David Lewis produced a body of philosophical writing that, in fourbooks and scores of articles, spanned every major philosophical area,with perhaps the greatest concentration in metaphysics, philosophy oflanguage, philosophical logic, and philosophy of mind. Despite thisastonishing variety, a newcomer to Lewis’s philosophy would bebest advised to begin with his metaphysics (especially: 1986a, 1986e,1999). There are several reasons. First, the majority of Lewis’swork either concerns, or substantially overlaps, topics inmetaphysics. Second, the metaphysical positions Lewis stakes out arestrikingly original and powerfully argued. Third, there is a coherenceand systematicity to this work that makes it a particularlyappropriate object for study, in that one sees trademark Lewisianphilosophical maneuvers clearly on display. (Indeed, if one wished tolearn how to do philosophy in a Lewisian style, the most efficient wayto do so would be to study his work in metaphysics.) Finally, andperhaps most interestingly, Lewis’s metaphysics exerted a profoundregulating influence on the rest of his philosophy: if some otherwiseattractive position on some philosophical problem could not be made tosquare with his overall metaphysical outlook, then it would have to beabandoned.

I should forestall one possible misunderstanding. You might thinkthat, given what I’ve just said, the way Lewis would recommenddoing philosophy is as follows: First you figure out what your basicmetaphysical commitments should be; then you turn your attention tovarious broad but non-foundational philosophical subject matters(personal identity, mental content, the nature of knowledge, theory ofvalue, etc.), and work out the consequences in each of these arenas ofyour fundamental metaphysical posits. Nothing could be further fromLewis’s preferred methodology. (Well, maybe relying on divinerevelation would be further….) What he in fact recommends is aholistic approach: we start with the total body of claims we areinclined to believe—whether on the basis of “commonsense” (an oft-invoked category, for Lewis) or ofscience—and try our best tosystematize it inaccordance with standards of theoretical goodness that are themselvesendorsed by common sense and/or science (and so are themselves, tosome extent, also up for grabs). A substantial portion of Lewis’soverall body of philosophical work can thus be seen as anextended—and breathtakingly ambitious—attempt at achievingtotal reflective equilibrium. Here is an especially succinctdescription of this approach:

One comes to philosophy already endowed with a stock of opinions. Itis not the business of philosophy either to undermine or to justifythese preexisting opinions, to any great extent, but only to try todiscover ways of expanding them into an orderly system. (1973b, p. 88)

Still, while Lewis’s method of philosophical inquiry is certainlynot “bottom-up”, in my opinion it is best to present theresults of that inquiry in a bottom-up fashion. That is whatthis essay, and ones to follow, will attempt to do. I will divide theterrain into four parts: Lewis’s fundamental ontology; his theoryof metaphysical modality; his “applied” metaphysics(covering such topics as laws of nature, counterfactuals, causation,identity through time, and the mind); and Lewisian methodology inmetaphysics. I’ll explain these distinctions shortly, but beadvised that the present essay will almost exclusively address thefirst of these four topics. Other aspects of Lewis’s thought arecovered in the general entry onDavid Lewis.

• 1. Lewisian metaphysics: an overview
• 2. Fundamental ontology: A simplified version
• 3. Perfectly natural properties and relations
• 4. Spatiotemporal relations and spacetime points
• 5. Humean Supervenience
• 6. Lewis v. Almost-Lewis
• 7. Some criticisms
• 8. Counterpart theory
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

In order to provide more depth, there are also supplementary documentsthat provide more detailed treatments of the following issues:Reduction,The Natural/Non-Natural Distinction,Physicalism,Spacetime Points,The Contingency of Humean Supervenience,Physical Magnitudes,Fundamental Entities, andCounterpart-Theoretic Semantics for Quantified Modal Logic.

1. Lewisian metaphysics: an overview

On a traditional conception, metaphysics aims to answer, in a suitablyabstract and fully general manner, two questions:

1. Whatis there?
2. What is it (that is, whatever it is that there is)like?

Lewis fully endorses this conception: for him, metaphysicians are notin the business merely of analyzing our “conceptualscheme” (except insofar as doing so is an effectivemethod for finding answers to metaphysical questions), norneed they pay any heed to the perennial philosophical calls for theabolition of their subject. They are, rather, engaged in anunproblematically factual inquiry into the nature of reality—onewhose recognizable epistemological pitfalls provide no grounds fordoubting its legitimacy:

Once the menu of well-worked-out theories is before us, philosophy isa matter of opinion. Is that to say that there is no truth to be had?Or that the truth is of our own making, and different ones of us canmake it differently? Not at all! If you say flatly that there is nogod, and I say that there are countless gods but none of them are ourworldmates, then it may be that neither of us is making any mistake ofmethod. We may each be bringing our opinions to equilibrium in themost careful possible way, taking account of all the arguments,distinctions, and counterexamples. But one of us, at least, is makinga mistake of fact. Which one is wrong depends on what there is. (Lewis1983a, p. xi)

We can begin to get a handle on Lewis’s audacious andcomprehensive answers to our two overarching questions bydistinguishing three components to his metaphysical program:

