First published Mon Sep 10, 2007; substantive revision Fri Oct 31, 2014

The first three sections of this entry examine a broad selection of problems considered to be metaphysical and discuss ways in which the purview of metaphysics has expanded over time. We shall see that the central problems of metaphysics were significantly more unified in the Ancient and Medieval eras. Which raises a question—is there any common feature that unites the problems of contemporary metaphysics? The final two sections discuss some recent theories of the nature and methodology of metaphysics. We will also consider arguments that metaphysics, however defined, is an impossible enterprise.

It is not easy to say what metaphysics is. Ancient and Medieval philosophers might have said that metaphysics was, like chemistry or astrology, to be defined by its subject-matter: metaphysics was the “science” that studied “being as such” or “the first causes of things” or “things that do not change”. It is no longer possible to define metaphysics that way, for two reasons. First, a philosopher who denied the existence of those things that had once been seen as constituting the subject-matter of metaphysics—first causes or unchanging things—would now be considered to be making thereby a metaphysical assertion. Second, there are many philosophical problems that are now considered to be metaphysical problems (or at least partly metaphysical problems) that are in no way related to first causes or unchanging things—the problem of free will, for example, or the problem of the mental and the physical.

The word ‘metaphysics’ is notoriously hard to define. Twentieth-century coinages like ‘meta-language’ and ‘metaphilosophy’ encourage the impression that metaphysics is a study that somehow “goes beyond” physics, a study devoted to matters that transcend the mundane concerns of Newton and Einstein and Heisenberg. This impression is mistaken. The word ‘metaphysics’ is derived from a collective title of the fourteen books by Aristotle that we currently think of as making up Aristotle's Metaphysics. Aristotle himself did not know the word. (He had four names for the branch of philosophy that is the subject-matter of Metaphysics: ‘first philosophy’, ‘first science’, ‘wisdom’, and ‘theology’.) At least one hundred years after Aristotle's death, an editor of his works (in all probability, Andronicus of Rhodes) titled those fourteen books “Ta meta ta phusika”—“the after the physicals” or “the ones after the physical ones”—the “physical ones” being the books contained in what we now call Aristotle's Physics. The title was probably meant to warn students of Aristotle's philosophy that they should attempt Metaphysics only after they had mastered “the physical ones”, the books about nature or the natural world—that is to say, about change, for change is the defining feature of the natural world.

This is the probable meaning of the title because Metaphysics is about things that do not change. In one place, Aristotle identifies the subject-matter of first philosophy as “being as such”, and, in another as “first causes”. It is a nice—and vexed—question what the connection between these two definitions is. Perhaps this is the answer: The unchanging first causes have nothing but being in common with the mutable things they cause. Like us and the objects of our experience—they are, and there the resemblance ceases. (For a detailed and informative recent guide to Aristotle's Metaphysics, see Politis 2004.)

Should we assume that ‘metaphysics’ is a name for that “science” which is the subject-matter of Aristotle's Metaphysics? If we assume this, we should be committed to something in the neighborhood of the following theses:

The subject-matter of metaphysics is “being as such”

The subject-matter of metaphysics is the first causes of things

The subject-matter of metaphysics is that which does not change

Any of these three theses might have been regarded as a defensible statement of the subject-matter of what was called ‘metaphysics’ until the seventeenth century. But then, rather suddenly, many topics and problems that Aristotle and the Medievals would have classified as belonging to physics (the relation of mind and body, for example, or the freedom of the will, or personal identity across time) began to be reassigned to metaphysics. One might almost say that in the seventeenth century metaphysics began to be a catch-all category, a repository of philosophical problems that could not be otherwise classified as epistemology, logic, ethics or other branches of philosophy. (It was at about that time that the word ‘ontology’ was invented—to be a name for the science of being as such, an office that the word ‘metaphysics’ could no longer fill.) The academic rationalists of the post-Leibnizian school were aware that the word ‘metaphysics’ had come to be used in a more inclusive sense than it had once been. Christian Wolff attempted to justify this more inclusive sense of the word by this device: while the subject-matter of metaphysics is being, being can be investigated either in general or in relation to objects in particular categories. He distinguished between ‘general metaphysics’ (or ontology), the study of being as such, and the various branches of ‘special metaphysics’, which study the being of objects of various special sorts, such as souls and material bodies. (He does not assign first causes to general metaphysics, however: the study of first causes belongs to natural theology, a branch of special metaphysics.) It is doubtful whether this maneuver is anything more than a verbal ploy. In what sense, for example, is the practitioner of rational psychology (the branch of special metaphysics devoted to the soul) engaged in a study of being? Do souls have a different sort of being from that of other objects?—so that in studying the soul one learns not only about its nature (that is, its properties: rationality, immateriality, immortality, its capacity or lack thereof to affect the body …), but also about its “mode of being”, and hence learns something about being? It is certainly not true that all, or even very many, rational psychologists said anything, qua rational psychologists, that could plausibly be construed as a contribution to our understanding of being.

Perhaps the wider application of the word ‘metaphysics’ was due to the fact that the word ‘physics’ was coming to be a name for a new, quantitative science, the science that bears that name today, and was becoming increasingly inapplicable to the investigation of many traditional philosophical problems about changing things (and of some newly discovered problems about changing things).

Whatever the reason for the change may have been, it would be flying in the face of current usage (and indeed of the usage of the last three or four hundred years) to stipulate that the subject-matter of metaphysics was to be the subject-matter of Aristotle's Metaphysics. It would, moreover, fly in the face of the fact that there are and have been paradigmatic metaphysicians who deny that there are first causes—this denial is certainly a metaphysical thesis in the current sense—others who insist that everything changes (Heraclitus and any more recent philosopher who is both a materialist and a nominalist), and others still (Parmenides and Zeno) who deny that there is a special class of objects that do not change. In trying to characterize metaphysics as a field, the best starting point is to consider the myriad topics traditionally assigned to it.

If metaphysics now considers a wider range of problems than those studied in Aristotle's Metaphysics, those original problems continue to belong to its subject-matter. For instance, the topic of “being as such” (and “existence as such”, if existence is something other than being) is one of the matters that belong to metaphysics on any conception of metaphysics. The following theses are all paradigmatically metaphysical:

“Being is; not-being is not” [Parmenides];

“Essence precedes existence” [Avicenna, paraphrased];

“Existence in reality is greater than existence in the understanding alone” [St Anselm, paraphrased];

“Existence is a perfection” [Descartes, paraphrased];

“Being is a logical, not a real predicate” [Kant, paraphrased];

“Being is the most barren and abstract of all categories” [Hegel, paraphrased];

“Affirmation of existence is in fact nothing but denial of the number zero” [Frege];

“Universals do not exist but rather subsist or have being” [Russell, paraphrased];

“To be is to be the value of a bound variable” [Quine].

It seems reasonable, moreover, to say that investigations into non-being belong to the topic “being as such” and thus belong to metaphysics. (This did not seem reasonable to Meinong, who wished to confine the subject-matter of metaphysics to “the actual” and who therefore did not regard his Theory of Objects as a metaphysical theory. According to the conception of metaphysics adopted in this article, however, his thesis [paraphrased] “Predication is independent of being” is paradigmatically metaphysical.)

The topics “the first causes of things” and “unchanging things”—have continued to interest metaphysicians, though they are not now seen as having any important connection with the topic “being as such”. The first three of Aquinas's Five Ways are metaphysical arguments on any conception of metaphysics. Additionally the thesis that there are no first causes and the thesis that there are no things that do not change count as metaphysical theses, for in the current conception of metaphysics, the denial of a metaphysical thesis is a metaphysical thesis. No post-Medieval philosopher would say anything like this:

I study the first causes of things, and am therefore a metaphysician. My colleague Dr McZed denies that there are any first causes and is therefore not a metaphysician; she is rather, an anti-metaphysician. In her view, metaphysics is a science with a non-existent subject-matter, like astrology.

