Metaphysics
METAPHYSICS
Physics is the scientific investigation of the fundamental nature of physical being. Metaphysics—at least within that tradition that traces itself back to Aristotle's eponymous treatise—is the philosophical investigation of the even more fundamental nature of being as such. Metaphysics is concerned with the contours of the categories of entity postulated or presupposed by any possible, acceptable, account of the world, whether of the physical world or of any other aspect of the world. The task of metaphysics is to lay out a complete, coherent ontology, embracing all that is necessary to capture the correct account of the world in any of the special inquiries—whether they be empirical, mathematical, modal, or moral.
The Changing Methods of Metaphysics
Traditionally, metaphysics was practiced as a top-down, a priori discipline, with Euclidean geometry as its model. The metaphysician begins with self-evident principles of a highly general nature, together with appropriate definitions, and proceeds to draw out the necessary consequences.
This approach is clearly exemplified in the work of two prominent eighteenth-century metaphysicians, Gottfried Wilhelm Leibniz and Benedict (Baruch) de Spinoza. Leibniz spun metaphysical gold out of the dross of the principles of noncontradiction and sufficient reason: His entire Monadology (1965), replete with an infinite collection of possible worlds, with the actual world (the best of all possible worlds) consisting of a myriad of mutually reflecting, simple, mind-like substances. Spinoza was even more self-consciously imitating Euclid, but his conclusions are almost diametrically opposed to those of Leibniz. Spinoza's ontology comprises exactly one substance (God-or-Nature), of which the mental and the physical realms are two aspects, and everything about the one Substance is absolutely necessary—only the actual is really possible.
In the light of its lofty aim, the conflicting conclusions of its practitioners, and their exaggerated claims to have achieved the aim with completeness and certainty, it is perhaps unsurprising that the discipline of metaphysics, so practiced, has been regularly contested. Empiricists, led by David Hume, have often attacked a priori metaphysics, contrasting its lackluster or conflicting results with the astonishing successes of empirical sciences, on the one hand, and of mathematics on the other.
At the end of the eighteenth century, Immanuel Kant, in response to Hume's critique, attempted a partial vindication of a priori metaphysics. According to Kant, metaphysics can play a legitimate role as handmaid to science and a less straightforward role in upholding ethics. Through an analysis of the cognitive needs of thinking, sensing beings, it can establish the presuppositions of Newtonianism—Euclidean space, absolute time, deterministic causation, and enduring interacting substances obeying conservation laws. In addition, if a metaphysical hypothesis—the existence of God or the freedom of the will—is required for the smooth and effective operation of morality, then that may be legitimately adopted as though it were true, as a postulate of practical rationality. Kant's compromise evidently failed to rein in the metaphysical spirit, his work unleashing a century's worth of metaphysical system-building in an increasingly problematic idealist tradition.
In the late nineteenth century, the appetite for idealist metaphysics began to fade. A realist assault on this tradition was launched by Alexius Meinong, Bertrand Russell, Gottlob Frege, and George Moore, and their style of argumentation, as much as the content of their conclusions, was influential in shaping the twentieth century's more circumspect approach to metaphysics. Rather more radically a group of scientifically minded thinkers—inspired by Ludwig Wittgenstein's Tractatus (1922), rallying under the banner of Logical Positivism and brandishing a verificationist criterion of meaning—declared all metaphysical discourse completely meaningless. They argued that sentences that cannot be either verified by observation or proven by pure logic and are not merely beyond our knowing but are strictly speaking, meaningless. Echoing Hume, they denied any legitimate space for metaphysics between a posteriori science and a priori logic. The shortcomings of Logical Positivism were rapidly exposed (mostly by its adherents and fellow empiricists such as Karl Popper), but its offspring—ordinary language philosophy—cast over the metaphysical enterprise a pall that did not lift until the 1960s. Metaphysics, cautiously revived by heirs of both movements (albeit with notable differences in methodology detailed below), is once again a flourishing discipline in the early twenty-first century.
Contemporary metaphysics is characterized by a bottom-up approach rather than the traditional top-down approach. The contemporary metaphysician begins with a problem or puzzle, often generated by some basic data or the consequences of such data. The different sources of this basic data characterize two broad traditions. One tradition—championed by Moore, mediated midcentury by philosophers such as P. F. Strawson, Arthur Prior, and Roderick Chisholm and embraced by contemporary philosophers such as Frank Jackson—takes as prime data the deliverances of everyday discourse and commonsense, so called "Moorean facts": for example, that I have two hands; that there is a piece of cheese in my left hand and a stick of chalk in my right; that the chalk and the cheese are distinct things; that cheese and chalk have the same color, and so on.
A different tradition, traceable back through the empiricists (such as Russell and Rudolph Carnap), mediated by Willard Quine, and embraced by philosophers such as John Smart, John Mackie, and David Armstrong, is less impressed with commonsense data. It takes the serious data to be constituted by the presuppositions and deliverances of extraordinarily successful scientific theories: that there is no role for the flow of time in a fundamental account of the world; that the fundamental laws are probabilistic rather than deterministic; that simultaneity is relative to motion; and that space–time may be non-Euclidean. The presuppositions and deliverances of the mathematical disciplines essential to science are also treated as serious data: for example, that there numbers, and an infinite class of such; that there are functions from numbers to numbers and that the infinite class of such functions is vastly bigger than the infinite class of numbers; that there can be no complete axiomatization of mathematical truth, and so on.
The two traditions overlap, of course, as exemplified in the work of prominent metaphysicians like David Lewis. Lewis (1981, 1986) draws extensively on both kinds of data, seeking an ontology compatible with and explanatory of both. However, if that's not possible, the data from the sciences usually trump those of commonsense.
To say that contemporary metaphysics is bottom-up is not to saddle it with a crude inductivism—the fallacious inference of general theories from finite data. The task of the contemporary metaphysician is not so much to prove an ontology, either from high-level first principles or from lower-level data, as to propose an ontology to accommodate and explain the data, to resolve apparent conflicts by explaining away the appearance of such, or explain why the data are misleading. The methodology is less like that of pure mathematics and more like that of science—conjecture and refutation—with the difference being the kind of data that require accommodation or furnish a counterexample.
