Today I read this sentence in the book review section of the New York Times: “An interesting , sciencey explanation of the Y chromosome in all it’s vagary and confusion, and the strange trip through the behaviors of the life span of the males of many species.” This is from Mark Morris in By the Book. It is semi-literate in several ways, including not being a complete sentence, but what caught my eye was the grammatical error of using “it’s” instead of “its”. I assume Mr. Morris initiated the error, but think of how many pairs of editorial eyes failed to detect and correct it! And this is the book review section of the New York Times! Is there really no hope for civilization? I would fire the people responsible. Are they trying to promote illiteracy? I felt more despair at this than the many other outrages I have seen recently in this country.
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The concept of intelligibility is often used by philosophers but not often analyzed. The OED gives this simple definition of “intelligible”: “able to be understood”, but it follows that up with a definition proper to philosophy: “able to be understood only by the intellect”. The intellect is the faculty that makes things intelligible; without it nothing would be. Clearly, intelligibility is a relational concept: something (we are not told what) is intelligible only if it is understood (possibly potentially) by someone, or by someone’s intellect. Logically, the concept is like being perceivable or knowable: a non-mental entity is said to be perceivable or knowable or intelligible in relation to a mind equipped with certain cognitive powers. We might paraphrase the dictionary definition by saying that something is intelligible if and only if it is graspable by the intellect (not by the senses or the faculty of knowing): it is intellectual apprehension. But what is that exactly? One tradition has it that intellectual apprehension belongs to the domain of the a priori—mathematics, logic, the forms, maybe philosophy itself. But it would be wrong to limit the concept to these areas, since the empirical world can be intelligible too, i.e. understood by the intellect. This is a special kind of cognition, distinct from perception and knowledge—superior, deeper, more penetrating. In it the world is made peculiarly transparent to the mind, not in a blur or superficially or inadequately. It is, we might say, an elevated type of insight, not to be identified with simply knowing brute facts.
What would count as paradigm instances of the intelligible? Mathematics is the standard example, both pure and applied. Numbers and geometric figures are inherently intelligible, but so is their application to the world: when we describe the world mathematically we make it intelligible, because we make it graspable by the intellect. Mathematical laws are the central examples. This doesn’t mean that everything in physics is intelligible, but the common assumption is that physics is our best hope of rendering the world intelligible–and mathematics is central to physics. However, there is another area of intelligibility that should be mentioned—belief-desire psychology. We make actions intelligible by relating them to beliefs and desires: actions are intelligible in the light of the beliefs and desires that lead to them. We render the action rational by describing it in this way, and hence we understand it; there is nothing brute or opaque about it. Just as with mathematics, there is a whiff of the a priori: the idea of rationality as a normative domain is invoked–hence the practical syllogism. In both cases an ideal structure is brought to bear on concrete reality, thereby rendering it intelligible. This is not something we detect with our senses; we apply it, by means of the intellect, to the things we perceive. We render the world intelligible rather than see it to be so.
I am inclined to suppose that these are the only cases of intelligibility in the natural world. Mere perceptual knowledge is never by itself intelligible knowledge; nor is causal knowledge, since it merely tells us what causes what, not what abstract principles underlie the causal connections. Physics might tell us that gravity causes motion, but without a mathematical law this does not render nature intelligible. Animals can have perceptual and causal knowledge, but they don’t have intelligible knowledge of the kind delivered by mathematical physics. Cartesian mechanism was supposed to make the physical world intelligible and it was a quantitative account of matter and motion. The case of biology is interesting: it is not generally thought of as having an a priori component, but it is supposed to provide understanding of the biological world. Does Darwin’s theory make evolution intelligible? It has a mathematical side because it uses the notion of frequency—advantageous traits lead to greater frequency in the population than disadvantageous ones. And we can quantify many aspects of animal behavior and genetic propagation. But there is also the teleological notion of function, which brings biology close to psychology: the heart beats as it does because that is its function (compare: a person beats a drum because he desires to). It is as if bodily organs desire to do what it is their function to do. Moreover, the standard way of understanding natural selection is analogous to intentional selection by agents—nature selects certain organisms to survive as selective breeders do. So biology falls under teleological conceptions and hence inherits the intelligibility that belongs to such conceptions (it is the same for theories that attribute evolution to God’s design). Thus biology is not a clear counterexample to the thesis that mathematics and teleology are the sole types of intelligibility. Merely knowing that clouds cause rain does not render the cloud-rain nexus intelligible: we must either treat it mathematically or conceive it teleologically to do that. In fact, the mathematical method works in this case because we can describe clouds as aggregates of water droplets subject to mathematically describable forces—rain thereby becomes intelligible.
Are these two modes of intelligibility unrelated? They certainly seem so at first glance: mathematics is one thing, psychology another. But perhaps there are some significant commonalities or areas of overlap. Psychology has its quantitative aspects, both scientific and common sense; in particular, we have the ideas of strength of desire and degree of belief. These are formalized in decision theory, a mathematical theory; so ordinary psychological understanding is capable of mathematical formulation in addition to being teleological. There is also a good deal of mathematics in the psychology of perception and elsewhere. We thus have a kind of double intelligibility in psychology, though the mathematical component is not as salient as it is in physics. In the case of mathematics itself, we can ask whether it has any teleological dimension, any built-in purpose. Formalists might say so, relying on the notion that mathematics reduces to symbolism and symbolism has a purpose; an instrumentalist view of mathematics would then be indicated. The same can be said for intuitionism: mathematics is a mental construction and that construction has a purpose—it is a kind of mental artifact that we employ in certain ways. Mathematics has a purpose and our application of it to the empirical world is the fulfillment of that purpose. Platonism, however, seems to banish purpose from mathematics, viewing it as a non-human objective realm of reality that pre-dates human existence. But that is not so clear on reflection: for there is an uncanny fit between mathematics as an abstract inquiry and the nature of empirical reality. For example, numbers are remarkably useful for counting objects, and geometry seems tailor made for describing objects in space. Is this just a happy accident? One could swear that mathematics was designed so as to be applied in these ways. Yet, according to Platonism, mathematical reality follows its own internal rules and was not constructed by human minds in any way. Its usefulness is therefore entirely contingent, extrinsic to its inner nature. Thus Platonism pulls away from the idea that mathematics has a purpose that is realized in its applications.