This feature of the contemporary conception of metaphysics is nicely illustrated by a statement of Sartre's:

I do not think myself any less a metaphysician in denying the existence of God than Leibniz was in affirming it. (1949: 139)

An anti-metaphysician in the contemporary sense is not a philosopher who denies that there are objects of the sorts that an earlier philosopher might have said formed the subject-matter of metaphysics (first causes, things that do not change, universals, substances, …), but rather a philosopher who denies the legitimacy of the question whether there are objects of those sorts.

The three original topics—the nature of being; the first causes of things; things that do not change—remained topics of investigation by metaphysicians after Aristotle. Another topic, discussed in the following subsection, occupies an intermediate position between Aristotle and his successors.

We human beings sort things into various classes. And we often suppose that the classes into which we sort things enjoy a kind of internal unity. In this respect they differ from sets in the strict sense of the word. (And no doubt in others. It would seem, for example, that we think of the classes we sort things into—biological species, say—as comprising different members at different times.) The classes into which we sort things are in most cases “natural” classes, classes whose membership is in some important sense uniform—“kinds”. We shall not attempt an account or definition of ‘natural class’ here. Examples must suffice. There are certainly sets whose members do not make up natural classes: a set that contains all dogs but one, and a set that contains all dogs and exactly one cat do not correspond to natural classes in anyone's view. And it is tempting to suppose that there is a sense of “natural” in which dogs make up a natural class, to suppose that in dividing the world into dogs and non-dogs, we “cut nature at the joints”. It is, however, a respectable philosophical thesis that the idea of a natural class cannot survive philosophical scrutiny. If that respectable thesis is true, the topic “the categories of being” is a pseudo-topic. Let us simply assume that the respectable thesis is false and that things fall into various natural classes—hereinafter, simply classes.

Some of the classes into which we sort things are more comprehensive than others: all dogs are animals, but not all animals are dogs; all animals are living organisms, but not all living organisms are animals …. Now the very expression “sort things into classes” suggests that there is a most comprehensive class: the class of things, the class of things that can be sorted into classes. But is this so?—and if it is so, are there classes that are “just less comprehensive” than this universal class? If there are, can we identify them?—and are there a vast (perhaps even an infinite) number of them, or some largish, messy number like forty-nine, or some small, neat number like seven or four? Let us call any such less comprehensive classes the ‘categories of being’ or the ‘ontological categories’. (The former term, if not the latter, presupposes a particular position on one question about the nature of being: that everything is, that the universal class is the class of beings, the class of things that are. It thus presupposes that Meinong was wrong to say that “there are things of which it is true that there are no such things”.)

The topic “the categories of being” is intermediate between the topic “the nature of being” and the topics that fall under the post-Medieval conception of metaphysics for a reason that can be illustrated by considering the problem of universals. Universals, if they indeed exist, are, in the first instance, properties or qualities or attributes (i.e., “ductility” or “whiteness”) that are supposedly universally “present in” the members of classes of things and relations (i.e., “being to the north of”) that are supposedly universally present in the members of classes of sequences of things. “In the first instance”: it may be that things other than qualities and relations are universals, although qualities and relations are the items most commonly put forward as examples of universals. It may be that the novel War and Peace is a universal, a thing that is in some mode present in each of the many tangible copies of the novel. It may be that the word “horse” is a universal, a thing that is present in each of the many audible utterances of the word. And it may be that natural classes or kinds are themselves universals—it may be that there is such a thing as “the horse” or the species Equus caballus, distinct from its defining attribute “being a horse” or “equinity”, and in some sense “present in” each horse. (Perhaps some difference between the attribute “being a horse” and the attribute “being either a horse or a kitten” explains why the former is the defining attribute of a kind and the latter is not. Perhaps the former attribute exists and the latter does not; perhaps the former has the second-order attribute “naturalness” and the latter does not; perhaps the former is more easily apprehended by the intellect than the latter.)

The thesis that universals exist—or at any rate “subsist” or “have being”—is variously called ‘realism’ or ‘Platonic realism’ or ‘platonism’. All three terms are objectionable. Aristotle believed in the reality of universals, but it would be at best an oxymoron to call him a platonist or a Platonic realist. And ‘realism’ tout court has served as a name for a variety of philosophical theses. The thesis that universals do not exist—do not so much as subsist; have no being of any sort—is generally called ‘nominalism’. This term, too is objectionable. At one time, those who denied the existence of universals were fond of saying things like:

There is no such thing as “being a horse”: there is only the name [nomen, gen. nominis] “horse”, a mere flatus vocis [puff of sound].

Present-day nominalists, however, are aware, if earlier nominalists were not, that if the phrase ‘the name “horse” ’ designated an object, the object it designated would itself be a universal or something very like one. It would not be a mere puff of sound but would rather be what was common to the many puffs of sound that were its tokens.

The old debate between the nominalists and the realists continues to the present day. Most realists suppose that universals constitute one of the categories of being. This supposition could certainly be disputed without absurdity. Perhaps there is a natural class of things to which all universals belong but which contains other things as well (and is not the class of all things). Perhaps, for example, numbers and propositions are not universals, and perhaps numbers and propositions and universals are all members of a class of “abstract objects”, a class that some things do not belong to. Or perhaps there is such a thing as “the whiteness of the Taj Mahal” and perhaps this object and the universal “whiteness”—but not the Taj Mahal itself—both belong to the class of “properties”. Let us call such a class—a proper subclass of an ontological category, a natural class that is neither the class of all things nor one of the ontological categories—an ‘ontological sub-category’. It may indeed be that universals make up a sub-category of being and are members of the category of being “abstract object”. But few if any philosophers would suppose that universals were members of forty-nine sub-categories—much less of a vast number or an infinity of sub-categories. Most philosophers who believe in the reality of universals would want to say that universals, if they do not constitute an ontological category, at least constitute one of the “higher” sub-categories. If dogs form a natural class, this class is—by the terms of our definition—an ontological sub-category. And this class will no doubt be a subclass of many sub-categories: the genus canis, the class (in the biological sense) mammalia, …, and so through a chain of sub-categories that eventually reaches some very general sub-category like “substance” or “material object”. Thus, although dogs may compose an ontological sub-category, this sub-category—unlike the category “universal”—is one of the “lower” ones. These reflections suggest that the topic “the categories of being” should be understood to comprehend both the categories of being sensu stricto and their immediate sub-categories.

Does the topic “the categories of being” belong to metaphysics in the “old” sense? A case can be made for saying that it does, based on the fact that Plato's theory of forms (universals, attributes) is a recurrent theme in Aristotle's Metaphysics. In Metaphysics, two of Plato's central theses about the forms come in for vigorous criticism: (i) that things that would, if they existed, be “inactive” (the forms) could be the primary beings, the “most real” things, and (ii) that the attributes of things exist “separately” from the things whose attributes they are. We shall be concerned only with (ii). In the terminology of the Schools, that criticism can be put this way: Plato wrongly believed that universals existed ante res (prior to objects); the correct view is that universals exist in rebus (in objects). It is because this aspect of the problem of universals—whether universals exist ante res or in rebus—is discussed at length in Metaphysics, that a strong case can be made for saying that the problem of universals falls under the old conception of metaphysics. (And the question whether universals, given that they exist at all, exist ante res or in rebus is as controversial in the twenty-first century as it was in the thirteenth century and the fourth century B.C.E.) If we do decide that the problem of universals belongs to metaphysics on the old conception, then, since we have liberalized the old conception by applying to it the contemporary rule that the denial of a metaphysical position is to be regarded as a metaphysical position, we shall have to say that the question whether universals exist at all is a metaphysical question under the old conception—and that nominalism is therefore a metaphysical thesis.

There is, however, also a case to made against classifying the problem of universals as a problem of metaphysics in the (liberalized) old sense. For there is more to the problem of universals than the question whether universals exist and the question whether, if they do exist, their existence is ante res or in rebus. For example, the problem of universals also includes questions about the relation between universals (if such there be) and the things that are not universals, the things usually called particulars. Aristotle did not consider these questions in the Metaphysics. One might therefore plausibly contend that only one part of the problem of universals (the part that pertains to the existence and nature of universals) belongs to metaphysics in the old sense. At one time, a philosopher might have said,

The universal “doghood” is a thing that does not change. Therefore, questions about its nature belong to metaphysics, the science of things that do not change. But dogs are things that change. Therefore, questions concerning the relation of dogs to doghood do not belong to metaphysics.