Given a finite amount of data, the number of potentially adequate metaphysical theories seems limited only by the imagination of practicing metaphysicians. To decide between theories we need more than data accommodation. Metaphysicians typically subscribe to Occam's Razor —the injunction to refrain from multiplying entities beyond necessity. The Razor, read as an endorsement of ontological abstemiousness, is sometimes considered a license to slash entities without regard for a complementary principle—the injunction to refrain from eliminating entities that are necessary. Necessary for what? For accommodating and explaining the data. The upshot of these two principles is, then, that a theory must explain the data; and, of two theories that both explain the data, the theory with fewer ontic commitments is to be preferred.
So, we begin with a domain of discourse—such as mind, or mathematics, or morality—and note that, on the surface at least, it supplies data that posit or presuppose an ontology. Our ordinary mind-talk, for example, presupposes mental states (experiences, thoughts, desires, emotions) along with physical states, and a rich network of causal interactions between them. Mathematics posits numbers, classes, functions, spaces, and a rich array of other abstract objects. Morality presupposes goods and evils, rights and obligations, virtues and vices. But there is often a problem with the entities posited or presupposed. For example, if the mind is something over and above the physical, how can it causally interact with the physical without violating physical laws? And if it is difficult to understand how the mind could affect physical states, it is even more difficult to see how numbers, existing outside space and time, could affect the mind. Whence, then, our knowledge of numbers? Finally, a good would have to be something the mere recognition of which would engage the will, and nothing (some will aver) could do that. The question arises, then, whether such things as minds, numbers, and goods should be counted among the indispensable building blocks of the universe. Is it coherent to postulate them? Are they consistent with the rest of what we know? And even if it is coherent, do we really need them to accommodate the data? Can they be explained, or explained away, in a complete, consistent account of the world? Already with the posing of such seemingly unavoidable questions, the enterprise of metaphysics is up and running.
A Spectrum of Metaphysical Approaches
Whenever entities are posited to explain the data provided by some domain of discourse, three broad responses, differing in ontological commitment, are possible. At one end of the spectrum we have realism, at the other, antirealism ; between, we have determinationism. Each can be divided into two subcategories.
The realist with respect to a domain accepts both the discourse and the data at face value; affirms the necessity of the entities postulated to explain the data, and adds that the entities really are basic—they are additional to (or "over and above") whatever else there may be. Realism comes in two broad varieties. Transcendent realism locates the posited entities outside the spatiotemporal, causal order. By contrast, immanent realism locates the entities within the spatiotemporal, causal order, typically ascribing them an indispensable causal role.
Most realists about numbers and other abstract entities have been of the transcendent variety, but recently, some number-realists have embraced immanence, espousing a role for abstract entities in the causal network. A transcendent realist theory of value is also usually ascribed to Plato—with the Form of the Good, like all the Forms, eternal and unchanging, existing "over and above" the transient realm of particular contingent beings. It is not hard to find naturalist theories of value that ascribe them a causal role, but as we will see below, there is an important sense in which naturalism about value is not fully realist—it does not posit value "over and above" the natural realm. A version of immanent value realism holds, like Platonic realism, that value is real, that it is something "over and above" the purely natural realm, but adds that value plays a causal role with respect to the motivational states of sensitive beings.
At the other end of the spectrum we have antirealism. The antirealist repudiates the entities in question, maintaining that the discourse that delivers the data is fundamentally misleading. But the data can be misleading in one of two very different ways. The data are recorded and delivered in what appear to be genuine, truth-bearing (or assertoric) claims. What masquerades as truth-bearing claims, however, might really be something else, and the nonassertoric antirealist says just that. Rather than being truth-bearing assertions, they might be expressions of desire, or moves in a language game, or instruments in the derivation of genuinely truth-bearing assertions. In ethics, nonassertoric antirealism is noncognitivism ; in the philosophy of science, instrumentalism ; in the philosophy of math, formalism ; in the philosophy of mind, the intentional stance theory ; and so on. Nonassertoric antirealism allows apparent reference to the purported entities while denying there are any such.
The assertoric antirealist, by contrast, accepts that the discourse consists of genuine truth-bearing assertions but rejects those assertions as untrue. In the metaphysics of the mind, this constitutes eliminativism concerning the entities. In the metaphysics of morality, it is known as the error theory. An increasingly popular variant of assertoric antirealism, especially with respect to abstract entities such as numbers, is fictionalism. The fictionalist thinks that the relevant claims are untrue but also thinks that there is a point in continuing the discourse just as though they were.
Between realism and antirealism lie a collection of approaches that share a doctrine of determination. Like the realist, the determinationist acknowledges the discourse and the data that suggest the disputed entities. Like the antirealist, however, the determinationist denies that the disputed entities are basic, holding that the truth about the higher level is fully determined by the truth about ontologically more fundamental entities. Determinationism also comes in two varieties, reductive and nonreductive. The reductionist holds either that the disputed entities are reducible to more basic entities (entity reduction) or that all the facts about the disputed entities are reducible to facts about undisputed entities (fact reduction).
A necessary and sufficient condition for entity education is that the (apparently) higher-level entities are identical to lower-level entities, that properties of the reducible entities are identical to properties of the lower-level entities, and consequently that truths about the reducible entities turn out to be truths about the entities to which they reduce. The reduced entities are nothing but the lower-level entities to which they are reduced. Thus, for example, logicism claims that numbers are reducible to classes: The number zero, for example, is simply identical to the empty class; the number one is identical to the class of all singleton classes, and so on. The identity theory of the mind claims that mental states are identical to physical states of the brain. The ethical naturalist claims that moral properties (such as the rightness of actions) are identical to natural properties (such as maximizing expected happiness).
A classic example of reduction without entity reduction can be found in Russell's justly famous theory of descriptions. In his Principles of Mathematics, Russell embraced Meinong's theory of nonexistent objects: that there are genuine objects—possibilia like the golden mountain and the King of France, and impossibilia like the round square—which have a range of features (the golden mountain is made of gold) but which lack the crucial feature of existence. In "On Denoting"—which set the tone for twentieth century analytic philosophy—Russell repudiated this ontology by showing that phrases that apparently denote such possibilia are not really denoting phrases at all. They do not denote particulars, and they do not denote anything else. Russell shows us a way of dispensing with nonexistent objects, but unlike the eliminativist, he does not repudiate the data or the discourse that suggest them. Rather, he shows how to translate the data into facts about properties. Nonexistents disappear from Russell's ontology theory, but the data that suggested them are fully accommodated. This is a kind of reduction without being a reduction of the problematic entities. It is a reduction of the facts about the purported entities while the entities are repudiated or "analyzed away." Let's reserve the term fact reduction for those cases in which every fact about some purported entities is equivalent to a fact about some other entities; there is no entity reduction, and the purported entities are repudiated.