First, he offers an account of what thefundamental ontologicalstructure of the world is. Is, andmustbe—although as we’ll see, that qualification turns out to bein a certain sense trivial. This account of fundamental ontology ofcourse presupposes that the word “fundamental”means something, and in particular manages to cleanlydistinguish a certain central core of one’s ontologicalcommitments from the rest. Suppose these commitments take the form ofviews about what entities (or “particulars”) there are,and what properties and relations they stand in. Then we candistinguish two questions. Are some entities more fundamental thanothers—with, perhaps, an elite group of entities being the mostfundamental? Are some properties/relations more fundamental thanothers—again, with, perhaps, an elite group being the mostfundamental? You might find a “yes” answer to bothquestions attractive. (E.g., chairs exist, but they are notfundamental-level entities—though perhaps quarks are. Likewise,some chairs have the property ofbeing made of oak; but thisis not a fundamental-level property—though perhaps the propertyof having such-and-such electric charge is.) As for Lewis’s ownviews, with respect to the second question they are fairlyunambiguous: He is quite clear that a proper ontology must include notjust particulars but also properties and relations (see especially1983b); he is equally clear that it is a perfectly objective anddeterminate matter which of these properties/relations are morefundamental (or, in his terminology, more “natural”) thanothers (ibid.); he is officially agnostic about whether someproperties/relations aremost fundamental, orperfectly natural (1986f). His views on the first questionare, to my eyes at least, more difficult to discern—but forreasons that, in the final analysis, probably do not matter. Seethe

Supplement onFundamental Entities

What’s more, to a very great extent he takes it that the route toa proper theory of fundamental ontology is by way ofa prioriphilosophical inquiry. (An important qualification will be notedshortly.)

Second, he offers an account ofmodality, his famous“realism” about possible worlds. Lewis, like manyphilosophers, takes talk of possibility and necessity to be bestexplicated as disguised quantification over possible worlds (andpossible inhabitants thereof), and he was endlessly ingenious atshowing how to use the resources provided by a theory of“possibilia” to produce analyses of a host of modallocutions. But his realism about possible worlds consists in much morethan inclusion of such entities into his ontology; indeed, it wouldprobably be better to call Lewis a “reductionist” aboutmodality—reductionist in a way that distinguishes him fromvirtually every other philosopher of modality. For a typical believerin possible worlds will, if asked to explain what they are, give anaccount thatuses modal notions at some crucial point.Perhaps she will say that possible worlds are maximalconsistent sets of sentences (in some appropriate language);or perhaps she will say that they are certain kinds of maximalproperties that reality as a wholecould have instantiated.Lewis says no such thing: he offers a characterization of possibleworlds—and thus of modality generally—inexplicitlynon-modal terms. This complete subordination of the modal to thenon-modal gives his philosophy of modality a quite radical character,and also sheds light on some of his seemingly independent views aboutthe modalities involved in such concepts as causation, law of nature,and chance. (For example, Lewis rejects philosophical accounts of lawsof nature that rely on any primitive modal notions.)

Third, Lewis offers an account of how facts about everything elsereduce to the sorts of facts laid out in his accounts offundamental ontology and modality. (Note that given the remarks in thelast paragraph, these reductions ultimately rest on facts aboutfundamental ontologyalone; no unanalyzed modal notions areinvolved in them.) Better: he offers an assortment of distinctiveapproaches for constructing such reductions, of which there are manyexamples but no single, canonical exposition. At this point I wish tomake just three observations about these strategies. First, they canbe seen to be directed at providing answers to a distinctivelymetaphysical kind of question, of the form, “What is it forsuch-and-such a fact to obtain?” Examples will pin down theidea:

• Question: What is it for an object to persist through time?Lewis’s answer: It is for that object to be constituted bythree-dimensional, instantaneous time-slices that exist at differenttimes. (Lewis 1988)
• Question: What is it for an object to have a certain propertyessentially? Lewis’s answer: It is for every one of thatobject’s counterparts in other possible worlds to have thatproperty. (Lewis 1968)
• Question: What is an event? Lewis’s answer: It is a certainkind of property of spacetime regions. (Lewis 1986d)
• Question: What is it for one event to be a cause of another?Lewis’s (preliminary) answer: It is for the second event tocounterfactually depend on the first, in the sense that had the firstnot occurred, the second would not have.^[1] (Lewis 1973a, 1986b)
• Question: What is an explanation of some event? Lewis’sanswer: It is a quantity of information about that event’s causes.(Lewis 1986c)

And so on. It is this kind of question—albeit not always phrasedin this way, and accompanied by definite views about what constitutesa philosophically appropriate answer—that animate what we mightcall Lewis’s “applied metaphysics”: the application ofhis basic positions in ontology and modality to a range of perennialmetaphysical topics. Note that thereductionist character ofhis approach comes out when we pursue the obvious follow-up questions:For example, what is it for one event to counterfactually depend onanother? Roughly, it is for the closest possible world in which thesecond does not occur to be a world in which the first does not occur.What is it for one world to be closer to actuality than another?We’ll skip the answer for now—but rest assured that it andthe answers to subsequent follow-up questions are designed to hangtogether in such a way as to collectively display how facts about whatcauses what ultimately reduce to facts about fundamental ontology. Andso it goes, for personal identity, free will, the mind, knowledge,ethics, laws of nature, you name it.

The second observation is that it remains far from clear whether wecan dispense with the notion of “reduce to” (or“determined by”, “fixed by”, etc.) in favor ofsome philosophically more sanitized alternative; see the

Supplement onReduction

The third observation I wish to make at this point is that Lewis isstrongly motivated by a desire for theoretical economy—both withrespect to ontology and with respect to ideology. His quest forontological economy shows up in the austerity of thekinds offundamental entities he admits into his ontology (he neither shows,nor cares to show, any economy with respect to theirnumber).His quest for ideological economy shows up in several places, butperhaps most notably in his utter rejection ofany unanalyzedmodal notions, and—something that hasn’t been mentionedyet—in his attempted reduction of set theory to mereology andplural quantification.