But no contemporary philosopher would divide the topics that way—not even if he or she believed that doghood existed and was a thing that did not change. A contemporary philosopher—if that philosopher concedes that there is any problem that can properly be called “the problem of universals”—will see the problem of universals as a problem properly so called, as a problem having the kind of internal unity that leads philosophers to speak of a philosophical problem. And the same point applies to the topic “the categories of being”: every philosopher who is willing to say that “What are the categories of being?” is a meaningful question will assign every aspect of that question to metaphysics

Let us consider some aspects of the problem of universals that concern changing things. (That is, that concern particulars—for even if there are particulars that do not change, most of the particulars that figure in discussions of the problem of universals as examples are things that change.) Consider two white particulars—the Taj Mahal, say, and the Washington Monument. And suppose that both these particulars are white in virtue of (i.e., their being white consists in) their bearing some one, identifiable relation to the universal “whiteness”. Suppose further that we are able to single out this relation by some sort of act of intellectual attention or abstraction, and that (having done so) we have given it the name “falling under”. All white things and only white things fall under whiteness, and falling under whiteness is what it is to be white. (We pass over many questions that would have to be addressed if we were discussing the problem of universals for its own sake. For example, both blueness and redness are spectral color-properties, and whiteness is not. Does this fact imply that “being a spectral color-property” is, as one might say, a second-order universal? If so, does blueness “fall under” this universal in the same sense as the sense in which a copy of Philosophical Studies falls under blueness?)

Now what can we say about this relation, this “falling under”? What is it about the two objects whiteness and the Taj Mahal that is responsible for the fact that the latter falls under the former? Is the Taj perhaps a “bundle” of universalia ante res, and does it fall under whiteness in virtue of the fact that whiteness is one of the universals that is a constituent of the bundle that it is? Or might it be that a particular like the Taj, although it indeed has universals as constituents, is something more than its universal constituents? Might it be that the Taj has a constituent that is not a universal, a “substrate”, a particular that is in some sense property-less and that holds the universal constituents of the Taj together—that “bundles” them? (If we take that position, then we may want to say, with Armstrong (1989: 94–96), that the Taj is a ‘thick particular’ and its substrate a ‘thin particular’: a thick particular being a thin particular taken together with the properties it bundles.) Or might the Taj have constituents that are neither universals nor substrates? Might we have been too hasty when we defined ‘particulars’ as things that are not universals? Could there perhaps be two kinds of non-universals, concrete non-universals or concrete individuals (those would be the particulars, thick or thin), and abstract non-universals or abstract individuals (‘accidents’ or ‘tropes’ or ‘property instances’), things that are properties or qualities (and relations as well), things like “the (individual) whiteness of the Taj Mahal”? Is the Taj perhaps a bundle not of universals but of accidents? Or is it composed of a substrate and a bundle of accidents? And we cannot neglect the possibility that Aristotle was right and that universals exist only in rebus. If that is so, we must ask what the relation is between the matter that composes a particular and the universals that inhere in it—that inhere simultaneously in “this” matter and in “that” matter.

The series of questions that was set out in the preceding paragraph was introduced by observing that the problem of universals includes both questions about the existence and nature of universals and questions about how universals are related to the particulars that fall under them. Many of the theories that were alluded to in that series of questions could be described as theories of the “ontological structure” of non-universals. We can contrast ontological structure with mereological structure. A philosophical question concerns the mereological structure of an object if it is a question about the relation between that object and those of its constituents that belong to the same ontological category as the object. For example, the philosopher who asks whether the Taj Mahal has a certain block of marble among its constituents essentially or only accidentally is asking a question about the mereological structure of the Taj, since the block and the building belong to the same ontological category. But the philosopher who asks whether the Taj has “whiteness” as a constituent and the philosopher who supposes that the Taj does have this property-constituent and asks, “What is the nature of this relation ‘constituent of’ that ‘whiteness’ bears to the Taj?” are asking questions about its ontological structure.

Many philosophers have supposed that particulars fall under universals by somehow incorporating them into their ontological structure. And other philosophers have supposed that the ontological structure of a particular incorporates individual properties or accidents—and that an accident is an accident of a certain particular just in virtue of being a constituent of that particular.

Advocates of the existence of ante res universals, and particularly those who deny that these universals are constituents of particulars, tend to suppose that universals abound—that there is not only such a universal as whiteness but such a universal as “being both white and round and either shiny or not made of silver”. Advocates of other theories of universals are almost always less liberal in the range of universals whose existence they will allow. The advocate of in rebus universals is unlikely to grant the existence of “being both white and round and either shiny or not made of silver”, even in the case in which there is an object that is both white and round and either shiny or not made of silver (such as a non-shiny white plastic ball).

The two topics “the categories of being” and “the ontological structure of objects” are intimately related to each other and to the problem of universals. It is not possible to propose a solution to the problem of universals that does not have implications for the topic “the categories of being”. (Even nominalism implies that at least one popular candidate for the office “ontological category” is non-existent or empty.) It is certainly possible to maintain that there are ontological categories that are not directly related to the problem of universals (“proposition”, “state of affairs”, “event”, “mere possibile”), but any philosopher who maintains this will nevertheless maintain that if there are universals they make up at least one of the higher ontological sub-categories. And it seems that it is possible to speak of ontological structure only if one supposes that there are objects of different ontological categories. So whatever metaphysics comprehends, it must comprehend every aspect of the problem of universals and every aspect of the topics “the categories of being” and “the ontological structure of objects”. For a recent investigation of the problems that have been discussed in this section, see Lowe (2006).

We turn now to a topic that strictly speaking belongs to “the categories of being”, but which is important enough to be treated separately.

Some things (if they exist at all) are present only “in” other things: a smile, a haircut (product, not process), a hole …. Such things may be opposed to things that exist “in their own right”. Metaphysicians call the things that exist in their own right ‘substances’. Aristotle called them ‘protai ousiai’ or “primary beings”. They make up the most important of his ontological categories. Several features define protai ousiai: they are subjects of predication that cannot themselves be predicated of things (they are not universals); things exist “in” them, but they do not exist “in” things (they are not accidents like Socrates' wisdom or his ironic smile); they have determinate identities (essences). This last feature could be put this way in contemporary terms: if the prote ousia x exists at a certain time and the prote ousia y exists at some other time, it makes sense to ask whether x and y are the same, are numerically identical (and the question must have a determinate answer); and the question whether a given prote ousia would exist in some set of counterfactual circumstances must likewise have an answer (at least if the circumstances are sufficiently determinate—if, for example, they constitute a possible world. More on this in the next section). It is difficult to suppose that smiles or holes have this sort of determinate identity. To ask whether the smile Socrates smiled today is the smile he smiled yesterday (or is the smile he would have smiled if Crito had asked one of his charmingly naïve questions) can only be a question about descriptive identity.

Aristotle uses ‘(prote) ousia’ not only as a count-noun but as a mass term. (He generally writes ‘ousia’ without qualification when he believes that the context will make it clear that he means ‘prote ousia’.) For example, he not only asks questions like “Is Socrates a (prote) ousia?” and “What is a (prote) ousia”?, but questions like “What is the (prote) ousia of Socrates?” and “What is (prote) ousia?” (Which question he is asking sometimes has to be inferred from the context, since there is no indefinite article in Greek.) In the count-noun sense of the term, Aristotle identifies at least some (protai) ousiai with ta hupokeimena or “underlying things”. Socrates, for example, is a hupokeimenon in that he “lies under” the in rebus universals under which he falls and the accidents that inhere in him. ‘To hupokeimenon’ has an approximate Latin equivalent in ‘substantia’, “that which stands under”. (Apparently, “to stand under” and “to lie under” are equally good metaphorical descriptions of the relations a thing bears to its qualities and accidents.) Owing both to the close association of (protai) ousiai and hupokeimena in Aristotle's philosophy and to the absence a suitable Latin equivalent of ‘ousia’ ‘substantia’ became the customary Latin translation of the count-noun ‘(prote) ousia’.