Finally, we have nonreductive determinationism, which has gained considerable currency through the notion of supervenience in philosophy of mind. All determination theories affirm that there can be no difference in one kind of entity without a difference in another, more basic kind. For example, a widely held view is that there can be no difference in the moral without some difference in the natural. Another is that there can be no difference in the mental without some difference in the physical. The higher-level entities are thus determined by the lower-level entities. What is characteristic of a supervenience theory as such is that it posits this determination, does not repudiate the higher-level entities, but also denies the reducibility of the higher-level entities to the lower-level entities.
Supervenience is naturally located between reductionism and realism. The supervenience theorist agrees with the realist and the fact reductionist that the higher-level entities cannot be reduced to the lower-level entities but agrees with the entity reductionist that the higher-level entities are not ontologically basic. There is thus a sense (weaker than the reductionist sense) in which supervening entities are "nothing over and above" the basic entities, but there is also a sense in which the supervening entities, while falling short of the independently real, enjoy some kind of autonomy denied reducible entities.
Those sympathetic to physicalism (viz., there is nothing over and above the physical) but skeptical that mental state kinds are identical to physical state kinds are attracted to the thesis of the nonreductive supervenience of the mental. Those sympathetic to naturalism (viz., there is nothing over and above the purely natural) but skeptical that moral properties are identical to natural properties are attracted to the nonreductive supervenience of the moral on the natural.
Supervenience theories share considerable common ground with emergence theories—lately enjoying something of a revival—and it is interesting that supervenience is popular in domains (such as philosophy of mind and philosophy of biology) where emergence theories also seem a promising compromise between realism and reductionism.
Whether or not there is logical space for nonreductive determinationism has not yet been satisfactorily settled. Like other attempts to forge middle paths between two clear alternatives, a supervenience theory embodies a certain instability, suggesting to some that, in the end, the supervenience advocate will either be forced to embrace the reductionism eschewed or lapse into a form of realism.
One particularly important determination theory is worth singling out for special attention since it has played a pivotal role in the history of metaphysics—namely, determination by the mental (or mind-dependence ). Broadly speaking, this is idealism, and it is a perennially attractive option—indeed, so attractive that idealism has often been taken to be the rival to realism. Bishop George Berkeley famously claimed that physical objects are nothing but (are identical to) congeries of experiences. The notorious problem of maintaining the intermittently observed tree in the quad in uninterrupted existence led Berkeley to posit an omniobserver, someone to keep a perpetual eye on things. A different response to this problem moves beyond actual experiences to various potential experiences. Physical differences that go undetected may be detectable by observers under suitable hypothetical conditions. (If you were in the quad, or having in-the-quad experiences, then you would have tree experiences.) An idealist could add those conditional states to the determination base. This move, from Berkeleian idealism to phenomenalism, might be a move from entity reduction to fact reduction, or it might be a move from entity reduction to supervenience. If physical objects "disappear" in the final analysis leaving behind the truths that appear to be about them, then we have fact reduction. If physical objects are not identified with anything else, reference to physical objects as genuine entities remains, and the totality of facts about such objects is determined by the actual and conditional facts about experiences, then we have a version of supervenience.
Faced with the fact that actual minds have various cognitive shortcomings, the idealist may also want to tidy up both actual and potential mental states in various ways. The physical facts are held to be determined not by the actual mental states of existing observers but by the mental states that ideal observers would have if they were ideally placed. Hence, variations on the basic idealist theme of mind dependence include positivism, ideal limit theories of truth, and related accounts such as internal realism. Many who regard Berkeleian idealism about the physical world as deeply implausible have embraced some version of idealism in other domains—with respect to mathematical entities, theoretical entities, God, possibilities, colors, values, and universals. This three-fold classification helps explain why there is a certain amount of confusion in debates about realism since antirealism and nonrealism (the disjunction of antirealism and determinationism) and are not usually defined or carefully distinguished.
A Problem in Metaphysics: Universals and Particulars
These patterns of opposition and compromise—realism versus antirealism, with determination seeking a middle way—have played out across the metaphysical spectrum. They find a particularly clear expression, however, in a problem of central concern to metaphysics since its very inception—the problem of universals and particulars, a problem the intrinsic interest of which proves prefatory to its myriad applications. For one's attitude toward universals and particulars has profound implications for one's attitude to a host of other problems—those of abstract entities, change, time, causation, identity, possibility, value, and morality.
Consider a stick of chalk (A ), a wedge of cheese (B ), and a chunk of chocolate (C ). A is chalk and B is not chalk—it follows that A and B are not identical. This is an application the principle of the indiscernibility of identicals, often associated with Leibniz: If entity X is identical to entity Y, then anything true of X is also true of Y. This in turn is a consequence of the principle of non contradiction : that no proposition can be both true and false. So much seems straightforward, yet this sort of easy observation intersects with a second, equally obvious fact, to create a puzzle: A is yellow and B is yellow. How can A and B, clearly distinct, be the same —that is, yellow? How can they be both the same and not the same? That's puzzling.
Whenever we strike an apparent contradiction (A and B are the same and are not the same), it is natural to make a distinction. A and B are not numerically the same (they are two) but they are qualitatively the same (they instantiate the property yellowness ). Properties are instantiated by particulars one at a time—they are monadic universals. But there are also universals that characterize couples and triples. Resemblance, for example, is not a property that particulars have or lack. Resemblance involves pairs—it is a dyadic relation. And betweenness, which characterizes triples, is a triadic relation, and so on. The problematic data can be accommodated, and the apparent inconsistency explained away, by an ontology that posits two radically different categories of being—particulars and universals—and a relation of instantiation (itself a universal) holding between particulars and universals.
