Inverted Positivism

I wish to introduce you to the work of an obscure Austrian philosopher. His name is Otto Otto and he lives in the suburbs of Vienna.  [1] He belongs to a group called the Vienna Oval by facetious analogy with the better-known Vienna Circle. Otto (you can take this to be his first or last name according to preference) is a positivist strict and pure, old school to the core. He accepts the verifiability criterion of meaning without dilution or compromise: every meaningful statement must be verifiable. He differs from other positivists, however, in two particulars: he doesn’t think that ordinary empirical statements are verifiable, and he does think that a priori truths are. In particular, he holds that analytic truths are the paradigm of verifiability. He thus maintains that analytic and other a prioristatements are straightforwardly meaningful while empirical statements are not. His reason for denying the verifiability of empirical statements is not eccentric: it lies in the power of skepticism. Skepticism teaches us that our ordinary statements of science and common sense are not rationally justifiable, i.e. not verifiable. According to the verifiability principle, then, they are not meaningful. Since we could be brains in a vat, we can’t justify statements about the external world, which means they are not verifiable; and hence they cannot be meaningful. However, we can justify analytic statements, because the skeptic cannot cast doubt on our acceptance of them: we know for sure, for example, that bachelors are unmarried males. So analytic statements are meaningful, but empirical statements are not. That is Otto’s considered position and he sees no reason to deviate from it.

            Now Professor Otto is not an unreasonable man: he is aware that his position might strike some as extreme, even perverse. For how can it be that science and common sense are literally meaningless? Here he is prepared to hedge a bit: they may be agreed to have a kind of secondary semantic status. Conventional positivists make this kind of compromise all the time: they accept that a priori statements are meaningful without being empirically verifiable, holding them to be tautologies devoid of real content; and they also recognize the existence of meaningful ethical statements. They accordingly speak of “cognitive meaning”, contrasting it with lesser kinds of meaning; they operate, in effect, with a semantic caste system. Likewise Otto and his comrades accept that empirical statements have a kind of second-class semantic status: they have a use, a role on communication, even if they lack meaning proper. They lack what Otto is pleased to call logical meaning or rational meaning or epistemic meaning, but they do have pragmatic meaning—meaning in the vernacular non-rigorous sense. They have the same status as tautologies in the rival positivist worldview: tautologies are not meaningful in the sense of being informative and fact stating, but only in the lesser sense that they are grammatically well-formed and composed of meaningful elements. Likewise Otto and his associates accept that empirical statements are grammatical and composed of meaningful elements, but they deny that such statements have the kind of serious substantial meaning possessed by statements you can rationally accept as true. They wonder what the point is of statements that cannot be used to express knowledge, as empirical statements cannot (because of skepticism). True, such statements are not literal nonsense, either by grammar or lexicon, but they can’t match a priori statements for their ability to express ascertainable knowledge. The latter statements are genuinely cognitive in the sense of being knowledge expressing, while empirical statements exist in a limbo of uncertainty. Otto privately condemns empirical statements as sheer nonsense, in his strict and pure sense, but he publicly concedes that they have a kind of degenerate meaning—just as the Circle positivists do the same for analytic statements and ethical statements. What Otto can’t fathom is why these putative positivists believe that empirical statements are meaningful and yet are not verifiable—given that they accept the verifiability theory of meaning. Don’t they see that no empirical statement can be established as true, or even asserted in preference to its negation, given that the skeptic is undeniably right? They fail to understand that a priori statements are the only kind that allow of conclusive verification, and hence qualify as meaningful. Even if they are mere tautologies—which Otto strongly contests—they are at least verifiable tautologies: you can at least know them to be true! You know them to be true by the exercise of reason and knowledge of meaning, whereas the senses can never deliver skepticism-proof knowledge. The problem of induction by itself shows that laws of nature cannot ever be known, so such statements are not verifiable, and hence not meaningful. On the other hand, we can know with certainty that bachelors are unmarried males and that 2 plus 2 equals 4. Thus the principle of verifiability shows that only a priori statements are meaningful in the gold-standard sense, with empirical statements trailing somewhere in the semantic dust. They are meaningful only in the sense that “Colorless green ideas sleep furiously” is meaningful, i.e. they are grammatical and composed of meaningful elements. Otto’s position is rather like the position that would have been taken by Popper had he been interested in criteria of meaningfulness: empirical statements can never be verified (though they may be falsified), and so cannot be strictly meaningful. Otto and friends adopt the simple view that meaning requires the possibility of knowledge, and only a priori statements can really be known to be true. They regard the rival band of positivists as sloppy weak-kneed thinkers who refuse to accept the problem of empirical knowledge—don’t they see that no empirical statement has ever been verified? Authentic positivism thus requires us to accept that empirical discourse is strictly meaningless save in a second-class by-courtesy-only sense. It is meaningful only in the way ethical discourse is meaningful, i.e. by dint of grammatical correctness and pragmatic utility.