Let’s take a somewhat closer look, now, at Lewis’s account offundamental ontology.

2. Fundamental ontology: A simplified version

It will be useful to start with a view that is almostLewis’s—almost, but not quite, as it is more opinionatedthan he would be comfortable with. Stating the view takes but a fewlines; providing the needed commentary will take longer. Thus,Almost-Lewis says the following:

The onlyfundamental entities that areparticularsare spacetime points.

What these particularsare like is given by what perfectlynatural monadic properties they instantiate, and what perfectlynatural relations they stand in to one another.

And that’s it. That is, the facts about what fundamentalparticulars there are, and what perfectly natural properties andrelations they instantiate, determine all other facts, even modalfacts. Almost-Lewis(and Lewis) believes, of course, inother particulars besidesspacetime points; it’s just that these particulars are notfundamental: what it is for them to exist is to be explained, somehow,in terms of facts about the fundamental entities. (See the

Supplement onFundamental Entities

for some qualifications about Lewis’s position.)

Notice one consequence: If the facts about what fundamentalparticulars there are, and what perfectly natural properties andrelations they instantiate, determineall other facts, thenthere is no reason to suppose that compositeparticulars—particulars that have other particulars as properparts—ever instantiate perfectly natural monadic properties. (Ofcourse, they can perfectly well instantiate the very-but-not-perfectlynatural property of havingparts that instantiatesuch-and-such a perfectly naturalrelation.) Thus, if, forexample, my laptop has a mass of 3 kg, that is so only in a slightlyderivative sense: the laptop is composed of parts whose masses add upto 3 kg.

Four questions demand attention: What are “perfectlynatural” properties and relations? What does it come to to saythat the fundamental particulars arespacetime points? Whatdoes it come to to say that they are spacetimepoints?Finally, what is the relationship between the fundamental ontologyposited by Almost-Lewis and Lewis’s own celebrated thesis ofHumean Supervenience? Let’s consider these topics in turn.

3. Perfectly natural properties and relations

Remember that laying out the foundations of one’s ontologyrequires two things: to say what, fundamentally,there is;and to say what itis like, presumably by stating somefacts about the fundamental entities. But not just any factsmatter. For example, it may be true of some of the fundamentalentities that they coexist with at least one pig; but saying so doesnothing to help articulate thefundamental structure ofreality. To do that, Lewis thinks, one needs adistinctionamong the properties and relations: some are special, in that it istheir pattern of instantiation among the fundamental entitiesthat constitutes the fundamental structure of reality—the“joints” along which nature is to be ultimately carved.These special properties and relations are the “perfectlynatural” ones.

(There are a variety of other uses to which Lewis puts the notion of“natural” properties, some of which show that what heneeds is a distinction that admits of gradations, with theperfectly natural properties at one extreme. See the

Supplement onThe Natural/Non-natural Distinction

for an overview.)

It is not enough merely toappeal to such a distinction; formetaphysics to do its job properly, it must also provide anaccount. Now, one way to proceed would be to provide a theoryof what properties and relations are, in which it is stipulated thatall such things are to count as “perfectly natural”. Onsuch an approach, while there may well be a property corresponding tothe predicate “has mass 5 kg” (for example), there willalmost certainly be no property corresponding to the predicate“is green” (let alone that familiar gerrymander, “isgrue”). Lewis favors a different approach. Given his commitmentto set theory, healready believes in things that, by hislights, deserve to be called the property of being green, and indeedthe property of being grue: these are merely certainsets—sets of actual and possible objects. (See thesection on Lewis’s modal metaphysics in the entry onDavid Lewis, and the supplement onThe Natural/Non-natural Distinction.) The question for him, then, is how todistinguish amongthese sets those that are perfectly natural. Here I will presentAlmost-Lewis as being, almost like Lewis, agnostic as between fourbroad alternatives. (Almost, because Lewis eventually decided that thefirst alternative, according to which natural properties and relationsare Aristotelian universals, is unworkable; see his 1986f for thereasons.)

• One could adopt atheory of universals of the kinddeveloped by David Armstrong (1978a,1978b): “…we couldcall a property [viz., set of actual and possible objects]perfectly natural if its members are all and only thosethings that share some one universal.” (1999 p. 13)
• One could treat “natural” as aprimitivepredicate of sets of actual and possible objects: “…aNominalist could take it as a primitive fact that some classes ofthings are perfectly natural properties; others areless-than-perfectly natural to various degrees; and most are not atall natural. Such a Nominalist uses ‘natural’ as aprimitive predicate, and offers no analysis of what he means inpredicating it of classes.” (1999, p. 14)^[2]
• One could define “natural” in terms of a suitablycomplex, and primitive, notion ofresemblance:“Alternatively, a Nominalist in pursuit of adequacy might preferto rest with primitive objective resemblance among things.…Then he could undertake to define natural properties in termsof the mutual resemblance of their members and the failure ofresemblance between their members and their non-members.” (1999,p. 14)
• One could adopt an ontology oftropes—roughly,property-instances, entities that occupy a sort of ontological halfwayhouse between particulars and properties. (See Lewis 1986f, Williams1953, Campbell 1990.)