Responses to this two-tiered ontology have traditionally been categorized as either nominalist or realist, with a third category—conceptualist —sometimes thrown rather awkwardly into the mix. The six-fold schema set out above suggests that the space of possibilities is much richer. With respect to universals, one might be antirealist (assertoric or nonassertoric), determinationist (reductive or nonreductive), or realist (transcendent or immanent). Further, any of those positions might be combined with one of the six distinct approaches to particulars. So in all there are thirty-six possible combinations, not just two or three. For example, one might be a transcendent realist about both universals and particulars, or an immanent realist about one and a reductionist about the other, or a reductionist about both universals and particulars (invoking some third category of entity to which both reduce), and so on. Not all of these combinations have been embraced, but many have. For the purposes of illustrating the approaches and the arguments that characterize them, a few of the more commonly held positions are sketched.
Realism about Particulars, Nonrealism about Universals
A particular, unlike a universal, lacks the mysterious capacity to be "fully present" in distinct particulars. We feel we understand particulars, perhaps because we are experientially acquainted with them. We do seem to be acquainted with concrete particulars—such as bits of chalk, cheese, and chocolate. But there are other purported entities that strike us as particular rather than universal that are not like these—for example, numbers, classes, propositions, and possibilities. And there are others that are difficult to categorize—such as space and time.
Particularism embraces realism about particulars—there are particulars, and particulars are not reducible to anything more basic—and adds that the only basic entities are particulars. It is thus a one-tier ontology with both considerable simplicity and commonsense in its favor. Particularism affirms that anything at all (universals, numbers, classes, possibilities, causation, space, time) is either eliminable or reducible to particulars. Concrete particularism is more austere, restricting fundamental being to concrete particulars, the paradigms of which are physical objects. The concrete particularist is a realist about concrete particulars and is typically an immanent realist, assigning particulars both spatiotemporal location and a role in the causal order. There are versions of transcendent realism about particulars although typically transcendent particulars will be abstract rather than concrete (for example, numbers, classes, and possibilities).
In what follows particularism is combined with five different versions of nonrealism about universals. These five accounts have all been called "nominalisms," but the nomenclature is not particularly perspicuous. Sometimes nominalism connotes concrete particularism ; at others, the broader doctrine of particularism. Sometimes it connotes antirealism about universals; at others, determinationism. Predicate nominalism, which holds that there are just particulars and the words (names) we call them by, is perhaps the clearest candidate for the title. Mereological nominalism combines concrete particularism with reduction of universals. Conceptualism, sometimes called "concept nominalism," is a version of idealism—reduction of universals to mental particulars. Extensionalism, sometimes called "class nominalism," is a reduction of universals not to concrete particulars but to classes of concrete particulars. Finally, resemblance theories are determinationist and may be of either the reductive or nonreductive kind. The determination base includes concrete particulars and resemblances between them.
predicate nominalism as an eliminativist particularism
The most austere version of nominalism—often called word or predicate nominalism —is naturally construed as concrete particularism combined with eliminativism about universals. It holds that there are concrete particulars and there are the predicates (words) we apply to them, and that is all. Simply put: Things are yellow because we call them "yellow." We call things by the same name—A and B are both called "yellow"—but there is no need to postulate a universal of yellowness instantiated by all things so called. (Distinct people are called "Brian," but we do not postulate a universal Brianness.)
The predicate nominalist repudiates universals rather than reducing them to particulars but accommodates the data by means of the following equivalences:
A is yellow ⇔ A is called "yellow."
B is yellow ⇔ B is called "yellow."
C is brown ⇔ C is called "brown."
On the left-hand side we have some Moorean facts, which apparently presuppose concrete particulars (A, B, C ) and universals (yellowness; brownness). However, the right-hand side supplants reference to a property with reference to a predicate. Since it is implausible to identify yellowness with the predicate "yellow," the position is plausibly construed as denying the universal yellowness: There is a word "yellow," we call a bunch of things "yellow," and if we call them "yellow," they are yellow (end of story).
Some criticisms of word nominalism are worth sketching because they involve argument kinds that crop up repeatedly in this area. The word nominalist's explanation of the data seems backwards. Distinct things are not made yellow by virtue of being called "yellow;" they are called "yellow" because they are one color, conventionally dubbed "yellow." If we call a person "Brian," then for any other similar person—for example, his identical twin—it is a matter of separate convention whether we also call him "Brian." But if we call a color sample on a chart "yellow," and another sample is qualitatively indistinguishable from that, the original convention covers the second color sample, and we call it "yellow," too.
Secondly, since there are only concrete particulars, words must also be concrete particulars. How many words are there on the following line?
yellow, yellow
There are two answers: two and one. There are two concrete words but only one dictionary entry at issue. We must distinguish between word-tokens and word-types. On the one hand, word-tokens are spatially located, unrepeatable, concrete particulars. A word-type, on the other hand, has distinct word-tokens as instances. Word-types look very like universals. Elimination of one universal—yellowness—has only been achieved at the cost of accepting another—the word-type "yellow."
To eliminate this word-type, the nominalist might deploy the complex predicate "called 'tokens of the word-type "yellow."'" But this launches a regress, for the same problem resurfaces for applications of this new predicate. Universals are eliminated at one level only to have them pop up in the shape of word-types at the next. Only if word-types at all levels are eliminable in favor of word-tokens will universals be exorcised, but that would require an infinite supply of word-tokens, and there are just not enough to go around. The nominalist might invoke possible word-tokens here, but that would launch the nominalist beyond the actual world into the problematic outer space of possibility—not a happy place for nominalists to venture.
Finally, chalk is called "yellow," but the cheese is also called "yellow." Calling involves many distinct particular-word pairs—it seems to be a dyadic relation linking particulars and word-tokens, and relations are universals. If one tries to eliminate this relation in favor of another word, we are again launched on a tiresome regress.
There is an alternative construal of predicate nominalism according to which yellowness is eliminated in favor of a different property—being called "yellow." But this would be neither elimination of universals (since both properties have an equal claim to being universals) nor a reduction of universals to particulars. It is simply a proposal to economize within the class of universals itself. As Lewis noted in a different context (possibility), it is not just the number of entities that fall within an ontological category that matters to ontic simplicity, but more importantly, it is the number of basic ontological categories countenanced. If there is something unsatisfactory about the category of universal, then whether you admit one, or a million, or an infinite array is immaterial—your attempt to eliminate universals fails.
mereological nominalism as entity reduction
Predicate nominalism is an eliminativist version of concrete particularism, but there are reductionist versions too—mereological nominalism, for example. Mereology is the theory of the part–whole relation. Some particulars are parts of other particulars. The top of the pen and the body of the pen are both proper parts of the pen, and the pen is the mereological sum of the body and the top. The pen continues to exist even when the top is removed and its parts are separated. Perhaps the chalk and the cheese are also parts of a particular, a spatially scattered whole made partly of chalk and partly of cheese.