Here an ingenious theist may spot his chance: God designed mathematics to be both an objective abstract structure and imbued with purpose! His relation to mathematics is like our relation to our machines: both are objective constituents of reality but both are also purposive. Mathematics is objective-cum-functional. So even Platonism may be understood (at a stretch) to incorporate a teleological dimension, though obscurely so; in which case, it shares something with psychology. The two are not then completely separate conceptually, though it would obviously be wrong to reduce one to the other. If so, we have a more unified or integrated theory of intelligibility than we might have hoped for: our two paradigm cases turn out to have more in common than appears at first sight. We might even speak of the “teleological-mathematical” as the cornerstone of intelligibility: this joint conceptual structure is the key to making nature intelligible to ourselves—transparent to the intellect. Where it applies we have intelligibility–otherwise we don’t.
And what about unintelligibility? What are the paradigm cases of that? Nonsense is surely at the top of the list—garbled speech, ungrammatical sentences, and rampant non sequitur. Here we can make no sense of what we hear: the words don’t add up to a semantically coherent whole. The purpose of words is to join with other words according to rules to produce meaningful sentences, but in nonsense speech this purpose breaks down. The combinatorial power of grammar, itself a type of computational structure, fails to apply to nonsensical products. There is an absence of both fulfilled purpose and mathematical order: it is like saying, “Zero plus addition over prime number equals infinity”—mathematical nonsense. In nonsense abstract form and purpose fail to apply. And the same is true of actions in general: a person’s actions are said to be unintelligible when we can discern no purpose in them, when even the abstract structure belief and desire fails to apply. We also find unintelligibility in science—quantum theory being the prime example. The idea of God playing dice with the universe is an expression of teleological chaos at the root of things—what could God’s purpose be in playing cosmic dice? We feel we cannot make sense of things if no agency could ever act as reality is thought to demand. In the case of the mysteries of mind we also use the notion of unintelligibility—for example, the nexus of consciousness and the brain is said to be unintelligible. Here again we have no coherent mathematics to apply and it is difficult to see how the brain can fulfill the purpose of producing consciousness. If we could see how an agent could build a brain so as to mathematically guarantee that consciousness would be the result, then we would regard the psychophysical nexus as intelligible; but we lack any such understanding, so we declare the connection unintelligible, at least for now. Thus the scaffolding of intelligibility applies in some areas but not in all, more or less dramatically. We can bring it to bear in some cases but not in every case. It is the idea (and ideal) of making intellectual sense—conformity to the paradigms of mathematics and commonsense psychology being the model.
We try to extend the paradigms into various corners of the world; sometimes we succeed, sometimes not. If we lacked these conceptual structures, nothing would be intelligible to us—we would at best have perceptual and causal knowledge (as we may presume is the state of animal cognition). The special type of comprehension that we call intellectual understanding is constituted by these two types of thinking—the mathematical and the teleological. They afford us a kind of transparency and order not available otherwise. And notice that they are not perceptually based: we don’t see the world as mathematically or teleologically ordered; we bring these notions tothe given, rather than deriving them from it. They are not licensed by strict empiricism. There is something projective at work here—imposed, self-generated. We make the world intelligible; we don’t find it to be so—except in the sense that we discover that things turn out that way. We apply our intellect to empirical reality and thereby render it intelligible; we don’t have impressions of intelligibility as we have impressions of color and shape. Intelligibility is not a sense datum.
Some strains of thought have it that the world is actually not intelligible at all, not as an objective trait of reality. Instead we force it into an appearance of intelligibility by imposing our own minds on it. Thus nothing is inherently teleological or mathematical: there is no purpose in psychology and the physical world is not a mathematical structure. Ideally, we should banish both ways of thinking from psychology and physics: no goals and no numbers. One need not agree with this point of view to appreciate its motivation: goals and numbers are not part of the given but a conceptual apparatus that we bring to bear in order to organize the facts. They are how weunderstand things not how things are in themselves (phenomenal not noumenal). Thus we cannot really make sense of the world, only our apprehension of it; in itself the world is without sense, not subject to intellectual comprehension at all. It is all, as the saying goes, just one damn thing after another, without rhyme or reason. To say that the world is intelligible can only mean that we can apply the apparatus of mathematics and teleology to it in order to organize our knowledge, but it is quite indifferent to these invocations. This is certainly an intelligible position to take on intelligibility, to be set beside the more realist position that goals and numbers are part of the fabric of objective reality. I won’t attempt to decide the issue, though I incline to the realist view.
 The same is true of exercises of theoretical reasoning, i.e. acquiring beliefs by rational processes: here we use logic, a normative discipline, as a means of rendering belief formation intelligible. It is like applying mathematics to empirical reality.
 It is sometimes supposed that the touchstone of intelligibility is conformity to commonsense categories and principles, as with the idea that causation works only by physical contact. But conformity to common sense is neither necessary nor sufficient for intelligibility: much of physics is not part of common sense but quite intelligible (the same is true of pure mathematics), and some commonsense categories are not intelligible (at least presently)—such as consciousness and free action, arguably. Moreover, common sense has little to do with specifically intellectual knowledge as opposed to practical knowledge.
 We can compare mathematics with morality in this respect: moral realism can be combined with a functional view of morality. Its truths are not dependent on the human mind, but they fit human life remarkably well, as if designed to do so. Morality is not irrelevant to human life, even if its basis is extra-human. Indeed, we need to be able to combine both moral realism and moral relevance in order to give a satisfactory account of morality, as we also do in the case of mathematics.
 I have not discussed the extremely controversial question of whether philosophy itself renders the world intelligible. The question turns on the nature of philosophy and the form of its findings. Let me just remark that concepts have a purpose and that the notion of a calculus of concepts is not to be rejected out of hand. On the other hand, philosophy is the domain of mystery par excellence.
Our Unified Universe
Imagine a universe in which mind, matter and mathematics all exist but stand in no interesting relation with each other. Minds don’t know any mathematics, mathematics has no application to matter (or mind), and mind and matter have no causal interaction or even correlation with each other. The three merely coexist in this universe as separate realms with no connection. It is not a unified universe but simply a three-element universe—a mere list not an organic whole. The parts don’t interlock and function together but merely exist alongside each other. In particular, the minds in this universe don’t understand mathematics and apply it to reality; mathematics simply exists abstractly, not even being true of the rest of the universe. Think of it as an ontological trinity without connecting relations: each realm has a robust existence but they are totally cut off from each other. They are a Many that does not correspond to a One (except the set consisting of all three). It would be hard to think of any design to this universe; it seems gratuitous, random, and pointless—just three types of being idly sitting beside each other (and not even that, because “beside” expresses a spatial relation). They are non-communicating cohabitants not collaborating members of a team. They leave each other completely alone in splendid isolation. If a super-being had created this universe, you would wonder what its purpose was—a cosmic storeroom perhaps? Each component has its own reality and set of truths, but there is no inter-category impingement and hence no higher unity.
