David Lewis

First published Thu Jul 23, 2009; substantive revision Thu Nov 18, 2021

David Lewis (1941–2001) was one of the most importantphilosophers of the 20th Century. He made significant contributions tophilosophy of language, philosophy of mathematics, philosophy ofscience, decision theory, epistemology, meta-ethics and aesthetics. Inmost of these fields he is essential reading; in many of them he isamong the most important figures of recent decades. And this listleaves out his two most significant contributions.

In philosophy of mind, Lewis developed and defended at length a newversion of materialism (see the entry onphysicalism). He started by showing how the motivations driving the identity theoryof mind andfunctionalism could be reconciled in his theory of mind. He called this an identitytheory, though his theory motivated the position now known asanalytic functionalism. And he developed detailed accounts of mental content (building onDavidson’sinterpretationism) and phenomenal knowledge (building on Nemirow’sability hypothesis) that are consistent with his materialism. The synthesis Lewis endedup with is one of the central positions in contemporary debates inphilosophy of mind.

But his largest contributions were in metaphysics. One branch of hismetaphysics was his Hume-inspired reductionism about the nomological.He developed a position he called “Humean supervenience”,the theory that said that there was nothing to reality except thespatio-temporal distribution of local natural properties. And he didthis by showing in detail howlaws, chances,counterfactual dependence,causation, dispositions and colours could be located within this Humean mosaic.The other branch of his metaphysics was hismodal realism. Lewis held that the best theory of modality posited concrete possibleworlds. A proposition is possible if and only if it is true at one ofthese worlds. Lewis defended this view in his most significant book,On the Plurality of Worlds. Alongside this, Lewis developed anew account of how to think about modal properties of individuals,namelycounterpart theory, and showed how this theory resolved several long-standing puzzlesabout modal properties.

1. Lewis’s Life and Influence

As we’ve already seen, part of Lewis’s significance camefrom the breadth of subject matter on which he made majorcontributions. It is hard to think of a philosopher since Hume who hascontributed so much to so many fields. And in all of these cases,Lewis’s contributions involved defending, or in many casesarticulating, a big picture theory of the subject matter, as well asan account of how the details worked. Because of all his work on thedetails of various subjects, his writings were a font of ideas evenfor those who didn’t agree with the bigger picture. And he wasalmost invariably clear about which details were relevant only to hisparticular big picture, and which were relevant to anyone who workedon the subject.

Lewis was born in Oberlin, Ohio in 1941, to two academics. He was anundergraduate at Swarthmore College. During his undergraduate years,his interest in philosophy was stimulated by a year abroad in Oxford,where he heard J. L. Austin’s final series of lectures, and wastutored by Iris Murdoch. He returned to Swarthmore as a philosophymajor, and never looked back. He studied at Harvard for his Ph.D.,writing a dissertation under the supervision of W. V. O. Quine thatbecame his first book,Convention. In 1966 he was hired atUCLA, where he worked until 1970, when he moved to Princeton. Heremained at Princeton until his death in 2001. While at Harvard he methis wife Stephanie. They remained married throughout Lewis’slife, jointly attended numerous conferences, and co-authored threepapers. Lewis visited Australia in 1971, 1975, every year from 1979 to1999, and again shortly before his death in 2001.

Lewis was a Fellow of the American Academy of Arts and Sciences, aCorresponding Fellow of the British Academy, and an Honorary Fellow ofthe Australian Academy of the Humanities. He received honorarydoctorates from the University of Melbourne, the University of York inEngland, and Cambridge University. His Erdös number was 3.

Lewis published four books:Convention (1969a),Counterfactuals (1973a),On the Plurality of Worlds(1986a) andParts of Classes (1991a). His numerous papershave been largely collected in five volumes:Philosophical PapersVol. I (1983a),Philosophical Papers Vol. II (1986b),Papers in Philosophical Logic (1998a),Papers inMetaphysics and Epistemology (1999a) andPapers in SocialPhilosophy (2000a). This entry starts with a discussion ofLewis’s first two books, then looks at his contributions tophilosophy of mind. Sections 5 and 6 are on his metaphysics, lookingin turn at Humean Supervenience and modal realism. Section 7 looksvery briefly at some of the many works that aren’t been coveredin the previous five categories.

2. Convention

David Lewis’s first book wasConvention (1969a; notethat all citations are to works by David Lewis, unless explicitlystated otherwise). It was based on his Harvard Ph. D. thesis, andpublished in 1969. The book was an extended argument that languagecould be entirely grounded in convention. There is a simple argumentthat this could not be so. Conventions are formed by agreement,agreements are made in language, so language must precede convention,not be grounded in convention. (In the foreward Quine contributes toConvention, Quine appears to express some sympathy for thisargument.) Lewis’s response is to deny that conventions requireanything like an agreement. Rather, on his view, conventions areregularities in action that solve co-ordination problems. We canstumble into such a regularity without ever agreeing to do so. Andsuch a regularity can persist simply because it is in everyone’sbest interest that it persist.

2.1 Analysis of Convention

Lewis viewed conventions as solutions to co-ordination problems (seeSection 3.2 of the entry onconvention). His thinking about these problems was heavily influenced by ThomasSchelling’s work on co-operative games inThe Strategy ofConflict (Schelling 1960). Many of the key ideas in Lewis’sbook come from game theory.

The simplest cases in which conventions arise are ones where we arerepeatedly playing a game that is purely co-operative, i.e. thepayoffs to each agent are the same, and there are multiple equilibria.In such a case, we may well hope for the equilibrium to persist. Atthe very least, we will prefer the persistence of the equilibrium toany one person deviating from it. And we will have this preferenceeven if we would prefer, all things considered, to be in some otherequilibrium state. In such a case, there may well be a practice ofcontinuing to play one’s part in the equilibrium that has beenreached. This is a regularity in action—it involves making movesin the repeated game. Given that everyone else is following theregularity, each agent has a reason to follow the regularity;otherwise it wouldn’t be an equilibrium. But if other agentsacted differently, agents would not be interested in following theregularity, since there are alternative equilibria. Because thesethree conditions are met, Lewis argued that the practice is really aconvention, even if there was never any explicit agreement to continueit.

The case we started with was restricted in two important ways. First,the case involved games that were perfectly repeated. Second, itinvolved games where the payoffs were perfectly symmetric.Lewis’s theory of convention involved getting rid of bothrestrictions.

Instead of focussing on repeated co-ordination problems, Lewis justfocussed on repeated situations which collectively constitute aco-ordination problem. Lewis does not identify situations with games.A repeated situation may come in different ‘versions’,each of which is represented by a different game. For example, it maybe that the costs of performing some kind of action differ ondifferent occasions, so the formal game will be different, but thedifferences are small enough that it makes sense to have a commonpractice. And Lewis does not require that there be identity ofinterests. InConvention he does require that there be largeoverlap of interests, but this requirement does not do much work, andis abandoned in later writing. With those requirements weakened, weget the following definition of convention.

A regularityR in the behaviour of members of a populationP when they are agents in a recurrent situationS isaconvention if and only if it is true that, and it is commonknowledge inP that, in almost any instance ofSamong members ofP,
almost everyone conforms toR;
almost everyone expects everyone else to conform toR;
almost everyone has approximately the same preferences regardingall possible combinations of actions;
almost everyone prefers that any one more conform toR,on condition that almost everyone conform toR;
almost everyone would prefer that any one more conform toR′, on condition that almost everyone conform toR′,
whereR′ is some possible regularity in the behaviourof members ofP inS, such that almost no one inalmost any instance ofS among members ofP couldconform to bothR′ and toR. (Lewis 1969:78)

This is clearly a vague definition, with many ‘almost’sscattered throughout. But Lewis, characteristically, thought this wasa feature not a bug of the view. Our intuitive notion of a conventionis vague, and any analysis of it should capture the vagueness. Theidea that analyses of imprecise folk concepts should be impreciserecurs throughout Lewis’s career.

The notion of ‘common knowledge’ that Lewis is workingwith here is not the standard modern notion. Lewis does not requirethat everyone know that everyone know etc., that all of theseconditions hold. Rather, when Lewis says that it is common knowledgethatp, he means that everyone has a reason to believe thatp, and everyone has a reason to believe everyone has a reasonto believe thatp, and everyone has a reason to believe thateveryone has a reason to believe everyone has a reason to believe thatp, and so on. That people act on these reasons, or are knownto act on these reasons, to form beliefs is unnecessary. And that thebeliefs people would get if they acted on their reasons are true isalso not part of the view. Hence it is necessary to specify truth aswell as common belief in the definition.

Lewis argues that this definition captures many of our ordinaryconventions, such as the convention of driving on the right side ofthe road in the United States, the convention of taking certain piecesof paper as payments for debts, and, most importantly, the conventionsgoverning the use of language.

2.2 Conventions of Language

In the final chapter ofConvention, Lewis gives his theory ofwhat it is for a community to speak a language (see the section onconventional theories of meaning in the entry onconvention), i.e., for a community to have adopted one language as their languageby convention. Lewis individuates languages largely by the truthconditions they assign to sentences. And his account of truthconditions is given in terms of possible worlds. So the truthcondition of an indicative sentence is the set of possible worlds inwhich it is true. Somewhat more abnormally, Lewis takes the truthcondition for an imperative to be the set of possible worlds in whichthe imperative is obeyed. (The account of language inConvention covers many different moods, but we will focushere on the account of indicatives.)

The focus on truth conditions is not because Lewis thinks truthconditions are all that there are to languages. He acknowledges thatlanguages also have ‘grammars’. A grammar, inLewis’s sense, is a lexicon (i.e. a set of elementaryconstituents, along with their interpretation), a generative component(i.e. rules for combining constituents into larger constituents), anda representing component (i.e. rules for verbally expressingconstituents). Lewis’s preferred interpretations are functionsfrom possible worlds to extensions. So we can sensibly talk about themeaning of a non-sentential constituent of the language, but thesemeanings are derived from the truth conditions of sentences, ratherthan determining the meanings of sentences. That’s because, aswe’ll see, what the conventions of language establish in thefirst instance are truth conditions for entire messages, i.e.,sentences.

Given this understanding of what a language is, Lewis goes on to saywhat it is for a population to speak a language. One natural approachwould be to say that speakers and hearers face a co-ordinationproblem, and settling on one language to communicate in would be asolution to that problem. When Lewis is analysing signalling, that isthe approach he takes. But he doesn’t think it will work forlanguage in general. The reason is that he takes conventions to beregularities in action, and it is hard to say in general what actionsare taken by hearers.

So instead Lewis says that a populationP speaks a languageL if and only if there is a convention of speaking truthfullyinL that persists amongstP. The parties to theco-ordination problem (and the convention that solves it) are thedifferent people who want to communicate inP. They solvetheir problem by speaking truthfully (on the whole) inL.

It might be wondered whether it could really be a convention to speaktruthfully inL. After all, there is no obvious alternativeto speaking truthfully. As Lewis points out, however, there are manynatural alternatives to speaking truthfully inL; we couldspeak truthfully inL′ instead. The existence ofalternative languages makes our use ofL conventional. Andthe convention can be established, and persist, without anyoneagreeing to it.