Starting with A, B, and C, there are at least four such distinct, albeit overlapping, mereological sums—(A +B ), (B +C ), (A +C ) and (A +B +C )—yielding at least seven distinct concrete particulars in total. Note that sameness of parts entails sameness of whole: ((A +B )+A ), for example, has just two parts, A and B, and so is identical to (A +B ). If there are n basic (nonoverlapping) concrete particulars, then, assuming the principle of unrestricted mereological composition (that every sum of concrete particulars is itself a concrete particular), there are 2n —1 concrete particulars. The principle is controversial, but one way of characterizing concrete particularism is this: The principle of unrestricted composition places an upper bound on the collection of entities.
Let S (F ) be the mereological sum of all particulars to which predicate F applies—S (yellow) is the sum of all yellow things. Plausibly, something is yellow if and only if it is a part of S (yellow). This suggests the following analysis:
X is F ⇔ X is a part of S (F )
Note that the analysis assumes that for any predicate F, the sum of all things with F is also a concrete particular. However, it does not assume unrestricted composition—for there may be collections of particulars to which no single predicate applies. This mereological analysis, if adequate, might allow us to identify the property F -ness with S (F ), a concrete particular.
Mereological nominalism accommodates quite a lot of data about properties such as water and yellow. But take two related properties such as water and single H2O molecule that involve the part–whole relation—a quantity of water has parts that are single H2O molecules. Mereological particularism entails that for something to be water, it has to be a part of S (water), and for something to be a single H2O molecule, it has to be part of the S (single H2O molecule). But these two sums are identical —sum all quantities of water, and sum all single molecules of water, and you arrive at the same whole. So mereological nominalism entails that to be water just is to be a single molecule of water—and that, unfortunately for the theory, is just false.
conceptualism as idealism about universals
The attraction of conceptualism is that it reduces universals to something concrete, particular, and also mind-friendly: concepts. Concepts are things that the mind can get a handle on whereas universals may be problematic in that respect. The beginning idea is that the cheese is yellow if and only if the cheese falls under the concept of yellow. Quite generally, where C (F ) is the concept of F, we have:
X is F ⇔ X falls under C (F ).
We can thus explain the data by appealing to a concept—an apparently familiar mental particular—rather than a mind-independent universal.
Our mental vocabulary (such as belief, thought, desire) suffers a pervasive state-content ambiguity. My belief that the cheese is yellow might be my state of believing, as in: "My belief that the cheese is yellow, given my aversion to yellow cheese, made me refuse it." But it might also be the content of my belief, as in: "My belief is just the same as yours: that the cheese is yellow." Our believings are distinct entities, but what we believe here is the same. Believings are mind-dependent (which believings there are depends on who believes what), but the common content of distinct believings does not depend on what you or I believe.
Concepts also suffer the state-content ambiguity—there are concept-graspings and there are the concepts grasped. Concepts in the state-sense are mind-dependent (which concept-graspings exist depends on who is grasping what), but the contents of such graspings do not appear to be mind-dependent.
The conceptualist may eschew concepts as contents of graspings in favor of a myriad different and individual graspings. But your grasping of yellow has something in common with mine. What is that? If we apply conceptualism to this datum then, as with predicate nominalism, we are launched on a regress and there will not be enough particular concept graspings to accommodate all the data.
extensionalism: reduction of universals to classes
For every predicate F that may or may not apply to a particular, there is the class of all and only the particulars to which F applies in fact, the extension of F —E (F ). In our example, class {A,B } is the extension of yellow, {C } the extension of brown. Something is yellow if and only if it is in the class of yellow things. So the following is an apparently necessary equivalence:
X is F ⇔ X is a member of E (F ).
This suggests identifying F -ness with its extension, E (F ). (After abandoning concrete particularism, Quine adopted extensionalism.)
Extensionalism is sometimes called "class nominalism," but the postulation of classes marks a real departure from concrete particularism. Classes may be particular, but they are not concrete. Classes are "over and above" the concrete particulars that are their members, and Nelson Goodman's criterion explains why. Starting with A, B, C there are at most seven concrete particulars. However, there are many more classes. There are seven nonempty classes of particulars. Each one pairs off with a mereological sum—{A,B } with A +B, {A } with A, and so on—but we cannot identify these classes with the corresponding concrete particulars. Classes are individuated by membership: They are identical if and only if they have exactly the same members (the principle of extensionality). So the singleton class {A } is a distinct entity from its sole member A. A piece of cheese is not a class consisting of a piece of cheese. Quite generally a class is not the mereological sum of its members.
Once we acknowledge classes of classes, the hierarchy of classes "over and above" the concrete particulars, A, B, C explodes into a vast and infinitely intricate structure, one massively exceeding the modest seven-member ontology of mereological sums countenanced by the concrete particularist. The two-membered class {{A,B },A }, for example, is distinct from the two-membered class {A,B }. The former has a member {A,B } that the latter lacks. Contrast this with ((A +B )+A ) and (A +B )—the same concrete particular.
Extensionalism, a radical departure from nominalism, thus has plenty of resources—but does it have enough to do justice to the data? Being a chordate is the property of being a heart-bearing animal; being a renate, the property of being a kidney-bearing animal. These are distinct properties. As it happens, these two properties have the same extension. Extensionalism thus entails that they are one and the same property. As generous as the ontology of classes is, it is not generous enough. This coextension problem is a classic example of an argument against a reduction thesis. The reduction base is shown to be insufficiently rich to capture all relevant entities.
A different criticism suggests that there are too many classes as well. A universal involves sameness. There are, however, "arbitrary" collections of concrete particulars exhibiting no genuine sameness. If the sameness of A and B (yellowness) reduces to the fact that both are members of {A,B }, why does not the fact that A and C are both members of {A,C } yield a genuine sameness there? The class theorist could bite this bullet and accept that all classes are universals. (Bullet-biting is a rather common response to recalcitrant data.) A different response would be to block the counterexample by declaring that only certain "natural" classes are genuine or have what it takes to be universals. (This response exhibits an ad hocness that is arguably worse than bullet-biting.)