The question whether there in fact are substances continues to be one of the central questions of metaphysics. Several closely related questions are: How, precisely, should the concept of substance be understood?; Which of the items (if any of them) among those we encounter in everyday life are substances?; If there are substances at all, how many of them are there?—is there only one as Spinoza contended, or are there many as most of the rationalists supposed?; What kinds of substances are there?—are there immaterial substances, eternal substances, necessarily existent substances?

It must be emphasized that there is no universally accepted and precise definition of ‘substance’. Depending on how one understood the word (or the concept) one might say either that Hume denied that there were any substances or that he held that the only substances (or the only substances of which we have any knowledge) were impressions and ideas. It would seem, however, that most philosophers who are willing to use the word ‘substance’ at all would deny that any of the following (if they exist) are substances:

Universals and other abstract objects. (It should be noted that Aristotle criticized Plato for supposing that the protai ousiai were ante res universals.)

Events, processes, or changes. (But some metaphysicians contend that substance/event is a false dichotomy.)

Stuffs, such as flesh or iron or butter. (Unfortunately for beginning students of metaphysics, the usual meaning of ‘substance’ outside philosophy is stuff. Aristotle criticized “the natural philosophers” for supposing that the prote ousia could be a stuff—water or air or fire or matter.)

The nature of being, the problem of universals, and the nature of substance have been recognized as topics that belong to “metaphysics” by almost everyone who has used the word. We now turn to topics that belong to metaphysics only in the post-Medieval sense.

Philosophers have long recognized that there is an important distinction within the class of true propositions: the distinction between those propositions that might have been false and those that could not have been false (those that must be true). Compare, for example, the proposition that Paris is the capital of France and the proposition that there is a prime between every number greater than 1 and its double. Both are true, but the former could have been false and the latter could not have been false. Likewise, there is a distinction to be made within the class of false propositions: between those that could have been true and those that could not have been true (those that had to be false).

Some Medieval philosophers supposed that the fact that true propositions are of the two sorts “necessarily true” and “contingently true” (and the corresponding fact about false propositions) showed that there were two “modes” in which a proposition could be true (or false): the mode of contingency and the mode of necessity—hence the term ‘modality’. Present-day philosophers retain the Medieval term ‘modality’ but now it means no more than “pertaining to possibility and necessity”. The types of modality of interest to metaphysicians fall into two camps: modality de re and modality de dicto.

Modality de dicto is the modality of propositions (‘dictum’ means proposition, or close enough). If modality were coextensive with modality de dicto, it would be at least a defensible position that the topic of modality belongs to logic rather than to metaphysics. (Indeed, the study of modal logics goes back to Aristotle's Prior Analytics.)

But many philosophers also think there is a second kind of modality, modality de re—the modality of things. (The modality of substances, certainly, and perhaps of things in other ontological categories.) The status of modality de re is undeniably a metaphysical topic, and we assign it to the “new” metaphysics because, although one can ask modal questions about things that do not change—God, for example, or universals—a large proportion of the work that has been done in this area concerns the modal features of changing things.

There are two types of modality de re. The first concerns the existence of things—of human beings, for example. If Sally, an ordinary human being, says, “I might not have existed”, almost everyone will take her to have stated an obvious truth. And if what she has said is indeed true, then she exists contingently. That is to say, she is a contingent being: a being who might not have existed. A necessary being, in contrast, is a being of which it is false that it might not have existed. Whether any objects are necessary beings is an important question of modal metaphysics. Some philosophers have gone so far to maintain that all objects are necessary beings, since necessary existence is a truth of logic in what seems to them to be the best quantified modal logic. (See Barcan 1946 for the first modern connection between necessary existence and quantified modal logic. Barcan did not draw any metaphysical conclusions from her logical results, but later authors, especially Williamson 2013 have.)

The second kind of modality de re concerns the properties of things. Like the existence of things, the possession of properties by things is subject to modal qualification. If Sally, who speaks English, says, “I might have spoken only French”, almost everyone will take that statement to be no less obviously true than her statement that she might not have existed. And if what she has said is indeed true, then “speaking English” is a property that she has only contingently or (the more usual word) only accidentally. Additionally there may be properties which some objects have essentially. A thing has a property essentially if it could not exist without having that property. Examples of essential properties tend to be controversial, largely because the most plausible examples of a certain object's possessing a property essentially are only as plausible as the thesis that that object possesses those properties at all. For example, if Sally is a physical object, as physicalists suppose, then it is very plausible for them to suppose further that she is essentially a physical object—but it is controversial whether they are right to suppose that she is a physical object. And, of course, the same thing can be said, mutatis mutandis, concerning dualists and the property of being a non-physical object. It would seem, however, that Sally is either essentially a physical object or essentially a non-physical object. And many find it plausible to suppose that (whether she is physical or non-physical) she has the property “not being a poached egg” essentially.

The most able and influential enemy of modality (both de dicto and de re) was W. V. Quine, who vigorously defended both the following theses. First, that modality de dicto can be understood only in terms of the concept of analyticity (a problematical concept in his view). Secondly, that modality de re cannot be understood in terms of analyticity and therefore cannot be understood at all. Quine argued for this latter claim by proposing what he took to be decisive counterexamples to theories that take essentiality to be meaningful. If modality de re makes any sense, Quine contended (1960: 199–200), cyclists must be regarded as essentially bipedal—for “Cyclists are bipedal” would be regarded as an analytic sentence by those who believe in analyticity. But mathematicians are only accidentally bipedal (“Mathematicians are bipedal” is not analytic by anyone's lights). What then, Quine proceeded to ask, of someone who is both a mathematician and a cyclist?—that person seems both essentially and only accidentally bi-pedal. Since this is incoherent, Quine thought that modality de re is incoherent.

Most philosophers are now convinced, however, that Quine's “mathematical cyclist” argument has been adequately answered by Saul Kripke (1972), Alvin Plantinga (1974) and various other defenders of modality de re. Kripke and Plantinga's defenses of modality are paradigmatically metaphysical (except insofar as they directly address Quine's linguistic argument). Both make extensive use of the concept of a possible world in defending the intelligibility of modality (both de re and de dicto). Leibniz was the first philosopher to use ‘possible world’ as a philosophical term of art, but Kripke's and Plantinga's use of the phrase is different from his. For Leibniz, a possible world was a possible creation: God's act of creation consists in his choosing one possible world among many to be the one world that he creates—the “actual” world. For Kripke and Plantinga, however, a possible world is a possible “whole of reality”. For Leibniz, God and his actions “stand outside” all possible worlds. For Kripke and Plantinga, no being, not even God, could stand outside the whole system of possible worlds. A Kripke-Plantinga (KP) world is an abstract object of some sort. Let us suppose that a KP world is a possible state of affairs (this is Plantinga's idea; Kripke says nothing so definite). Consider any given state of affairs; let us say, Paris being the capital of France. This state of affairs obtains, since Paris is the capital of France. By contrast, the state of affairs Tours being the capital of France does not obtain. The latter state of affairs does, however, exist, for there is such a state of affairs. (Obtaining thus stands to states of affairs as truth stands to propositions: although the proposition that Tours is the capital of France is not true, there nevertheless is such a proposition.) The state of affairs x is said to include the state of affairs y if it is impossible for x to obtain and y not to obtain. If it is impossible for both x and y to obtain, then each precludes the other. A possible world is simply a possible state of affairs that, for every state of affairs x, either includes or precludes x; the actual world is the one such state of affairs that obtains.

Using the KP theory we can answer Quine's challenge as follows. In every possible world, every cyclist in that world is bipedal in that world. (Assuming with Quine that necessarily cyclists are bipedal. Apparently he had not foreseen adaptive bicycles.) Nevertheless for any particular cyclist, there is some possible world where he (the same person) is not bipedal. Once we draw this distinction, we can see that Quine's argument is invalid. More generally, on the KP theory, theses about de re essential properties need not be analytic; they are meaningful because they express claims about an object's properties in various possible worlds.