Our universe is not like this; indeed, the universe described is the negation of ours. We have the same set of basic categories, but our categories interact in substantial and meaningful ways. Our minds do grasp mathematics, mathematics does apply to the world, and mind and matter interact in manifold ways. We can picture our universe as a triangle with mathematics at the apex and mind and matter at the two base angles. A line connects mind to mathematics with an arrow pointing upwards (this is understanding mathematics); the opposite line connects mathematics to matter with an arrow pointing downwards (this is mathematics applying to the world); and the two base angles are connected by arrows pointing both ways representing causal interaction. This last involves perception of matter by mind, dependence of mind on brain, and possibly the origin of mind in matter. In virtue of these relations the three-part structure functions in a certain way: mind and matter enjoy causal commerce and are deeply connected, while mind uses mathematics to describe and explain the world by exploiting the fact that mathematics applies to the world. It might be said that matter causes mind, which understands mathematics, which applies to matter. Mathematics is not cut off from mind and matter at all, as in the previous universe, and mind and matter are closely intertwined. This is not mere cohabitation but close collaboration.
None of the relations I have described is philosophically unproblematic; in fact, they constitute some of the deepest problems of philosophy. How does the mind come to grasp and know mathematical truth, especially given a Platonist understanding of it? This can’t be a causal relation, but then how does the mind make the connection? Similarly, why is mathematics applicable to the world? If mathematical truth concerns an autonomous abstract world, why is there an uncanny fit between it and empirical reality? How is mathematical physics even possible? And the mind-body problem is too well known to need exposition: how does psychophysical interaction occur? Is the mind the same as the body or separate from it? Nevertheless, these relations evidently exist, puzzling and mysterious as they are. They lead to a variety of familiar theories: materialism declares all three realms to be variations on matter, so that all the inter-category relations reduce to physical relations; idealism makes all three mental, thus eliminating ontological gulfs (matter and numbers being mental constructions); and dualism (or pluralism) affirms the reality of all three and lives with the accompanying mysteries, maybe invoking divine assistance (pre-established harmony and so on). These problems don’t arise for the list-like universe, because the problematic relations don’t even obtain there; but that is not our universe. Our universe consists of interlocking parts in which ontological chasms are routinely crossed: we do know mathematics, mathematics applies to extra-mathematical reality, and mind and matter are on intimate terms. Our universe is structured by these relations: psychophysical causation, mathematical knowledge, mathematical application. The first relation has received much attention, but the other two should not be neglected.
I submit that our universe qualifies as an organic unity, unlike the unstructured universe. I don’t mean that it is literally a living thing, only that it works as a unified whole (as a machine does): it has parts that work together. One might venture to suggest that mathematics exists in order to be known and applied to the empirical world, while mind owes its efficacy (and maybe its existence) to the material world. In the other universe each category is irrelevant to its companions, but in our universe each category feeds off the others in a kind of cosmic dance (we might picture mathematics as being rather pleased that it is known by minds and applicable to matter). Our universe is unified, a One that encompasses a Many. It is not a mere random set but a functioning totality. An animal body consists of an interacting assemblage of organs not merely a collection of them, so that it constitutes a higher unity; the universe is similar in that its parts do not sit idly by content with their own internal reality but feed into each other to produce results not obtainable otherwise. Physics is one such result, as is science generally (psychology too has its mathematical side). Material civilization is another. These are not possible in the list-like universe, because the requisite relations don’t obtain. This universe seems logically possible, but it is a far cry from our universe with its rich internal structure. If it had been designed by a super-being, one could see the point: the whole arrangement was set up to exploit the relations between the different parts, not as a mere exercise in ontological fecundity. If you wanted to produce beings like us, such a universe would be necessary—not the universe in which disunity reigns. We are psychophysical beings who know and apply mathematics, but this human nature requires the existence of the relations I have been harping on. The mental beings in the alternative universe would have a very different nature, having no commerce with matter and no inkling of the mathematical realm. They would be vastly inferior to us in both power and knowledge, knowing only their own mind and being incapable of shaping the material world (or being shaped by it). The architecture of our universe, by contrast, delivers real dividends and does not provoke the reaction “What is the point?” If you were a god with a strong interest in mathematics and science (but not much concerned with morality), this would be an interesting project to undertake–while the unstructured universe would seem an exercise in futility.
These reflections edge us in a theistic direction, but not of the traditional Judeo-Christian kind. The emissaries of the god who created our unified universe are not Jeremiah, John the Baptist and Jesus, but Euclid, Pythagoras and Plato. This god has little discernible interest in sin, suffering, and salvation, but it evidently has a strong interest in mathematical knowledge and its applications. Its proudest products are Cantor, Godel, Gauss, Newton, et al. It also apparently believes that the psychophysical nexus is the beating heart of things—seeing, acting, feeling—not disembodied contemplation and self-directed introspection. Thus this super-being (let’s not call it “God” or “a god”) created a universe in which these ideals could be realized: a world of embodied minds and knowable mathematical order. And who is to say that these are not worthwhile aims? So we might try to convert the considerations of this essay into an argument for the existence of such a being—only a designer like this can account for the organic structure present in our universe. The disparate parts had to be brought coherently together, which was no easy feat, and is not built into the very ideas of mind, matter and mathematics. On the evidence, this being is not keen to reveal its existence, being more like a scientist conducting experiments than a caring father figure interested in our moral condition (perhaps at this moment the being is saying to itself, “Rumbled at last!”). At any rate, there is a challenge here to explain why the universe in which we live isn’t of the unconnected variety—why it seems so well designed for knitting the separate parts together. There is nothing random or pointless about it. The parts fit harmoniously together, nicely enabling certain things not possible otherwise, such as science and civilization. Even morality finds a place, given the need for concrete moral action and the possibility of a utilitarian calculus (though no doubt our super-being prefers actual calculus). Pythagoras was the true prophet, though (temporarily?) eclipsed by religions of a more worldly and practical bent.
There are two ways to render the universe metaphysically unified. One is to claim that everything is made of the same stuff—hence materialism and idealism. The other is to claim that the various parts of the universe, whether of the same stuff or not, are interrelated in such a way that an organic whole is the outcome. It appears that our universe is of the latter kind, unlike other universes that may be conceived. Perhaps in the logical space of possible universes ours stands out for its organic unity, fortunately for us.
 This isn’t to say that there are no areas of disconnect: we may not understand all of mathematics, some of it may have no application to the world, and mind and matter may harbor aspects that have no bearing on each other. So the links are partial not total; still they exist and are significant.
 As an exercise read Paul Benacerraf’s “Mathematical Truth” and Thomas Nagel’s “What is it Like to be a Bat?” in tandem—the structural parallels should stand out. The best conceptions of mind and mathematics leave their relation to the human organism deeply problematic.