2.3 Later Revisions

In “Languages and Language” (1975b), Lewis makes two majorrevisions to the picture presented inConvention. He changesthe account of what a convention is, and he changes the account ofjust what convention must obtain in order for a population to speak alanguage.

There are two changes to the account of convention. First, Lewis nowsays that conventions may be regularities in action and belief, ratherthan just in action. Second, he weakens the third condition, which wasapproximate sameness of preferences, to the condition that (almost)each agent has a reason to conform when they believe others conform.The reason in question may be a practical reason, when conformityrequires action, or an epistemic reason, when convention requiresbelief.

InConvention, the conventions that sustained language wereregularities amongst speakers. As we noted, it would be more naturalto say that the conventions solved co-ordination problems betweenspeakers of a language and their hearers. That is what the new accountof what it is for a population to speak a language does. ThepopulationP speaks the languageLiff there areconventions of truthfulness and trust inL. Speakers aretruthful inL if and only if they only utter sentences theybelieve are true sentences ofL. Hearers are trusting inL if and only if they take the sentences they hear to be(generally) true sentences ofL.

The old account took linguistic conventions to be grounded inco-ordination between speakers generally. We each communicate inEnglish because we think we’ll be understood that way giveneveryone else communicates that way, and we want to be understood. Inthe new account there is still this kind of many-way co-ordinationbetween all the speakers of a language, but the most basic kind ofco-ordination is a two-way co-ordination between individual speakers,who want to be understood, and hearers, who want to understand. Thisseems like a more natural starting point. The new account also makesit possible for someone to be part of a population that uses alanguage even if they don’t say anything because theydon’t have anything to say. As long as they are trusting inL, they are part of the population that conforms to thelinguistic regularity.

John Hawthorne (1990) argued that Lewis’s account cannot explainthe intuitive meaning of very long sentences. While not accepting allof Hawthorne’s reasons as to why very long sentences are aproblem, in “Meaning Without Use: Reply to Hawthorne”(1992a) Lewis agreed that such sentences pose a problem to his view.To see the problem, letL be the function from each sentenceof English to its intuitive truth condition, and letL* bethe restriction of that function to sentences that aren’t verylong. Arguably we do not trust speakers who utter very long sentencesto have uttered truths, under the ordinary English interpretation oftheir sentences. We think, as Lewis said, that such speakers are“trying to win a bet or set a record, or feigning madness orraving for real, or doing it to annoy, or filibustering, or making anexperiment to test the limits of what it is humanly possible to sayand mean.” (Lewis 1992a: 108) That means that while there may bea convention of truthfulness and trust inL*, there is noconvention of trust inL in its full generality. So the“Languages and Language” theory implies that we speakL*, notL, which is wrong.

Lewis’s solution to this puzzle relies on his theory of naturalproperties, described below in Section 4.6. He argues that somegrammars (in the above sense of grammar) are more natural than others.By default, we speak a language with a natural grammar. SinceL has a natural grammar, andL* doesn’t, otherthings being equal, we should be interpreted as speakingLrather thanL*. Even if other things are not quite equal,i.e. we don’t naturally trust speakers of very long sentences,if there is a convention of truthfulness and trust inL inthe vast majority of verbal interactions, and there is no otherlanguage with a natural grammar in which there is a convention oftruthfulness and truth, then the theory will hold, correctly, that wedo speakL.

3. Counterfactuals

David Lewis’s second book wasCounterfactuals (1973a).Counterfactual conditionals were important to Lewis for severalreasons. Most obviously, they are a distinctive part of naturallanguage and it is philosophically interesting to figure out how theywork. But counterfactuals would play a large role in Lewis’smetaphysics. Many of Lewis’s attempted reductions of nomic ormental concepts would be either directly in terms of counterfactuals,or in terms of concepts (such as causation) that he in turn defined interms of counterfactuals. And the analysis of counterfactuals, whichuses possible worlds, would in turn provide motivation for believingin possible worlds. We will look at these two metaphysical motivationsin more detail in section 4, where we discuss the relationship betweencounterfactuals and laws, causation and other high-level concepts, andin section 5, where we discuss the motivations for Lewis’s modalmetaphysics.

3.1 Background

To the extent that there was a mid-century orthodoxy aboutcounterfactual conditionals, it was given by the proposal in NelsonGoodman (1955). Goodman proposed that counterfactual conditionals werea particular variety of strict conditional. To a first approximation,If it were the case thatp, it would be the case thatq (hereafterp □→q) is truejust in case Necessarily, eitherp is false orq istrue, i.e. □(p ⊃q). Goodman realised thatthis wouldn’t work if the modal ‘necessarily’ wasinterpreted unrestrictedly. He first suggested that we needed torestrict attention to those possibilities where all facts‘co-tenable’ withp were true. More formally, ifS is the conjunction of all the co-tenable facts, thenp□→q is true if and only if □((p∧ S) ⊃q).

Lewis argued that this could not be the correct set of truthconditions forp □→q in general. Hisargument was that strict conditionals were in a certain senseindefeasible. If a strict conditional is true, then adding moreconjuncts to the antecedent cannot make it false. But intuitively,adding conjuncts to the antecedent of a counterfactual can change itfrom being true to false. Indeed, intuitively we can have longsequences of counterfactuals of ever increasing strength in theantecedent, but with the same consequent, that alternate in truthvalue. So we can imagine that (3.1) and (3.3) are true, while (3.2)and (3.4) are false.

(3.1) If Smith gets the most votes, he will be the next mayor.
(3.2) If Smith gets the most votes but is disqualified due toelectoral fraud, he will be the next mayor.
(3.3) If Smith gets the most votes, but is disqualified due toelectoral fraud, then launches a military coup that overtakes the citygovernment, he will be the next mayor.
(3.4) If Smith gets the most votes, but is disqualified due toelectoral fraud, then launches a military coup that overtakes the citygovernment, but dies during the coup, he will be the next mayor.

If we are to regardp □→q as true if andonly if □((p ∧ S) ⊃q), then the Smust vary for different values ofp. More seriously, we haveto say something abouthow S varies with variation inp. Goodman’s own attempts to resolve this problem hadgenerally been regarded as unsuccessful, for reasons discussed inBennett (1984). So a new solution was needed.

3.2 Analysis

The basic idea behind the alternative analysis was similar to thatproposed by Robert Stalnaker (1968). Let’s say that anA-world is simply a possible world whereA is true.Stalnaker had proposed thatp □→q wastrue just in case the most similarp-world to the actualworld is also aq-world. Lewis offered a nice graphic way ofthinking about this. He proposed that we think of similarity betweenworlds as a kind of metric, with the worlds arranged in somelarge-dimensional space, and more similar worlds being closer to eachother than more dissimilar worlds. Then Stalnaker’s idea is thatthe closestp-world has to be aq-world forp □→q to be true. Lewis consideredseveral ways of filling out the details of this proposal, three ofwhich will be significant here.

First, he rejected Stalnaker’s presupposition that there is amost similarp-world to actuality. He thought there might bemany worlds which are equally similar to actuality, with nop-world being more similar. Using the metric analogysuggested above, these worlds all fall on a common‘sphere’ of worlds, where the centre of this sphere is theactual world. In such a case, Lewis held thatp □→q is true if and only if all thep-worlds on thissphere areq-worlds. One immediate consequence of this isthat Conditional Excluded Middle, i.e., (p □→q) ∨ (p □→ ~q) is not atheorem of counterfactual logic for Lewis, as it was forStalnaker.

Second, he rejected the idea that there must even be a sphere ofclosestp-worlds. There might, he thought, be closer andcloserp-worlds without limit. He called the assumption thatthere was a sphere of closest worlds the “LimitAssumption”, and noted that we could do without it. The newtruth conditions are thatp □→q is trueatw if and only if there is ap ∧q-world closer tow than anyp ∧¬q-world, or that there is nop world.

Third, he considered dropping the assumption that w is closer toitself than any other world, or even the assumption that w is amongthe worlds that are closest to it. When we think in terms ofsimilarity (or indeed of metrics) these assumptions seem perfectlynatural, but some philosophers have held that they have bad prooftheoretic consequences. Given the truth conditions Lewis adopts, theassumption that w is closer to itself than any other world isequivalent to the claim thatp ∧q entailsp □→q, and the assumption that w isamong the worlds that are closest to it is equivalent to the claimthatp □→q andp entailq. The first of these entailments in particular has beenthought to be implausible. But Lewis ultimately decided to endorse it,in large part because of the semantic model he was using. When wedon’t think about entailments, and instead simply ask ourselveswhether any other world could be as similar to w as w is to itself,the answer seems clearly to be no.

As well as offering these semantic models for counterfactuals, in thebook Lewis offers an axiomatisation of the counterfactual logic heprefers (see Table 6 in Section 3.3 of the entrylogic of conditionals), as well as axiomatisations for several other logics that makedifferent choices about some of the assumptions we’ve discussedhere. And he has proofs that these axiomatisations are sound andcomplete with respect to the described semantics.

He also notes that his preferred counterfactual logic invalidatesseveral familiar implications involving conditionals. We alreadymentioned that strengthening the antecedent, the implication of(p ∧r) □→q byp□→q, is invalid on Lewis’s theory, and gavesome natural language examples that suggest that it should be invalid.Lewis also shows that contraposition, the implication of ~q□→ ~p byp □→q, andconditional syllogism, the implication ofp □→r byp □→q andq□→r, are invalid on his model, and givesarguments that they should be considered invalid.

3.3 Similarity

InCounterfactuals, Lewis does not say a lot about similarityof worlds. He has some short arguments that we can make sense of thenotion of two worlds being similar. And he notes that on differentoccasions we may wish to use different notions of similarity,suggesting a kind of context dependency of counterfactuals. But thenotion is not spelled out in much more detail.

Some reactions to the book showed that Lewis needed to say more here.Kit Fine (1975) argued that given what Lewis had said to date, (3.5)would be false, when it should be true.

(3.5) If Richard Nixon had pushed the button, there would have been anuclear war.

(‘The button’ in question is the button designed to launchnuclear missiles.) The reason it would be false is that a world inwhich the mechanisms of nuclear warfare spontaneously failed but thenlife went on as usual, would be more similar, all things considered,to actuality than a world in which the future consisted entirely of apost-nuclear apocalypse.

In “Counterfactual Dependence and Time’s Arrow”(1979c), Lewis responded by saying more about the notion ofsimilarity. In particular, he offered an algorithm for determiningsimilarity in standard contexts. He still held that the particularmeasure of similarity in use on an occasion is context-sensitive, sothere is no one true measure of similarity. Nevertheless there is, hethought, a default measure that we use unless there is a reason toavoid it. Here is how Lewis expressed this default measure.