We can also use the notion of possible worlds to define many other modal concepts. For example, a necessarily true proposition is a proposition that would be true no matter what possible world was actual. Socrates is a contingent being if there is some possible world such that he would not exist if that world were actual, and he has the property “being human” essentially if every possible world that includes his existence also includes his being human. Kripke and Plantinga have greatly increased the clarity of modal discourse (and particularly of modal discourse de re), but at the expense of introducing a modal ontology, an ontology of possible worlds.

Theirs is not the only modal ontology on offer. The main alternative to the KP theory has been the ‘modal realism’ championed by David Lewis (1986). Lewis's modal ontology appeals to objects called possible worlds, but these “worlds” are concrete objects. What we call the actual world is one of these concrete objects, the spatiotemporally connected universe we inhabit. What we call “non-actual” worlds are other concrete universes that are spatiotemporally isolated from ours (and from each other). There is, Lewis contends, a vast array of non-actual worlds, an array that contains at least those worlds that are generated by an ingenious principle of recombination, a principle that can be stated without the use of modal language (1986: 87). For Lewis, moreover, “actual” is an indexical term: when I speak of the actual world, I refer to the world of which I am an inhabitant—and so for any speaker who is “in” (who is a part of) any world.

In the matter of modality de dicto, Lewis's theory proceeds in a manner that is at least parallel to the KP theory: there could be flying pigs if there are flying pigs in some possible world (if some world has flying pigs as parts). But the case is otherwise with modality de re. Since every ordinary object is in only one of the concrete worlds, Lewis must either say that each such object has all its properties essentially or else adopt a treatment of modality de re that is not parallel to the KP treatment. He chooses the latter alternative. Although Socrates is in only the actual world, Lewis holds, he has ‘counterparts’ in some other worlds, objects that play the role in those worlds that he plays in this world. If all Socrates' counterparts are human, then we may say that he is essentially human. If one of Hubert Humphrey's counterparts won (the counterpart of) the 1968 presidential election, it is correct to say of Humphrey that he could have won that election.

In addition to the obvious stark ontological contrast between the two theories, they differ in two important ways in their implications for the philosophy of modality. First, if Lewis is right, then modal concepts can be defined in terms of paradigmatically non-modal concepts, since ‘world’ and all of Lewis's other technical terms can be defined using only ‘is spatiotemporally related to’, ‘is a part of’ and the vocabulary of set theory. For Kripke and Plantinga, however, modal concepts are sui generis, indefinable or having only definitions that appeal to other modal concepts. Secondly, Lewis's theory implies a kind of anti-realism concerning modality de re. This is because there is no one relation that is the counterpart relation—there are rather various ways or respects in which one could say that objects in two worlds “play the same role” in their respective worlds. Socrates, therefore, may well have non-human counterparts under one counterpart relation and no non-human counterparts under another. And the choice of a counterpart relation is a pragmatic or interest-relative choice. But on the KP theory, it is an entirely objective question whether Socrates fails to be human in some world in which he exists: the answer must be Yes or No and is independent of human choices and interests.

Whatever one may think of these theories when one considers them in their own right (as theories of modality, as theories with various perhaps objectionable ontological commitments), one must concede that they are paradigmatically metaphysical theories. They bear witness to the resurgence of metaphysics in analytical philosophy in the last third of the twentieth century.

Long before the theory of relativity represented space and time as aspects of or abstractions from a single entity, spacetime, philosophers saw space and time as intimately related. (A glance through any dictionary of quotations suggests that the philosophical pairing of space and time reflects a natural, pre-philosophical tendency: “Had we but world enough, and time …”; “Dwellers all in time and space”.) Kant, for example, treated space and time in his Transcendental Aesthetic as things that should be explained by a single, unified theory. And his theory of space and time, revolutionary though it may have been in other respects, was in this respect typical of philosophical accounts of space and time. Whatever the source of the conviction that space and time are two members of a “species” (and the only two members of that species), they certainly raise similar philosophical questions. It can be asked whether space extends infinitely in every direction, and it can be asked whether time extends infinitely in either of the two temporal “directions”. Just as one can ask whether, if space is finite, it has an “end” (whether it is bounded or unbounded), one may ask of time whether, if it is finite, it had a beginning or will have an end or whether it might have neither, but rather be “circular” (be finite but unbounded). As one can ask whether there could be two extended objects that were not spatially related to each other, one can ask whether there could be two events that were not temporally related to each other. One can ask whether space is (a) a real thing—a substance—a thing that exists independently of its inhabitants, or (b) a mere system of relations among those inhabitants. And one can ask the same question about time.

But there are also questions about time that have no spatial analogues—or at least no obvious and uncontroversial analogues. There are, for example, questions about the grounds of various asymmetries between the past and the future—why is our knowledge of the past better than our knowledge of the future?; why do we regard an unpleasant event that is about to happen differently from the way we regard an unpleasant event that has recently happened?; why does causation seem to have a privileged temporal direction? There do not seem to be objective asymmetries like this in space.

There is also the question of temporal passage—the question whether the apparent “movement” of time (or the apparent movement of ourselves and the objects of our experience through or in time) is a real feature of the world or some sort of illusion. In one way of thinking about time, there is a privileged temporal direction marking the difference between the past, present, and future. A-theorists hold that time is fundamentally structured in terms of a past/present/future distinction. Times change from past to present to future, giving rise to passage. (The name ‘A-theorist’ descends from J.M.E. McTaggart's (1908) name for the sequence past/present/future which he called the ‘A-series’.) Within the A-theory, we might further ask whether the past and future have the “same sort of reality” as the present. Presentist A-theorists, like Prior 1998, deny that the past or future have any concrete reality. Presentists typically think of the past and future as, at best, akin to abstract possible worlds—they are the way the world was or will be, just as possible worlds are ways the actual world could be. Other A-theorists, like Sullivan (2012), hold that the present is metaphysically privileged but deny that there is any ontological difference between the past, present, and future. More generally, A-theorists often incorporate strategies from modal metaphysics into their theories about the relation of the past and the future to the present.

According to B-theories of time, the only fundamental distinction we should draw is that some events and times are earlier or later relative to others. (These relations are called ‘B-relations’, a term also derived from McTaggart). According to the B-theorists, there is no objective passage of time, or at least not in the sense of time passing from future to present and from present to past. B-theorists typically maintain that all past and future times are real in the same sense in which the present time is real—the present is in no sense metaphysically privileged.

It is also true, and less often remarked on, that space raises philosophical questions that have no temporal analogues—or at least no obvious and uncontroversial analogues. Why, for example, does space have three dimensions and not four or seven? On the face of it, time is essentially one-dimensional and space is not essentially three-dimensional. It also seems that the metaphysical problems about space that have no temporal analogues depend on the fact that space, unlike time, has more than one dimension. For example, consider the problem of incongruent counterparts: those who think space is a mere system of relations struggled to explain our intuition that we could distinguish a world containing only a left hand from a world containing only a right hand. So it seems there is an intuitive orientation to objects in space itself. It is less clear whether the problems about time that have no spatial analogues are connected with the one-dimensionality of time.

Finally, one can raise questions about whether space and time are real at all—and, if they are real, to what extent (so to speak) they are real. Might it be that space and time are not constituents of reality as God perceives reality but nevertheless “well-founded phenomena” (as Leibniz held)? Was Kant right when he denied spatial and temporal features to “things as they are in themselves”?—and right to contend that space and time are “forms of our intuition”? Or was McTaggart's position the right one: that space and time are wholly unreal?

