distal environment, but the attributes we see them as possessing are not their actual physical attributes; they are (in one sense) mental attributes (or possibly topic-neutral attributes). We see objective particulars, but we don’t see them as having attributes objectively possessed (i.e. the attributes they actually objectively exemplify).[1] Perception is both objective and subjective, depending on which facet of it we are discussing. In the matter of perceptual reference to specific objects the senses are objective, but in the matter of perceptual description (general attributes ascribed) the senses are not objective. In yet other terms, perception is exogenous and endogenous, distal and proximate, “external” and “internal”. Thus naïve realism about the objects of perception doesn’t entail naïve realism about how these objects are perceived, and subjectivism about how objects are perceived doesn’t entail subjectivism about the objects perceived. In fact it turns out that this combination of objectivity and subjectivity is precisely what we should expect of perception, given its function and limitations.

            I won’t spend much time defending the first part of the hybrid theory—the identification of perceptual objects with objective physical particulars. When an ordinary object is before me in my visual field and acts on my senses in the normal way, we can say truly that it is the object I am seeing. It is the very object that I can also sense in other ways—by touch, taste, etc.—and it is the same object that is described by physics and chemistry, biology and geography. It is a three-dimensional solid object located in physical space consisting of atoms and subject to gravity and other forces; it might have been there long before perceiving organisms ever evolved and it will survive their extinction. Its properties are precisely those ascribed to it in objective physical science, whatever those may be. It is completely mind-independent. Yet it is the (direct!) object of perceptual reference—what the perceptual system singles out as a subject of predication (attribution, characterization). It is what is seen: not some intermediary will-o’-the-wisp entity but a real concrete inhabitant of objectivity reality. Nor is there any other object that is simultaneously seen along with this concrete object; it is the only object referred to by the perceptual system. So yes, we see bunches of atoms, assemblages of electrons, protons, and neutrons, collocations of strings or quarks—things that have nothing of the mind built into them. The objects of perception are just the ordinary physical particulars of the natural world, neither more nor less; and nothing else!

            This much will be assented to by most theorists of perception today (not so in the heyday of sense-datum theory); far more controversial is the second part of the theory. It will be supposed that the properties attributed by vision (say) are precisely those objectively possessed by the distal particulars that constitute the objects of sight. For example, I may see an object as round and being round is exactly what that object is—objectively, in reality, as things mind-independently stand. I see the physical particular itself and my eyes ascribe to it the very properties it really has. Maybe I also see it as frightening or delicious-looking, which are mind-involving, but the core of my perceptual representation consists of attributions of objectively instantiated properties—shape, distance, relative position, texture, and so on. I see an object as having edges and by God it has edges! But are things really that simple? Do we see things exactly as they objectively are? Let’s start with color and other secondary qualities: don’t these really have their origin in the mind? Certainly there is a long tradition that supposes so. Again, I won’t go into this question in detail, but it surely is possible that color in objects consists of a disposition to give rise to sensory experiences of a certain sort.  And isn’t the way an organism sees color a result of its specific sensory make-up? The same color might elicit fear in one animal but joy in another, depending on what the object means to the animal (is it predator or prey?). Couldn’t there be creatures that by stipulation project colors onto objects with no detriment to the claim that they nevertheless perceive objective physical particulars? This may be admitted but denied that primary qualities are mentally projected: things surely have shape independently of whether they are perceived to have shape! That may well be so, but is it the same shape? We are familiar with the idea that visual geometry is Euclidian while physical geometry is not, so that how we perceive figure differs from how figure objectively is. Also, there is that old point of Plato’s, namely that nothing in nature is ever perfectly circular or rectangular or straight. These are ideals dealt with in pure geometry, but they don’t apply to the empirical world. But don’t we see things in accordance with this natural geometry? The discus looks round, the picture frame rectangular, etc. We see and feel edges as smooth and continuous while in (microscopic) reality they are bumpy and discontinuous. We see things as solid when they are not, being mainly empty space; or empty when they have tiny particles in them, like air. We perceive spatial relations egocentrically, which they are not intrinsically. Then we have that old chestnut: the circular coin that looks elliptical from an angle. An elliptical representation surely enters into such a perception (no matter what we think), but the coin itself lacks this property. All perceptions come with a mode of presentation (visual constancies provide a good example), but modes of presentation are not part of the reality that we perceive—they are not objective features of the physical world. It is hard to think of any perceptual encounter that is free of subjective elements, i.e. mental representations that incorporate the perspective of the subject. We don’t perceive the world sub specie aeternitatus. We never perceive the world just as it objectively is sans any subjective intrusion; no organism does. We always bring a point of view (the Lebenswelt).