            What view does Otto’s school of positivism take of metaphysical discourse? One might think they would be tolerant of it since it purports to be a priori, but actually they are as intolerant of it as their rivals in central Vienna. The reason is simple: such statements are never rationally justifiable. No metaphysician can ever establish the truth of his assertions: there is no method of acquiring metaphysical knowledge. It isn’t the lack of empirical content that is the problem—that applies equally to mathematical knowledge—but the problem of not having any effective method of delivering knowledge. No proof procedures and no simple unfolding of meaning, just endless wrangling and futile dispute. So metaphysics is as meaningless as the other positivists maintain but for a different reason. Empirical justification is neither here nor there; what matters is that there be some method for finding out the truth. As to ethics, Otto is ambivalent: he is inclined to regard it as a priori, and he accepts that ethical reasoning is rational, but he is disturbed at the lack of consensus about ethical questions. He is apt to call ethical statements “quasi-meaningful”: they have emotive meaning, to be sure, and they permit rational inference, but they lack the kind of certainty we find in mathematics, logic, and analytic truth. Ethical statements are not as meaningful as statements in these areas, though they are a lot more meaningful than statements of physics, say, with its unverifiable induction-based statements of natural law. Nothing meaningful is unjustifiable, so ethics squeaks in by comparison with science: after all, it has a strong a priori component. But science is stuck in unverifiable limbo: for none of it can be proved. Here Otto is a Popperian: Hume was right about induction, and that means that scientific theories can never be rationally established (though they may be refuted). As Otto likes to say, science never expresses genuine propositions—things that can be true or false—though it can bandy around sentences that are instrumentally useful and are clearly grammatical.

            Otto suspects that the other positivists are unduly influenced by religion. They see that religion is not an area of rational inquiry in good standing, and that it is dubiously meaningful, so they naturally seek to ban it. But they wrongly locate the central defect of religion: it isn’t that it lacks empirical credentials but that it lacks any procedure for establishing its claims. It doesn’t have the methodological clarity of the analytic, the logical, and the mathematical. In fact, it does have empirical criteria of justification; it is just that these criteria tend to undermine its truth (all those alleged miracles never pan out empirically). The reason it is not meaningful is that its claims are not susceptible to rational demonstration—not rationally verifiable. Faith is not rational demonstration, so faith cannot supply meaning. The other positivists wrongly contrast religion with science, thinking that science supplies the paradigm of the meaningful for the true positivist; but science is not strictly meaningful by correct positivist standards. Rather, religion and science are both condemned to semantic destitution, according to the proper form of positivism—the kind that links meaning with rational provability. The problem with religious claims is just that there is no rational way to demonstrate them. If they were analytic everything would be fine (the ontological argument was a valiant effort in that direction), but they clearly are not—they don’t just spell out what the word “God” means. Nor are they mathematical in nature. So there is no way to justify them by rational criteria. The positivists were right to find a tight connection between meaning and knowledge, but they wrongly located this connection in empirical knowledge—of which there is no such thing. They were logical empiricists where they should have been logical rationalists: pure reason can establish the truth of propositions, and hence guarantee meaning, but the senses combined with induction are impotent to establish anything, so they cannot be the source of meaning. Skepticism disproves classical positivism, but it leaves Otto’s version of positivism untouched, or so he contends.  [2]

  [1] Why the double “Otto”? The palindromic possibilities, the economy (two letters, a whole name), the contempt for custom: and why not? Nabokov cannot be the only one.

  [2] Did I mention that Otto Otto is a mathematician by training and also an accomplished logician? He is also fond of compiling synonyms. Empirical science leaves him cold because of its lack of formal rigor and its inconclusive methods. This may have something to do with his insistence that real meaning lies in the a priori sciences; he is certainly snooty about the mathematical capabilities of members of the Vienna Circle (those mathematical illiterates, as he refers to them). In fact, he lumps them together with the metaphysicians in their shared lack of methodological scruples. Empirical science is far too much like metaphysics, in his book.

Mental and Physical Events

Identity of properties is one thing; identity of particulars is another. Particulars can be identical without their properties all being identical. This is obvious: Superman is identical to Clark Kent but the property of being a flying man is not identical to the property of being a journalist. It is just that a single man has both these properties. This distinction has been thought useful in characterizing the relationship between the mind and the brain: hence the distinction between type identity theories and token identity theories. A type identity theory would say that the property of pain is identical to the property of C-fiber firing; a token identity theory would say that every particular instance of pain is identical with an instance of some kind of brain event or another—it need not always be C-fiber firing. The properties are different but they apply to the same particular (so a dualism of particulars is false). Thus we have “non-reductive materialism” and “anomalous monism”.  [1] Two sets of properties, one set of particulars: mental properties are not identical to physical properties, but every instance of the former is an instance of the latter. Here is an analogy for the token identity theory: each member of the set of soldiers has a certain rank—private, corporal, captain, colonel, etc.—and (we can suppose) a certain civilian occupation—lawyer, teacher, greengrocer, tailor, etc. For any instance of the former set of attributes, we can say that he or she is identical to someone with an attribute drawn from the latter set of attributes. That is, every soldier is token identical to someone of a certain civilian occupation—what has the former property also has the latter—but it would be quite wrong to identify military ranks and civilian occupations. The property of being a colonel is not identical to the property of being a lawyer, say. No one would be a “civilianist” about military ranks, holding that ranks are type identical with civilian occupations. Yet there are no soldiers who fail (we are supposing) to also have a (prior) civilian occupation: there is no dualism here of soldiers and non-military workers—as if each soldier has a kind of shadow civilian counterpart. No, he or she just is a particular civilian worker. The same people can have different attributes. Just so events can have both the attribute of being a pain and the attribute of being a C-fiber firing—without the attributes being identical. Thus we have a weaker version of materialism, one that avoids the problems encountered by type identity theories. We have materialism without reductionism.