If these problems about space and time belong to metaphysics only in the post-Medieval sense, they are nevertheless closely related to questions about first causes and universals. First causes are generally thought by those who believe in them to be eternal and non-local. God, for example—both the impersonal God of Aristotle and the personal God of Medieval Christian, Jewish, and Muslim philosophy—is generally said to be eternal, and the personal God is said to be omnipresent. To say that God is eternal is to say either that he is everlasting or that he is somehow outside time. And this raises the metaphysical question of whether it is possible for there to be a being—not a universal or an abstract object of some other sort, but an active substance—that is everlasting or non-temporal. An omnipresent being is a being that does not occupy any region of space (not even the whole of it, as the luminiferous ether of nineteenth-century physics would if it existed), and whose causal influence is nevertheless equally present in every region of space (unlike universals, to which the concept of causality does not apply). The doctrine of divine omnipresence raises the metaphysical question whether it is possible for there to be a being with this feature. Ante res universals are said by some of their proponents (precisely those who deny that universals are constituents of particulars) to have no relations to space and time but “vicarious” ones: the ante res universal “whiteness” may be said to be present where each white particular is, but only in a way analogous to the way in which the number two is present where each pair of spatial things is. But it is doubtful whether this is a position that is possible for a metaphysician who says that a white thing is a bundle composed of whiteness and various other universals. Those who believe in the existence of in rebus universals are fond of saying, or have been in recent years, that these universals (‘immanent universals’ is a currently popular name for them) are “multiply located”—“wholly present” at each place at which the things that fall under them are present. And by this they certainly do not mean that whiteness is present in many different regions of space only vicariously, only as a number might be said to be present wherever there are things in that number, only in virtue of bearing the non-spatial relation “being had by” to a multitude of particulars each of which is present in a single region of space. All theories of universals, therefore, raise questions about how things in various ontological categories are related to space. And all these questions have temporal analogues.

Related to questions about the nature of space and time are questions about the nature of objects that take up space or persist through time, and these questions form yet another central theme in post-medieval metaphysics. Are some or all objects composed of proper parts? Must an object have proper parts in order to “fill up” a region of space—or are there extended simples? Can more that one object be located in exactly the same region? Do objects persist through change by having temporal parts?

Much work on persistence and constitution has focused on efforts to address a closely knit family of puzzles—the puzzles of coincidence. One such puzzle is the “problem of the statue and the lump”. Consider a gold statue. Many metaphysicians contend that there is at least one material object that is spatially co-extensive with the statue, a lump of gold. This is easily shown, they say, by an appeal to Leibniz's Law (the principle of the non-identity of discernibles). There is a statue here and there is a lump of gold here, and—if the causal story of the statue's coming to be is of the usual sort—the lump of gold existed before the statue. And even if God has created the statue (and perforce the lump) ex nihilo and will at some point annihilate the statue (and thereby annihilate the lump), they further argue, the statue and the lump, although they exist at exactly the same times, have different modal properties: the lump has the property “can survive radical deformation” and the statue does not. Or so these metaphysicians conclude. But it has seemed to other metaphysicians that this conclusion is absurd, for it is absurd to suppose (these others say) that there could be spatially coincident physical objects that share all their momentary non-modal properties. Hence, the problem: What, if anything, is the flaw in the argument for the non-identity of the statue and the lump?

A second puzzle in this family is the “problem of Tib and Tibbles”. Tibbles is a cat. Call his tail “Tail”. Call all of him but his tail “Tib”. Suppose Tail is cut off—or, better, annihilated. Tibbles still exists, for a cat can survive the loss of its tail. And it would seem that Tib will exist after the “loss” of Tail, because Tib lost no part. But what will be the relation between Tib and Tibbles? Can it be identity? No, that is ruled out by the non-identity of discernibles, for Tibbles will have become smaller and Tib will remain the same size. But then, once again, we seem to have a case of spatially coincident material objects that share their momentary non-modal properties.

Both these constitution problems turn on questions about the identities of spatially coincident objects—and, indeed, of objects that share all their (proper) parts. (A third famous problem of material constitution—the problem of the Ship of Theseus—raises questions of a different sort.) Some metaphysicians contend that the relation between the lump and the statue, on the one hand, and the relation between Tib and Tibbles, on the other, cannot be fully understood in terms of the concepts of parthood and (non-) identity, but require a further concept, a non-mereological concept, the concept of “constitution”: the pre-existent lump at a certain point in time comes to constitute the statue (or a certain quantity of gold or certain gold atoms that first constituted only the lump come to constitute them both); pre-existent Tib at a certain point in time comes to constitute Tibbles (or certain cat-flesh or certain molecules …). (Baker 2000 is a defense of this thesis.) Others contend that all the relations between the objects that figure in both problems can be fully analyzed in terms of parthood and identity. For a more thorough overview of the solutions to these puzzles and different theories of constitution in play, see Rea (ed.) 1997 and Thomson 1998.

Questions about causation form yet a fourth important category of issues in the “new” metaphysics. Of course, discussion of causes go back to Ancient Philosophy, featuring prominently in Aristotle's Metaphysics and Physics. But Aristotle understood ‘cause’ in a much broader sense than we do today. In Aristotle's sense, a ‘cause’ or ‘aiton’ is an explanatory condition of an object—an answer to a “why” question about the object. Aristotle classifies four such explanatory conditions—an object's form, matter, efficient cause, and teleology. An object's efficient cause is the cause which explains change or motion in an object. With the rise of modern physics in the seventeenth century, interest in efficient causal relations became acute, and it remains so today. And when contemporary philosophers discuss problems of causation, they typically mean this sense.

One major issue in the metaphysics of causation concerns specifying the relata of causal relations. Consider a mundane claim: an iceberg caused the Titanic to sink. Does the causal relation hold between two events: the event of the ship hitting the iceberg and the event of the ship sinking? Or does it hold between two sets of states of affairs? Or does it hold between two substances, the iceberg and the ship? Must causal relations be triadic or otherwise poly-adic? For example, one might think that we are always required to qualify a causal claim: the iceberg, rather than the captain's negligence, was causally responsible for the ships foundering. And can absences feature in causal relations? For example, does it make sense to claim that a lack of lifeboats was the cause of a third class passenger's death?

We might further ask whether causal relations are objective and irreducible features of reality. Hume famously doubted this, theorizing that that our observations of causation were nothing more than observations of constant conjunction. For example, perhaps we think icebergs cause ships to sink only because we always observe ship-sinking events occurring after iceberg-hitting events and not because there is a real causal relation that holds between icebergs and foundering ships.

Contemporary metaphysicians have been attracted to other kinds of reductive treatments of causation. Some—like Stalnaker and Lewis—have argued that causal relations should be understood in terms of counterfactual dependencies (Stalnaker 1968 and Lewis 1973). For example, an iceberg's striking the ship caused its sinking at time t if and only if in the nearest possible worlds where the iceberg did not strike the ship at time t, the ship did not sink. Others have argued that causal relations should be understood in terms of instantiations of laws of nature. (Davidson (1967) and Armstrong (1997) each defend this view albeit in different ways.) All of these theories expand on an idea from Hume's Treatise in attempting to reduce causation to different or more fundamental categories. (For a more complete survey of recent theories of causation, see Paul and Hall 2013.)

Debates about causation and laws of nature further give rise to a related set of pressing philosophical questions—questions of freedom. In the seventeenth century, celestial mechanics gave philosophers a certain picture of a way the world might be: it might be a world whose future states were entirely determined by the past and the laws of nature (of which Newton's laws of motion and law of universal gravitation served as paradigms). In the nineteenth century the thesis that the world was indeed this way came to be called ‘determinism’. The problem of free will can be stated as a dilemma. If determinism is true, there is only one physically possible future. But then how can anyone ever have acted otherwise? For, as Carl Ginet has said (1990: 103), our freedom can only be the freedom to add to the actual past; and if determinism holds, then there is only one way that the given—the actual—past can be “added to”. But if determinism does not hold, if there are alternative physically possible futures, then which one comes to pass must be a mere matter of chance. And if it is a mere matter of chance whether I lie or tell the truth, how can it be “up to me” whether I lie or tell the truth? Unless there is something wrong with one of these two arguments, the argument for the incompatibility of free will and determinism or the argument for the incompatibility of free will and the falsity of determinism, free will is impossible. The problem of free will may be identified with the problem of discovering whether free will is possible—and, if free will is possible, the problem of giving an account of free will that displays an error in one of (or both) these arguments.