            This is not remotely surprising given how perceptual systems evolved. Perception evolved in conjunction with (inseparably from) the organism’s motor system, and the motor system is a practical capacity. Like all biological systems the sensorimotor system obeys principles of economy and has inherent limitations; it doesn’t build in more than is necessary to achieve its biological purpose (survival, reproduction). Perceptual representational primitives are geared to practical ends not to ideal science, so they suffice to carry out their function if they approximate to objective reality; complete veridicality is not in their job description. Getting the exact geometry of the physical world right is not their aim, so long as there is an adequate correlation between how they represent things and how things objectively are. We don’t find systematic radical discrepancies between perceptual content and objective reality, because that would thwart the purposes of the sensorimotor system; but it can tolerate small degrees of inaccuracy or coarseness or opacity. Animals don’t need “microspical eyes” (to use Locke’s phrase). As long as the perceived external object is represented in practically useful ways, the sensorimotor system is doing its job; it can get by with non-veridical representations as long as they make no difference to practical outcomes. Indeed too much accuracy and precision might interfere with the smooth functioning of the organism (compare vagueness). Of course the human visual system evolved from much simpler visual systems and inherits many of their design features, so we should expect it to have the pragmatic character of earlier systems. Thus some degree of objectivity is desirable, but not complete veridicality, absolute precision. The mind generates perceptual primitives that suit its biological purposes, and these map onto objective reality without necessarily coinciding with it. Thus the properties attributed to external objects by the sensorimotor system are not possessed by those objects as they are independently. Those smooth surfaces that we see and touch are not possessed by physical objects as such; their surfaces are granular and discontinuous—so they are not parts of physical objects objectively considered. The data of sense consist of attributes cobbled together by the mind (ultimately the genes) over the long course of evolution, so sense-datum theory is not wrong on this score (however mangled its expression tended to be).[2] We perceive objects as we represent them for our specific purposes not as they independently are (precisely, objectively, absolutely). Of course objects are disposed to cause in us perceptions that only approximate to their intrinsic objective properties, so they have these dispositional properties; but the properties we attribute are not identical with any properties of the object in itself. Yet we are seeing that object: it is the particular that our perception singles out for comment (so to speak). So our perceptual states have two sides: the objective physical particular that is singled out and the mind-contributed property that is attributed to that particular. We are both locked in our head (as in the traditional sense-datum theory) and oriented to outer reality (as naïve realism supposes). But we are not completely locked in our head, because of the correlations and approximations I have mentioned. We are not a mirror but we are not a black box either.

            There is a question about how mental the perceptual attributes are, and hence how subjective perception is. Earlier sense-datum theorists tended to take sense-data as completely mental—assuming that perceived shape and color were themselves mental phenomena (though not all did this: some took them to be neutral between mental and physical). I would say they are not mental at all, not strictly speaking anyway. I don’t think color properties are really mental properties, despite being projected by the mind. I also believe that geometrical attributes are not themselves mental: being circular, say, is not a property of the mind. They are “abstract” for want of a better word. My point has just been that the attributes ascribed by the perceptual system to physical particulars are not in general identical to attributes objectively possessed by those particulars, so how we see things is not (precisely) how they are objectively. I don’t say that these attributes are mental or subjective, though it is true that they are projected by the mind (they are probably lurking somewhere in the genes). Certainly they are not derived from external objects in the manner of classical empiricism. They are “subjective” only in the sense that they have their origin in the mind not in the sense that they are attributes of the mind (like pain or belief). What I have chiefly wanted to urge is that it is perfectly consistent to maintain a hybrid view of perception, and that both sides of this composite picture are plausible. Perception is of (de re) physical particulars outside the perceiving subject and yet it is as of (de dicto) properties that fail to coincide with the properties objectively possessed by such particulars. Perceptual reference is to physical particulars, but perceptual predication is not of physical properties (i.e. those objectively possessed by physical particulars). So both naïve realism and the sense-datum theory are partly wrong and partly not wrong.[3]

Colin McGinn     

[1] I am adopting some of the terminology developed by Tyler Burge in his Perception: First Form of Mind (2022).

[2] See J.L. Austin’s Sense and Sensibilia (1962) on the mangling.

[3] Burge doesn’t discuss the hybrid theory, though it seems to me consistent with his overall position (except that he tends towards attribute veridicality). I should note that a projective view of perceptual properties is consistent with the existence of perceptual constancies with respect to such properties.