            But do we? Is token identity theory really a form of materialism? Is it strong enough for that? And is it an adequate account of the relationship between the mind and the brain? Consider this question (which I have never seen asked): could any other type of mental event than pain have a token that is identical with a token of C-fiber firing? Could a tickle or a sensation of red be identical to an instance of C-fiber firing—in addition to instances of pain? Evidently, both colonels and corporals can be identical to people who are teachers in civilian life, so can both token pains and token tickles both be identical to tokens of the type C-fiber firing? Generally, is it possible for instances of every type of mental event to be identical to instances of the same physical type? Might every mental token be identical to a token of an identical physical type? Evidently, nothing in logic precludes this: token identity theory is consistent with total homogeneity at the physical level. There is nothing but C-fiber firing to “realize” every mental type. If that were so, then properties of the brain would have nothing to do with properties of the mind. In the same way civilian occupations have nothing to do with military ranks: these properties are determined by quite different factors (or could be). Nothing about being a tailor makes you into a colonel rather than a corporal, since tailors can be both (they can be trained to be both). Similarly, the mental type of a mental token is not determined by its physical type—it might not even be correlated with that type. Of course, if type identity were true, then we would have such determination, but not if we only have token identity. Token identity is entirely neutral on what determines mental properties: it could be acts of God or human convention or the color of your hair. Two people could have completely different mental lives while having all their physical properties in common—they could still be such that all their mental tokens are identical to physical tokens. A given mental type can be “multiply realized”, as we have been taught, but as a matter of logic it is also true that the same physical type can be “multiply manifested”, i.e. correlated with different mental types. At any rate, token identity in no way rules this out. We may then wonder whether it deserves the name “materialism”, since it is silent on what makes an organism have the mind it has. Mere token identity is a very weak relation, hardly qualifying as a less unpalatable version of classic type identity: for it says nothing about the nature or fixation of mental properties, i.e. what makes the mind the mind. What kind of mind you have has nothing to do with what kind of brain you have, according to token identity theory; the theory merely rules out the possibility that mental tokens float free of physical tokens—as soldiers might be thought (falsely) to float free of people with prior civilian lives. A monism of mental tokens allows for any old theory of mental types, or none. It is not a theory of mental types at all.

            This point may be conceded (the “uniform realization” point) but it may be suggested that we need to strengthen the token identity theory in a familiar way—by invoking supervenience. We can assert that mental types are strongly dependent on brain types, so that brain type entails mental type—physical properties fix mental properties. All right, let’s go ahead and assert that: the question then is what makes it true. The crucial point is that type identity explains this but token identity does not: if mental types are physical types, then of course you can’t have one without the other; but if they aren’t, the question is left hanging. Without type identity (or something close to it) supervenience looks like a mere stipulation devoid of rationale. It leaves open the question of why the dependence goes in one direction only: why doesn’t the mind also determine the brain? How can the properties be dependent one way but not the other? We certainly don’t have supervenience in the case of the soldiers, for the obvious reason that civilian occupation doesn’t determine military rank (or shape determine color, etc.), so why is the mental case different? No answer is given—a mere logical possibility is asserted. And surely we would want to say that there must be some internal relation between the brain and the mind—something about brain properties that underlies and explains supervenience. Absent a specification of what this might be, supervenience only gives us materialism by main force: it is what we need to wheel in to bulk up token identity into something looking more like classic materialism. More strongly put, unexplained supervenience is mere postulation not a theory of the mind-brain relation. It (purportedly) fills the gap left by abandoning type identity theory but without really supplying any filler. But token identity alone is hopelessly weak as a theory of the mind-brain relation. We may note that the asymmetry of dependence postulated by supervenience is also exaggerated at best: for there must be somedetermination from the mental to the physical, as a matter of hard necessity. For example, pain is necessarily linked to withdrawal behavior (or a disposition to it), but withdrawal behavior must be physically produced by the nervous system—so pain must fix some physical aspects of the organism feeling pain (viz. a physical withdrawal mechanism). It is not completely neutral about the condition of the body. Maybe C-fibers are in fact the only ones that can figure in a causal sequence that culminates in withdrawing a limb from the painful stimulus, even though this fact is not transparent to us; in that case there is partial supervenience from the mental to the physical.  [2] And then we will have mutual dependence between mental and physical types, which encourages a type identity theory after all. It turns out that token identity plus supervenience is not sufficient to capture the nature of the mind-brain relation, and that we must move in a more type-committed direction. So token identity alone is no good, and one-way supervenience is no good either; we can’t avoid assuming something like type identity (possibly type composition). Maybe the brain descriptions (and the mental descriptions too) have to go beyond our commonsense categories, but we can’t avoid assuming a close relation of types—and identity seems the only clear way to go. Of course, this will lead to the classic objections to type identity theory, but that is just the old familiar mind-body problem making itself felt. My point is that the attempt to circumvent the objections to type identity by retreating to token identity (with or without supervenience) is doomed, because (a) that is not really a form of materialism and (b) we evidently need to postulate a stronger relation between mind and brain than can be supplied by those theories.