 There is a question about other animals—do they know mathematics too? You might be tempted to say no, but that would be rash: animals live in a mathematically describable world and must be sensitive to mathematical facts. Animals need to be aware of amounts, plurality, size, distance, speed, and so on in order to function successfully (consider migrating birds). True, they are not taught arithmetic at school, but their brains must be capable of elaborate calculations. So let’s not exclude them from the realm of the cognitively mathematical; there can be many ways of “knowing” mathematics.
There are many types of event: physical, chemical, astronomical, biological, psychological, social, economic, historical, cultural. Each type of event has its own science or field of study, so that disciplines are identified via types of event. In general, these disciplines describe, predict, and explain the events that form their subject matter. Naturally, this involves dealing with certain types of object in which the events participate—material bodies, molecules, stars, organisms, psychological subjects, social groups, economic institutions, historical figures, cultures. So the sciences all deal with characteristic types of events and their associated objects, as their names suggest. They are event-specific. But philosophy is not like this: it has no class of events to call its own. There are no philosophical events that form the subject matter of philosophy; the very phrase “philosophical event” is an oxymoron. What would it even be for an event to be philosophical? Of course, there are such events as philosophical conferences or philosophical publishing events (“It was a philosophical event when Philosophical Investigations was published in 1953”), but these are not what philosophy is about. It might be said that philosophy is about other kinds of event and object, those dealt with in the sciences—physical, psychological, biological, etc. It is about what other subjects are about, while having no subject matter to call its own. While physics, say, is about physical things, philosophy is not about philosophical things—a class of distinctively philosophical entities. It may postulate philosophical entities—platonic forms, immaterial spirits, Fregean truth-values, Meinongian subsistent beings—but it isn’t about a certain class of events and objects recognized to exist in the world. There are no specifically philosophical events whose nature it strives to discover.
To the cynical this may suggest a lack of legitimate subject matter—philosophy is about nothing! The sciences are about things we can point to and identify, but philosophy has the null subject matter—it is just hot air devoid of any real anchor. Not only does it make no progress; it has no object of investigation on which progress could be made. Indeed, that is why it makes no progress—it isn’t about anything. But this dismissive attitude is far too quick: for philosophy isn’t alone in lacking a specific ontology of events on which to work. There are no logical events or moral events or mathematical events either. Does that mean that logic, morality, and mathematics have no legitimate subject matter? Not a specific type of event, to be sure, but does that exhaust the possibilities? Logic is about logical relations, morality is about right and wrong, mathematics is about mathematical truth: it is just that these subject matters are not event-like. There is no such thing as a number turning even or a moral value coming into existence or a logical entailment being derailed. What these subjects are about is a controversial question, but we are not required to suppose that they must be about events or about nothing—maybe they are about structures or properties or concepts or facts. Events happen, but not everything real is a happening. Philosophy belongs with these subjects in being about no distinctive class of events, but that doesn’t prevent it from being about structures or properties or concepts or facts. In fact, I believe that philosophy is about logical reality, and logic is not directed at events either.
A more positive response to the recognition that philosophy is not about philosophical events is that this provides a neat way to define the nature of philosophy. It belongs to that class of intellectual inquiries that do not deal with events; it is not event-directed. Sometimes it is said that philosophy is about thought, or again about language, but on one interpretation this cannot be true: it cannot be about episodes of thought, or episodes of language, or else it would be about a particular class of events—as psychology is. It cannot be about mental acts or speech acts, since acts are events. It could be about the structure or content of thought or language, but not their occurrence—not concrete happenings. This conception is partly prompted by a desire to find something solidly empirical for philosophy to be about, but that is precisely the wrong move: it tries to assimilate philosophy to the empirical sciences that traffic in concrete events. That is the exact opposite of what philosophy does. If philosophy were about events of ordinary linguistic usage, then there would be philosophical events; but there are no philosophical events, so philosophy can’t be about that. There are events of ordinary linguistic usage, but they are the subject matter of other disciplines—linguistics, sociology—not philosophy as such. This is like supposing that morality is about events of moral (or immoral) action, but it is not about such events—rather, it is about the rules and principles that should guide action. Morality is not concerned with the description, prediction, and explanation of actions deemed moral or immoral—that is a matter for the psychology of behavior. Maybe speech acts could provide useful data for philosophy, but they are not its proper subject matter in the way that physical events are the proper subject matter of physics or speech behavior is the proper subject matter of psycholinguistics. The same is true for mathematical acts and the proper subject matter of mathematics—mathematics is not about events of doing mathematics. This is why there are no mathematical events, though there are events with a mathematical subject matter (e.g. actual calculations).
More to the point, it might be wondered how this fact about philosophy relates to the traditional idea that philosophy is an a priori science (like logic and mathematics—or even morality under some interpretations). It relates closely, but the ideas are not identical. The a priori claim is epistemological; the event claim is ontological or semantic. To say that philosophy is an a priori discipline is to say that the knowledge it produces is gained independently of experience (as the phrase goes); to say that philosophy is not about philosophical events is to make an ontological or semantic claim concerning the type of reality with which philosophy is occupied. Putting both claims together, we could say that philosophy is a priori precisely because it is not about events, that being the mark of the a posteriori. In any case, the claims are different, though related. Perhaps if there were philosophical events (whatever that might mean) philosophy would not be a priori, since those events would interact with our senses to produce philosophical knowledge; but the very oddity of that supposition shows how bizarre it is to think that there are philosophical events. In this sense it is quite wrong to hold that philosophy is “continuous with science”, as if philosophy has the same general shape as science but brings its own subject matter. We can say that biology is continuous with physics and chemistry, but in that sense philosophy is not continuous with those disciplines—as if it were concerned with a special more rarified type of event. The same can be said of logic, morality, and mathematics—none of these are “continuous with science” if that means they share science’s general preoccupation with events. Obviously, this is connected to the fact that the sciences seek causal explanations, events being the stuff of causation, but these non-event disciplines are not in that line of business. We canreasonably claim that philosophy is continuous with logic, morality, and mathematics, since all these disciplines are dedicated to aspects of reality that go beyond events; and indeed the affinity is generally recognized.