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Impersonal Identity

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Impersonal Identity

We normally think that bodily survival depends upon identity through time. The body of an animal may change over time, but the body remains one and the same through these changes; the animal doesn’t acquire a numerically distinct body as it goes through life. Even in death the body remains one and the same object (though the organism may be no more). The body of the animal survives death by being identical to an earlier body, going back to the womb. Only when nothing identical to the earlier body exists does the body cease to exist. But what should we say about fission cases? Suppose the body divides into two, either naturally or by artificial intervention: then we have a problem with identity as a criterion of survival. For we cannot say that the later bodies are each identical with the earlier body, since they are not identical with each other; and it seems funny to say that one body could be identical to two bodies taken together. Yet it would surely be an exaggeration to claim that in such a case we have no survival—as if fission cases are just like incineration cases. It seems right on balance to say that the fission of a body allows for survival without identity. That position is reinforced by noting that fission might be succeeded by fusion: the pieces might be put back together again just as they were in the pre-fission body. Surely that would be the very same body that had recently divided into two. The original body had survived even though for a while nothing was identical to it. Bodily survival does not logically require bodily identity over time.

            This conclusion applies to more than just animal bodies. You can divide a statue into two for purposes of ease of transportation, later to be reassembled, and the case is clearly one of survival without identity (the statue survives as two pieces). Likewise for a rock or a plant. Similarly for a club or nation: such social entities can divide and remain in existence. Secession is not cessation. If a club decides to operate henceforward as two clubs, this is not like disbanding the club altogether; it might just be a convenience so to divide, as when a tennis club decides to split into a doubles club and a singles club. The reason for this is that fission involves continuity: the parts of the original entity survive as separate entities. Wherever there is fission there will be survival without identity, because identity is a very demanding relation; there are relations that fall short of it where we still have continued existence. Identity obeys Leibniz’s law, but mere survival does not. If you take apart your bicycle, you don’t destroy it utterly; it may be expressly designed to be taken apart. Nor do you destroy a cake by cutting it into pieces, even though the original cake is not identical to any of its pieces (they are not identical to each other). There is nothing strange or paradoxical here: given fission, survival without identity is what we should expect.

            The survival of persons follows the same pattern. Generally survival coincides with identity through time, but in fission cases (split brain) these come apart. Then we have survival in the shape of erstwhile parts that persist, as when the two halves of the brain are implanted into different bodies. The original brain is not identical with either hemisphere, and it is odd to say that it is identical with both together.[1] But nothing here is surprising once personal fission has been mooted: brains can be divided, and when they are we have survival without identity. Suppose Jekyll resides in one half of a person’s brain and Hyde in the other. When the brain is split and the halves placed in different bodies two persons are formed, but the original person survives the procedure (unlike the case in which the original brain is simply burned to ashes). Nothing here shows anything distinctive or remarkable about persons as such; certainly they are not the onlythings that can survive without benefit of identity. If persons were simple indivisible entities, then fission would not be possible for them; but evidently this is not the case. In fact, the idea of split personality already provides space for such a possibility, given that the two (or more) personalities might come to inhabit distinct bodies. The potential for fission is present in cases of split personality, and it provides an example of survival without identity if the personalities come to occupy distinct bodies. I think this is implicit in our ordinary concept of a person, because we recognize that conflicting psychological traits can coexist inside the same human organism (as with selfish and unselfish traits). All is not harmony within, as many a human story illustrates. Once we envisage dividing an individual into separate unified psychological wholes we are preparing the ground for survival without identity. This is not some startling piece of anti-commonsense philosophy but part of our ordinary folk psychology—which is the story of Jekyll and Hyde makes sense to us. It is true of each of us that if we had our brains suitably rejigged and placed in different bodies, then we would survive without any future person being identical with the person we now are. In this respect we are like the rest of nature.

[1] Even if it were, we could still destroy one and have a case of survival without identity.

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Subjects and Persons

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Subjects and Persons

 

Are persons and subjects identical? Both these concepts are hard to define, but we can fix ideas by saying that subjects are centers of consciousness and persons are constituted by memories, personality traits, and mental and physical capacities. Elsewhere I have given an argument showing that they are not identical, because we can conceive of cases in which the same subject persists while the associated person changes.[1] An implication of this is that subjects and persons, though non-identical, exist in the same place (at the same time). In fact, we are already committed to the spatial coincidence of several distinct entities associated with persons: a particular aggregate of material stuff; a collection of biological cells; a body; a living organism—and in addition subjects and persons. All these have differing identity conditions, so that each can perish while the others survive. The aggregate of matter can go out of existence while the collection of cells persists, and the organism can survive the total replacement of its cells; arguably, too, the person can outlive the organism it was once attached to (say by being uploaded into another organism). All this is very familiar. The question I want to consider here is whether subjects and persons have different conditions of survival: are there cases in which one can survive without the other? I will be particularly interested in fission cases.