It is of the first importance to avoid big, widespread, diverseviolations of law.
It is of the second importance to maximize the spatio-temporalregion throughout which perfect match of particular factprevails.
It is of the third importance to avoid even small, localized,simple violations of law.
It is of little or no importance to secure approximate similarityof particular fact, even in matters that concern us greatly. (Lewis1979c: 47–8)

Lewis argues that by this measure, worlds in which the mechanisms ofnuclear warfare spontaneously fail will be less similar to the actualworld than the post-nuclear apocalypse. That’s because thefailure of those mechanisms will either lead to divergence from theactual world (if they fail partially) or widespread, diverseviolations of law (if they fail completely). In the former case,there’s a violation of law that isn’t made up for in anincrease in how much spatio-temporal match we get. In the latter casethe gain we get in similarity is only an expansion of thespatio-temporal region throughout which perfect match of particularfact prevails, but that doesn’t help in getting us closer toactuality if we’ve added a big miracle. So in fact the nearestworlds are ones where a nuclear war occurs, and (3.5) is true.

One way to see the effects of Lewis’s ordering is to workthrough its implication for an important class of cases. When theantecedent of a counterfactual is about the occurrence ornon-occurrence of a particular eventE at timet,the effect of these rules is to say that the nearest worlds are theworlds where the following claims all hold, witht* being aslate as possible.

There is an exact match of particular fact with actuality up tot*.
There is a small, localized law violation att*.
There is exact conformity to the laws of actuality aftert*.
The antecedent is true.

So we find a point just beforet where we can make theantecedent true by making a small law violation, and let the laws takeover from there. There is something intuitively plausible about thisway of viewing counterfactuals; often we do aim to talk about whatwould have happened if things had gone on in accordance with the laws,given a starting point slightly different from the one that actuallyobtained.

Jonathan Bennett (2003) notes that when the antecedent of aconditional is not about a particular event, Lewis’s conditionsprovide the wrong results. For instance, if the antecedent is of theformIf one of these events had not happened, thenLewis’s rules say that the nearest world where the antecedent istrue is always the world where the most recent such event did nothappen. But this does not seem to provide intuitively correct truthconditions for such conditionals. This need not bother Lewis’slarger project. For one thing, Lewis was not committed to there beinga uniform similarity metric for all counterfactuals. Lewis could saythat his default metric was only meant to apply to cases where theantecedent was about the happening or non-happening of a particularevent at a particular time, and it wouldn’t have seriouslyundermined his larger project. Indeed, as we’ll see in Section5.2 below, the counterfactuals he was most interested in, and forwhich these criteria of similarity were devised, did have antecedentsconcerning specific events.

4. Philosophy of Mind

In “Reduction of Mind” (1994b), David Lewis separates hiscontributions to philosophy of mind into two broad categories. Thefirst category is his reductionist metaphysics. From his firstpublished philosophy paper, “An Argument for the IdentityTheory” (1966a), Lewis defended a version of the mind-brainidentity theory (see the entry on theidentity theory of mind). As he makes clear in “Reduction of Mind”, this became animportant part of his global reductionism. We’ll look at hismetaphysics of mind in sections 4.1–4.3.

The second category is his theory of mental content. Following DonaldDavidson in broad outlines, Lewis held that the contents of aperson’s mental states are those contents that ’fit’the typical causal profile of the state. For example, a stateisn’t constituted by the combination of adesire for some end plus a belief that waving will bring about thatend, unless it typically causes waving. In thisrespect Lewis’s views resembledinterpretationist theories of beliefs. But he differed from other interpretationists inseveral ways. We will focus here on two of them. Lewis held thatmental contents are typicallyproperties, notpropositions. And he held that a theory of mental contentrequires aninegalitarian theory of properties. We’lllook at his theory of content in sections 4.4–4.6.

4.1 Ramsey Sentences

The logical positivists faced a hard dilemma when trying to make senseof science. On the one hand, they thought that all meaningful talk wasultimately talk about observables. On the other hand, they respectedscience enough to deny that talk of unobservables was meaningless. Thesolution was to ‘locate’ the unobservables in theobservation language; in other words, to find a way to reduce talk ofunobservables to talk about observables.

Lewis didn’t think much of the broader positivist project, buthe was happy to take over some of their technical advances in solvingthis location problem. Lewis noted that this formal project, theproject of trying to define theoretical terms in an already understoodlanguage, was independent of the particular use we make of it. Allthat really matters is that we have some terms introduced by a newtheory, and that the new theory is introduced in a language that isgenerally understood. In any such case it is an interesting questionwhether we can extract the denotation of an introduced term from thetheory used to introduce it.

The term-introducing theory could be a scientific theory, such as thetheory that introduces terms like ‘electron’, and thelanguage of the theory could be observation language. Or, moreinterestingly, the term-introducing theory could be folk psychology,and the language of the theory could be the language of physics. If wehave a tool for deriving the denotations of terms introduced by atheory, and we have a way of treatingfolk psychology as a theory (i.e., a conjunction of sentences to which folk wisdom is committed),we can derive the denotations of terms like ‘belief’,‘pain’, and so on using this theory. Some of Lewis’simportant early work on the metaphysics of mind was concerned withsystematising the progress positivists, especially Ramsey and Carnap,had made on just this problem. The procedure is introduced in“An Argument for the Identity Theory”,“Psychophysical and Theoretical Identifications” (1972a)and “How to Define Theoretical Terms” (1970c). There areimportant later discussions of it in “Reduction of Mind”and “Naming the Colours” (1997c), among many others.

In the simplest case, where we have a theory T that introduces one newnamet, Lewis says thatt denotes thexsuch that T[x], where T[x] is the sentence we get by(a) converting T to a single sentence, perhaps a single longconjunction, and (b) replacing all occurrences oft with thevariablex. That is, if there is a uniquex suchthat T[x],t denotes it, andt isdenotationless otherwise. (Note that it isn’tmeaningless, but it isdenotationless.)

The simplest case is not fully general in a few respects. First,theories often introduce many terms simultaneously, not just one. Sothe theory might introduce new termst₁,t₂, …,t_n. No problem,we can just quantify overn-tuples, wheren is thenumber of new terms introduced. So instead of looking at∃₁x T[x], where ∃₁means ‘exists a unique’ andx is an individualvariable, we look at ∃₁xT[x], wherex is a variable thatranges overn-tuples, and T[x] is thesentence you get by replacingt₁ with the firstmember ofx,t₂ with the secondmember ofx, …, andt_nwith then^th member ofx.Although this is philosophically very important, for simplicityI’ll focus here on the case where a single theoretical term isto be introduced.

The simplest case is not general in another, more important, respect.Not all theoretical terms are names, so it isn’t obvious that wecan quantify over them. Lewis’s response, at least in the earlypapers, is to say we can alwaysreplace them with names thatamount to the same thing. So if T says that allFs areGs, and we are interested in the term ‘G’, thenwe’ll rewrite T so that it now saysGness is a propertyof allFs. In the early papers, Lewis says that this is aharmless restatement of T, but this isn’t correct. Indeed, inlater papers such as “Void and Object” (2004d) and“Tensing the Copula” (2002a) Lewis notes that somepredicates don’t correspond to properties or relations. There isno property of being non-self-instantiating, for instance, though wecan predicate that of many things. In those cases the rewriting willnot be possible. But in many cases, we can rewrite T, and then we canquantify into it.

The procedure here is often called Ramsification, or Ramseyfication.(Both spellings have occurred in print. The first is in the title ofBraddon-Mitchell and Nola (1997), the second in the title of Melia andSaatsi (2006).) The effect of the procedure is that if we had a theoryT which was largely expressed in the language O, except for a fewtermst₁,t₂, …,t_n, then we end up with a theory expressedentirely in the O-language, but which, says Lewis, has much the samecontent. Moreover, if the converted theory is true, then the T-termscan be defined as the substitutends that make the converted sentencetrue. This could be used as a way of eliminating theoretical termsfrom an observation language, if O is the observation language. Or itcould be a way of understanding theoretical terms in terms of naturallanguage, if O is the old language we had before the theory wasdeveloped.

In cases where there is a uniquex such that T[x],Lewis says thatt denotes thatx. What if there aremany suchx? Lewis’s official view in the early papersis that in such a caset does not have a denotation. In“Reduction of Mind”, Lewis retracted this, and said thatin such a caset is indeterminate between the many values. In“Naming the Colours” he partially retracts the retraction,and says thatt is indeterminate if the different values ofx are sufficiently similar, and lacks a denotationotherwise.

A more important complication is the case where there is no realiserof the theory. Here it is important to distinguish two cases. First,there is the case where the theory is very nearly realised. That is, atheory that contains enough of the essential features of the originaltheory turns out to be true. In that case we still want to say thatthe theory manages to provide denotations for its new terms. Second,there are cases where the theory is a long way from the truth. Thescientific theory of phlogiston, and the folk theory of witchcraft,are examples of this. In this case we want to say that the terms ofthe theory do not denote.

As it stands, the formal theory does not have the resources to makethis distinction. But this is easy to fix. Just replace the theory Twith a theory T*, which is a long disjunction of various importantconjuncts of T. So if T consisted of three claims,p₁p₂ andp₃, and it is close enough to true if two of themare true, then T* would be the disjunction (p₁∧p₂) ∨ (p₁ ∧p₃) ∨ (p₂ ∧p₃). Lewis endorses this method in“Psychophysical and Theoretical Identifications” Thedisjuncts are propositions that are true in states that would count asclose enough to the world as described by T that T’s termsdenote. Note that in a real-world case, some parts of T will be moreimportant than others, so we won’t be able to just ‘countthe conjuncts’. Still, we should be able to generate a plausibleT* from T. And the rule in general is that we apply the above strategyto T* rather than T to determine the denotation of the terms.

4.2 Arguing for the Identity Theory

Lewis’s first, and most important, use of Ramsification was toargue for the mind-brain identity theory, in “An Argument forthe Identity Theory”. Lewis claims in this paper that hisargument does not rely on parsimony considerations. The orthodoxargument for the identity theory at the time, as in e.g. J. J. C.Smart (1959), turned on parsimony. The identity theory and dualismexplain the same data, but the dualist explanation involves moreontology than the identity theory explanation. So the identity theoryis preferable. Lewis says that this abductive step is unnecessary. (Heeven evinces concern that it is unsound.) Lewis offers instead anargument from the causal efficacy of experience. The argument issomething like the following. (I’ve given the argument thatpains are physical, a similar argument can be given for any other kindof experience.)

Pains are the kind of thing that typically have such-and-suchphysical causes and such-and-such physical effects, where the‘such-and-such’s are filled in by our folk theory ofpain.
Since the physical is causally closed, the things that havesuch-and-such physical causes and such-and-such physical effects arethemselves physical.
So, pains are physical.

The first premise is analytically true; it follows from the way wedefine theoretical terms. The second premise is something we learnfrom modern physics. (It isn’t clear, by the way, that we canavoid Smart’s parsimony argument if we really want to argue forpremise 2.) So the conclusion is contingent, since modern physics iscontingent, but it is well-grounded. Indeed, if we change the secondpremise a little, drawing on neurology rather than physics, we candraw a stronger conclusion, one that Lewis draws in“Psychophysical and Theoretical Identifications”.

Pains are the kind of thing that typically have such-and-suchphysical causes and such-and-such physical effects, where the‘such-and-such’s are filled in by our folk theory ofpain.
Neural state N is the state that has such-and-such physical causesand such-and-such physical effects.
So, pains are instances of neural state N.