Returning now to Almost-Lewis’s fundamental ontology, the optionsseem to be these: It might be that a spacetime point (or sequence ofpoints) instantiates a perfectly natural property (respectively,relation) by instantiating a universal, in the sense of Armstrong. Itmight be that it has it by having as one part a certain kind of trope,in roughly the sense of Williams. (Whence we must amend slightly, andtake thesetropes to be the fundamental entities.) It mightbe that it has it by belonging to a special sort of set of (actual andmerely possible) spacetime points—special either on account ofthe resemblances that unite its members and distinguish them fromnon-members, or on account of simplybeing perfectly natural.Regardless of which one chooses, Lewis thinks, one’s theory ofnatural properties and relations ought to respect fourphilosophically-motivated constraints:

First, an adequate theory should beminimal, in the sensethat it posits just enough perfectly natural properties and relationsfor their distribution among the fundamental particulars to fully anddeterminately fix the nature of all of reality: “The guidingidea, roughly, is that the world’s universals should comprise aminimal basis for characterizing the world completely. Universals thatdo not contribute at all to this end are unwelcome, and so areuniversals that contribute only redundantly.” (1999, p. 12) Itis clear from the surrounding text that Lewis takes this constraint togovern the various alternatives to a universals account of naturalness.^[3]

Second, perfectly natural properties and relations are, Lewis thinks,non-modal. What, exactly, this means will need to come in formore discussion. For the moment, we can take it tomean roughly this (though trouble for this characterization quicklyarises): the instantiation of a perfectly natural property by one(fundamental) particular, or of a relation by several, placesabsolutely no constraints of a logical or metaphysical kind on theinstantiation of any other perfectly natural property or relation bythat or any other particular or particulars.

Third, they areintrinsic to the particulars that instantiatethem—which, all too roughly, means that they characterize whatthose particulars are like, independently of what any other distinctparticular is like. More: The intrinsic nature of any particular isexhausted by what perfectly natural properties it instantiates.^[4] This assumption also allows a theory of natural properties andrelations to yield, in a fairly simple way, a definition of“perfect duplicate” applicable to any possible objectsx andy (not necessarily inhabiting the samepossible world):x andy are perfect duplicates iffthey share exactly the same perfectly natural properties.^[5] A definition of “intrinsic” follows: a propertyP is intrinsic iff any two duplicatesx andy (taken from any possible worlds) either both haveP or both fail to haveP. Of course, what we reallyhave here is a tight circle that puts on display how the expressions“intrinsic”, “perfect duplicate”, and“perfectly natural” can be interdefined, with the help ofthe modal notion of metaphysical possibility. (See Lewis 1983c andLangton & Lewis 1998 for discussion of various strategies forbreaking out of this circle.)

The fourth constraint is purely negative: it is that it should be leftto the empirical sciences to fill in the details aboutwhichperfectly naturalmonadic properties there are (at least, inactuality:philosophy might teach us, or at least give ussome reason to believe, that there are, in other possible worlds,so-called “alien” properties, perfectly natural propertiesnot instantiated in the actual world). Not just any empirical sciencewill do: given, in particular, the first of the four theses, it isreally the job of fundamental physics to fill in these details. Thespecial sciences get no say.

What about perfectly natural relations? Here matters are less clear.Lewis certainly thinks that spatiotemporal relations are perfectlynatural; what is less obvious is whether, by his lights, physics couldrationally lead us toreject this claim. For now I willsimplify, and have Almost-Lewis add afifthconstraint—one that is in tension at least with the spirit ofthe fourth, and that the real Lewis certainly rejects. It is this: notonly are spatiotemporal relations perfectly natural, they are theonly perfectly natural relations. (The onlypossibleones—though remember that given Lewis’s reductionism aboutmodality, that is an idle addition.)

The picture that emerges is this: Reality consists of a multitude ofspacetime points. Each of these stands in spatiotemporal relations tosome others (though not toall others). Each instantiates variousperfectly natural, non-modal monadic properties. That is all there is;anything putatively “extra”—facts about laws ofnature, or about persisting macro-objects, or about causation, orabout mentality, or about ethics, or about sets, etc.—mustsomehow reduce to that stuff. For Almost-Lewis, this picture capturesa fundamental truth about the nature of existence. It is roughly rightthat it is also anecessary truth—a status that wouldseem to fall out automatically, given Lewis’s reductionist accountof modality. The only unfinishedphilosophical business is towork out the right theory of natural properties and relations, and towork out the details of the reduction for particular cases.

4. Spatiotemporal relations and spacetime points

The foregoing Almost-Lewisian thesis about spatiotemporal relations istoo strong to be tenable: we now have reasonably good reasons, drawnfrom quantum physics, for holding that even in the actual world, thereare perfectly natural relations other than the purely spatiotemporalones. (Roughly: the relations—whatever exactly they amountto—coded up in the quantum mechanical wave-function.) Two pointsin its defense are, however, worth brief mention: First, seeminglyobvious counterexamples—involving such basic physical relationsasbeing more massive than—in factaren’tcounterexamples, since Lewis can deny that they are genuinelyfundamental orperfectly natural, on the basis that factsabout their obtaining reduce to facts about the distribution ofmonadic perfectly natural properties. (Still, they will certainly turnout to bevery natural.) Second, if we could at leastmaintain, as acontingent thesis, that the only perfectlynatural relations are spatiotemporal ones, then we could plausiblysettle an unresolved and deeply vexed question about the content ofphysicalism (the doctrine, to put it rather too crudely, that allthere is to the actual world is physical stuff), as explained inthe supplementary document

Physicalism

At any rate, the thesis that spatiotemporal relations are at leastamong the perfectly natural relations allows us to clarifyand simplify Almost-Lewis’s position. Specifically, we can saythat all that it comes to to say that the fundamental entities arespacetime points is that they stand in perfectly naturalspatiotemporal relations to one another. For more, see thesupplementary document on

Spacetime Points

To say that they are spacetimepoints, finally, is to saythat they have no proper parts.