            We tacitly assume that physical types play some role in fixing mental types when we intuitively rule out the possibility that the same physical type may underlie different mental types in instances of token identity. We don’t even consider the possibility that token pains and tickles and sensations of red might all be identical to physical tokens of C-fiber firing, even though that is not logically precluded by token identity theories—because we assume that the mental is fixed in some way by the physical (hence the appeal of type identity theories). But mere token identity is quite compatible with homogeneity at the physical level combined with heterogeneity at the mental level (the analogue of soldiers of different military ranks all coming from people of the same civilian occupation).  [3] But that is not a satisfactory account of the relation between mental and physical events; and supervenience as commonly understood is not sufficient to remedy the problem. Type identity seems like the only way to go—with all the problems that are attendant upon that. Token identity theory is thus an inadequate refuge from those problems. It is too much like saying that all mental events fall under physical descriptions like “occurring n miles from the equator”: that is no doubt true, but it is not a form of materialism. Many types of mental token could correspond to the same such description (all those at a certain latitude, say), but that is not a theory of what makes mental types the types they are. The brain needs to be brought into closer proximity to the mind than that, but token identity alone is not equipped to do it. Type identity, however, is.  [4]

C

  [1] Davidson’s “Mental Events” serves as a classic expression of this type of theory.

  [2] Valves are similar: they can be made of very different materials, but they all require a physical mechanism consisting of opening and closing. Likewise all tables require a flat raised stable surface, which are physical features, despite varying widely in physical composition. Not all physical facts are compositional facts.

  [3] If we were to observe this situation obtaining in the brain, we would surely conclude that mind and brain have little to do with each other. The same mental type can co-occur with different physical types (“multiple realization”) and the same physical type can co-occur with different mental types (“uniform realization”). The fact that each mental token is identical with some physical token would not alter our opinion. In fact, we observe quite strong correlations and these lead us, reasonably enough, to postulate type identities; but this is not part of the logic of token identity theories. So token identity theory cannot be construed as a relaxing of type identity theory that preserves its spirit while avoiding its difficulties.  

  [4] The type of type identity might be very different from any currently envisaged or even imaginable by us: it might have to be expressed using concepts quite alien to concepts we now use to think about mind and brain. In particular, C-fiber firing may be a far more exotic thing (by our standards) than we realize; it may have hidden depths. Type identity and mysterianism are not incompatible doctrines: the brain might have properties currently mysterious to us that are type identical with mental properties.

Identity

Philosophical logicians usually distinguish between qualitative and numerical identity. The former can hold between one object and another, meaning exact similarity (we can also define a notion of partial qualitative identity). Numerical identity (which from now on I will simply call identity) is supposed to relate objects only to themselves: nothing can be identical, in this sense, to an object that is not it. It is supposed that every object stands in this relation to itself, using “object” in the most capacious sense to include numbers, properties, functions, processes, etc.  Identity appears to hold even between fictional objects and themselves—Sherlock Holmes is identical to himself. So the relation of identity is absolutely universal; moreover, it is necessary—everything is necessarily identical to itself. This is not true of qualitative identity, since it can be contingent that two objects are exactly similar. It is commonly accepted that the identity relation holds trivially of everything: just by being something an object is self-identical. For this reason some people have felt that identity is a pseudo relation—that there is something suspicious about it. It does seem exceptionally uninformative to be told that an object is identical to itself (tell me something I don’t know!). Anyway it is supposed that we know what we are talking about: we know what “identical” means in this special sense—to the point that we can recognize the concept as fishy in some way. But do we really know what identity is in the intended sense? Do we have a genuine concept of identity? Can we articulate what we mean by the word?

            It might be thought that we have a number of possible avenues of explication available: Leibniz’s law, a famous dictum of Frege’s, and the involvement of sortal concepts in identity.    [1] Taking the last first, it is sometimes said that identity statements are incomplete without the specification of a sortal, as in “Hesperus is the same planetas Phosphorous”; accordingly, identity is sortal relative, or at least sortal dependent. Thus we can explicate the nature of identity by saying that it essentially involves the kinds of objects—same planet, same animal, same number. It is not just an elusively bare abstract relation that holds indifferently of everything thing there is (and is not); it has specific concrete substance (in the Aristotelian sense of “substance” as well). But this doctrine cannot be right: it confuses identity statements and identity facts. Maybe statements of identity need sortal supplementation (or maybe not    [2]), but the nonlinguistic fact of identity surely does not. How can an object’s identity with itself depend on its kind? What does that even mean? Does it mean that there is no relation of identity except one that incorporates a sortal kind—as with planet-identity, animal-identity, and number-identity? But it is hard to see what this is supposed to mean: aren’t these all instances of identity tout court? Isn’t there an overarching relation of simple numerical identity? Nor is it clear how much elucidation this doctrine affords: we are still left wondering what the import and point of identity is supposed to be. I am the same human being as myself: big deal, what’s the point of saying that? We have a bunch of sortal-relative identity relations, but we still don’t know what they are exactly—and why objects bother to instantiate them. What does it mean to say that x is the same F as y? What is this sameness with oneself?