So, at least in the second argument, Lewis is defending a kind ofidentity theory. Pains just are instances of neural states. I’llfinish up this survey of Lewis’s metaphysics of mind with a lookat two complications to this theory.

4.3 Madmen and Martians

Pain is defined by its causal role. Central to that role is that weare averse to pain, and try to avoid it. But not all of us do. Some ofus seek out pain. Call them madmen. A good theory of pain shouldaccount for the possibility of madmen.

The simplest way to account for madmen would be to simply identifypain with a neural state. So Lewis’s identity theory iswell-placed to deal with them. But there is a complication. Not everycreature in the universe who is in pain has the same neural states asus. It is at least possible that there are creatures in which somesilicon state S plays the pain role. That is, the creatures are averseto S, they take S to be an indicator of bodily damage, and so on.Those creatures are in pain whenever they are in state S. Call anysuch creature a Martian. A simple identification of pain with neuralstate N will stipulate that there couldn’t be any Martians. Thatwould be a bad stipulation to make.

The possibility of madmen pushes us away from a simple functionaldefinition of pain. Some creatures have pains that do not play thepain role. The possibility of Martians pushes us away from a purelyneural definition of pains. Some creatures have pains that are notlike our neural pain states. Indeed, some of them might have painswithout having any neural states at all. Lewis’s way ofthreading this needle is to say that pains, like all mental states,are defined for kinds of creatures. Pains in humans are certain neuralstates. They are the neural states that (typically, in humans) havethe functional role that we associate with pain. In other kinds ofcreatures pains are other states that (typically, in those creatures)play the pain role. The details of these views are worked out in“Mad Pain and Martian Pain” (1980c).

4.4 Constitutive Rationality

The contents of a mental state are, according to Lewis, the contentsthat best make sense of the state. As he sometimes puts it, they arethe contents that ‘fit’ the state. Part of what it is tofit a state is to rationalise the behavior that the state typicallycauses. So constraints of rationality, especially concerning whatactions are rational given that one is in a mental state, arepartially constitutive of mental content.

Put this broadly, Lewis’s position is indebted to DonaldDavidson’s work, and Lewis frequently acknowledges the debt. ButLewis differs from Davidson in several respects. I’ll brieflymention four of them here, then look at two substantial changes in thenext two sections. (The primary sources for the discussion in thissection are “Radical Interpretation” (1974c) andespecially its appendices inPhilosophical Papers: Volume I(1983a), and “Reduction of Mind”.)

First, Lewis does not think that fit requires that one’s beliefsare typically true. Rather, it requires that beliefs are (typically)rational. If the subject is surrounded by misleading evidence, falsebeliefs fit better than true ones.

Second, Lewis does not give a particularly special place to thesubject’s verbal behaviour in considering which content fits. Inparticular, we don’t first ask what assignment of contents totheir words best makes sense of their verbal behavior, and then saythat the central aspect of fit for mental states involves dispositionsto produce words with the same contents as belief states. Rather,Lewis follows Grice (among others) in taking mental content to bemetaphysically primary, and linguistic content to be determined bymental states (see the section on meaning in the entry onGrice).

Third, Lewis believes innarrow content. Indeed, there is a sense in which he thinks narrow content isprimary. He holds thatSwampman has contentful states, thereby disagreeing with Davidson (amongothers). And he thinks that we share many beliefs (most clearlymetalinguistic beliefs) with denizens ofTwin Earth.

Finally, Lewis’s theory of mental content, like his theory ofmind in general, is anti-individualistic. What matters is thefunctional role that a state typically has in creatures of a certainkind, not what role it has in this creature. So there might be amadman who does not attempt to get what they desire. A purefunctionalist may say that such a person has no desires, sincedesires, by definition, are states that agents attempt to satisfy.Lewis says that as long as this state typically leads tosatisfaction-attempts in creatures of this kind, it is a desire.Indeed, if a state typically leads to attempts to getX, itis a desire forX, even if little about the role the stateplays in this particular agent would suggest it is a desire forX.

4.5De Se Content

Some of our beliefs and desires are about specific individuals. Imight, for instance, believe that BW is a crook and desire that he bepunished. Some of our beliefs and desires are self-directed. I might,for instance, believe that I am not a crook and desire that I not bepunished. If I know that I am BW, then I should not have all of thosebeliefs and desires. But I might be ignorant of this. In somecircumstances (e.g., amnesia, or receiving deceptive information aboutyour identity) it is no sign of irrationality to not know who you are.And if you don’t know you areX, you may ascribedifferent properties to yourself and toX.

Lewis’s way of handling this problem was exceedingly simple. Hisoriginal version of interpretationism had it that belief-states wereultimately probability distributions over possible worlds, anddesire-states were ultimately utility functions, again defined overpossible worlds. In “AttitudeDe Dicto andDeSe” (1979b), he argued that this isn’t correct.Beliefs and desires are, at the end of the day, probability andutility functions. (Or at least they are approximations to thosefunctions.) But they are not defined over possible worlds. Rather,they are defined over possible individuals.

What that means for belief and desire is easiest to express using thelanguage of possible worlds. The standard view is that propositionsare (or at least determine) sets of possible worlds, and that thecontent of a belief is a proposition. To believe something then is tolocate yourself within a class of possible worlds; to believe that youinhabit one of the worlds at which the proposition is true.Lewis’s view is that properties are (or at least determine) setsof possible individuals, and that the content of a belief is aproperty. To believe something then is to locate yourself within aclass of possible individuals; to believe that you are one of theindividuals with the property. More simply, beliefs are theself-ascriptions of properties.

Within this framework, it is easy to resolve the puzzles we addressedat the top of the section. If I believe that BW is a crook, Iself-ascribe the property of inhabiting a world in which BW is acrook. (On Lewis’s theory, beliefs that are not explicitlyself-locating will be beliefs about which world one is in.) If Ibelieve I am not a crook, I self-ascribe the property of not being acrook. Since there are possible individuals who are (a) not crooks but(b) in worlds where BW is a crook, this is a consistentself-ascription. Indeed, I may even have strong evidence that I haveboth of these properties. So there is no threat of inconsistency, oreven irrationality here.

Lewis’s suggestion about how to think of self-locating mentalstates has recently been very influential in a variety of areas. AdamElga (2001, 2004) has extensively investigated the consequences ofLewis’s approach for decision theory. Andy Egan (2007) hasdeveloped a novel form of semantic relativism using Lewis’sapproach as a model. Daniel Nolan (2007) has recently argued thatLewis’s approach is less plausible for desire than for belief,and Robert Stalnaker (2008) argues that the view makes the wrongjudgments about sameness and difference of belief across agents andtimes.

4.6 Natural Properties

One classic problem for interpretationism is that our dispositionsmassively underdetermine contents. I believe that (healthy) grass isgreen. But for some interpretations of ‘grue’, ascribing to me the belief that grass is grue will fit mydispositions just as well. As Lewis points out towards the end of“New Work For a Theory of Universals” (1983e), if we areallowed to change the interpretations of my beliefs and desires at thesame time, the fit can be made even better. This looks like a problemfor interpretationism.

The problem is of course quite familiar. In different guises it isGoodman’s grue/green problem, Kripkenstein’s plus/quus problem, Quine’sgavagai problem, andPutnam’s puzzle of the brain in a vat with true beliefs (Goodman 1955, Wittgenstein1953, Kripke 1982, Quine 1960, Putnam 1981). One way or another it hasto be solved.

Lewis’s solution turns on a metaphysical posit. Some properties,he says, are morenatural than others. The natural propertiesare those that, to use an ancient phrase, carve nature at the joints.They make for objective resemblance amongst the objects that havethem, and objective dissimilarity between things that have them andthose that lack them. The natural properties, but not in general theunnatural properties, are relevant to the causal powers of things.Although science is in the business of discovering which naturalproperties are instantiated, when Lewis talks about natural propertieshe doesn’t mean properties given a special role by nature. It isnot a contingent matter which properties are natural, because itisn’t a contingent matter which properties make for objectivesimilarity.

Some properties are perfectly natural. Other properties are lessnatural, but not all unnatural properties are alike. Green things area diverse and heterogeneous bunch, but they are more alike than thegrue things are. And the grue things are more alike than some othereven more disjunctive bunches. So as well as positing perfectlynatural properties, Lewis posits a relation of more and less naturalon properties. He suggests that we just need to take the perfectlynatural as primitive, and we can define the naturalness of otherproperties in terms of it. The idea is that the naturalness of aproperty is a function of the complexity of that property’sdefinition in terms of perfectly natural properties. It isn’t atall obvious that this suggestion will capture the intuitive idea, andLewis does not defend it at any length.

Natural properties will play a major role for Lewis. We’vealready seen one place where it turns out they are needed; namely, insaying what it is for two worlds to have an ‘exact match’of spatiotemporal regions. What Lewis means by that is that theregions are intrinsic duplicates. And the way he analyses intrinsicduplication in (1983e) is that two things are duplicates if they havethe same intrinsic properties. We will see many other uses of naturalproperties as we go along, particularly in the discussion of Humeansupervenience in section 5.

But as Lewis (1983e) makes clear, natural properties play many moreroles in his larger philosophy, including in the theory ofrationality, the theory of mental content, the theory of linguisticcontent, and the theory of laws. It is rational to have a belief witha more natural rather than a less natural content. If two differentassignments of beliefs and desires would make equally good sense of anagent’s dispositions, the more natural assignment is the correctone. If two different interpretations of the words of a publiclanguage would make equally good sense of speakers’ practices,the more natural interpretation is the correct one. And laws aresimple generalisations, where simplicity is defined in part in termsof naturalness.

There is some scholarly dispute about the relationship between thefour theses set out in the last four sentences of the precedingparagraph. Williams (2007) argues that the thesis about laws isexplanatorily prior to some of the theses about rationality andcontent. Sider (2001) argues that the third thesis is a standalonepart of Lewis’s theory. Schwarz (2014), however, argues that itisn’t even a part of Lewis’s theory. Weatherson (2003)endorses Sider’s view, but later Weatherson (2013) endorsesSchwarz’s critique of Sider’s interpretation, whilearguing that a qualified version of the third thesis can neverthelessbe derived from the first two. (A version of Schwarz’s paper hadbeen in circulation since 2006, so it well precedes Weatherson’s2013 paper, despite the slightly later publication date.)Janssen-Lauret and MacBride (2020) respond to Schwarz, arguing thatevidence from Lewis’s recently available correspondence supportsthe view that Lewis took naturalness to play a central role indetermining the reference of individual words.

This topic, natural properties, was one of very few topics where Lewishad a serious change of view over the course of his career. Of course,Lewis changed the details of many of his views, in response tocriticism and further thought. But the idea that some properties couldbe natural, could make for objective similarity, in ways that mostsets of possibilia do not, is notably absent from his writings before“New Work”. Indeed, as late as “Individuation byAcquaintance and by Stipulation” (1983c), he was ratherdismissive of the idea. But natural properties came to play centralroles in his metaphysics and, as we see here, his theory of mind. AsLewis notes in “New Work”, much of the impetus for hischange of view came from discussions with D. M. Armstrong, and fromthe arguments in favour of universals that Armstrong presented in his(1978).