Being a priori and being concerned with something other than events are connected characteristics, but the latter is fundamental. When philosophy concerns itself with events of the ordinary type, as with the question of the relation between mental events and physical events, it is not concerned with some proprietary type of philosophical event; it is concerned with the nature of the relation between the two ordinary types of event—that is its proper subject matter. This is why the subject matter of philosophy includes all types of event but not a specific type of event peculiar to it. According to one tradition, philosophy is concerned exclusively with concepts, understood abstractly, and this well captures the sense in which it is not the study of a certain type of event. The obvious fact that there are no philosophical events dramatizes the point that philosophy is not as other sciences. We could say that it is a “formal science”, but it is more illuminating to say that it has no event-like subject matter. As remarked, I think that its subject matter is logical reality, and that is far removed from the world of passing events and perishable happenings. Trying to reconfigure philosophy so that it resembles the event orientation of the sciences only leads to distortion, confusion, and cynicism.
 See my “Philosophy Defined” and Truth By Analysis. According to this conception of science and philosophy, the science of events could be completed without any philosophical problem being resolved: all events could be described, predicted, and explained without making a start on the problems of philosophy. This shows that science will never take the place of philosophy.
 It would be wrong to suppose that philosophy is identical with the union of all event-directed sciences, since that would simply make it a very inclusive empirical science. In order to study philosophy one would need to master all the sciences and no more.
“All happy families resemble one another, each unhappy family is unhappy in its own way.” This famous remark by Tolstoy usually provokes a wry smile and a sage nod, but is it true and what exactly does it mean? We may paraphrase it thus: there is only one kind of family happiness, but there are many kinds of family unhappiness. Families are such that happiness in them comes in only one variety, but unhappiness in families has several varieties. This has the look of a proposition about families as such, but families themselves are various. Do we mean families with children, and how many children and of what sex, or are we including childless marriages? Must the parents be married? Must they be of different sexes? What of single parent families? Does happiness come in several forms if the family varies along these dimensions, or is Tolstoy’s statement to be limited to traditional families of a man, a woman, and three children of both sexes? Does the same point apply to couples before marriage: are all happy engagements alike while unhappy engaged couples come in different varieties? And what about romantic partners not contemplating marriage and family?
But why limit ourselves to family units at all—couldn’t we say the same about any social grouping? Are happy friendships all happy in the same way but unhappy ones variable in their mode of unhappiness? What about clubs or regiments or dinner parties or motorcycle gangs or rock bands? If these social units admit of the distinction Tolstoy identifies, it has nothing essentially to do with families, but applies equally to people forming groups of any kind. The trouble is that we are not told what it is about families in particular that generates the asymmetry in question, and it is not obvious what Tolstoy had in mind (or any of his sage assenters). Is it that happy families all have a strong but fair father, while unhappy families can have a flighty mother or a delinquent son or a disobedient daughter? That is hardly plausible: more plausible is the proposition that happy families contain happy members while unhappy ones contain at least one unhappy member—but then all unhappy families are unhappy in the same way. And what about the individual: can’t we equally say that all happy individuals are happy in the same way but unhappy individuals can be unhappy in different ways? Is it that my happiness resembles your happiness but that my unhappiness is unique to me? But surely I can be happy in virtue of something that doesn’t make you happy (e.g. being a kite surfer) and also unhappy about the same thing you are unhappy about (e.g. being short of funds). Whence the asymmetry? People vary, so what makes one person happy may not make another happy, and the same for unhappiness. Why should happiness be uniform but unhappiness multiform? And is it that Tolstoy’s statement is intended to apply only to family happiness—only it exemplifies the uniformity of happiness and variety of unhappiness? This takes us back to what is meant by “family” and whether the point generalizes to other social groups.
I can see one possible rationale for Tolstoy’s statement, but it doesn’t apply to families in particular or even to all social units; nor is it clearly true. This is that there are more things to be unhappy about than things to be happy about. As a rough generalization, people are happy when they are safe, well fed, and loved, though some may crave worldly success and plaudits; but they can be unhappy about virtually anything—their looks, weight, height, popularity, job, spouse, home, national politics, tennis game, literacy, numeracy, teeth, lack of riches, state of the world, death, the neighbors, etc. Happiness is found in a small number of things while unhappiness can be found all over the place. That seems right as a rough generalization about human nature: it explains why people who seem to have it pretty good can still find things to complain about. So happy people will converge in the things they are happy about, more or less, while unhappy people will tend to diverge in their cause of discontent. There are just so many things to be irritated about, disappointed in, furious over, and pissed with—while happiness seems to flow from just a few sources. Thus happy people will tend to be happy about the same things while unhappy people will vary in their list of peeves and grievances. This is the grain of truth in Tolstoy’s remark, but it has nothing particularly to do with families, happy or unhappy. Families will tend to he happy when their members are safe, well fed, and loved; unhappy families may be unhappy because of a domineering father or a feckless mother or a reckless son or a depressed daughter or a deceased pet or a paucity of bathrooms. There are not many things in this world to be thankful for, but of things to complain about there is no end. Consequently, one person’s happiness tends to resemble another person’s happiness while unhappiness can differ widely from person to person. Tolstoy doesn’t tell us the relative proportions of happy and unhappy families, but according to the explanation just given we might predict that unhappiness will preponderate, simply because there are so many causes of unhappiness to choose from. The same is true for human beings in general.
 But not for animals as far as I can see: they are not constantly seeking reasons to be miserable, or even naturally prone to bouts of depression; on the whole, they seem pretty happy, short of starvation and abuse. Tolstoy could not make his statement about, say, chimpanzee or elephant families.
The Concept of Miracle
Where do we get the concept of the miraculous? Why does that concept seem compelling to us? Why do we take to it so readily? It is not, to be sure, from the observation of miracles, in the style of empiricism—we don’t have perceptions of actual miracles. Nor, presumably, is it innate: what would be the use of a concept so inapplicable? Apparently it is a complex concept, so it could be constructed from simpler components, but why does it grip us—why this concept and not any of the indefinitely many other concepts that we might construct? Why does it seem so natural, so inevitable? It is a conceptual universal, but nothing about the world to which we apply it suggests its necessity. What explains its presence in the human conceptual scheme? Even those who reject its application most fervently are familiar with the concept itself.
Here is how the OED defines “miracle”: “an extraordinary and welcome event that is not explicable by natural or scientific laws, attributed to divine agency”. This is too narrow for our purposes, since not all supernatural events are thought to be welcome, nor assigned to divine agency. Some are unwelcome and assigned to malign forces—the Devil is deemed capable of devilish “miracles”, i.e. extraordinary events not explicable by natural or scientific law. The broader concept we are interested in connotes the uncanny, the inexplicable, the exempt from natural law—the weird, the spooky. How does that idea enter our thoughts? Whence the concept of magic, whether for good or ill? Might it simply never have occurred to us? Is it just a dispensable historical accident, a piece of cultural detritus with no discernible foundation? Or does it have deep roots in our experience of the world, including ourselves?