One upshot is that my original statement of Almost-Lewis’sontology needs an amendment: for it was misleading to say thataccording to him, the fundamental particulars arespacetimepoints. That’s true, but it wrongly suggests that he is making achoice of one fundamentalkind of particular, distinguishedfrom other possible choices by the essential nature of its members.Not so. It is more accurate to describe his fundamental ontologythus:

• There are particulars.
• They are, or are wholly composed of,simples—particulars have no other particulars as properparts.
• These simples have various perfectly natural monadicproperties.
• They stand in various spatiotemporal relations to oneanother.
• And that is all.

5. Humean Supervenience

Almost-Lewis’s theses about what fundamental ontology comprises,and how all other facts reduce to facts about it, bears a very closerelationship to Lewis’s celebrated thesis of Humean Supervenience(hereafter: “HS”). But they are not the same, and thedifferences are worth keeping track of. Here is a typical statement ofHS (slightly stronger, as we’ll see, than the version Lewisofficially endorses): No two possible worlds differ with respect towhat is true at them, without differing with respect to thegeometrical arrangement of their spacetime points, or with respect towhich perfectly natural properties are instantiated at those points.^[6] (Note that so stated, HS is automatically metaphysicallynecessary.) Thus, HS is asupervenience claim,logically weaker than Almost-Lewis’s claim of reduction. It isalso a claim that—for some good reasons and some badreasons—Lewis accepts only in a weaker form that ismetaphysicallycontingent. More significantly, it is no partof HS that facts about possible worldsthemselves reduce toanything else; whereas both Almost-Lewis and Lewis are explicit intheir commitment to this further claim. Having said all this, it willbe worth remembering in what follows that Almost-Lewis’s position(which, remember, incorporates Lewis’s modal realism)entails HS. So, any doubts about HS will carry over toAlmost-Lewis’s fundamental ontology.

6. Lewis v. Almost-Lewis

Let’s consider now the most salient ways in which Lewis’s ownpositions about fundamental ontology diverge from those ofAlmost-Lewis.

First, Lewis takes the lessons quantum physics teaches seriouslyenough to withhold endorsement of Almost-Lewis’s fifth thesis,that the only perfectly natural relations are spatiotemporalrelations.

Second, Lewis is agnostic as to whether, in addition to spacetimepoints, there might be (in this, or other possible worlds) fundamentalentities that areoccupants of such points. But agnosticismon this score is probably a bad idea: the proposed possibility is notclearly intelligible, nor it is clear what its motivation could be.For more, see the supplementary document on

Spacetime Points

Third, on a plausible story about whatnon­-fundamentalentities there are, it will turn out that on Almost-Lewis’s view,everything that exists is composed of simples (parts, that themselveshave no proper parts). Lewis is also agnostic on this score: he takesit to be at least an epistemic possibility that there is“gunk”: something, every proper part of which itself has aproper part (see for example Lewis 1991). Lewis says relatively littleeither about the status of this possibility (in particular, is it morethan merely epistemic?), or about its potential ramifications for hisvarious positions in metaphysics. To keep things simple, I willdiscount it for the remainder of this main essay.

Fourth, Lewis holds that his thesis of Humean Supervenience is, atbest, onlycontingently true. Of course, given that herecognizes the (metaphysical) possibility of perfectly natural,non-spatiotemporal relations, heshould treat HS as at bestcontingent. But he advances reasons for doing so of a quite differentsort. They are not particularly good reasons, and so we will pass themby; but see the supplementary document on

The Contingency of Humean Supervenience

for discussion.

7. Some criticisms

What, finally, should we make of Lewis’s conception of fundamentalontology? A complicated question; I will limit discussion to just twoimportant worries. Let’s begin by noting the obvious influence ofa certain scientifically-informed conception of the world in shapingLewis’s picture of reality. Lewis himself is quite explicit aboutthis influence:

The picture is inspired by classical physics. Humean Superveniencedoesn’t actually say that physics is right about what localqualities there are, but that’s the case to keep in mind. But ifwe keep physics in mind, we’d better remember that physicsisn’t really classical. …The point of defending HumeanSupervenience is not to support reactionary physics, but rather toresist philosophical arguments that there are more things in heavenand earth than physics has dreamt of. (1994, p. 474)

But there is a less acknowledged influence of first-order predicatelogic—an influence that is not entirely salutary. It isundoubtedly tempting, for philosophers steeped in the use offirst-order logic as a clarifying tool, to assume that the properrepresentation of the ultimate structure of reality must be by meansof some (interpreted) first-order language—a language whosevariouspredicates could be taken to express the variousfundamental properties and relations that characterizereality at its most basic level. But if we look to physicsinstead—as we surely ought to—we find that the basicrepresentational tools arevariables, that correspond tophysical magnitudes. Taking seriously the picture offundamental ontology suggested by these representations turns out tomatter quite a bit: in particular, there are reasons to think thatnone of the first three theses about natural properties andrelations—that they are minimal, non-modal, andintrinsic—is tenable without some modification. Thisissue—which we will mostly pass over in what follows, exceptwhere it matters—is explored in more detail in thesupplementary document on

Physical Magnitudes

The second significant source of concern about Lewis’s conceptionof fundamental ontology is the role—or rather lackthereof—thatmodal notions have in it. This concern hastwo aspects. First, one might hold that some, at least, of thefundamental properties and relations that characterize reality havemodal aspects that are ontologically basic. Considermass:one might hold that it is metaphysically impossible for there to be aworld containing just two massive particles, accelerating away fromeach other—and that this impossibility somehow flows from thenature of mass itself.