5. Humean Supervenience

Many of David Lewis’s papers in metaphysics were devoted tosetting out, and defending, a doctrine he called “HumeanSupervenience”. Here is Lewis’s succinct statement of theview.

It is the doctrine that all there is to the world is a vast mosaic oflocal matters of particular fact, just one little thing and thenanother. (Lewis 1986b: ix)

The doctrine can be factored into two distinct theses. The first isthe thesis that, in John Bigelow’s words, “truthsupervenes on being”. That is, all the truths about a worldsupervene on the distribution of perfectly natural properties and relations inthat world. The second is the thesis that the perfectly naturalproperties and relations in this world areintrinsic properties of point-sized objects, and spatiotemporal relations. Lewis held thatthe first of these was necessary and a priori. (See, for instance,“Parts of Classes” (1991a), “Reduction ofMind”, “Truthmaking and Difference-making” (2001d).)The second is contingently true if true at all. Indeed, modern physicssuggests that it is not true (Maudlin 2007: Ch. 2). Lewis was aware ofthis. His aim in defending Humean supervenience was to defend, as heput it, its “tenability” (1986a: xi). We will return atthe end of this section to the question of why he might have wanted todo this. For now, we will focus on how he went about this project.

The primary challenge to Humean supervenience comes from those whohold that providing a subvenient basis for all the truths of thisworld requires more than intrinsic properties of point-sized objectsand spatiotemporal relations. Some of these challenges come fromtheorists who think best physics will need non-spatiotemporalrelations in order to explainBell’s Theorem. But more commonly it comes from those who think that grounding themodal, the nomic or the mental requires adding properties andrelations to any Humean mosaic constructed from properties found infundamental physics. (I’m using ‘mental’ here tocover all the properties that Lewis considered mental, broadlyconstrued. This includes contents, since Lewis thought content wasgrounded in mental content, and value, since he thought values weregrounded in idealised desires. So it’s a fairly broad category,and there is a lot that isn’t obviously reducible to fundamentalphysics. As we’ll see, Lewis attempts to reduce it allstep-by-step.)

We’ve discussed in the previous section how Lewis aimed toreduce the mental to the nomic. (Or at least much of it; we’llreturn to the question of value in section 7.5.) We’ll discussin the next section his distinctive modal metaphysics. In this sectionwe’ll look at how he attempted to locate the nomic in the Humeanmosaic. Lewis’s aim was to show that nomic properties andrelations could be located in the Humean mosaic by locating them asprecisely and as explicitly as he could. So the location projectrevealed a lot about these nomic features. We’ll spend the nexttwo subsections looking at the two important parts of this project.Notably, they are two parts where Lewis refined his views severaltimes on the details of the location.

5.1 Laws and Chances

Lewis’s reductionist project starts withlaws of nature. Building on some scattered remarks by Ramsey and Mill, Lewis proposeda version of the ‘best-system’ theory of laws of nature.There is no paper devoted to this view, but it is discussed in section3.3 ofCounterfactuals, in “New Work For a Theory ofUniversals”, extensively in Postscript C to the reprint of“A Subjectivist’s Guide to Objective Chance” in(1986b), and in “Humean Supervenience Debugged”(1994a).

The simple version of the theory is that the laws are the winners of a‘competition’ among all collections of truths. Some truthsare simple, e.g. the truth that this table is brown. Some truths arestrong; they tell us a lot about the world. For example, theconjunction of every truth in this Encyclopedia rules out a largechunk of modal space. Typically, these are exclusive categories;simple truths are not strong, and strong truths are not simple. Butthere are some exceptions. The truth that any two objects areattracted to one another, with a force proportional to the product oftheir masses and inversely proportional to the distance between them,is relatively simple, but also quite strong in that it tells us a lotabout the forces between many distinct objects. The laws, says Lewis,are these simple but strong truths.

Two qualifications are needed before we get to Lewis’s 1973 viewof laws. It is collections of truths, not individual truths, that aremeasured and compared for simplicity and strength. And it is not everytruth in the winning collection (or best system), but only thegeneralisations within it, that are laws. So even if the best systemincludes particular facts about the Big Bang or its immediateaftermath, e.g. that the early universe was a low entropy state, thosefacts are not laws on Lewis’s view.

In “New Work For a Theory of Universals”, Lewis notesanother restriction that is needed. If we measure the simplicity ofsome truths by the length of their statement in an arbitrarily chosenlanguage, then any truth at all can be made simple. LetFx betrue if and only ifx is in a world where every truth in thisEncyclopedia is true. ThenEverything is F is simplystateable in a language containingF, and is presumablystrong. SoEverything is F will be a law. But this kind ofconstruction would clearly trivialise the theory of laws.Lewis’s solution is to say that we measure the simplicity of aclaim by how easily stateable it is in a language where all predicatesdenoteperfectly natural properties. He notes that this moverequires that the natural properties are specified prior to specifyingthe laws, which means that we can’t reductively specifynaturalness in terms of laws. (In any case, since Lewis holds thatlaws are contingent (1986a: 91) but which properties are natural isnot contingent (1986a: 60n), this approach would not be open toLewis.)

In “Humean Supervenience Debugged”, Lewis notes how toextend this theory to indeterministic worlds. Some laws don’tsay what will happen, but what will have a chance of happening. If thechances of events could be determined antecedently to the laws beingdetermined, we could let facts about chances be treated more or lesslike any other fact for the purposes of our ‘competition’.But, as we’ll see, Lewis doesn’t think the prospects fordoing this are very promising. So instead he aims to reduce laws andchances simultaneously to distributions of properties.

Instead of ranking collections of truths by two measures, strength andsimplicity, we will rank them by three, strength, simplicity and fit.A collection of truths that entails that what does happen has (atearlier times) a higher chance of happening has better fit than acollection that entails that what happens had a lower chance ofhappening. The laws are those generalisations in the collection oftruths that do the best by these three measures of strength,simplicity and fit. The collection will entail various‘history-to-chance’ conditionals. These are conditionalsof the formIf H_t then P_t(A) = x, whereH_t is a proposition about the history of the worldtot, andP_t is the function frompropositions to their chance att. The chance ofAatt inw isx if and only if there is somesuch conditionalIf H_t then P_t(A) = x,whereH_t is the history ofw tot.

The position that I’ve sketched here is the position that Lewissays that he originally was drawn towards in 1975, and that heendorsed in print in 1994. (The dates are from his own description ofthe evolution of his views in (1994a).) But in between, in both(1980a) and Postscript C to its reprinting in (1986b), he rejectedthis position because he thought it conflicted with a non-negotiableconceptual truth about chance. This truth was what he called the“Principal Principle”.

The Principal Principle says that a rational agent conforms theircredences to the chances. More precisely, it says the following istrue. Assume we have a numberx, propositionA, timet, rational agent whose evidence is entirely about times upto and includingt, and a propositionE that (a) isabout times up to and includingt and (b) entails that thechance ofA att isx. In any such case,the agent’s credence inA givenE isx.

An agent who knows what happens aftert need not be guided bychances att. If I’ve seen the coin land heads, thatits chance of landing heads was 0.5 at some earlier time is no reasonto have my credence in heads be 0.5. Conversely, if all I know is thatthe chance is 0.5, that’s no reason for my conditional credencein heads to be 0.5 conditional on anything at all. Conditional on itlanding heads, my credence in heads is 1, for instance. But giventhese two restrictions, the Principal Principle seems like a goodconstraint. Lewis calls evidence about times aftert‘inadmissible’, which lets us give a slightly more concisesummary of what the Principal Principle says. For agents with noinadmissible evidence, the rational credence inA,conditional on the chance ofA beingx, combinedwith any admissible evidence, isx.

The problem Lewis faced in the 1980s papers is that the best systemsaccount of chance makes the Principal Principle either useless orfalse. Here is a somewhat stylised example. (I make no claims aboutthe physical plausibility of this setup; more plausible examples wouldbe more complicated, but would make much the same point.) Lett be some time before any particle has decayed. LetA be the proposition that every radioactive particle willdecay before it reaches its actual half-life. Att,A has a positive chance of occurring. Indeed, its chance is 1in 2ⁿ, wheren is the number ofradioactive particles in the world. (Assume, again for the sake of ourstylised example, thatn is finite.) But ifAoccurred, the best system of the world would be different from how itactually is. It would improve fit, for instance, to say that thechance of decay within the actual half-life would be 1. So someone whoknows that the chance ofA is 1 in 2ⁿknows thatA won’t happen.

Lewis calledA an ‘undermining’ future; it has achance of happening, but if it happens the chances are different. Theproblem with underminers is that they conflict with the PrincipalPrinciple. Someone who knows the chance ofA should, by thePrincipal Principle, have credence 1 in 2ⁿ thatA will happen. But given the chance ofA, it ispossible to deduce ~A, and hence have credence inA.This looks like an inconsistency, so like any principle that implies acontradiction, the Principal Principle must be false. The most obviousway out is to say that information about the chance ofA isinadmissible, since it reveals something about the future, namely thatA doesn’t occur. But to say that chances areinadmissible is to make the Principal Principle useless. So given thebest systems theory of laws and chances, the Principal Principle iseither false or useless. Since the Principal Principle is neitherfalse nor useless, Lewis concluded in these 1980s papers that the bestsystems theory of laws and chances was false.

The problem with this was that it wasn’t clear what couldreplace the best systems theory. Lewis floated two approaches in thepostscripts to the reprinting of (1980a), one based on primitivechances, and the other based on history-to-chance conditionals beingnecessary. But neither seemed metaphysically plausible, and althougheach was consistent with the Principal Principle, they made it eithermysterious (in the first case) or implausible (in the second). Abetter response, as set out in “Humean SupervenienceDebugged”, was to qualify the Principal Principle. Lewis saidthat what was really true was the “New Principle”. Hisproposal was based on ideas developed by Ned Hall (1994) and MichaelThau (1994).

We’ll explain the New Principle by starting with a special caseof the old Principle. LetT be the ‘theory ofchance’ for the world, the conjunction of all history-to-chanceconditionals. And letH be the history of the world tot. AssumingT is admissible, the old PrincipalPrinciple says that the credence inA givenH ∧T should be the chance ofA att. The NewPrinciple says that the credence inA givenH ∧T should be the chance ofA givenT att. That is, whereC is the agent’s credencefunction, andP is the chance function, and the agent has noinadmissible evidence, it should be thatC(A |H ∧T) =P(A |T).This compares to the old principle, which held thatC(A |H ∧T) =P(A).

That’s the special case of the New Principle for an agent withno inadmissible evidence. The general case follows from this specialcase. In general, assuming the agent has no inadmissible evidence, therational credence inA givenE is the expectedvalue, givenE, of the chance ofA givenH∧T. That is, whereC is the agent’scredence function, andP is the chance function, it should bethe sum across all possible combinations ofH andTofC(H ∧T |E)P(A |H ∧T).