Let’s grant that in fission cases (brain bisection and subsequent relocation of the hemispheres) we have survival without identity. My question then is whether in such cases we also have survival of the subject sans identity: does the conscious subject survive in the form of two subjects of consciousness, as the person survives in the form of two persons? Our intuitions are clear about survival of the person, but are they equally clear about survival of the subject? The basis of these intuitions in the case of persons concerns the relationship between the brain and the person: the person as a psychological entity is distributed between the two hemispheres, so we can understand how each hemisphere can form the basis of a person (memories, personality traits, etc.). Thus we have no trouble accepting that brain bisection is not the end of the person. We can survive this operation, as we can survive losing part of our brain but retaining enough to constitute our (partial?) survival. We see what can survive and we understand the mechanism whereby survival occurs (it isn’t like incineration). But the same is not true of the conscious subject; here things are not so clear. What is it in the brain that gets bisected in such a way as to lead to two complete subjects? And what exactly is it that survives? What kind of parts does the subject have that allows for it to be divided into these parts? Do we even have a clear idea of what such division would amount to? Thus we have no articulable intuition comparable to that in the case of the survival of persons under fission. Maybe two brand new subjects emerge from the operation—we have way of telling. We can’t point to a brain structure and observe that it is plainly divisible into two, since the subject and the person are not the same. What if the conscious subject corresponds to a brain structure that cannot be divided into two to yield the survival of the original? It doesn’t have the analogue of two hemispheres, i.e. something capable of preserving a person-like entity in two bodies. What if the subject is simply not a divisible entity at all? We really have no idea, so we don’t have the conviction that it could allow for survival under fission. It might simply die when bisection of its neural correlate occurs. Thus we can be gratified that qua person we could survive fission but not convinced that qua conscious subject we could also survive fission. The subject is a different entity and it doesn’t automatically inherit the survival capabilities of persons; at any rate, we have no solid intuition that it does. The metaphysics of the subject might well preclude what the metaphysics of the person permits. What if the subject is based in a single (remarkable!) neuron that cannot be divided into two to yield two functionally equivalent neurons? Then we don’t have the possibility of survival under division of the physical basis in question—as we do for the person.

Someone might retort that it doesn’t matter; only the person matters. Why should I care if the conscious subject can’t survive under fission? If I must have the operation done I will be comforted to know that the person I am will survive, but I might not care whether the conscious subject I also am will survive. But this is too sanguine: for I will surely care that my own consciousness will survive the operation; it is what I centrally am. My personality may change and my memories fade without losing my identity, but if a numerically distinct center of consciousness comes to occupy my body then in a very real sense I no longer exist. If your conscious self replaces mine (while leaving my personhood intact) I shall feel that I have lost my essence; it’s not like having some else’s kidney put into my body. I care whether I survive! Perhaps we should say that both subject and person matter and not try to decide which matters more, since we may want to preserve our personhood as well as our subject-hood. The difference is that in the one case fission is clearly compatible with survival, while in the other case this claim is far more problematic; we don’t really have any clear idea of what the latter kind of fission might consist in. We only have a very schematic idea of what the conscious subject is (vide Hume) while the concept of a person has more structure (memories, projects, personality, etc.). It is even epistemically possible that our lives are populated by many successive conscious subjects that merge imperceptibly together. The concept of the pinpoint unstructured self has its intuitive appeal, with nothing to distinguish one self from another. In any case, survival without identity is harder to make sense of in the case of the conscious subject as such. The person is marked as to gender, for example, yet the conscious subject does not appear to be; so we know what must survive for fission to be a case of personal survival. But what has to survive in order that the conscious subject survives? One wants to say: merely the thing itself. Attributes matter in the one case but not in the other.

Thus if we are interested in the question of what it takes for us to survive, we need to consider two entities (not counting the living organism)—the person and the subject of consciousness—and different answers may be indicated in the two cases. Certainly we should not assume that what matters is preserved under fission just because this is true for persons; it may not be true for subjects (or organisms/animals). I am myself inclined to say that the preservation of the person matters less, simply because one’s personal profile changes considerably over a single life, from childhood to old age: but one remains the same animal and the same subject of consciousness throughout one’s life. So fission cases have less significance for the survival of what we are than has been recognized. We are animals and subjects of consciousness as well as persons, but only persons allow for clear cases of survival without identity.

[1] See my “I Am Not a Person”.

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Does Arithmetic Rest on a Mistake?