            Here we reach for Frege’s famous dictum: identity is that relation a thing has to itself and to no other thing. This is ritually intoned, as if it contains self-evident wisdom, but it is not critically examined. The thought is that other equivalence relations don’t satisfy the definition because they can relate an object to other objects: for example, I am the same height as myself, but also the same height as other people—whereas I am identical to myself, but not identical to anyone else. The identity relation can only relate an object to itself, but other equivalence relations can hold between an object and itself and other objects. There are three problems here. First, what about a universe empty save for one object? In such a universe sameness of height does not relate me to other objects, since there are none—so it would count as the identity relation according to Frege’s dictum. Intuitively, what have other objects got to do with my self-identity? Not relating me to other objects can hardly count as essential to my identity with myself. Second, the dictum is circular if offered as a definition: for we need to understand what is meant by “other things”. Surely this phrase means “things not identical to the given thing”, but then the concept of identity is being presupposed: you already have to grasp what identity is before you can understand Frege’s dictum. Third, and most telling, the dictum doesn’t single the identity relation out even in the actual world; other relations satisfy Frege’s condition. Take the part-whole relation: certain objects stand in this relation to me, but they don’t stand in this relation to anyone else. My right arm is part of me but not part of anyone else—so the part-whole relation holds between me and parts of me but not between me and parts of other objects. You might object that the part-whole relation doesn’t relate me to myself but only to parts of me (unlike the same-height relation), but consider the relation of improper part: that does relate me to myself but not to anyone else—I am not a part, proper or improper, of anyone else. Yet part-hood and identity are not the same relation. This could have been expected on intuitive grounds, because Frege’s dictum is very general—identity is being said to be anyrelation that relates an object to itself but not to anything else. That is unlikely to single identity out uniquely, save per accidens (this why it fails for the single-object universe). The dictum fails to capture the specific idea of numerical identity. Not that Frege meant it as a strict definition (he was too circumspect for that) but more as a useful heuristic; in any case, it doesn’t help with the task of giving the notion of identity clear content. We can’t complacently cite the dictum as explaining what that concept consists in.

            Third, we have Leibniz’s law of the indiscernibility of identicals: does this tell us what we are talking about when we talk of identity? The law has the advantage of being true, indeed necessarily true, but it is limited as a method for explaining the concept of identity. It offers only a necessary condition to begin with, and the converse principle is far from self-evident on a natural understanding of it (i.e. the identity of indiscernibles). But the main problem is one of triviality: what precisely does this law assert? It is awkward to state because we have to say something like, “If two objects are (numerically) identical, then they must share all their properties”. Two objects? We blushingly shift to using variables: “If x and y are identical, then they must share all their properties”. But this is scarcely any better—x AND y? What is really meant is just that an object is always exactly similar to itself: an object is always qualitatively identical to itself. Where there is numerical identity there is qualitative identity. True enough, but does it help with understanding the concept of (numerical) identity? We are being told that objects always have the properties they have and no others—again, that is hardly news. But worse, it uses qualitative identity to explain numerical identity: it derives the latter concept from the former. Construed as an effort to get a handle on identity proper, it invokes qualitative identity, stating weakly that objects are always exactly like themselves. Surely we are entitled to expect something better—something meatier, more apropos (but see below). So we are still lacking any decent account of what this alleged special relation of numerical identity comes to—some kind of elucidation, analysis, insight. Instead we just have the identity relation staring blankly and inarticulately back at us, hoping we will somehow get the hang of it. It seems unnervingly self-effacing.

            At this point the disturbing figure of the skeptic enters the conversation: what if there is no such relation as identity? It is proving so elusive because it isn’t really there. What do we mean when we say an object is identical to itself—what are we thinking? Nothing, according to the skeptic: our wheels are spinning, our thought process deceiving us. It might be contended, skeptically, that the concept has its origin in certain epistemic and linguistic practices but that it has no reference in objective reality; it is a kind of illicit projection, a phantasm of the intellect. Things are not round and heavy and red and self-identical: that last is just not a real property of things, but a reification of our epistemic and linguistic practices. We often don’t know that we are dealing with a single object and can therefore discover the truth of a statement of the form “x is identical to y”, but that doesn’t imply that the real world contains objective identity relations. The concept of identity is useful to us in recording our epistemic dealings with the world, but it shouldn’t be taken to denote a genuine constituent of objective reality—for what kind of constituent is it? Do we see or touch it, or need it in our scientific theories, or feel it in ourselves? Why not just admit that it isn’t part of a truly objective conception of things (perhaps rather like the commonsense concept of an object). There are objective similarities between things to be sure, and we can speak of things as indistinguishable, but the idea of numerical identity is a chimera. So says the skeptic, and he is not without rational grounds for his opinion. However, the position is extreme and I am inclined to suggest something weaker, though in the spirit of the skeptical position. This is that talk of numerical identity is best interpreted as an extension of the concept of qualitative identity, which is perfectly meaningful: to say that an object is identical to itself is just to say that it is exactly similar to itself. Two distinct objects can be exactly similar, thus warranting talk of identity between them (“these two balls are identical”), and a single object can be exactly similar to itself too. So there is not an extra primitive relation in the world called “numerical identity”; this talk is really just the application of the concept of qualitative identity to solitary objects. Every object is qualitatively identical to itself—that is, every object is self-identical in just the sense that two objects can be said to be identical. There is really just the concept of qualitative identity, and it can hold between distinct things or one thing and itself. Of course, statements of qualitative identity between an object and itself are trivially true, but then so is the proposition that every object is self-identical. An advantage of this way of seeing things is that we need not recognize any ambiguity in the word “identical”: it always means so-called qualitative identity. And there is little intuitive plausibility in the view that “identical” varies in meaning as between a numerical and a qualitative sense. If this position is correct, there is no identity relation such as philosophical logicians have supposed—no separate kind of identity; there is just a single relation of similarity—but objects can stand in this relation to themselves. To be self-identical is to be self-similar. I am completely similar to myself, hence “self-identical”. We can easily specify what this identity relation consists in: the sharing of properties. We know what properties are and we know what sharing them is—well, that is what identity is all about. This relation can hold between several objects and it can hold between a single object and itself. If I say that I am identical to myself, I am saying that I am exactly similar to myself—just as I can be similar to other people (perhaps exactly similar). The statement is no doubt peculiar, because hardly disputable, but it is the interpretation that makes the most sense of identity talk; it’s either that or skepticism about the whole concept. We could try maintaining, feebly, that the concept of numerical identity is primitive and inexplicable—simply not capable of any articulation—but that seems unattractive in the light of the alternatives. It is preferable to hold that so-called numerical identity is analyzable as reflexive qualitative identity. After all, that relation clearly exists and has a clear content—why introduce anything further?