An explanatory asymmetry argument against extensionalism is often deployed. It is claimed that A 's being yellow explains A 's membership of the class of yellow particulars, not the other way around. This claim contradicts the extensionalist's claim that these facts are really one and the same. The extensionality principle, however, entails that if X is a member of a class C, then that very class could not have lacked X —any class C * that lacks X is necessarily distinct from C. That A is a member of {A,B } is necessary. That A is yellow is, by contrast, contingent. No contingent fact explains a necessary fact, and so the argument fails. Even though it fails, it suggests a different argument. It follows, by the indiscernibility of identicals, that a contingent fact (such as A 's being yellow) cannot be a necessary fact (such as A 's being a member of {A.B }). But extensionalism entails they are the same fact. Call this the necessary extension problem.
The coextension and necessary extension problems are closely related. The reason chordate and renate cannot be identified with the class that is their common extension is that their extensions might well have differed from each other. And that presupposes that they have their extensions contingently, not necessarily. Since chordate and renate differ in their possible extensions, one way of modifying extensionalism would be to expand the reduction base to include possibilia. Two accounts have predominated. One embraces possible but nonactual particulars and takes the extension of property P to be the class of actual and nonactual particulars that have P. (This presupposes that particulars are world-bound—no particular appears in more than one possible world.) Another is to include possible but nonactual worlds with common or overlapping domains of particulars. In each possible world W, the property P has an extension in W. The property P thus induces a function F (P ) from worlds to extensions—and a reductionist might identify P with the function F (P ). These accounts are both reductionist, presupposing different accounts of possibility. They go well beyond the domain of concrete particulars entertained by traditional extensionalists, and they are both known as intensional accounts of universals.
Despite the richness of the framework of worlds and functions, however, it may still not be rich enough to capture all the data. Being triangular is the property of being a plane figure with three angles. Being trilateral is the property of being a plane figure with three sides. Because each logically necessitates the other, these properties induce the very same function from worlds to classes of concrete particulars (or classes of possibilia), and so even these intensionalist accounts render them identical. If they are not identical, then we need something more discriminating than functions from worlds to classes of particulars with which to identify them.
resemblance theories: reduction and supervenience
An important group of theories claim that property facts are determined by facts about resemblance. A crude version of the resemblance theory invokes paradigms, and resemblance to such paradigms—namely, where P (F ) is a specified paradigm of F :
X is F ⇔ X resembles P (F ).
The shortcomings of the paradigm account are numerous. It entails, for example, that the designated paradigm of yellowness is necessarily yellow (since everything necessarily resembles itself). It also entails that anything resembling P (F ) in any respect at all is F. A far more promising account draws on the notion of similarity circle —a class such that all the members of the class resemble every member of the class, and nothing outside the class also resembles every member of the class. Provided that there is sufficient variety in particulars, similarity circles carve out what are, intuitively, the genuine universals without the necessity for privileging any particular. This might be regarded as a reduction of universals to classes of particulars plus resemblances, but it can also be regarded as a supervenience thesis: Properties supervene on a basis consisting of resemblance and the domain of particulars. There can be no difference in properties without some difference in the structure of resemblances—same resemblance structure, same properties.
As Russell famously noted, any account that grounds properties in resemblance faces a problem. Resemblance is a relation between particulars and as such seems to be a universal. It might be considered an ontological saving to reduce myriad universals to one, but as noted in the context of word nominalism, what is important is the number of nonempty ontological categories.
This criticism of resemblance theories can be generalized to any attempt to reduce universals to something "else." Suppose we reduce property P to some entity Reduct(P ): the class of P s; the mereological sum of P s; the concept of P ; the similarity circle that corresponds to P, and so on. The reductionist says that for X to be P is for X to bear some suitable relation R to Reduct(P ). But the reductionist is then forced either to admit one universal—the relation R —or to apply the theory to R itself, launching an unhappy regress.
Resemblance theorists might employ the tu quoque, charging that the realist faces a similar regress. Assume realism: For X to be yellow is for X to instantiate (I ) the universal yellowness (Y ). But then, for X to instantiate Y is for a certain triple—X,Y,I —to stand in a relation, I *. I * cannot be I. For one thing I, is a dyadic relation, and I * is a triadic relation. For another, this would involve a relation taking itself as one of its own relata. So I * is distinct from I. We can repeat the argument to obtain a third relation I **, and so on. So the realist is thus as much involved in a regress as any of the reductionist rivals.
The realist might appeal to the category response: The regress is damaging to the particularist because it shows that the category of relation cannot be done away with. That's an internal inconsistency. But the realist about universals does not object to that category being nonempty, and even an infinite class of distinct instantiation relations constitutes no embarrassment for realism as such. Of course, a realist who wants to keep the number of universals down to a small or finite collection might be embarrassed.
Finally, the resemblance theorist may run out of the kind of variety in actual objects required to set properties apart. (Renate and chordate are still coextensive.) To increase the variety and block a coextension objection, the resemblance theorist might take a now familiar tack—embracing relations of resemblance between possible as well as actual particulars. As with the related attempts to deflect counterexamples by invoking possibilia, this constitutes a significant and not entirely unproblematic expansion of the reduction base. Certainly it violates the original nominalistic spirit that inspired it.
Realism about Both Particulars and Universals
One explanation for this apparent failure to eliminate or reduce universals is realism—that universals are neither eliminable, nor reducible, nor supervenient. That this is no proof of realism is obvious—we may not have exhausted all possible alternatives. However, realism about universals conjoined with realism about particulars does explain these failures, as well as providing an explanation of the ubiquitous Moorean facts of predication.
transcendent realism about universals
What is often called ante rem realism, or Platonic realism, is a transcendent realism: that irreducible universals exist of necessity, beyond contingency in general, and beyond the contingent causal network in particular. One powerful explanatory principle, typically embraced by transcendent realists (Plato perhaps) states that any meaningful predicate, whether simple or complex, applies to things in virtue of designating a genuine universal. So not only contingent predicates such as "black" and "raven" designate universals, so, too, do predicates that apply of necessity (such as "self-identical"); predicates that apply to nothing (such as "unicorn"); predicates that apply to nothing of necessity (such as "self-distinct"); and finally, not only simple predicates (such as "black" and "raven") designate universals, but so do complex predicates (such as "black raven," "not black," "black or raven," "black if and only if a raven," and so on). Since predicates apply to universals themselves (e.g., yellowness is a pretty color ), universals are instances of other universals. This unrestricted transcendent realism makes the domain of universals a largely a priori affair.