I once compared the emergence of consciousness from the brain to the miracle of converting water into wine. Why did I do that? It was because the concept of the miraculous suggests itself when considering the way consciousness arises from the physical world: this seems uncanny, contrary to natural law, freakish, inexplicable. I emphasized that this can only be an appearance—consciousness is not really miraculous. The mind is not objectively a miracle; rather, it is a mystery that looks like a miracle. But now I want to invert that thought and make a speculative suggestion: we get the concept of a miracle from our sense of ourselves as conscious beings. We strike ourselves as freakish and uncanny, at least when we reach a certain level of self-consciousness, and we then project this idea onto things outside of us. The dependence of mind on body appears unintelligible, extraordinary, possibly a sign of divine agency (assuming we find consciousness a “welcome event”). So it is not so much that the brain is like water and the mind is like wine; rather, water is like the brain and wine is like the mind. The emergence of mind from matter is the paradigm of the miraculous–everything else is projection and extension. Thus the concept arises spontaneously in us as a consequence of our very nature, at least as that nature strikes us; it isn’t just an adventitious eccentricity of culture. We don’t regard the mind-brain connection as miraculous because we alreadyhave the concept of a miracle from some other source; we derive the concept of the miraculous from our apprehension of ourselves as psychophysical beings. This is why it is universal and deep seated. This is why the concept seems so familiar, so easy to grasp. No wonder people often feel that the supernatural is all around them and ever-present—because it is part of our nature (as we apprehend ourselves). We see the world as spooky because we are spooky. In fact, of course, we are not objectively spooky, just deeply mysterious; but we convert a mystery into a miracle and then spread the concept outwards. After all, if we are a miracle inside, why can’t there be miracles outside? When someone miraculously rises from the dead (allegedly) isn’t this just like the way conscious life rises from dead matter, even when that matter resides in a living brain? There is that peculiar sense of getting something from nothing that attends all putative miracles. And the miracle of consciousness does occur all the time—every time a baby is conceived, every time we wake from sleep, every time our brain causes a thought. So why can’t external miracles happen regularly too? Clearly they are possible because they happen all the time in our own lives. Is water turning into wine any more impossible than brain chemicals turning into consciousness? In fact, it looks a lot more possible, what with water and wine both being liquids and all.
The form of explanation I am suggesting resembles Hume on causation and the origins of animism. Hume couldn’t find a source for the concept of causation in external objects (no impression of necessary connection), so he sought it within the mind in our habit of anticipation; we then project this inner impression outwards and populate the world with causal relations. It is not that we derive our concept of causation from external objects and then project it inwards; we get the idea from our inner feeling of expectation and then project it outwards. By analogy, we sense miracle within ourselves (erroneously but intelligibly) and then project it onto the outside world. We are under the illusion that we are miraculous and we suppose that we are not alone in this. In the case of animism, we attribute the qualities of living things to inanimate objects, mistakenly assimilating them to ourselves: we find intention and will where they do not objectively exist. We have a first-person awareness of life and we spread it around indiscriminately—as we have a first-person awareness of the (seemingly) miraculous and then ascribe it to the world outside. No doubt we are motivated to do this in various ways, but the cognitive groundwork is prepared by our knowledge (sic) of ourselves. The idea of miracle is all too familiar from our ordinary experience. Presumably other animals don’t have the concept of a miracle, because they don’t have the kind of self-consciousness that gives rise to it; but we humans apprehend ourselves as enigmas, which we then convert into the idea of a miracle. Suppose that dualism were really true and that causal interaction takes place in the pineal gland: that would strike us as a type of miracle and God might be invoked to make sense of it. This could be the origin of the concept of the miraculous, and it would be an intelligible explanation of how the general concept arises. But the same is true even if we don’t accept that kind of metaphysics, because emergence is mysterious anyway. The enigma of emergence is readily converted into the idea of miracle, and then projection does the rest.
The obvious next question is whether the concept of God has a similar type of origin. I won’t go into this deeply, but I will make a couple of suggestions. The concept of God is clearly a compound of other concepts: omnipotence, omniscience, moral perfection, immateriality, and infinity. The last two are the hardest to explain in that both concepts are difficult to account for: where do we get them? We obviously don’t see and touch immaterial spirits and derive the concept by abstraction; and the concept of an infinite being is likewise not derived from perceptual acquaintance with such entities. A plausible hypothesis is that we derive them from knowledge of our own nature, or at least the kind of limited awareness we have of our nature. We certainly don’t experience our own consciousness as material, so it is at least intelligible that we could form the idea of an immaterial being on this basis—even if we are not rightly so described. Crudely, we have an illusion of immateriality. In the case of infinity we have more than an illusion of infinity: we ourselves are infinite beings. I don’t mean that as spatial beings we are infinitely divisible; I mean that we have attributes that are characterized by infinity—namely, language and thought. I intend nothing mystical here; I am just making the familiar point that language and thought admit of infinitely many combinations of primitive elements. And we are aware of this fact about ourselves: we know that we have this kind of infinite potential. So we have no trouble forming the idea of an infinite being, combining it with the other attributes that define God. We thus come by the idea of an immaterial infinite being via contemplation of our own make-up: this concept is not alien to us. So it is not that we have an antecedent idea of God that we subsequently apply to ourselves, casting ourselves in his exalted image; rather, we use ourselves as model to construct the complex idea of God, which we then proceed to project onto the world. Whether the world really contains anything answering to this concept is another question, but the concept itself has its origin in our own nature. How else could we get it? The concept of the supernatural is ultimately based on a distorted picture of ourselves, as a result of partial understanding and incorrigible projection. Religion begins at home.
 Does anyone ever really get over the discovery that his or her precious consciousness, in all its glory, is the result of that furrowed and frightful thing called the brain? The miracle seems almost cruel in its absurdity!
 Let me stress that this is a speculative proposal—other theories might be suggested. The advantage of the present proposal is that it finds a firm place for the concept of the supernatural in the natural world. We don’t want to discover that only the existence of the supernatural can explain the presence of that concept in our minds—not if we want a secular psychology anyway.