            What are the consequences of this revision in the way we think of identity? All those puzzles of identity must now be recast in terms of self-similarity, as must the idea of a criterion of identity. This may not (should not) make a difference to the substantive issues, but to be clear in our mind we should think in the recommended terms. There is nothing real to identity over and above self-similarity. And since philosophy is very largely concerned with questions of identity, particularly the identity of concepts and properties, the revision must have an impact on how we understand philosophical questions. Concepts (meanings, intensions, properties) can be exactly similar to themselves, this being what concept identity comes down to. If the concept of knowledge, say, has a property not possessed by the concept of true justified belief, then the two concepts cannot be identical; for then the concept of knowledge would not be qualitatively identical to the concept of true justified belief. Identity is always qualitative identity, so concepts can’t be identical unless they share the same qualities (this is Leibniz’s law in another form). In a way the concept of identity already contains Leibniz’s law, because what it means to say that x is identical to yis defined as sharing the same properties. It is not some further tacked on thesis that identical objects are always exactly alike: self-identity simply is sharing the same properties—x being identical to x just is x being qualitatively identical to x. This is why Leibniz’s law is so self-evident: it is really a kind of tautology. This is as it should be.    [3]

    [1] I have consigned to a footnote another familiar attempt to explicate identity because the attempt barely gets off the ground and is lamentably confused, namely that identity is a relation between signs. That is, for objects to be identical is for them to be the single denotation of two terms. The trouble, obviously, is that object identity can’t depend on language. Still, the suggestion is helpful in illustrating what a substantive account of identity might look like: at least we are given a nontrivial analysis of the concept (just a wrong one). Compare: identity is the co-reference of ideas in God’s mind—substantive enough but none too plausible.

    [2] The sortals go into the fixation of reference not the type of identity relation involved, as in “that elephant is identical to that elephant” said while pointing to different parts of the same elephant. But objects cannot be incomplete in the way bare demonstratives are.

    [3] Old hands will see the imprint of several philosophical logicians on what I write here (Geach, Wiggins, Kripke, and others). It should be evident that what I say is radical to the point of heretical—I myself have always assumed that numerical identity is transparently a concept in good standing. I am as shocked as anyone by the skeptical reflections herein sketched (contrast my Logical Properties (2000), chapter 1). 

Philosophical Destruction

The destructive impulse is particularly conspicuous in philosophy. We are forever refuting, criticizing, rejecting, disagreeing, ridiculing, dismantling, tearing down, cutting to pieces, grinding to a fine powder, annihilating, and otherwise smashing to smithereens (or sometimes mildly amending and carefully reformulating). We also construct and create, but a lot of the time our aims are less positive. Why is this? It doesn’t seem to be so in other disciplines, or at least not to the same degree: physicists and biologists don’t spend most of their time ripping each other to shreds, or even correcting and revising what others have to say. They are too busy in the lab or field, discovering things, contributing to human knowledge; but we philosophers always seem to be at each other’s throats. Thus critical acumen is much prized in our field—so-and-so is said to be very “sharp” and a demon with the deft counter-example. Reputations can be built around one “devastating” criticism. Entire philosophies can be primarily destructive: empiricism, positivism, ordinary language philosophy, Wittgenstein in both his periods, Quine much of the time, Berkeley’s idealism, Hume’s skepticism, existentialism, neurophilosophy. There is nothing wrong with that: philosophy really is a highly critical discipline. The whole subject is infused with negativity. Is it because philosophy is so hard? Is it that philosophical problems are so resistant to solution? It’s easier to criticize than to construct, destroy rather than create. We are frustrated by our chosen subject, but we can at least vent our frustrations in bouts of mutual destruction, otherwise known as civilized debate. This can be enjoyable enough, thrillingly ego-driven, and even fairly amusing—better than banging your head against a brick wall. I get a kick out of it anyway. The predominant feeling you have when trying to construct something in philosophy is a sense of vulnerability: someone is going to destroy what you have struggled to create, undermining your carefully constructed arguments, and gutting you intellectually. This is not a fun feeling; better to rip into someone else and watch the feathers fly. Yes, it’s faintly discreditable, a bit of a cop-out, but at least you are achieving something with your time (that arduous education has not gone completely to waste). Or you could just become an historian.