Van Inwagen (1998) defends the position that, although the modern problem of free will has its origin in philosophical reflections on the consequences of supposing the physical universe to be governed by deterministic laws, the problem cannot be evaded by embracing a metaphysic (like dualism or idealism) that supposes that agents are immaterial or non-physical. This leads into our next and final sample of topics from the “new” metaphysics.

If it is natural both to pair and to oppose time and space, it is also natural to pair and to oppose the mental and the physical. The modern identity theory holds that all mental events or states are a special sort of physical event or state. The theory is parsimonious (among its other virtues) but we nevertheless exhibit a natural tendency to distinguish the mental and the physical. Perhaps the reason for this is epistemological: whether our thoughts and sensations are physical or not, the kind of awareness we have of them is of a radically different sort from the kind of awareness we have of the flight of a bird or of a flowing stream, and it seems to be natural to infer that the objects of the one sort of awareness are radically different from the objects of the other. That the inference is logically invalid is (as is so often the case) no barrier to its being made. Whatever the reason may be, philosophers have generally (but not universally) supposed that the world of concrete particulars can be divided into two very different realms, the mental and the material. (As the twentieth century passed and physical theory rendered “matter” an increasingly problematical concept, it became increasingly common to say “the mental and the physical”.) If one takes this view of things, one faces philosophical problems that modern philosophy has assigned to metaphysics.

Prominent among these is the problem of accounting for mental causation. If thoughts and sensations belong to an immaterial or non-physical portion of reality—if, for example, they are changes in immaterial or non-physical substances—how can they have effects in the physical world? How, for example, can a decision or act of will cause a movement of a human body? How, for that matter, can changes in the physical world have effects in the non-physical part of reality? If one's feeling pain is a non-physical event, how can a physical injury to one's body cause one to feel pain? Both questions have troubled “two realm” philosophers—or ‘dualists’, to give them their more usual name. But the former has troubled them more, since modern physics is founded on principles that assert the conservation of various physical quantities. If a non-physical event causes a change in the physical world—dualists are repeatedly asked—does that not imply that physical quantities like energy or momentum fail to be conserved in any physically closed causal system in which that change occurs? And does that not imply that every voluntary movement of a human body involves a violation of the laws of physics—that is to say, a miracle?

A wide range of metaphysical theories have been generated by the attempts of dualists to answer these questions. Some have been less than successful for reasons that are not of much intrinsic philosophical interest. C. D. Broad, for example, proposed (1925: 103–113) that the mind affects the body by momentarily changing the electrical resistance of certain synapses in the brain, (thus diverting various current pulses, which literally follow the path of least resistance into paths other than those they would have taken). And this, he supposed, would not imply a violation of the principle of the conservation of energy. But it seems impossible to suppose that an agent could change the electrical resistance of a physical system without expending energy in the process, for to do this would necessitate changing the physical structure of the system, and that implies changing the positions of bits of matter on which forces are acting (think of turning the knob on a rheostat or variable resistor: one must expend energy to do this). If this example has any philosophical interest it is this: it illustrates the fact that it is impossible to imagine a way for a non-physical thing to affect the behavior of a (classical) physical system without violating a conservation principle.

The various dualistic theories of the mind treat the interaction problem in different ways. The theory called ‘dualistic interactionism’ does not, of itself, have anything to say about the problem—although its various proponents (Broad, for example) have proposed solutions to it. ‘Occasionalism’ simply concedes that the “local” counterfactual dependence of the behavior of a physical system on a non-physical event requires a miracle. The theory of pre-established harmony, which substitutes “global” for local counterfactual dependence of voluntary physical movements on the mental states of agents, avoids problems with conservation principles—but secures this advantage at a great price. (Like occasionalism, it presupposes theism, and, unlike occasionalism, it entails either that free will does not exist or that free will is compatible with determinism.) ‘Epiphenomenalism’ simply denies that the mental can affect the physical, and contents itself with an explanation of why the mental appears to affect the physical.

In addition to these dualistic theories, there are monistic theories, theories that dissolve the interaction problem by denying the existence of either the physical or the non-physical: idealism and physicalism. (Present-day philosophers for the most part prefer the term ‘physicalism’ to the older term ‘materialism’ for reasons noted above.) Most current work in the philosophy of mind presupposes physicalism, and it is generally agreed that a physicalistic theory that does not simply deny the reality of the mental (that is not an “eliminativist” theory), raises metaphysical questions. Such a theory must, of course, find a place for the mental in a wholly physical world, and such a place exists only if mental events and states are certain special physical events and states. There are at least three important metaphysical questions raised by these theories. First, granted that all particular mental events or states are identical with particular physical events or states, can it also be that some or all mental universals (‘event-types’ and ‘state-types’ are the usual terms) are identical with physical universals? Secondly, does physicalism imply that mental events and states cannot really be causes (does physicalism imply a kind of epiphenomenalism)? Thirdly, can a physical thing have non-physical properties—might it be that mental properties like “thinking of Vienna” or “perceiving redly” are non-physical properties of physical organisms? This last question, of course, raises a more basic metaphysical question, ‘What is a non-physical property?’ And all forms of the identity theory raise fundamental metaphysical questions, ontological questions, questions like, ‘What is an event?’ and ‘What is a state?’.

As is obvious from the discussion in Section 3, the scope of metaphysics has expanded beyond the tidy boundaries Aristotle drew. So how should we answer our original question? Is contemporary metaphysics just a compendium of philosophical problems that cannot be assigned to epistemology or logic or ethics or aesthetics or to any of the parts of philosophy that have relatively clear definitions? Or is there a common theme that unites work on these disparate problems and distinguishes contemporary metaphysics from other areas of inquiry?

These issues concerning the nature of metaphysics are further connected with issues about the epistemic status of various metaphysical theories. Aristotle and most of the Medievals took it for granted that, at least in its most fundamental aspects, the ordinary person's picture of the world is “correct as far as it goes”. But many post-Medieval metaphysicians have refused to take this for granted. Some of them, in fact, have been willing to defend the thesis that the world is very different from, perhaps radically different from, the way people thought it was before they began to reason philosophically. For example, in response to the puzzles of coincidence considered in Section 3.3, some metaphysicians have maintained that there are no objects with proper parts. This entails that composite objects—tables, chairs, cats, and so on—do not exist, a somewhat startling view. And as we saw in Section 3.1, other metaphysicians have been happy to postulate the reality of concrete merely possible worlds if this posit makes for a simpler and more explanatorily powerful theory of modality. Perhaps this contemporary openness to “revisionary” metaphysics is simply a recovery of or a reversion to a pre-Aristotelian conception of a “permissible metaphysical conclusion”, a conception that is illustrated by Zeno's arguments against the reality of motion and Plato's Allegory of the Cave. But no matter how we classify it, the surprising nature of many contemporary metaphysical claims puts additional pressure on practioners to explain just what they are up to. They raise questions of the methodology of metaphysics.

One attractive strategy for answering these questions emphasizes the continuity of metaphysics with science. On this conception, metaphysics is primarily or exclusively concerned with developing generalizations from our best-confirmed scientific theories. For example, in the mid-twentieth century, Quine (1948) proposed that that the “old/intermediate” metaphysical debate over the status of abstract objects should be settled in this way. He observed that if our best scientific theories are recast in the “canonical notation of (first-order) quantification” (in sufficient depth that all the inferences that users of these theories will want to make are valid in first-order logic), then many of these theories, if not all of them, will have as a logical consequence the existential generalization on a predicate \(F\) such that \(F\) is satisfied only by abstract objects. It would seem, therefore, that our best scientific theories “carry ontological commitment” to objects whose existence is denied by nominalism. (These objects may not be universals in the classical sense. They may, for example, be sets.) Take for example the simple theory, ‘There are homogeneous objects, and the mass of a homogeneous object in grams is the product of its density in grams per cubic centimeter and its volume in cubic centimeters’. A typical recasting of this theory in the canonical notation of quantification is:

\(\exists Hx\) & \(\forall x(Hx \rightarrow Mx = Dx \times Vx)\)

(‘\(Hx\)’: ‘\(x\) is homogeneous’; ‘\(Mx\)’: ‘the mass of \(x\) in grams’; ‘\(Dx\)’: ‘the density of \(x\) in grams per cubic centimeter’; ‘\(Vx\)’: ‘the volume of \(x\) in cubic centimeters’.) A first-order logical consequence of this “theory” is

\(\exists x\exists y\exists z(x = y \times z)\)

That is: there exists at least one thing that is a product (at least one thing that, for some \(x\) and some \(y\) is the product of \(x\) and \(y\)). And a product must be a number, for the operation “product of” applies only to numbers. Our little theory, at least if it is recast in the way shown above, is therefore, in a very obvious sense, “committed” to the existence of numbers. It would seem, therefore, that a nominalist cannot consistently affirm that theory. (In this example, the role played by ‘the predicate F’ in the abstract statement of Quine's “observation” is played by the predicate ‘…=…×…’.)