The New Principle is, Lewis argues, consistent with the best systemstheory of laws and chances. Lewis had originally thought that anyspecification of chance had to be consistent with the PrincipalPrinciple. But in later works he argued that the New Principle was aclose enough approximation to the Principal Principle that a theory ofchances consistent with it was close enough to our pre-theoreticnotion of chance to deserve the name. So he could, and did, happilyendorse the best systems theory of laws and chance.

5.2 Causation

In “Causation” (1973b), Lewis put forward an analysis ofcausation in terms of counterfactual dependence. The idea was that eventB was counterfactually dependent oneventA if and only if the counterfactualHad A notoccurred, B would not have occurred was true. Then eventC causes eventE if and only if there is a chainC,D₁, …,D_n,E such that each member in the chain (exceptC) iscounterfactually dependent on the event before it. In summary,causation is the ancestral of counterfactual dependence.

The reasoning about chains helped Lewis sidestep a problem that manythought unavoidable for a counterfactual theory of causation, namelythe problem of pre-empting causes. Imagine that Suzy throws a rock,the rock hits a window and the window shatters. Suzy’s throwcaused the window to shatter. But there is a backupthrower—Billy. Had Suzy not thrown, Billy would have thrownanother rock and broken the window. So the window breaking is notcounterfactually dependent on Suzy’s throw. Lewis’ssolution was to posit an event of the rock flying towards the window.Had Suzy not thrown, the rock would not have been flying towards thewindow. And had the rock not been flying towards the window, thewindow would have not shattered. Lewis’s thought here is that itis Suzy’s throwing that causes Billy to not throw; once she hasthrown Billy is out of the picture and the window’s shatteringdepends only on what Suzy’s rock does. So we avoid this problemof pre-empters.

Much of the argumentation in “Causation” concerns thesuperiority of the counterfactual analysis to deductive-nomologicaltheories. These arguments were so successful that from a contemporaryperspective they seem somewhat quaint. There are so few supporters ofdeductive-nomological theories in contemporary metaphysics that amodern paper would not spend nearly so much time on them.

After “Causation” the focus, at least of those interestedin reductive theories, moved to counterfactual theories. And it becameclear that Lewis had a bit of work left to do. He needed to say moreabout the details of the notion of counterfactual dependence. He didthis in “Counterfactual Dependence and Time’s Arrow”(1979c), as discussed in section 2. He needed to say more about thenature of events. In “Events” (1986g) he said that theywere natural properties of regions of space-time. (At this stage heassumed that events were the relata of the causal relation. Thisassumption is criticised by L. A. Paul (2000), and in (2004d) Lewisdrops it.) And prodded by Jaegwon Kim (1973), he needed to add thatA andB had to be wholly distinct events forB to counterfactually depend onA. The alternativewould be to say that an event’s happening is caused by anyessential part of the event, which is absurd.

But the biggest problem concerned what became known as “latepre-emption”. In the rock throwing example above, we assumedthat Billy decided not to throw when he saw Suzy throwing. But we canimagine a variant of the case where Billy waits to see whetherSuzy’s rock hits, and only then decides not to throw. In such acase, it is the window’s shattering, not anything prior to this,that causes Billy not to throw. That means that there is no eventbetween Suzy’s throw and the window’s shattering on whichthe shattering is counterfactually dependent.

Lewis addressed this issue in “Redundant Causation”, oneof the six postscripts to the reprinting of “Causation” in(1986b). He started by introducing a new concept: quasi-dependence.B quasi-depends onA if and only if there is aprocess starting withA*, and ending withB* , andB* counterfactually depends onA*, and the processfromA* toB* is an intrinsic duplicate of theprocess fromA to B, and the laws governing the process fromA* toB* (i.e. the laws of the world in whichA* andB* happen) are the same as the laws governingthe process fromA toB. In short, quasi-dependenceis the relation you get if you start with dependence, then add all ofthe duplicates of dependent processes. Causation is then the ancestralof quasi-dependence. Although the window’s shattering does notdepend on Suzy’s throw, it does quasi-depend on it. That’sbecause there is a world, with the same laws, with a duplicate ofSuzy’s throw, but Billy determined not to throw, and in thatworld the window shatters in just the same way, and depends onSuzy’s throw.

Eventually, Lewis became unsatisfied with the quasi-dependence basedtheory. In “Causation as Influence” (2000a, 2004a) he setout several reasons for being unhappy with it, and a new theory tosupersede it.

One argument against it is that it makes causation intrinsic to thepairC andE, but some cases, especially cases ofdouble prevention, show that causation is extrinsic. Doubleprevention occurs when an event, call itC, preventssomething that would have preventedE from happening.Intuitively, these are cases of causation. Indeed, when we look at thedetails we find that many everyday cases of causation have thispattern. But thatC causesE does not depend on theintrinsic natures ofC andE. Rather, it depends onthere being some threat toE, a threat thatCprevents, and the existence of threats is typically extrinsic toevents.

Another argument is that quasi-dependence cannot account for what cameto be known as ‘trumping pre-emption’. Lewis illustratedthis idea with an example from Jonathan Schaffer (2000). The troopsare disposed to obey all orders from either the Sergeant or the Major.But they give priority to the Major’s orders, due to theMajor’s higher rank. Both the Major and the Sergeant order thetroops to advance, and they do advance. Intuitively, it is the Major,not the Sergeant, who caused the advance, since the Major’sorders have priority. But the advance does quasi-depend on theSergeant’s orders, since in a world where the Majordoesn’t make an order, the advance does depend on theSergeant.

Lewis’s alternative theory relied on changing the definition ofcounterfactual dependence. The theory in “Causation” wasbased on what he came to call ‘whether-whether’dependence. What’s crucial is thatwhetherBhappens depends counterfactually onwhetherAhappens. The new theory was based on what we might call‘how-how’ dependence. Lewis says thatB dependsonA if there are large families of counterfactuals of theformIfA had happened in this way, thenB wouldhave happened in that way, and the ways in whichB wouldhappen are systematically dependent on the ways in whichAhappens. How muchA influencesB depends on how bigthis family is, how much variation there is in the wayBchanges, and how systematic the influence ofA onBis. He then defines causation as the ancestral of this notion ofcounterfactual dependence.

On this new theory, causation is a degree concept, rather than an‘all-or-nothing’ concept, since counterfactual dependencecomes in degrees. Sometimes Lewis says we properly ignore smallamounts of causation. For instance, the location of nearby parked carsinfluences the smashing of a window by a rock in virtue of smallgravitational effects of the cars on the flight of the rock. Butit’s very little influence, and we properly ignore it most ofthe time.

There are two other notable features of “Causation asInfluence”. It contains Lewis’s most comprehensive defenceof the transitivity of causation. This principle was central toLewis’s theory of causation from the earliest days, but had comeunder sustained attack over the years. And the paper has a briefattack on non-Humean theories that take causation to be a primitive.Lewis says that these theories can’t explain the variety ofcausal relations that we perceive and can think about. These passagesmark an interesting change in what Lewis took to be the primaryalternatives to his counterfactuals based reductionism. In 1973 theopponents were other kinds of reductionists; in 2000 they were thenon-reductionists.

5.3 Why Humean Supervenience

Given these concepts, a number of other concepts fall into place.Dispositions are reduced to counterfactual dependencies, though as is made clearin “Finkish Dispositions” (1997b), the reduction is not assimple as it might have seemed. Perception is reduced to dispositionsand causes. (See, for instance, “Veridical Hallucination andProsthetic Vision” (1980d).) We discussed the reduction ofmental content to dispositions and causes in section 4. And wediscussed the reduction of linguistic content to mental content insection 1. Values are reduced to mental states in “DispositionalTheories of Value” (1989b).

But we might worry about the very foundation of the project. Westarted with the assumption that our subvenient base consists ofintrinsic properties of point-sized objects and spatiotemporalrelations. But Bell’s inequality suggests that modern physicsrequires, as primitive, other relations between objects. (Or itrequires intrinsic properties of dispersed objects.) So Humeansupervenience fails in this world.

Lewis’s response is somewhat disarming. Writing in 1986, part ofhis response is scepticism about the state of quantum mechanics.(There is notably less scepticism in “How Many Lives HasSchrödinger’s Cat” (2004b).) But the larger part ofhis response is to suggest that scientific challenges to Humeansupervenience are outside his responsibility.

Really, what I uphold is not so much the truth of Humean supervenienceas thetenability of it. If physics itself were to teach methat it is false, I wouldn’t grieve ... What I want to fight arephilosophical arguments against Humean supervenience. Whenphilosophers claim that one or another common-place feature of theworld cannot supervene on the arrangement of qualities, I make it mybusiness to resist. Being a commonsensical fellow (except whereunactualized possible worlds are concerned) I will seldom deny thatthe features in question exist. I grant their existence, and do mybest to show how they can, after all, supervene on the arrangement ofqualities. (1986b: xi)

We might wonder why Lewis found this such aninterestingproject. If physics teaches that Humean supervenience is false, whycare whether there are also philosophical objections to it? There aretwo (related) reasons why we might care.

Recall that we said that Humean supervenience is a conjunction ofseveral theses. One of these is a thesis about which perfectly naturalproperties are instantiated in this world, namely local ones. Thatthesis is threatened by modern physics. But the rest of the package,arguably, is not. In particular, the thesis that all facts superveneon the distribution of perfectly natural properties and relations doesnot appear to be threatened. (Though see Maudlin (2007: Ch. 2) for adissenting view.) Nor is the thesis that perfectly natural propertiesand relations satisfy a principle of recombination threatened bymodern physics. The rough idea of the principle of recombination isthat any distribution of perfectly natural properties is possible.This thesis is Lewis’s version of the Humean principle thatthere are no necessary connections between distinct existences, andLewis is determined to preserve as strong a version of it as hecan.

Although physics does not seem to challenge these two theses, severalphilosophers do challenge them on distinctively philosophical grounds.Some of them suggest that the nomic, the intensional, or the normativedo not supervene on the distribution of perfectly natural properties.Others suggest that the nomic,intentional, or normative properties are perfectly natural, and as a consequenceperfectly natural properties are not freely recombinable. Thephilosophical arguments in favour of such positions rarely turn on theprecise constitution of the Humean’s preferred subvenient base.If Lewis can show that such arguments fail in the setting of classicalphysics, then he’ll have refuted all of the arguments againstHumean superveience that don’t rely on the details of modernphysics. In practice that means he’ll have refuted many, thoughnot quite all, of the objections to Humean supervenience.

A broader reason for Lewis to care about Humean supervenience comesfrom looking at his overall approach to metaphysics. When faced withsomething metaphysically problematic, sayfree will, there are three broad approaches. Some philosophers will argue thatfree will can’t be located in a scientific world-view, so itshould be eliminated. Call these ‘the eliminativists’.Some philosophers will agree that free will can’t be located inthe scientific world-view, so that’s a reason to expand ourmetaphysical picture to include free will, perhaps as a new primitive.Call these ‘the expansionists’. And some philosophers willreject the common assumption of an incompatibility. Instead they willargue that we can have free will without believing in anything thatisn’t in the scientific picture. Call these ‘thecompatibilists’.