            But let us analyze the destructive impulse in philosophy further: what is philosophical destruction? What are you aiming to do, and for what purpose? The OED puts us on the right track (as always): “destroy” is defined as “put an end to the existence of (something) by damaging or attacking it”. We are informed that the English word derives from an Old French word destruire, which is constructed from de expressing reversal and struere meaning “build”. Thus “destroy” literally means, “de-build”. It is like “depopulate” or “desegregate” or “deactivate” or “deconstruct”. This suggests that you cannot destroy what has not been built (though that concept is quite flexible and is not limited to human artifacts): it sounds funny to speak of destroying a heap or a wreck or a mess or even a random chunk of rock—for none of these things bespeaks constructive purpose. You primarily destroy what has been created, generally with a purpose in mind: human artifacts, human lives, animals, plants, buildings, systems of thought, arguments. Destroying is the opposite of building. Also, according to the dictionary, it involves two elements: existence and damaging by attacking. First, the thing destroyed has to exist: you can’t destroy what has no existence (fictional characters, hallucinated rabbits, meaningless jumbles of words). Second, the destruction (the “putting out of existence”) is accomplished by means of an aggressive act—attacking and damaging. This latter point is important: there is no avoiding the involvement of violence in philosophical criticism. You can’t destroy (demolish, decimate) an argument or a position without doing violence to it—as you can’t destroy a material object without doing violence to it. We may as well own up to this and not pussyfoot around: philosophical destruction is inherently aggressive, necessarily a form of attack (not on the person, of course, but on the position being destroyed). The aim is to put that position out of existence, i.e. refute it—overtly and publicly. Ultimately this means that we want to destroy belief in that position: we want to take existent beliefs and put them out of existence. That is what it is to put a philosophical position out of existence—to destroy belief in it. If I am trying to refute a certain position, I am aiming to destroy whatever belief others may have in that position: I am trying to eliminate a part of the other’s mind, or a component of his or her mental state. This is why it is apt to speak of destruction in connection with philosophical (and other intellectual) criticism: criticism is not intended to leave your mind unchanged, your beliefs happily intact. Let me be a touch melodramatic: refutation is murdering beliefs—putting them out of commission, consigning them to the Big Sleep. It is outright belief annihilation.    [1] So there is always something pugilistic and gladiatorial at play in philosophical disputation: a life is at stake, namely the life of the participants’ beliefs (opinions, commitments). Something is liable to go out of existence during a philosophical argument. No wonder there is resistance, tension, risk, fear, self-defense, and an atmosphere of combat: something’s very existence is at stake, often beliefs that have taken a lifetime to arrive at (all that work and puff!). We can also note that there is something godlike about the activity: the creative artist is often compared to God on account of her ability to bring things into being apparently from nowhere, but the power to destroy is also a feat of existence alteration—putting things out of existence. God has this power too, in abundance, and we humans can exercise it ourselves in more limited ways. No doubt the literal murderer relishes exercising this awesome power. Just so the philosophical “murderer” can relish his power to destroy positions and belief in them: look how I just annihilated that poor shmuck’s position! We humans have power over existence (as existence has power over us) and philosophical creation and destruction partake of that power. Don’t you think the positivists relished the destructive power of their philosophy? They put those babbling metaphysicians to the guillotine! They didn’t have much constructively to put in its place (the dirty little secret of positivism), but they could certainly do a tremendous amount of damage to existing belief. Their weapon of choice was the verification principle: wielding this sharp-edged sword they could cut traditional philosophical thought to pieces. It was a rotting zombie anyway, in their considered opinion, so it may as well be put out of its misery. On a lesser scale of destructive euphoria, we have the work of Strawson on Russell’s theory of descriptions, Quine’s “Two Dogmas of Empiricism”, Gettier on the analysis of knowledge, Kripke on the description theory of names, and Grice on conversational implicature—to pick some examples pretty much at random. And there is nothing in principle wrong with such destruction (or purported destruction)–with such aggression and annihilation; as I remarked, it is an essential part of philosophy. Philosophy is supposed to be destructive (though not only destructive).    [2]

            And here we run up against a further category of philosophical destruction (perhaps my personal favorite): destroying the destroyer. The positivist gunman swaggers into town ready to do some serious destroying: in his sights lie all traditional metaphysics, much of morality, and a good deal of science. Then the wily sheriff (silent, gruff) steps nimbly forward to stem this tide of destruction, revealing the blustering stranger as a fake and a wimp—a no-account loud-mouthed nobody. His draw is slow and his aim shaky: he gets handily refuted before he can do much damage (though there was that unfortunate business with the town drunk in the saloon, poor old Jeb). This is what was so gratifying about Grice on implicature and Kripke on necessity: they destroyed the would-be destroyers. They wielded superior weapons and exhibited superior skills, and the opposition went down. In so doing they resurrected ideas deemed extinct, bringing traditional questions back to life. For it is never a happy moment when a philosopher kills off an idea that doesn’t deserve that fate; and we welcome the savior who restores to life what had been thought extinguished for good. Even the problem of consciousness has been thought extinguished, only to come roaring back to life once certain misguided ideas have been exploded. So we must always be on the lookout for opportunities to reverse previous acts of wanton destruction (or alleged destruction). I would say the same for a lot of what Wittgenstein has been thought to have terminated; ditto for Quine. So I particularly relish the dismantling of such would-be destroyers. Destruction sometimes needs to be destroyed in turn.