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Does Arithmetic Rest on a Mistake?

 

How can the statement “1 + 1 = 2” be true? How can the operation of adding 1 to itself produce the number 2? There is only one number 1, so how could it by itself give rise to the distinct number 2? If you add the number 1 to itself, all you get is the number 1. It’s like adding Socrates to Socrates and hoping to get Plato (or “double Socrates”, whatever that may be). If anything we have the oddity “Socrates + Socrates = Socrates”. The Concise OED has an instructive definition of “add”: “to join to or put with something else”; the Shorter OED gives “join to or unite (one thing to another) as an increase or supplement”. Both stipulate that the added things must be distinct (“something else”, “another”): but 1 is not distinct from itself, so it can’t properly be added to itself. And how would doing that “increase” anything? In our initial statement we have two occurrences of the numeral “1” denoting the self-same number, asserting that this number added to itself gives 2 as sum. What is this strange kind of addition, and if it were to exist how could it yield the number 2? If “+” expresses a function, it would appear to have the same number occur in both argument places—yet we are told that this single number yields 2 as value of the function from 1 as argument. Notice that no one ever utters the sentence “1 added to itself equals 2”, because that makes the incoherence obvious—as with “Socrates added to himself equals Plato (or some other entity distinct from Socrates)”. On the face of it, then, arithmetic contains an absurdity—but one that escapes notice and goes unchallenged. What is going on?

            We must first observe that ordinary language contains two sorts of number word: adjectival and nominal. The arithmetical language we have been considering is nominal: nouns, singular terms and proper names that denote numbers conceived as objects. These terms form the subject of sentences to which predications are directed. But in much ordinary speech the adjectival use dominates: “five dogs”, “three cats”, “one car”. Here we are not using number words to denote objects but as components of predicates; they modify count nouns or sortals. In the adjectival use we can say things like, “One cat and one dog together add up to two animals”; or more formally, “One dog + one cat = two animals”. There is nothing puzzling here: there are many dogs and cats subject to counting and they can feature in equations (one dog and one cat are clearly distinct things). We are not trying to get two things out of one or engaging in peculiar acts of addition. We said nothing here about the object 1 and adding it to itself; we spoke only of the number of cats and dogs. I conjecture that people tend to hear the pure mathematical nominal statement as short for, or closely related to, the applied adjectival statement; and this leads them to overlook the peculiarities of the former kind of statement, logically speaking. Probably when we are drilled in early school years in academic arithmetic we are introduced to its formulas by means of adjectival paraphrases that lull the mind into a sense of familiarity, while actually changing the thought in fundamental ways. An ontology of cats and dogs is covertly replaced by an ontology of numbers denoted by proper names. Thus children don’t protest, “But you can’t produce 2 just by combining 1 with itself!”

            Abetting these adjectival uses in overlooking the logical problems inherent in “1 + 1 = 2”, we have sign-object confusion: we see two signs for 1 and conjure two number 1’s to go with them. This gives us the illusion that 1 can be converted into 2 by being added to itself. That clearly won’t work for “4 + 4 = 8” and infinitely many sentences like it, since there are not eight occurrences of “4” here; but anyway the fallacy is too blatant to bamboozle the mind for long. There is just the number 4 here, denoted twice, and it can’t be converted into 8 by being added to itself: 4 put together with itself gives just the same old number 4. In addition to this there is vagueness and uncertainty about what precisely these mathematical objects are, which allows the mind to imagine that they can increase in magnitude simply by self-adding. One has to focus on the logical character of the statements in question to see how peculiar they are, as standardly understood. In any case there are several factors that induce us to overlook the actual intended content of these sentences, the main one being the availability of adjectival counterparts to them, which are perfectly kosher.

            The problem I have indicated infects certain attempts to define the natural numbers. Leibniz’s approach, endorsed by Frege, has it that each number is composed of a series of 1’s (apart from zero). Thus “1 + 1 + 1 = 3”: we can define 3 in this manner, and so on for all numbers. But adding 1 to 1 is not a method for generating a new number; it is simply a way to remain stuck at the number 1. We can add 2 to 1 to get 3 because these are different numbers, but adding a number to itself can’t produce a new number. Non-identity is the essence of counting. It might be thought that there is a way out by exploiting the adjectival paraphrase as follows: the statement “one collection + another collection + one more collection = three collections” is perfectly meaningful, allowing us to identify these three entities with the number 3. That is not adding one thing to itself, but rather adding three distinct things together (as it might be, collections of dogs, cats, and mice). But really this says nothing like the original statement containing tokens of “1” that all denote the same number; it merely gives the false impression that such a statement makes sense by sounding similar to it.