Discrete and Continuous
Philosophy is awash in grand dichotomies—particular and general, mind and body, fact and value, finite and infinite, being and nothingness. Reality is held to divide into two large categories and the relations between them are mapped. But there is one dichotomy that is seldom discussed by philosophers, though it is generally recognized elsewhere: that between the discrete and the continuous. These concepts are not easy to define, though they are widely accepted at an intuitive level, no doubt because they pervade our everyday experience. The discrete consists of separate, distinct, self-contained objects that can be distinguished and counted: animals, mountains, tables, cells, atoms, words, concepts, numbers, propositions, gods. The continuous consists of undivided, unbroken, uninterrupted, seamless, smooth, homogeneous…what? Not objects or things–for then they would be discrete–but what we call mediums or manifolds or dimensions or magnitudes: stuff of some sort. Space and time are the paradigms, but we also regard other things as continuous: intensity of emotion, milk and honey, geometrical figures, colors, motion, fundamental matter. Of course, things that seem continuous have sometimes been discovered to be discrete, as with the atomic theory of matter or the quantum theory of energy; but we have a clear idea of what continuity might be even in these cases. We have a commonsense concept of the continuous that meshes with our ordinary perception of things, in which discrete objects are perceived to be internally continuous (possibly falsely). We thus feel ourselves to be surrounded by two kinds of being: discrete separated entities that can be counted, on the one hand, and smoothly varying continua that can only be measured, on the other. There are the discrete objects in space and time and the continuous mediums of space and time. The latter require their own mathematics, which nowadays involves the real numbers, infinitesimals, the concept of a limit, and calculus. We employ the modern notion of a dense array of points between any two of which there is always a third (this may be viewed as a way to discretize continuity). There is even a distinctive type of paradox associated with continuity (Zeno et al). So we accept a kind of ontological dualism: two kinds of being with different essential natures. Descartes used the concept of extension to unite space and matter, but that concept papers over the deep difference between the discrete and the continuous, both of which can be said to have extension—though we should note that not everything that is continuous is physical, e.g. emotional strength. The discrete-continuous distinction cuts across the mental-physical distinction, and brings its own brand of dualism.
Like other dualisms, this one invites philosophical scrutiny. How solid is the distinction? Might we not view each as a special case of the other? Is one derivable or emergent from the other? Are there illusions of continuity and discreteness? Is it possible to be a monist with respect to one or the other type of being? For instance, we are told that in the first moments after the big bang the temperature was so high that no particles could exist, so there were no discrete objects then—they came into being only when the universe cooled. Then wasn’t physical reality entirely continuous at that early point? If so, our current discrete universe emerged from a continuous universe, rather as we suppose that mind emerged from matter (which took more than mere cooling). Might not other universes stay at that initial high temperature and never evolve into discrete universes? On the other hand, it has been maintained that continuity is a mathematical fiction—everything real consists of discrete entities with no smooth transitions anywhere. Motion is really jerky and jumpy, space and time are particulate, and the mind is purely digital. Or we could just decide to eliminate entities that don’t meet our ontological expectations: there is no such thing as motion, space and time are unreal, and there are no emotions to vary continuously. We have the usual panoply of philosophical options to choose from: dualism, monism, reductionism, elimination, and invocations of God to get over ontological humps (e.g. the miracle of discrete entities springing from continuous stuff). Our experience suggests a dualism of the discrete and the continuous, but maybe reality is not so constituted; maybe in the noumenal world all is discrete (or all continuous). Continuity certainly presents problems of understanding, and it was only in the nineteenth century that mathematicians began to be comfortable with it (but at what cost—is a smooth line really reducible to a collection of points?). And why is the universe made this way to begin with? Why the ontological division? Wouldn’t it be simpler to make a universe that was just one way or the other? Why did God introduce continuity at all, given that his main purpose was to create discrete moral beings like us? What has continuity got to do with morality? We appear to live in a mixed world, but this doesn’t seem like a logical necessity—unless it really is once you get down to basics (maybe space and time couldn’t exist without their smooth structure). It is all quite puzzling—the mark of a good philosophical problem.
That was about the metaphysics of the discrete and continuous, but there is also the epistemology. Do we know about these things in the same way? Do we perceive continuity as we perceive discreteness? How do we get the concepts? There is a kind of primitive impression of continuity in vision that exists side by side with impressions of discreteness, but what exactly does this amount to? Is it just an absence of perceptible discreteness or is it a positive sense datum in itself? Is the child’s mind a continuous visual blur until sensations of discreteness supervene? What does it mean to say that a surface looks continuous—does it look as if all potential gaps have been filled? What if we look closer and see that the object is made up of lots of little discrete entities? Were we under an illusion? But is it even possible to see a discrete object without some parts of the visual field giving an impression of continuity? The gaps between objects look to be filled with continuous space and the objects themselves look like they are composed of continuous matter. And the cognitive mechanisms that process perception must recognize the discrete-continuous distinction: they deliver different kinds of mental representation to handle the sensory input. Is consciousness itself continuous or discrete or both? Is it quantized or infinitely divisible? Are the features of the brain that account for consciousness discrete properties of neurons or continuous features? Neural firings are discrete, but electrical charges can vary as continuous magnitudes—do both contribute to generating consciousness? Behaviorism in effect treated the mind as continuous, because behavior is just a type of motion, but how does that square with the discrete character of so much of the mind, particularly language and concepts? There is no such thing as applying half a concept, but the body can move half a meter. Your utterances must be either meaningful or not, but your voice can be louder or softer. How do we derive the discrete mental notions from concepts of continuous bodily motion? That is like trying to define atomic structure in terms of motions of matter—a sort of category mistake.
The natural position to take is that the world contains two sorts of ontological structure corresponding to two types of mathematics: discrete structure and continuous structure. The former can be dealt with using finite mathematics (or the mathematics of discrete infinity), while the latter requires the infinite mathematics of the continuum. Space and time have a continuous structure, while atoms and species have a discrete structure. This is just an irreducible fact. The two coexist and intermingle. Correspondingly, we have two sorts of phenomenology and mental representation geared to these objective structures—discrete cognition and continuous cognition. These might be conceived as distinct modules located somewhere in the brain. We know how to handle continuous magnitudes and we know how to handle discrete objects. When we see an object in motion we separate it from its surroundings as a distinct individual thing (using our discrete module) and we also track its movement through space as a continuous path with no gaps or interruptions (using our continuous module). We are capable of seeing the world in both ways simultaneously. The dualism is present but it is integrated, fused. It is rather like the perception of shape and color: different properties, different perceptual modules, but a unified perception. Just as there is a division of primary and secondary qualities despite perceptual unity, so there is a division of discrete and continuous properties despite perceptual unity. We see the same object as a discrete entity and as moving through a space without internal discreteness. Phenomenology thus recapitulates ontology. The distinction between discrete and continuous deserves a place in the pantheon of philosophical dualities.
 We could call it the problem of the granular and the gradual: are both equally real, and how do they meet up? The grainy and the graded, the chopped up and the smoothed out, the lumpish and the soupy: which form does reality prefer, and how does it combine them?