Second, one might hold that it is one thing to state a thesisconcerning what the fundamental structure of realityin facthappens to be; but that it isanother, separate matter tostate how realitycould be. Indeed, most metaphysicians, Isuspect, take it to be just blindingly obvious that these areconceptually distinct tasks. Granted that one’s views on whatthere is, and what it is like, will have ramifications for one’sviews on what therecould be and what itcould belike (most obviously, because thingscould be the way theyare; but there may be more interesting and subtle connectionsas well); still, the project of laying out the former views does notautomatically complete the project of laying out thelatter.

Of course there is a sense in which Lewis agrees: he takes it asobvious, after all, that he must supply an account of modality. Butthe strikingly reductionist character of that account shows that suchagreement as there is is mighty thin.

8. Counterpart theory

So far, this entry focused on the general shape of Lewis’smetaphysics. In this section, we turn to one of Lewis’s more specificmetaphysical doctrines: counterpart theory. We will begin with anoverview of the theory, review its motivation, some applications, andthen turn to criticism and objections. In a supplementary document, wereviewCounterpart-theoretic Semantics for Quantified Modal Logic.

Counterpart theory was originally introduced in Lewis (1968) as aformal theory about possible worlds and their inhabitants, but thelabel quickly came to be used for a loosely defined approach towardstrans-world identity and the interpretation of modal or temporaldiscourse. For the modal case, the central idea is that adere modal claim like ‘Joe Biden might be immaterial’is understood as saying that at some possible world, someone whosufficiently resembles Joe Biden in certainrespects—acounterpart of Biden—isimmaterial. Accordingly, ‘Biden is necessarily material’is understood as saying that all of Biden’s counterparts at allworlds are material.

While counterpart theory was Lewis’s invention, it was also aproduct of its time, the 1960’s, when quantified modal logic was“in the air” and questions about essentialism and theso-called problem oftransworld identity gained attention (e.g. Quine 1953, Hintikka 1962).^[7] The counterpart-theoretic approach does, however, bear a strikingsimilarity to certain views of Leibniz concerning essential andaccidental properties.^[8] (See Mondadori (1973) for a counterpart-theoretic interpretation ofLeibniz.)

8.1 Motivation and applications

Lewis assumed that modal statements in ordinary language can beanalysed in terms of quantification over possible worlds andindividuals: ‘it is possible that there are talkingdonkeys’ is analysed as ‘there are possible worlds atwhich there are talking donkeys’. Lewis’s modal realismpromises to turn this into a reductive analysis ofmodality. Statements about what is or is not the case at some possibleworld are ultimately reduced to non-modal statements. That there is aworld with talking donkeys, for example, means that there is aspatiotemporally isolated aggregate of things that has a genuinetalking donkey as part.

A problem now arises forde re statements about what ispossible or necessary for a particular individual. Since Joe Bidenmight have had three arms, there should be a world where he has threearms. But if Biden werepart of another world, then thatworld and our world would have a part in common. Lewis denies thatdifferent worlds can share parts. Even if we allowed for overlappingworlds, it is hard to see how the other world could have a three-armedBiden as a part, given that this part is also part of our world, whereBiden has two arms (compare Lewis 1986e, 199ff.). So ‘Bidenmight have had three arms’ is not analysed as stating that thereis a world which contains a three-armed Biden as part. Rather, it saysthat there is a world that contains a three-armedrepresentative orcounterpart of Joe Biden.

What makes one object a counterpart of another? According to Lewis,this is a matter of qualitative similarity in certain respects: acounterpart of Biden is an individual that sufficiently resembles theactual Biden in relevant respects, and more so than any other objectin its world. Sometimes Lewis drops the second clause (e.g. Lewis1968, 114–115), and at one point he merely suggests (withoutexplanation) that counterparthood “usually involve[s]similarity” (Lewis 1986e, 8).

The relevant respects of resemblance need not match intuitivejudgements of overall similarity (Lewis 1986e, 254f.), and they can behighly extrinsic. For example, they might give high weight tosomeone’s origin (Lewis 1986e, 244f. and 252), or to a causalconnection to an epistemic subject (Lewis 1983e).

Lewis does not think there is a once-and-for all correct answer towhich respects of resemblance are relevant. He rejects the idea thatthings have primitive essences which somehow determine or constrainwhat is possible for them. Rather, it is ultimately up to us whichrespects of similarity we prioritize. Often this choice is not fullysettled, leaving the counterpart relation vague and context-sensitive(see Lewis 1971, 209–11; Lewis 1973b, 41; Lewis 1983d, 42–3;Lewis 1986e, 251–5; Lewis 2003, 27–8).

For example, Lewis suggests that when we talk about people, we oftenrequire the counterparts to have a very similar origin, while allowingfor different careers and lifespan. In such a context, we might judgethat Biden might have died as an infant. In other contexts, however,we may wonder what would have been the case if Biden had been born todifferent parents, relaxing the requirement of similar origin (seee.g., Lewis 1973b, 41).

Since the counterpart relation is determined by similarity, everythingis its own counterpart. Other than that, Lewis imposes few generalrestrictions on the counterpart relation. In Lewis (1968), he suggeststhat nothing can be a counterpart of a different object in the sameworld, but this assumption is later dropped (Lewis 1986e, 232,fn.22). Unlike strict trans-world identity, counterparthood is notassumed to be transitive, symmetric, or functional. An object can havemultiple counterparts at a world, and different objects can have acommon counterpart.