            It might be said that we could save arithmetic by reformulating it adjectivally, ridding ourselves of nominal expressions and an ontology of numbers as objects. That sounds like a solid move in principle, but it won’t be able to save all of arithmetic as it now exists, because that subject has now taken on a life of its own. We would need to be able to restate all propositions about numbers in adjectival terms—for example, propositions affirming primes, cubes, successors, etc. How can theorems about numbers as such be represented in a language that declines to refer to them? What is called “number theory” will find it difficult to reformulate itself using only numerical adjectives and count nouns—how can we even say that a certain number is even? Adjectival arithmetic is fine in the market place, but it won’t do to encompass nominalized academic arithmetic.

            Could we ban all equations of the form “n + n = m” but keep the rest of pure arithmetic? There will still be infinitely many true equations to play with, such “5 + 3 = 8”. This doesn’t add any number to itself. But unfortunately the problem persists under the surface: for implicit in such a statement is an addition of one number to itself, viz. 3 added to 3, since 3 is part of 5 and so gets added to 3 (with 2 added to the result to give 8). Hidden in “5 + 3” is the addition “3 + 3”—as also is “4 + 1”. So we can’t avoid commitment to such equations even when they don’t appear on the surface; they lurk beneath because they are built into the whole conception. Numbers can always be broken down so as to generate them. You can’t have arithmetic, as it now exists, without these kinds of equations, despite their manifest weirdness (they don’t even fit the dictionary definition of “add”). One might even say that they claim a metaphysical impossibility: adding an object to itself (itself an impossible operation) to produce a quite distinct object (impossible ontologically). This is what you get if you nominalize adjectives illicitly. Here is an analogy: talk of large and small objects is common, as in “Jumbo is a small elephant” and “Mickey is a large mouse” (attributive adjectives). There is no logical problem about such sortal-relative adjectives in their proper grammatical position, but if we try to abstract them away from this position in order to form nominal expressions we get ourselves into trouble. Thus we might elect to speak of an entity called “largeness” and regard it as self-subsistent, as if “large” had a meaning independently of the nouns to which it is usually linked. Then we would wonder how a single animal could have both largeness and smallness at the same time, given that Jumbo is a large mammal but a small elephant (small for an elephant). Similarly, number words originally belong with count nouns, in which position they are unproblematic; but if you abstract them from that context and nominalize them, you find that the ontology thus created produces monsters like “1 + 1”. You can certainly add one cat to one dog and get two animals, but if you try to add the object 1 to itself to get the object 2 you run into incoherencies. In effect, there has been an illicit reification—of attributive adjectives or of numerical adjectives. Singular terms have been introduced and objects assigned to them, along with certain operations (like addition): but the coherence of the whole structure has not been demonstrated. In fact, the structure is built on equations that have no clear sense—or else are demonstrably nonsensical.

            So what is the status of arithmetic as it is commonly understood? Is it simply nonsense? Are its propositions analogous to “Largeness is larger than smallness” or “Largeness added to largeness equals even larger largeness”? That is, does it consist of mangled adjectives forced to dress up as pseudo proper names? Should it therefore be dropped, eschewed, and ridiculed? That seems harsh. Perhaps a form of fictionalism will serve to save it: arithmetical facts in the shape of adjectival constructions have been converted into propositions about fictional entities, obeying fictional laws. Names have been introduced and formulas manufactured, so that we end up with the likes of “1 + 1 = 2”. We drill kids in this discourse, as we drill them in other fictional discourse masquerading as fact (e.g. religion) and they are forced to accept it at face value. People end up believing in the Holy Trinity, a piece of transparent nonsense; and they end up believing that there are objects that when added to themselves produce other greater objects, which is scarcely more credible than the Holy Trinity nonsense. So maybe the whole shebang is carefully curated fiction presented as sober truth. And there is no denying that the edifice rests on perfectly sensible foundations in the use of number words in adjectival form; it is not pure nonsense. Nor is nonsense always and necessarily pernicious; it may even be useful (“useful fictions”, e.g. the average man). Is it an accident that Charles Dodgson was both a mathematician and a creator of delightful nonsense? Arithmetic, as we have it, is a human construction, according to fictionalism, like the creatures of the Jaberwocky, and it does not need literal truth in order to captivate the human mind. And it’s sort of true, given its sterling adjectival origins. We can carry on cheerfully intoning such nonsense as “1 + 1 = 2” while accepting that we are engaging in metaphysical quackery. The whole history of mathematics is littered with controversy about the reality of this or that newly created mathematical entity (zero, the infinitesimal, the irrational, the negative, etc.): is it inconceivable that the arithmetic of positive whole numbers is also steeped in ontological mud?