Realisms and Anti-Realisms
We reflexively speak of realism and anti-realism, as if we had a dichotomy of positions: you are either a realist or an anti-realist about a given subject matter. But this is too simple: there is a range of positions going from one extreme to another, depending upon the ostensible relation between the subject matter in question and human knowledge and experience. Consider material objects: the further the nature of such objects is removed from human knowledge and experience the more of a realist one becomes, and the closer the more of an anti-realist. Suppose you hold that material objects have only unknowable properties, so that their nature is totally distinct from anything revealed to the human mind. Then you hold an extreme realist view of material objects—they are maximally unrelated to human knowledge. The objects are objectively a certain way, but that way transcends the capacities of the human mind. But you might hold to a weaker thesis, namely that the properties of objects are knowable and yet independent of the mind: objects would be that way even if no minds existed, though all properties are in principle knowable. This also would be a realist thesis. You might even hold that all properties of objects are actually known and still be a realist about them.
But you might want to go a step further towards the mind: every property of an object must be the categorical basis of a disposition for the object to appear in a certain way. This position combines a non-identity thesis with respect to properties and their disposition to appear with a limit to properties that form the basis of such dispositions; if a putative property fails to correlate with any such disposition, it is deemed not to exist. Next you might choose to dispense with the categorical bases and simply identify properties with dispositions to appear: to be square, say, is just to have a disposition to appear square. Now you are moving into phenomenalist territory–objects as possibilities of sensations. That sounds decidedly anti-realist, but you are not quite there yet: for it might be supposed that the features of sensations that define material objects are not known to the subject of experience. This possible position is not typically recognized in the area of philosophy dedicated to these questions, but it exists in logical space. Thus it might be supposed that sensations are identical to brain processes, so that being square is identified with a disposition to cause certain brain processes in subjects (those correlated with its seeming that there is something square there). But these brain processes are not known to the subject, so objects are both dependent on sentient beings and yet removed form such beings’ knowledge. This strikes us as a weak form of anti-realism about material objects; and we can envisage variations on this theme that detect hidden aspects to conscious experience. A stronger form of anti-realism maintains, familiarly, that properties of objects are identical to dispositions to produce experiences that appear a certain way (“sense-data”). And then we have the most extreme anti-realist thesis of all, namely that so-called material objects have no existence save that of actually producing experiences with a certain appearance—to be square is just to actually appear square to someone at some time. We thus move from the thesis that material objects have a completely unknown nature to the thesis that they are nothing but fully known experiences—but this movement goes through a number of intermediate steps, not an abrupt switch from realism to anti-realism. That dichotomy does not do justice to the range of philosophical positions available to the theorist of material objects.
We can run a similar gamut for realism and anti-realism about the mind. A strong realist might hold that mental states exist but are never revealed in behavior, being cut off completely from third-person knowledge: the properties of mental states are completely unknowable to the outside observer, so that their existence and nature is independent of any behavioral evidence that might be adduced. Or they might be thought to be knowable via behavior but not identical to behavior (or dispositions to behavior). Or they might be thought to be the categorical basis of dispositions to behavior. Or they might be taken to be the dispositions themselves. Now we are squarely in anti-realist behaviorist territory, but again there is a neglected position here: what if the aspects of behavior that constitute mental states are hidden to observers? It might be supposed that they are the muscular and neural events that underlie observable behavior, so that they are not the evidence we normally use to ascribe mental states to others. This position combines an ontological claim about the nature of mental states—they are identical to episodes of behavior—but it removes them from ordinary third-person observation. The standard behaviorist position is that mental states are identical to observable behavior (under some notion of observation). This position is clearly anti-realist because it ties the mental facts to our evidence for asserting these facts, but the weaker behaviorist position doesn’t claim this connection to evidence—it is quasi anti-realist. Once again, the usual dichotomy of realist and anti-realist fails to capture the full range of options. We have gone from maximally realist to maximally anti-realist, as gauged by proximity to evidence, via a number of intermediate positions. The usual dichotomy is too crude.
The moral case follows a similar pattern. You could hold that some moral truths are completely unknowable, or even that all are (though that is certainly hard to credit). Or you could hold that, though knowable, moral truths are not mental in nature. Or you could hold that moral values are dispositions to elicit approval, or just approval itself. The neglected position would be that moral facts reduce to mental facts but that mental facts have a hidden aspect that constitutes moral facts (substitute for “facts” here anything you like). That is, moral facts might be mind-dependent and yet inaccessible to the subject, because the relevant mental states have a hidden aspect—as it might be, brain states or some other inaccessible property. What if you thought that moral approval is really an unconscious matter inaccessible to the conscious mind? Again, we have a range of conceivable positions, differing in strength, not a simple dichotomy. If someone says he is a moral realist, we need to ask what specific kind of realism he has in mind; and similarly for the moral anti-realist. There are clearly degrees of inaccessibility relating facts and our knowledge of them, and these define different kinds of metaphysical position. The same situation obtains for the mathematical and modal cases, though I won’t spell out how this goes, as it should be obvious by now.
The case of time is instructive. An extreme realist view would be that we can’t know anything of the past and the future, even though these stretches of time exist as determinately as the present. A less extreme view is that some facts about the past and future can be known but these facts have nothing intrinsically to do with what obtains in the present—they are in no way constituted by present facts. The anti-realist will insist, by contrast, that past and future facts are constituted by present facts or else do not exist at all; but again there is room for two strengths of position here—do these present facts provide our evidence for assertions about the past and future, or are they merely present whether evidential or not? That is, might they be currently inaccessible present facts? Maybe the past consists in current microphysical facts of which we have no knowledge, or the future consists of current facts of divine dispensation about which we are ignorant. This is recognizably anti-realist, though there is no claim of reduction to evidence. The stronger kind of anti-realism claims that past and future reduce to current evidence, presumably observable evidence of the kind we typically rely on to make statements about other times. This in turn can be regarded as mental in nature, as when it is held that the past reduces to present facts about sense data and not to external physical traces. There is thus no such thing as the anti-realist about the past, since a number of different positions can qualify for that description; and similarly for the realist about the past. What we really have is the comparative locution “A is more realist than B”, and likewise for “anti-realist”.
This also shows that it is not a helpful formulation to describe the realism versus anti-realism dispute as a contest between truth-condition semantics and assertion-condition semantics. That distinction is indeed dichotomous, but the distinction of metaphysical realism and anti-realism is not; so we had better not try to formulate the latter in terms of the former. We should not, here as elsewhere, let the metaphysical debate take a linguistic turn.
 I will mention that nominalism admits of varying strengths of anti-realism depending on how symbols are conceived. If symbols are observable marks on paper, then we get a close proximity between numbers and sensory evidence; but if instead they are viewed as internal mental entities in an unconscious language of thought, then we get distance between numbers and perceptual evidence, since such symbols are not perceived at all.