Lewis delivered counterpart theory as part of his modal realism, butthe core idea can be separated from this background, and even from theassumption of world-bound agents. (See e.g. Stalnaker 1986,Heller 1998, Sider 2002, Wang 2015, Woodward 2017; also Lewis 1986e,237f. and 259f.) Many philosophers who reject modal realism have cometo appreciate counterpart theory because of its explanatory andpuzzle-solving power. We will give a few examples.

First, counterpart theory promises to explain the widespreadelusiveness and context-dependence of essentialist judgements (Lewis1983d, 42–3; Lewis 1986e, §4.5; cf. Kaplan 1979,100–2). Could London have been located in Scotland? Could it havebeen founded in the 16th century? The answers aren’t obvious.For Lewis, this is not because we have imperfect access toLondon’s true essence, but simply because we have not settledexactly which other-worldly cities should qualify as counterparts ofLondon. A London counterpart is a city that sufficientlyresembles London, but the relevant resemblance criteria areoften vague and context-dependent.

Second, counterpart theory might offer an answer to certain puzzlesabout identity. Is a statue identical to the piece of clay from whichit is formed? Is a person identical to their body? Lewis says yes.However, intuitively persons and bodies, or statues and pieces ofclay, seem to differ in their modal properties: the piece of claycould survive squashing, the statue could not. According to Lewis, theexplanation is that when we refer to an object as a statue, we givemore weight to similarity with respect to shape than when we think ofthe same object as a piece of clay (see Lewis 1971; Lewis 1986e,252ff.; Lewis 2003, 27–8; and Robinson 1982).

In this context, Lewis suggests that different ways of referring to anobject can “evoke” different similarity standards, andthereby different counterpart relations, even within a single context(cf. Lewis 1986e, 258ff; Lewis 2003). This idea also helps tomake sense of conditionals like ’If I were you, I’d hateme’, where ‘I’ and ‘me’ in theconsequent intuitively pick out different individuals in the imaginedperson-swapping scenario, both of which somehow represent the speaker(see Lewis 1973b, 43; Kocurek 2018).

Third, counterpart theory might offer an answer to puzzles involvingpossible fission or time-travel. These might be analysed as scenariosin which an individual has multiple counterparts relative to the samecounterpart relation. Lewis intuits that he “might have beentwins” (Lewis 1973, 40–1), because the fetus from which hedeveloped might have undergone fission. (See also Schwarz 2014, Karmo1983.)

Fourth, counterpart theory offers a way to accept haecceitisticintuitions without subscribing to haecceitism. Lewis assumes that alltruths supervene on qualitative truths: no two worlds agree in allqualitative respects, while disagreeing with respect to who playswhich roles. A world of two-way eternal recurrence might look like acounterexample: intuitively, we could have lived in any of the epochsof such a world; these seem to be distinct possibilities, but they donot correspond to any qualitative difference. Lewis suggests that thedifferent epochs really do represent different possibilities for us,because we have counterparts in each of them. Here, too, Lewis invokesmultiple counterparthood relative to the same counterpart relation.(See Lewis 1986e, 230–5.)

Fifth, the fact that the counterpart relation need not be anequivalence relation has also been used to diffuse certain puzzles.Consider an ordinary bicycle. Intuitively, such an object does nothave all its parts essentially: the bike could have had a differentchain, for instance. On the other hand, arguably it could not havebeen composed ofentirely different parts. A bike made ofentirely different parts would have been a different bike. But thiscreates a puzzle (see Chisholm 1967, Chandler 1976): if the bike had adifferent chain, it would still be an ordinary bike that does not haveall its parts essentially; it could have had a different saddle (say).Iterating this line of thought, we can create a sequence that leadsfrom the actual bike to a bike composed of entirely different parts.Each possible bike in the sequence could have been the next bike inthe sequence. But didn’t we say that it is impossible that mybike is composed of entirely different parts? Counterpart theoryoffers a natural answer: a counterpart of a counterpart need not be acounterpart (see Lewis 1968, 28f; Lewis 1986e, 243–6;Ramachandran 2020).

So far, we have focused on metaphysical modality. The central ideaof counterpart theory has also been applied to other intensionalconstructions.

For example, Sider (1996, 2001) and Hawley (2001) argue for atemporal application, on which ‘Joe Biden won the election’ isanalysed as saying that a past counterpart of Biden won theelection. The temporal counterpart relation is here assumed to relateshort-lived temporal “stages” (see Schwarz 2014 for an alternative),and is not a matter of qualitative similarity. As in the modal case,this approach has been advertised as solving a range of puzzles, aswell as explaining the vagueness and context-dependence of temporaljudgements. Williams (2008) considers adopting the same perspective onidentity across space.

Several authors (including Lewis) have suggested applyingcounterpart theory to epistemic modality. Consider the followingpuzzle from Ninan (2018). A lottery has only two tickets, one blue andone red. The tickets are numbered 1 and 2, but we don’t knowwhich color goes with which number. We know that the blue ticket won,but we don’t know the number of the winning ticket. So, ticket1 might be the winner, and likewise for ticket 2. Yet even thoughone of them is the red ticket it doesn’t seem to follow that thered ticket is such that it might be the winner. Ninan suggests thatdiffering counterpart relations are evoked by different ways ofpicking out the tickets. (See also Lewis 1983e, Stalnaker 1986, Shaw2015, Rabern 2018, among others.)