Perhaps the greatest threat to unrestricted transcendent realism is Russell's paradox. Particulars have properties (such as being honest or cowardly), but properties also have properties (honesty is virtue, chalkiness is a universal, a piece of chalk is not a universal), and those properties have properties in turn (virtue is good, being a universal is something all universals have in common, being a particular is a universal not a particular).
By unrestricted realism the two predicates—being a universal and being a concrete particular —designate two universals, U and P. All universals have U in common. U is a universal, and so U itself has U. U is self-predicating. However, P is not a concrete particular (it is a universal), and so P is non-self-predicating. Given unrestricted realism, the meaningful predicate non-self-predicating designates a universal, N. Each universal either has N or lacks N. If N has N, then N is non-self-predicating—but then N does not self-predicate and so N lacks N (contradiction). If N lacks N, then N is not non-self-predicating; that is, N is self-predicating, and so N has N (contradiction again).
Russellian paradoxes can be constructed for just about any account of universals, including the most austere version of predicate nominalism. (The predicate "short" is called "short," but the predicate "long" is not called "long." Call the former "self-predicating" and the latter "non-self-predicating." Is the predicate "non-self-predicating" called "non-self-predicating"? Paradox ensues.) Russellian paradoxes are thus too pervasive, the realist might claim, for them to be peculiarly damaging to realism. Still, short of embracing paradoxes, the realist has an obligation to deflect them.
Any adequate realist answer to Russellian paradoxes must involve some restriction on the predicates: namely, not every apparently meaningful predicate necessarily designates a universal. Russell's theory of types is a classic restriction. Type theory stratifies entities. Simplifying somewhat: particulars are type-0 entities, properties of particulars are type-1 entities, properties of (type-1) properties are type-2 entities, and so on. A type-0 entity may either have or lack a type-1 property, and a type-1 property may have or lack a type-2 property, but no property either has or lacks a property of the same type. A property is always one type higher than the highest type of entity to which it can be sensibly applied or denied. Thus, the question of whether a universal P has or lacks itself does not arise. It is neither true nor untrue that P lacks P. The very attempt to apply P to itself is a category error (like the attempt to apply the color green to the number 7), and so the predicates "self-predicating" and "non-self-predicating" are literally meaningless. (The notion of a category error took on a life of its own long after Russell's theory of types lost the attention of most philosophers.) The paradox is blocked because there are no universals of self-predication or of non-self-predication.
The chief worry about a type theory is that it rules itself out as unsayable—to state it one must violate its strictures. Take the claim no universal can be applied to, or denied of, a universal of the same type. This makes a perfectly general claim about all universals. What type does the universal of being a universal (U ) belong to? It cannot consistently be assigned a level. It is this problem that undergirds the famous theme of Wittgenstein's Tractatus, that philosophy consists of things that can be shown but cannot be said.
immanent realism about universals
An important group of restricted realist theories trace their ancestry to Aristotle. Not every predicate picks out a universal, and it is a contingent matter, to be settled a posteriori, what universals there are. In rebus realism is a version of immanent realism. It begins with the simple idea that universals exist only in their instances. If a universal is not instantiated, it does not exist. Consequently, a predicate must apply to a particular for it to designate a genuine universal. This instantiation condition prohibits universals such as unicornhood. It also rules out various truth-functional combinations of universals. Even if black and raven are both universals, the predicate "not black and a raven" does not designate a universal (since all ravens are black).
Armstrong, a prominent advocate of immanent realism, places two further conditions on a predicate for it to designate a universal. Firstly, the predicate must apply in virtue of a genuine identity in the particulars. Even if yellow and raven are both universals, the disjunctive predicate "yellow or a raven" does not pick out a universal, despite being instantiated, because there is no qualitative identity exemplified by a yellow submarine and a black raven. Secondly, Armstrong draws on a condition inspired by the Eleatic Stranger in Plato's Sophist, who makes the intriguing suggestion (known as the Eleatic Principle ) that the mark of being is causal power. Armstrong requires that to be real, a universal must feature in causal laws. (Universals must do some work for their living.)
The Eleatic Principle gives natural science a crucial role in delineating the ultimate constituents of being. Interestingly, it also suggests an immanent realism that denies the instantiation condition. Michael Tooley has argued, within the same immanent realist framework, that there could be properties that play a genuine role in the causal order, because they enter into basic causal laws, but that could remain uninstantiated. If causal power is the mark of the real, it would be hard to deny them ontic standing, but if so, they are not in rebus universals—they exist independently of their exemplification by particulars. Clearly, there is wide scope for other, quite different versions of both transcendent and immanent realism about universals.
Realism about Universals, Reductionism about Particulars
If one embraces realism about universals, then, for the sake of simplicity, it would be worthwhile exploring the reduction or particulars to universals. Every particular X comes along with a bundle (or a class) of properties, B (X )—the class of all the properties it has. Further, an object X has property P if and only if P is a member of B (X ). This suggests that we embrace just one entity (the bundle) rather than two (the particular and its bundle). The bundle theory identifies a particular with the bundle of its properties.
This bundle theory faces problems analogous to the reduction of universals to classes of particulars—both too many classes and not enough classes. Firstly, there are too many classes. The class {golden, mountain} does not pick out any actual concrete particular—the golden mountain does not exist. This fact, however, may not be considered entirely undesirable. Meinong famously argued that metaphysics needs to accommodate data pertaining to the nonactual as well as to the actual. To explain the nonexistence of the golden mountain, the golden mountain must be an object with a specific nature, a nature that it possesses of necessity. If being golden and mountainous were contingent properties of the golden mountain, then who is to say that Kilimanjaro is not the golden mountain? The bundle theory thus dovetails nicely with this theory of possible objects.
The bundle theorist still owes us an account of the distinction between concrete existent particulars (Kilimanjaro) and merely possible particulars (the golden mountain). Meinong thought that it is their completeness that sets them apart. Kilimanjaro is complete—for every property, Kilimanjaro either has it or lacks it. The golden mountain is incomplete—it is a mountain, and it is made of gold, but for many properties (e.g., more than 1 mile high ), it neither has the property nor lacks it. But this will not do—we could specify complete bundles of properties that do not correspond to any concrete particular.