 

Colin McGinn                

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Intuitive Knowledge

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Intuitive Knowledge

 

The OED defines “intuition” as “immediate apprehension by the intellect alone” (among other meanings). Intuitive knowledge, then, is knowledge by the intellect alone—knowledge by pure intellection. The senses play no part in it. Empirical knowledge, by contrast, is defined as knowledge by means of the senses, perhaps allowing a contribution by the intellect in addition to sense experience. Intuitive knowledge is often regarded as problematic, even unintelligible, while empirical knowledge is thought to be pellucid and paradigmatic. Thus empiricism has enjoyed ascendancy over rationalism since its inception in the seventeenth century. I will argue that this assessment is mistaken. The subject is large, but I will keep it brief.

            The first point to note is that intuitive knowledge employs a single mental faculty in producing knowledge—the faculty of intellect. Its inputs are intellectual and so are its outputs; it doesn’t go outside itself. However, empirical knowledge employs a pair of faculties of very different nature: intellect in which the knowledge is stored, and the senses that yield sensations. Somehow sensations are supposed to produce states of knowledge. But how can sensations, which are non-propositional, give rise to knowledge, which is propositional? How could sensations constitute knowledge? The two are like chalk and cheese.  Only by attempting to reduce intellect to sensation, which is hopeless. Call this the problem of epistemic mismatch. Second, skepticism stands in the way of basing knowledge of the world on experience, since the two are not logically connected—as with dreams, evil demons, and brains in a vat. Sense experience cannot justify such knowledge claims, so it can hardly be a sound basis for knowledge. Intuitive knowledge has no such problem and is generally regarded as certain (e.g. knowledge of logical laws). There is thus no such thing as empirical knowledge (true justified belief). Third, it is completely unclear what sense experience is such that it can produce knowledge. If we take it to be concept-infused, we impose intellect on sense from outside; if we rigorously exclude concepts from it, the residue will be incapable of creating knowledge (the bare “given”). More basically, it is impossible to say, or discern, what sense experience actually contains: the more you stare at it the more it looks impotent to justify our typical claims about the world. Blooming buzzing confusion can’t yield propositional knowledge of reality. The only way to save empiricism is to inject it with rationalism by invoking intellect. Maybe sensations can somehow trigger knowledge but they can’t act as justifiers of knowledge (“only knowledge can justify knowledge”).

            Here is another way to look at the matter. The senses evolved in collaboration with the motor system to form the sensorimotor system. This system operates to regulate the organism’s relation to its environment and exists independently of cognition. It is not designed to produce knowledge or to interact with the intellect (all animals have it). The empiricist in effect believes that this primitive system can also give rise to propositional knowledge and is indeed its only legitimate basis. But seen from the proper biological perspective, this claim is vastly implausible; the intellectual system might never have evolved while the sensorimotor system would still be doing its job. It would be completely accidental if the senses could perform both functions. Perhaps there is some sort of epistemic hookup between the senses and the intellect, but the idea that knowledge of the world can be exhaustively explained by sensory inputs is quixotic at best. One can certainly imagine a rationalist philosopher (Plato?) holding that no knowledge can be derived from sensation, i.e. sensations can play no justificatory role. This isn’t to say that states of sensory seeming can’t function as justifications, as in “It seems to me that there’s a book on my desk”, but the states so reported are heavily imbued with concepts and capacities drawn from the intellectual faculty; they aren’t simply raw data existing antecedently to the operations of intellect. We really have no clear idea of what empirical knowledge could be construed in the traditional way (“impressions”, “ideas”, “sense-data”, etc.). So as a theory of knowledge, supposedly superior to rationalist theories, empiricist theories are woefully under-described, if not demonstrably incoherent. It is simply not true that knowledge is “based on experience”.

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Ears

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Ears

 

It began over a year ago when a small red patch appeared on the top of my right ear. At first it was diagnosed as inflammation of the cartilage probably brought on by wearing too tight headphones. The cure was not to put any pressure on it and wait for the inflammation to die down. After several months it had increased in size and painfulness, so I returned to the dermatologist. This time a biopsy revealed skin cancer (squamous cell). Now it was necessary to perform surgery. This was duly done: a five-hour MOHs procedure followed by a three-hour reconstruction (local anesthetic). I won’t specify the details but it was all pretty brutal (twenty odd stitches, serious pain). I lost half my ear. The cause: sun damage, possibly a result of playing tennis in the Florida sun.