An alternative to counterpart theory is to interpret terms forordinary individuals as denoting (partial) functions from worlds toindividuals, or aggregates of individuals at different worlds; a modalpredication like ‘Biden might have been three-armed’ is theninterpreted as saying that the function assigned to ‘Biden’ has athree-armed value for some world, or that the aggregate assigned to ‘Biden’ has a three-armed part located in some world. A temporalanalogue of this view (with aggregates) is Lewis’s preferred accountof temporal discourse. In Lewis (1986f, 244) he endorses a similarview for events—but see Bernstein (2014), Kaiserman (2017), andMcDonnell (2016) for reasons to prefer a counterpart-theoretictreatment.^[9]

The counterpart-theoretic analysis is more flexible insofar as iteasily allows for cases of multiple counterparts or asymmetriccounterparthood, which are difficult to model with trans-worldaggregates. Lewis argues that this added flexibility is more importantin the modal case than in the temporal case (Lewis 1971, 209; Lewis1983d, 40–2; Lewis 1986e, 217–20).

8.2 Reactions and criticisms

Some early criticisms of counterpart theory seem to rest onmisunderstandings. For example, Plantinga (1974, 115f.) and Salmon(1981, 232–38) complain that according to Lewis, all things have alltheir properties essentially, since there is no world in which thesevery things exist and have different properties. Kripke (1980)similarly complains that according to Lewis, when we say that Humphreymight have won the election, we are “not talking about somethingthat might have happened toHumphrey, but to someoneelse” (45, fn. 13). In response, Lewis points out thaton his view it is indeed Humphrey himself who might have won, invirtue of having a winning counterpart, cf. Lewis (1986e, 194–6,246; 1983d, 41–2). More generally, while his account impliesthat ordinary objects exist at only one world in a technical,mereological sense of ‘existing at a world’ – theyare not literally part of multiple worlds – it allows existenceat multiple worlds in a more neutral sense in which existing at aworld merely means being represented by the world as existing.According to counterpart theory, Humphrey is represented as winning,and as existing, by any world with a suitable Humphreycounterpart. (See also Hazen 1979, 320–4.)

One possible limitation of Lewis’s account is that hiscounterpart relation is assumed to be a qualitative similarityrelation. Feldman (1971) points out that “I could have beenquite unlike what I in fact am” is intuitively true, which seemsto require having non-similar counterparts. Lewis responds that thereare two similarity relations involved: at the relevant worlds, thereis someone who is similar to me in some respect (perhaps with respectto origin), but dissimilar from me in other respects (see Lewis1983d, 43; Lewis 1986e, 230–235). Heller (2005), Stalnaker(1986), and Fara (2009) offer further considerations against analysingcounterparthood in terms of qualitative similarity.

Another limitation of Lewis’s original presentation is that itdoes not allow imposing constraints on the choice of counterparts fordifferent individuals. Suppose we hold that Elizabeth II isessentially the daughter of George VI, and suppose there are worlds atwhich both Elizabeth and George have multiple counterparts, perhaps indifferent epochs of eternally recurring time. Some Elizabethcounterpart will then not be the daughter of some George counterpart.By Lewis’s 1968 account, ‘Elizabeth might not have beenGeorge’s daughter’ then comes out true, contrary to oursupposition. This problem was raised in Hazen (1979). Hazen suggests arevised analysis in terms of sets of counterpart functions. Lewis(1983d, 44–5) instead suggests that we should understand‘Elizabeth might not have been George’s daughter’ asa de re claim about the pair (or fusion) of Elizabeth and George.Hazen (2012) argues that neither proposal fully avoids theproblem.

The most common objection to counterpart theory is probably that itgives rise to a deviant and counter-intuitive modal logic. Lewis(1968) gives translation rules from the language of quantified modallogic to an extensional first-order language. These translation rulesinvalidate the “necessity of identity” and the“necessity of distinctness”, as well as familiarprinciples of modal logic such □(A ∧ B) → □A.Conversely, they do validate controversial principles such as theConverse Barcan Formula and the “necessity of existence”.It has also been argued that the rules can’t be extended to alanguage with a well-behaved ‘actually’ operator.

Whether these are genuine problems is a matter of debate. In fact,authors in mathematical logic have come to appreciatecounterpart-theoretic interpretations of modal logic as overcomingcertain problems of standard Kripke semantics. There are also ways ofreformulating Lewis’s translation rules so as to avoid thesupposedly problematic features. See the supplementary document:

Counterpart-theoretic Semantics for Quantified Modal Logic

for further details.

Lewis himself had no interest in preserving traditional principles ofmodal logic. He always remained skeptical about the prospects offormalising modal discourse with boxes and diamonds. (seee.g. Lewis 1983d, 45; Lewis 1986e, 12–13). He thus rejectedthe presupposition in these objections, that “the language ofboxes and diamonds affords a good regimentation of ordinary modalthought” (Lewis 1986e, 12).

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• Corsi, Giovanna, 2002, “Counterpart Semantics. A Foundational Study on Quantified Modal Logics”, Amsterdam, Institute for Logic, Language, and Computation, Research Report PP-2002-20.
• Schwarz, Wolfgang, 2013,Generalising Kripke Semantics for Quantified Modal Logics, manuscript available online.
• Sider, Ted, 2008,Beyond the Humphrey Objection, manuscript available online.
• David Kellog Lewis, by Peter King (Oxford University).
• Obituary of David Lewis, by Tim Crane, published inThe Independent, October 23,2001.

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Lewis, David |logic: modal |metaphysics |ontological commitment |properties |reduction, scientific

Acknowledgments

Many thanks to Phillip Bricker for extraordinarily acute and helpfulcomments on an earlier draft of this entry. Also, for his valuablehelp on the supplement on fundamental entities.