Quine's work on nominalism inspired a much broader program for approaching ontological questions. According to “neo-Quineans”, questions about the existence of abstract objects, mental events, objects with proper parts, temporal parts, and even other concrete possible worlds are united to the extent that they are questions about the ontological machinery required to account for the truth of our best-confirmed theories. Still, many questions of the new and old metaphysics are not questions of ontology. For example, many participants in the debate over causation are not particularly worried about whether causes and effects exist. Rather, they want to know “in virtue of what” something is a cause or effect. Few involved in the debate over the mental and physical are interested in the question whether there are mental properties (in some sense or other). Rather, they are interested in whether mental properties are “basic” or sui generis—or whether they are grounded, partially or fully, in physical properties.

Is there a unified methodology for metaphysics more broadly understood? Some think the task of the metaphysician is to identify and argue for explanatory relations of various kinds. According to Fine (2001), metaphysicians are in the business of providing theories of which facts or propositions ground other facts or propositions, and which facts or propositions hold “in reality”. For example, a philosopher might hold that tables and other composite objects exist, but think that facts about tables are completely grounded in facts about the arrangements of point particles or facts about the state of a wave function. This metaphysician would hold that there are no facts about tables “in reality”; rather, there are facts about arrangements of particles. Schaffer 2010 proposes a similar view, but holds that metaphysical grounding relations hold not between facts but between entities. According to Schaffer, the fundamental entity/entities should be understood as the entity/entities that grounds/ground all others. On Schaffer's conception we can meaningfully ask whether a table is grounded in its parts or vice versa. We can even theorize (as Schaffer does) that the world as a whole is the ultimate ground for everything.

Another noteworthy approach (Sider 2012) holds that the task of the metaphysician is to “explain the world” in terms of its fundamental structure. For Sider, what unites (good) metaphysics as a discipline is that its theories are all framed in terms that pick out the fundamental structure of the world. For example, according to Sider we may understand ‘causal nihilism’ as the view that causal relations do not feature in the fundamental structure of the world, and so the best language for describing the world will eschew causal predicates.

It should be emphasized that these ways of delimiting metaphysics do not presuppose that all of the topics we've considered as examples of metaphysics are substantive or important to the subject. Consider the debate about modality. Quine (1953) and Sider (2012) both argue from their respective theories about the nature of metaphysics that aspects of the debate over the correct metaphysical theory of modality are misguided. Others are skeptical of the debates about composition or persistence through time. So theories about the nature of metaphysics might give us new resources for criticizing particular first-order debates that have historically been considered metaphysical, and it is common practice for metaphysicians to regard some debates as substantive while adopting a deflationist attitude about others.

It may also be that there is no internal unity to metaphysics. More strongly, perhaps there is no such thing as metaphysics—or at least nothing that deserves to be called a science or a study or a discipline. Perhaps, as some philosophers have proposed, no metaphysical statement or theory is either true or false. Or perhaps, as others have proposed, metaphysical theories have truth-values, but it is impossible to find out what they are. At least since the time of Hume, there have been philosophers who have proposed that metaphysics is “impossible”—either because its questions are meaningless or because they are impossible to answer. The remainder of this entry will be a discussion of some recent arguments for the impossibility of metaphysics.

Let us suppose that we are confident that we are able to identify every statement as either “a metaphysical statement” or “not a metaphysical statement”. (We need not suppose that this ability is grounded in some non-trivial definition or account of metaphysics.) Let us call the thesis that all metaphysical statements are meaningless “the strong form” of the thesis that metaphysics is impossible. (At one time, an enemy of metaphysics might have been content to say that all metaphysical statements were false. But this is obviously not a possible thesis if the denial of a metaphysical statement must itself be a metaphysical statement) And let us call the following statement the “weak form” of the thesis that metaphysics is impossible: metaphysical statements are meaningful, but human beings can never discover whether any metaphysical statement is true or false (or probable or improbable or warranted or unwarranted).

Let us briefly examine an example of the strong form of the thesis that metaphysics is impossible. The logical positivists maintained that the meaning of a (non-analytic) statement consisted entirely in the predictions it made about possible experience. They maintained, further, that metaphysical statements (which were obviously not put forward as analytic truths) made no predictions about experience. Therefore, they concluded, metaphysical statements are meaningless—or, better, the “statements” we classify as metaphysical are not really statements at all: they are things that look like statements but aren't, rather as mannequins are things that look like human beings but aren't.

But (many philosophers asked) how does the logical positivist's central thesis

The meaning of a statement consists entirely in the predictions it makes about possible experience

fare by its own standards? Does this thesis make any predictions about possible experiences? Could some observation show that it was true? Could some experiment show that it was false? It would seem not. It would seem that everything in the world would look the same—like this—whether this thesis was true or false. (Will the positivist reply that the offset sentence is analytic? This reply is problematic in that it implies that the multitude of native speakers of English who reject the logical positivists' account of meaning somehow cannot see that that sentence is true in virtue of the meaning of the word “meaning”—which is no technical term but a word of ordinary English.) And, therefore, if the statement is true it is meaningless; or, what is the same thing, if it is meaningful, it is false. Logical positivism would therefore seem to say of itself that it is false or meaningless; it would be seem to be, to use a currently fashionable phrase, “self-referentially incoherent”.

Current advocates of ‘metaphysical anti-realism’ also advocate a strong form of the thesis that metaphysics is impossible. Insofar as it is possible to find a coherent line of argument in the writings of any anti-realist, it is hard to see why they, like the logical positivists, are not open to a charge of self-referential incoherency. Indeed, there is much to be said for the conclusion that all forms of the strong thesis fall prey to self-referential incoherency. Put very abstractly, the case against proponents of the strong thesis may be put like this. Dr. McZed, a “strong anti-metaphysician”, contends that any piece of text that does not pass some test she specifies is meaningless (if she is typical of strong anti-metaphysicians, she will say that any text that fails the test represents an attempt to use language in a way in which language cannot be used). And she contends further that any piece of text that can plausibly be identified as “metaphysical” must fail this test. But it invariably turns out that various sentences that are essential components of McZed's case against metaphysics themselves fail to pass her test. A test-case for this very schematic and abstract refutation of all refutations of metaphysics is the very sophisticated and subtle critique of metaphysics (it purports to apply only to the kind of metaphysics exemplified by the seventeenth-century rationalists and current analytical metaphysics) presented in van Fraassen 2002. It is a defensible position that van Fraassen's case against metaphysics depends essentially on certain theses that, although they are not themselves metaphysical theses, are nevertheless open to many of the criticisms he brings against metaphysical theses.

The weak form of the thesis that metaphysics is impossible is this: there is something about the human mind (perhaps even the minds of all rational agents or all finite rational agents) that unfits it for reaching metaphysical conclusions in any reliable way. This idea is at least as old as Kant, but a version of it that is much more modest than Kant's (and much easier to understand) has been carefully presented in McGinn 1993. McGinn's argument for the conclusion that the human mind is (as a matter of evolutionary contingency, and not simply because it is “a mind”) incapable of a satisfactory treatment of a large range of philosophical questions (a range that includes all metaphysical questions), however, depends on speculative factual theses about human cognitive capacities that are in principle subject to empirical refutation and which are at present without significant empirical support. For a different defense of the weak thesis, see Thomasson 2009.