            At the same time the ear was declared healed a lump appeared in my neck. This was duly scanned and biopsied: it was more cancer. The cancer in my ear had evidently spread to my neck and was now growing apace. A full-scale operation was quickly scheduled. This was performed two weeks ago. Again, I will spare you the gory details except to say that it was an eleven-hour operation requiring a hospital stay and subsequent daily home visits from a nurse. Full recovery is not guaranteed. It is presently difficult to eat and my right shoulder is compromised.

            I relay all this in order to encourage readers to protect their ears from the sun, especially if they live in a place with a lot of it. It is easy to neglect the ears while protecting the face. Sunscreen is not enough, especially if you spend time doing water sports (as I do). Wear a broad-brimmed hat (not a baseball cap). Ideally use a fabric covering such as a skullcap or full-face sun protection balaclava (as I have done for some years). Apparently my experiences are not uncommon and you don’t want to share them.

 

Co

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Blindsight and Empiricism

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Blindsight and Empiricism

 

Imagine a person with blindsight in every sense: no conscious perceptual experience at all but able to receive information subconsciously from the external world. This person nevertheless has ordinary fully conscious reason: she is capable of forming beliefs that count as knowledge in virtue of the informational input. It would not occur to her to suppose that all her knowledge rests on conscious experience; she would not be a traditional empiricist. She might indeed be a rationalist about her powers of knowing, supposing the intellect to be the sole mental faculty implicated in the generation of knowledge (she could still allow that causal relations to the environment are involved). So there is nothing necessary about conscious sensory experience in the production of knowledge of the external world (subliminal perception makes the same point). Sensory qualia are not essential to knowledge of the physical world. On the other hand, the apparatus of reason is essential: concepts, judgment, reasoning, and propositions. You can’t be blind about these things and still know in the ordinary sense. If someone were to claim that sensations of pain and pleasure were the essence of knowledge of physical things, we could quickly refute them by pointing out that a knower could very well lack such sensations and still know, so long as other faculties remained intact—in no way is knowledge based on sensations of pain and pleasure. The same could be said of emotion: it is not essential to the enterprise of knowledge despite its presence in the mind of the typical human knower. Pain, pleasure, and emotion no doubt have a function, but it is clearly not to serve as a foundation for human knowledge. The case of the blindsighted knower shows that the same is true of sensory experience: this too is not the indispensable foundation of human knowledge.[1]

            This suggests that all knowledge conforms to the basic tenets of rationalism: the mental faculty involved in producing knowledge is uniformly reason. It isn’t that some knowledge arises purely from reason and some knowledge consists in a kind of refinement or distillation of sense experience—a different kind of cognitive state—but rather that all knowledge is composed of the same basic materials, though no doubt about different things. Thus mathematical knowledge is essentially the same as knowledge of physical things in its intrinsic nature—viz. an activity of intellect—though the subject matter of the two is different. There is not intellectual knowledge and sensory knowledge, as if the latter is infused with sense experience while the former is not; rather, all knowledge is an affair of the intellect in its inner composition (however differently caused). Moreover, there is no sense in which one type of knowledge mimics or copies sensation; sensation is not internal to any kind of knowledge. There are not two types of knowledge as there are two types of swans (black or white): all knowledge is as the rationalist supposes. Empiricism only seems plausible because we tacitly imbue sensation with the products of the intellect, but this is to presuppose rationalism not find an alternative to it.

            It is quite true that some of our knowledge is about sensation, but that does not imply that this knowledge is itself a form of sensation; it is as intellectual as any knowledge we have. We must not transfer to the medium what belongs to the message, i.e. the subject matter. Our knowledge of sensation (Hume’s “impressions”) is not a version of sensation; it is the application of reason to a certain type of subject matter. Human reason is essentially homogeneous not an amalgam of a sense-based faculty and an intellect-based faculty; and the nature of this faculty corresponds closely to traditional rationalist conceptions from Plato onwards. Simply put, and without any attempt at argumentation, it consists of a set of innate ideas organized by a logical faculty into propositional structures of arbitrary complexity. The rational faculty receives inputs of various kinds, to be sure, but it operates in much the same way across the board. Empiricism is an inadequate theory of the nature of this faculty, and it mistakes the inessential for the essential in the production of knowledge.[2]       

 

[1] See my “Intuitive Knowledge”.

[2] Plato regarded sense experience as incapable of producing genuine knowledge, relegating it to the realm of mere “opinion”; but he could have gone further and rejected it as any kind of justifying basis for our knowledge claims. Experience is just the wrong kind of thing to provide a basis for reason to work on (as I argue in “Intuitive Knowledge”).

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