            We should distinguish two sorts of destructive philosophical act: destroying existing philosophical theories and destroying common sense (or possibly parts of accepted science). Philosophers are generally perfectly comfortable with the first sort of destruction, but the second is regarded as far more problematic. Preventing commonsense belief from destruction may involve destroying the arguments of anti-commonsense philosophers. It is, of course, controversial what counts as part of common sense (Berkeley’s idealism being a famous case), but we usually know if commonsense belief is being criticized. Overtly nihilist positions are typically destructive of common sense, intentionally so: asserting that nothing exists must surely count as destructive in this way. This is the analogue of destroying noncombatants in a war: other philosophers are soldiers in wars of mutual destruction, but ordinary folk are the equivalent of peaceful civilians. They are more likely to be invoked in the battle against opposing philosophers than made victims of destruction themselves. Scorched earth tactics against civilians are not most philosophers’ style, while the belief systems of other philosophers are considered fair game. If you go into philosophy, this sort of aggressive action is only to be expected. You can avoid it only by not sticking your neck out, possibly limiting yourself to destructive philosophy and never venturing anything constructive of your own (though you must cover yourself against destroyer destroyers). Frege is a good example of a philosopher who does the opposite: though he certainly offers criticisms of positions he is against (e.g. psychologism), he mainly tries to construct something positive. He erects an impressive edifice, systematic and precise, thus exposing his creation to possible destructive criticism (Russell’s paradox was surely a heavy blow). He is perhaps the most constructive analytical philosopher ever. Wittgenstein, by contrast, is relatively destructive. Russell lies somewhere in between. Quine is largely destructive, with occasional gleams of creativity. Kripke is a bit of both. Socrates was entirely negative. Plato and Aristotle leaned positive. And so on: each philosopher in the canon can be considered as a destroyer or as a creator. I myself am quite fond of a bit of philosophical destruction, but I also have a weakness for construction—so I am well aware of destructive efforts aimed in my direction (again, nothing wrong with that).    [3]

            What are the devices of philosophical destruction, its techniques and technology? They are well known to the trained philosopher: the detection of fallacies, the exposure of non-sequiturs (both subtle and gross), producing counterexamples, exposing use-mention confusions and type-token errors, and so on. With these weapons we carry out our destructive work, and valuable work it is. Logic is best seen in this light: it is a device of destruction, the equivalent of a deadly weapon of war. It isn’t used much for constructive purposes (not counting logicism and ascriptions of logical form), but it is the bread and butter of discursive demolition. Logic is what we wield when we set about demolishing a position—its main purpose is destructive. It is concerned with exposing logical fallacies rather than constructing logical arguments; its function veers negative. It is all about what does not follow. This should be built into the way logic is taught: it is a machine for winnowing out faulty reasoning. It isn’t a method for having new ideas but a device for destroying existing ideas (bad ones). I mean this in a broad sense of “logic”—not just propositional and predicate calculus but informal logic too (also induction and abduction). Logic is concerned with evaluating reasoning, and evaluation implies criticism, which implies destruction. Accusing someone of begging the question, say, is a destructive act: what the speaker just said has been reduced to rubble. Again, we should not pussyfoot around about this: philosophical expertise is like the expertise of a demolition man—both are good at destroying buildings, physical or intellectual. Both do valuable work, by clearing sites of rickety old buildings so that new ones can replace them. Philosophical destruction, recognized as such, is nothing to regret or feel ashamed of. It is the engine of truth.    [4]

    [1] There are echoes of Popper’s “critical philosophy” here—the emphasis on refutation and falsification instead of verification. Popper thinks that scientific progress occurs mainly by a process of elimination, much like natural selection: we don’t proceed by confirming good theories but by falsifying bad ones. Destruction of accepted theories is thus the engine of scientific advance. We might call this “discovery by destruction”. Philosophy, for a Popperian, is similar: the elimination of theories that fail to stand up to criticism. The counterexample is the engine of philosophical advance. Aggressive criticism is the means of achieving philosophical truth.   

    [2] Let me indulge in a medical analogy: it is part of medicine to destroy pathogens, the better to improve health. This destruction is essential to medicine and not at all sinister. Wittgenstein compared philosophy to therapy, which emphasizes improvement on the part of the patient; but he never explicitly drew attention to the point that destruction can also be part of the process (though he was himself flagrantly destructive). In fact, even Freudian psychotherapy has a destructive component, since harmful neuroses and repressions need to be destroyed (talking was supposed to do that). Isn’t psychiatry really concerned with the destruction of mental illness, using drugs, ECT, brain surgery, behavioral modification, and what- not?

    [3] If I ask myself what are my favorite examples of philosophical destruction, the answer comes back: Frege’s criticism of Mill’s theory of numbers, and Leibniz’s criticism of Locke’s theory of ideas. And who could not love Chomsky’s demolition of Skinner’s Verbal Behavior (though this is not strictly philosophy)? These all contributed massively to human thought.

    [4] Of course, there is a psychology and sociology of intellectual destruction in academic culture that can only be described as deplorable. I cannot even bring myself to discuss this lamentable subject. Its chief defect is confusion(the harshest word in my vocabulary).