Are there enough bundles of properties to accommodate all particulars, or does the bundle theory face a coextension problem? A bundle theory of particulars entails the Identity of indiscernibles (the converse of the indiscernibility of identicals): If X and Y are qualitatively identical (share all properties), then X and Y are numerically identical. This principle would be trivially true provided conditions such as being identical to X were genuine properties. But the bundle theorist cannot start with properties that presuppose antecedently given particulars. The bundling properties would have to be purely qualitative. But then it does seem possible for distinct particulars to share all their purely qualitative properties. (Quantum theory, for example, entails that it is possible for two bosons to share their fundamental quantum states—including the state corresponding to location.) That is incompatible with the bundle theory.
An essential property of a particular is a property without which that particular would not exist. It is controversial whether there are essential properties, and if so, which properties of any given particular are essential. However, there is widespread agreement that not every property of a particular is essential to it. At least some properties are such that an item could lose them without going out of existence. The bundle theory suffers an analogue of the necessary extension problem. Classes by their nature are necessary, eternal, and unchanging. So the bundle theory would appear to entail super-essentialism : that every property of a particular is essential to it; that if a particular lost a property, it would cease to be.
Rejecting Realism about Universals and Particulars
The space of possibilities is not restricted to reduction in one of two directions. Universals and particulars might both be reduced to some third, more basic, kind of entity. One prominent example of such an approach is trope theory.
A trope (this patch of brownness, that instance of sweetness) is a particularized universal—a particular instantiation of a universal by a particular. Put like that, of course, tropes apparently presuppose both particulars and universals. They appear to be nonbasic entities. But it is a characteristic move in metaphysics to take as ontologically basic something that has hitherto been assumed to be derivative and reverse the ontological order.
Tropes have the advantage of incorporating both particularity and qualitative character in their nature and are thus promising building blocks. The proposal is that particulars and universals are both classes of tropes, albeit different kinds of classes: Particulars are classes of co-located tropes—tropes occupying the same space and time—and universals are classes of exactly resembling tropes. A particular X has property P just in case the class of co-located tropes that make up X overlaps with the class of resembling tropes that constitute P.
Trope theory has the advantages of simplicity and comprehensiveness. Further, it avoids the co-extension problem that besets extensionalism. No redness trope is identical to a roundness trope. So even if redness and roundness always go together (they are always co-located) the class of all roundness tropes is a distinct class from that of redness tropes.
Trope theory retains the necessary extension problem. Classes have their members by necessity, but a concrete particular does not have its properties by necessity. By identifying predication with the intersection of two classes, trope theory implies that all predications are necessary. Again, such problems may be avoidable by invoking possible worlds, but only at the cost of expanding the reduction base to something that makes the resulting reduction rather costly in terms of ontological resources.
The Future of Metaphysics
The proposed schema for locating metaphysical theories is applicable in all of the various domains of the discipline, and the argument patterns for realism, antirealism, and determinationism bear important similarities across those domains. The basic data might involve claims about time, causation, possibility, the fundamental truths of arithmetic, mental states, spatial relations, value, morality, and so on. Theorists will take the data and lay out an ontology to explain them, or explain them away, either taking the surface ontology at face value, explaining it in terms of something more basic, or occasionally eliminating it altogether.
The modern metaphysician, aware of the underdetermination of theory by data, rarely expects or demands that the arguments conclusively establish any metaphysical proposal. Rather, the metaphysician will examine each metaphysical proposal on its explanatory merits, assessing first its explanatory adequacy with respect to the existing data, searching for new data to test and probe the proposal, and then turning to the more inherently contestable issues of theoretical elegance, economy, and overall coherence with other metaphysical theories. Inevitably, a considerable degree of fallibility and uncertainty remains. Still, that acknowledged, the future of metaphysics is no less secure than the future of science: Human beings can and will continue to probe the fundamental nature of the world right up to the limits of their cognitive abilities. Their doing so will, inescapably, implicate them in the enterprise of metaphysics.
See also Aristotle; Armstrong, David M.; Berkeley, George; Carnap, Rudolf; Chisholm, Roderick; Frege, Gottlob; Gödel, Kurt; Goodman, Nelson; Hume, David; Kant, Immanuel; Leibniz, Gottfried Wilhelm; Lewis, David; Mackie, John Leslie; Meinong, Alexius; Metaphysics, History of; Metaphysics, Nature of; Moore, George Edward; Newton, Isaac; Plato; Popper, Karl Raimund; Prior, Arthur Norman; Quine, Willard Van Orman; Russell, Bertrand Arthur William; Smart, John Jamieson Carswell; Spinoza, Benedict (Baruch) de; Strawson, Peter Frederick; Wittgenstein, Ludwig Josef Johann.
The Encyclopedia contains two additional general articles on this subject: Metaphysics, History of , and Metaphysics, Nature of . It also features the following articles: Absolute, The ; Apeiron/Peras ; Appearance and Reality ; Arche ; Being ; Categories ; Causation: Metaphysical Issues ; Chance ; Chaos Theory ; Continuity ; Cosmos ; Determinism, A Historical Survey ; Dialectic ; Emanationism ; Essence and Existence ; Eternal Return ; Eternity ; Hen/Polla ; Idealism ; Identity ; Infinity in Theology and Metaphysics ; Logos ; Macrocosm and Microcosm ; Materialism ; Monad and Monadology ; Monism and Pluralism ; Naturalism ; Nature, Philosophical Ideas of ; Nomos and Phusis ; Nothing ; Nous ; Ontology ; Panpsychism ; Personal Identity ; Personalism ; Persons ; Pessimism and Optimism ; Possibility ; Relations, Internal and External ; Solipsism ; Substance and Attribute ; Time ; Unconscious ; Universals, A Historical Survey ; Vitalism ; Voluntarism ; Why .
Differing schools of metaphysical thought are represented in the articles Aristotelianism ; Augustinianism ; Cartesianism ; Hegelianism ; Neoplatonism ; Ockhamism ; Platonism and the Platonic Tradition ; Scotism ; Spinozism ; Stoicism ; Thomism .
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Graham Oddie (2005)