As the above quote makes clear, Lewis was a compatibilist about mostquestions in metaphysics. He certainly was one about free will.(“Are We Free to Break the Laws?” (1981a).) And he was acompatibilist about most nomic, intentional and normative concepts.This wasn’t because he had a global argument for compatibilism.Indeed, he was an eliminativist about religion (“Anselm andActuality” (1970a), “Divine Evil” (2007)). And insome sense he was an expansionist about modality. Lewis may havecontested this; he thought introducing more worlds did not increasethe number of kinds of things in our ontology, because we are alreadycommitted to there being at least one world. As Melia (1992: 192)points out though, the inhabitants of those worlds include all kindsof things not found in, or reducible to, fundamental physics. Theyinclude spirits, gods, trolls and every other consistent beastimaginable. So at least when it came to what there is, as opposed towhat there actually is, Lewis’s ontology was ratherexpansionist.

For all that, Lewis’s default attitude was to accept that muchof our common-sense thinking about the nomic, the intentional and thenormative was correct, and that this was perfectly compatible withthis world containing nothing more than is found in science, indeedthan is found in fundamental physics.

Compatibilists should solve what Frank Jackson calls ‘thelocation problem’ (Jackson 1998). If you think that there are,say, beliefs, and you think that having beliefs in one’smetaphysics doesn’t commit you to having anything in yourontology beyond fundamental physics, then you should, as Jackson putsit, be able tolocate beliefs in the world described byfundamental physics. More generally, for whatever you accept, youshould be able to locate it in the picture of the world youaccept.

This was certainly the methodology that Lewis accepted. And since hethought that so much of our common sense worldview was compatible withfundamental physics, he had many versions of the location problem tosolve. One way to go about this would be to find exactly what thecorrect scientific theory is, and locate all the relevant propertiesin that picture. But this method has some shortcomings. For one thing,it might mean having to throw out your metaphysical work whenever thescientific theories change. For another, it means having yourmetaphysics caught up in debates about the best scientific theories,and about their interpretation. So Lewis took a somewhat differentapproach.

What Lewis’s defence of Humean supervenience gives us is arecipe for locating the nomic, intentional and normative properties ina physical world. And it is a recipe that uses remarkably fewingredients; just intrinsic properties of point-sized objects, andspatio-temporal relations. It is likely that ideal physics will havemore in it than that. For instance, it might have entanglementrelations, as are needed to explain Bell’s inequality. But it isunlikely to have less. And the more there is in fundamental physics,theeasier it is to solve the location problem, because thewould-be locator has more resources to work with.

The upshot of all this is that a philosophical defence of Humeansupervenience, especially a defence like Lewis’s that shows usexplicitly how to locate various folk properties in classical physics,is likely to show us how to locate those properties in more up-to-datephysics. So Lewis’s defence of Humean supervenience thengeneralises into a defence of the compatibility of large swathes offolk theory with ideal physics. And the defence is consistent with therealist principle that truth supervenes on being, and with the Humeandenial of necessary connections between distinct existences. And that,quite clearly, is a philosophically interesting project.

6. Modal Realism

This entry has been stressing Lewis’s many and diversecontributions to philosophy. But there is one thesis with which he isassociated above all others: modal realism. Lewis held that this worldwas just one among many like it. A proposition,p is possiblytrue if and only ifp is true in one of these worlds.Relatedly, he held that individuals like you or I (or this computer)only exist in one possible world. So what it is for a proposition likeYou are happy to be true in another world is not for you tobe happy in that world; you aren’t in that world. Rather, it isfor yourcounterpart to be happy in that world.

Lewis wrote about modal realism in many places. As early asCounterfactuals he wrote this famous passage.

I believe, and so do you, that things could have been different incountless ways. But what does this mean? Ordinary language permits theparaphrase: there are many ways things could have been besides the waythey actually are. I believe that things could have been different incountless ways; I believe permissible paraphrases of what I believe;taking the paraphrase at its face value, I therefore believe in theexistence of entities that might be called ‘ways things couldhave been.’ I prefer to call them ‘possible worlds.’(1973a: 84)

And Lewis used counterpart theory throughout his career to resolvemetaphysical puzzles in fields stretching frompersonal identity (“Counterparts of Persons and Their Bodies” (1971c)) totruthmaker theory (“Things qua Truthmakers” (2003b)). Indeed, Lewis’soriginal statement of counterpart theory is in one of his firstpublished metaphysics papers (“Counterpart Theory and QuantifiedModal Logic” (1968)).

But the canonical statement and defence of both modal realism andcounterpart theory is inOn the Plurality of Worlds (1986a),the book that grew out of his 1984 John Locke lectures. This sectionwill follow the structure of that book.

The little ‘argument by paraphrase’ fromCounterfactuals is a long way from an argument forLewis’s form of modal realism. For one thing, the argumentrelies on taking a folksy paraphrase as metaphysically revealing;perhaps we would be better off treating this as just a careless mannerof speaking. For another, the folksy paraphrase Lewis uses isn’tobviously innocuous; like many other abstraction principles it couldbe hiding a contradiction. And the argument does little to show thatother possible worlds are concreta; talking of them as ways thingscould be makes them sound like properties, which are arguablyabstracta if they exist at all. The first three chapters ofPlurality address these three issues. The fourth chapter isan extended discussion of the place of individuals in modal realism.We’ll look at these chapters in order.

6.1 A Philosophers’ Paradise

The short argument fromCounterfactuals that I quoted seemsdeeply unQuinean. Rather than saying that possible worlds existbecause they are quantified over in the best paraphrase of ourtheories, Lewis says they exist because they are quantified over injust oneparaphrase of our theories. To be sure, he says this is a permissibleparaphrase. On the other hand, there is vanishingly little defence ofits permissibility.

In the first chapter ofPlurality Lewis takes a much moreorthodox Quinean line. He argues, at great length, that the bestversion of many philosophical theories requires quantification overpossibilities. In traditional terms, he offers an extendedindispensability argument for unactualised possibilities. But traditional terms are perhapsmisleading here. Lewis does not say that possibilities are absolutelyindispensable, only that they make our philosophical theories so muchbetter that we have sufficient reason to accept them.

There are four areas in which Lewis thinks that possible worlds earntheir keep.

Modality: Traditional treatments of modal talk interms of operators face several difficulties. They can’t, atleast without significant cost, properly analyse talk about contingentexistence, or talk about modal comparatives, or modal superveniencetheses. All of these are easy to understand in terms of quantificationacross possibilities.
Closeness: Our best theory of counterfactuals,Lewis’s theory, relies on comparisons between possible worlds.Indeed, it relies on comparisons between this world and other worlds.Such talk will be hard to paraphrase away if worlds aren’treal.
Content: Lewis argues, in part followingStalnaker (1984), that our best theory of mental and verbal contentanalyses content in terms of sets of possibilities. This, in turn,requires that the possibilities exist.
Properties: We often appear to quantify overproperties. The modal realist can take properties to be sets ofpossibilia, and take such quantification at face value. In hisdiscussion of properties here, Lewis expands upon his theory ofnatural properties that he introduced in “New Work for a Theoryof Universals”, and that we discussed in section 3.

After arguing that we are best off in all these areas of philosophy ifwe accept unactualised possibilities, Lewis spends the rest of chapter1 saying what possible worlds are on his view. He isn’t yetarguing for this way of thinking about possible worlds; that will comein chapter 3. For now he is just describing what he takes to be thebest theory of possible worlds. He holds that possible worlds areisolated; no part of one is spatio-temporally related to any otherworld. Indeed, he holds that lack of spatio-temporal relation (orsomething like it) is what marks individuals as being in differentworlds. So his theory has the somewhat odd consequence that therecould not have been two parts of the world that aren’tspatio-temporally connected. He holds that worlds are concrete, thoughspelling out just what the abstract/concrete distinction comes to inthis context isn’t a trivial task. And he holds that worlds areplenitudinous, there are enough of them to do the work needed for ananalysis of modality. This requires at least that they satisfy aprinciple of recombination. But since it is possible that things aredifferent in kind to anything that actually exists, plenitude impliesthat there are worlds that can’t be made by simply putting partsof this world together. (Alastair Wilson (forthcoming) has a good survey ofthe complicated relationship between plenitude and recombination.)

6.2 Paradox in Paradise?

Chapter 2 deals with several objections to modal realism. Some ofthese objections claim that modal realism leads to paradox. Otherobjections claim that it undermines our ordinary practice. We willlook at two examples of each.

Peter Forrest and D. M. Armstrong (1984) argue that modal realismleads to problems given the principle of recombination. Anunrestricted principle of recombination says that for any things thatcould exist, there is a world in which there is a duplicate of all ofthem. Forrest and Armstrong apply the principle by taking the thingsto be the different possible worlds. A world containing a duplicate ofall the worlds would, they show, be bigger than any world. But by theprinciple it would also be a world. Contradiction. Lewis’ replyis to deny the unrestricted version of the principle. He insists thatthere is independent reason to qualify the principle to those thingswhose size and shape permits them to be fit into a single world.Without an unrestricted principle of recombination, there is no way tocreate the large world that’s at the heart of Forrest andArmstrong’s paradox.

David Kaplan argued that there could be no cardinality of the worlds.Kaplan did not publish this argument, so Lewis replies to the versionpresented by Martin Davies (1981: 262). On Lewis’s theory, everyset of worlds is a proposition. For any proposition, says Kaplan, thatproposition might be the only proposition being thought by a person atlocationl at timet. So for each proposition, thereis a world where it (alone) is thought by a person at locationl at timet. That means there is a one-onecorrespondence between the sets of worlds and a subset of the worlds.Contradiction. Lewis’s reply is to deny that every propositioncan be thought. He claims that functionalism about belief, plus therequirement that beliefs latch onto relatively natural properties,mean that most propositions cannot be thought, and this blocks theparadox.

Peter Forrest (1982) argues that modal realism leads to inductivescepticism. According to modal realism, there are other thinkers verymuch like us who are deceived by their surroundings. Given this, weshould doubt our inductive inferences. Lewis’s reply is thatmodal realism does not make inductive challenges any worse than theywere before. It is common ground that inductive inference is fallible.That is, it is common ground that these inferences could fail.Thinking of the possibilities of failure as concrete individuals mightfocus the mind on them, and hence make us less confident, but does notseem to change the inference’s justificatory status.Lewis’s argument seems hard to dispute here. Given the mutuallyagreed upon fact that the inference could fail, it’s hard to seewhat epistemological cost is incurred by agreeing that it does failfor someone kind of like the inferrer in a distant possible world.

Robert Adams (1974) argues that modal realism leads to surprisingresults in moral philosophy. The modal realist says that the waythings are, in the broadest possible sense, is not a contingentmatter, since we can’t change the nature of the pluriverse.Hence we cannot do anything about it. So if moral requirements flowfrom a requirement to improve the way things are, in this broadestpossible sense, then there are no moral requirements. Lewis rejectsthe antecedent of this conditional as something that only an extremeutilitarian could accept. What is crucial about morality is thatwe not do evil. Even if their actions won’t make adifference to the nature of the pluriverse, a virtuous agent will notwant to, for instance, cause suffering. By rejecting the view that inour moral deliberations we should care about everyone, possible andactual, equally, Lewis avoids the problem.

6.3 Paradise on the Cheap?

In chapter 3 Lewis looks at the alternatives to his kind of modalrealism. He takes himself to have established that we need to havepossible worlds of some kind in our ontology, but not that thesepossible worlds must be concrete. In particular, they can be abstract,or what he calls “ersatz” possible worlds. Lewis does nothave a single knock-down argument against all forms of ersatzism.Instead he divides the space of possible ersatzist positions intothree, and launches different attacks against different ones.

Lewis starts with what he calls “linguistic ersatzism”.This is the view that ersatz possible worlds are representations, andthe way they represent possibilities is something like the way thatlanguage represents possibilities. In particular, they representpossibilities without resembling possibilities, but instead in virtueof structural features of the representation.

He levels three main objections to linguistic ersatzism. First, ittakes modality as a primitive, rather than reducing modality tosomething simpler (like concrete possible worlds). Second, itcan’t distinguish qualitatively similar individuals in otherpossible worlds. Lewis argues that will mean that we can’talways quantify over possibilia, as we can in his theory. Third, itcan’t allow as full a range of ‘alien’, i.e.uninstantiated, natural properties as we would like. Sider (2002) hasreplied that some of these challenges can be met, or at least reducedin intensity, if we take the pluriverse (i.e. the plurality of worlds)to be what is represented, rather than the individual worlds.

The second theory he considers is what he calls “pictoralersatzism”. This is the view that ersatz possible worlds arerepresentations, and the way they represent possibilities is somethinglike the way that pictures or models represent possibilities. That is,they represent by being similar, in a crucial respect, to what theyare representing. The pictoral ersatzist, says Lewis, is caught insomething of a bind. If the representations are not detailed enough,they will not give us enough possibilities to do the job that possibleworlds need to do. If they are detailed enough to do that job, andthey represent by resembling possibilities, then arguably they willcontain as much problematic ontology as Lewisian concrete possibleworlds. So they have the costs of Lewis’s theory without anyobvious advantage.

The final theory he considers is what he calls “magicalersatzism”. Unlike the previous two theories, this theory isdefined negatively. The magical ersatzist is defined by their denialthat possible worlds represent, or at least that they represent ineither of the two ways (linguistic and pictoral) that we are familiarwith. And Lewis’s primary complaint is that this kind of theoryis mysterious, and that it could only seem attractive if it hides fromview the parts of the theory that are doing the philosophical work.Lewis argues that as soon as we ask simple questions about therelationship that holds between a possibility and actuality if thatpossibility is actualised, such as whether this is an internal orexternal relation, we find the magical ersatzist saying things thatare either implausible or mysterious.

It isn’t clear just who is a magical ersatzist. Lewis wrote thatat the time he wrotePlurality no one explicitly endorsedthis theory. This was perhaps unfair to variousprimitivistsabout modality, such as Adams (1974), Plantinga (1974) and Stalnaker(1976). Given the negative definition of magical ersatzism, and giventhe fact that primitivists do not think that possible worlds representpossibilities via any familiar mechanism, it seems the primitivistsshould count as magical ersatzists, or, as Lewis calls them,“magicians”. In any case, if magical ersatzism, in all itsvarieties, is objectionably mysterious, that suggests ersatzism is introuble, and hence if we want the benefits of possible worlds, we haveto pay for them by accepting concrete possible worlds.

6.4 Counterparts or Double Lives?

The last chapter ofPlurality changes tack somewhat. Insteadof focussing on different ways the world could be, Lewis’s focusbecomes different ways things could be. The chapter defends, andexpands upon, Lewis’s counterpart theory.

Counterpart theory was first introduced by Lewis in “CounterpartTheory and Quantified Modal Logic” (1968) as a way of makingmodal discourse extensional. Instead of worrying just what a nameinside the scope of a modal operator might mean, we translate thelanguage of quantified modal logic into a language without operators,but with quantifiers over worlds and other non-actual individuals. Soinstead of saying □Fa, we say∀w∀x ((Ww ∧Ixw∧Cxa) ⊃Fx). That is, for allwandx, ifw is a world, andx is inw, andx is a counterpart ofa, thenFx. Or, more intuitively, all ofa’scounterparts areF. The paper shows how we can extend thisintuitive idea into a complete translation from the language ofquantfied modal logic to the language of counterpart theory. In“Tensions” (1974a) Lewis retracts the claim that it is anadvantage of counterpart theory over quantified modal logic that it isextensional rather than intensional, largely because he finds thedistinction between these two notions much more elusive than he hadthought. But he still thought counterpart theory had a lot ofadvantages, and these were pressed in chapter 4.

The intuitive idea behind counterpart theory was that individuals, atleast ordinary individuals of the kind we regularly talk about, areworld-bound. That is, they exist in only one world. But they do nothave all of their properties essentially. We can truly say of anon-contender, say Malloy, that he could have been a contender. In thelanguage of possible worlds, there is a possible worldw suchthat, according to it, Malloy is a contender. But what in turn doesthis mean? Does it mean that Malloy himself is inw? Notreally, according to counterpart theory. Rather, a counterpart ofMalloy’s is a contender inw. And Malloy himself hasthe modal propertycould have been a contender in virtue ofhaving a counterpart inw who is a contender. This way ofthinking about modal properties of individuals has, claims Lewis, anumber of advantages.

For one thing, it avoids an odd kind of inconsistency. Malloy mightnot only have been a contender, he might have been 6 inches taller. Ifwe think that is because there is a world in which Malloy himself is 6inches taller, then it seems like we’re saying that Malloy canhave two heights, his actual height and one 6 inches taller. And thatlooks inconsistent. The obvious way out of this is to say that hebears one height in relation to this world, and another to anotherworld. But that turns height from an intrinsic property into arelation, and that seems like a mistake. Lewis thinks this problem,what he dubs the ‘problem of accidental intrinsics’, is areason to deny that Malloy himself is in multiple worlds.

For another, it allows us a kind of inconstancy in our modalpredications. Could Malloy have been brought by a stork, or must hehave had the parents he actually had? In some moods we think one, inother moods we think another. Lewis thinks that counterpart theory canreflect our indecision. There is a world with someone brought by astork who has a life much like Malloy’s. Is he one ofMalloy’s counterparts? Well, he is according to some counterpartrelations, and not according to others. When one of the formerrelations is contextually salient, it’s true to say that Malloycould have been brought by a stork. When more demanding counterpartrelations are salient, he isn’t one of Malloy’scounterparts, and indeed all of Malloy’s counterparts share hisparents. (More precisely, all of his counterparts have parents who arecounterparts of Malloy’s actual parents.) In those contexts, itis true to say that one’s parentage is essential. Throughout hiscareer, Lewis uses this inconstancy of the counterpart relation toresolve all manner of metaphysical puzzles, from puzzles aboutpersonal identity (1971c) to puzzles about truthmakers (2003b). Thefinal section ofPlurality is Lewis’s most extendedargument that this variability of the counterpart relation is astrength, not a weakness, of the theory.

7. Other Writings

Lewis wrote a lot that isn’t covered by the broad categorieswe’ve discussed so far. The point of this section is to providea sample of that material. It isn’t close to beingcomprehensive. It doesn’t include his treatment ofqualia in (1988h) and (1995b). It doesn’t include his contributions tocausal decision theory in (1979e) and (1981b). It goes very quickly over his many papers inethics. And it skips his contributions to debates about non-classicallogics, such as (1982c) and (1990). We’ve tried to restrictattention to those areas where Lewis’s contributions weregroundbreaking, influential, and set out a new positive theory.Shockingly, there is a lot to cover that meets those constraints, andis not included in the above survey of the major themes of hisphilosophy.

7.1 Mathematics and Mereology

Parts of Classes (1991a) and “Mathematics isMegethology” (1993d) consider the distinctive philosophicalproblems raised byset theory. As Lewis notes, it is widely held that all of mathematics reduces toset theory. But there is little consensus about what the metaphysicsof set theory is. Lewis puts forward two proposals that might,collectively, help to clarify matters.

The first proposal is what he calls theMain Thesis:“The parts of a class are all and only its subclasses”(1991a: 7). By ‘class’ here, Lewis does not mean‘set’. Classes are things with members. Some classes areproper classes, and hence not sets. And one set, the null set, has nomembers, so is not a class. Individuals, for Lewis, are things withoutmembers. Since the null set has no members, it is an individual. Butthe overlap between the sets and the classes is large; most sets wethink about are classes.

The big payoff of the Main Thesis is that it reduces the mysteries ofset theory to a single mystery. Any class is afusion of singletons, i.e., sets with one member. If we understand what a singleton is, andwe understand what fusions are, then we understand all there is toknow about classes, and about sets. That’s because any set isjust the fusion of the singletons of its members.

But singletons are deeply mysterious. The usual metaphors that areused to introduce sets, metaphors about combining or collecting orgathering multiple things into one are less than useless when it comesto understanding the relationship between a singleton and its member.In (1993d), Lewis settles for a structuralist understanding ofsingletons. He also says that he “argued (somewhat reluctantly)for a structuralist’ approach to the theory of singletonfunctions” in (1991a), though on page 54 of (1991a) he appearsto offer qualified resistance to structuralism.

One of the technical advances of (1991a) and (1993d) was that theyshowed how a structuralist account of set theory was even possible.This part of the work was co-authored with John P. Burgess and A. P.Hazen. Given a large enough universe (i.e., that the cardinality ofthe mereological atoms is aninaccessible cardinal), and given plural quantification, we can say exactly what constraintsa function must satisfy for it to do the work we want the singletonfunction to do. (By ‘the singleton function’ I mean thefunction that maps anything that has a singleton onto its singleton.Since proper classes don’t have singletons, and nor do fusionsof sets and objects, this will be a partial function.) Given that, wecan understand mathematical claims made in terms of sets/classes asquantifications over singleton functions. That is, we can understandany claim that would previous have used ‘the’ singletonfunction as a claim of the formfor all s:…s…s…, where the termss go where we would previously have referred to‘the’ singleton function. It is provable that thistranslation won’t introduce any inconsistency into mathematics(since there are values fors), or any indeterminacy (sincethe embedded sentence …s…s… hasthe same truth value for any eligible value fors).

Should we then adopt this structuralist account, and say that we haveremoved the mysteries of mathematics? As noted above, Lewis isuncharacteristically equivocal on this point, and seemed to change hismind about whether structuralism was, all things considered, a good ora bad deal. His equivocation comes from two sources. One worry is thatwhen we work through the details, some of the mysteries of set theoryseem to have been relocated rather than solved. For instance, if weantecedently understood the singleton function, we might have thoughtit could be used to explain why the set theoretic universe is solarge. Now we have to simply posit a very large universe. Another isthat the proposal is in some way revisionary, since it takes ordinarymathematical talk to be surreptitiously quantificational.Parts ofClasses contains some famous invective directed againstphilosophers who seek to overturn established science on philosophicalgrounds.

I’m moved to laughter at the thought of howpresumptousit would be to reject mathematics for philosophical reasons. How wouldyou like the job of telling the mathematicians that they mustchange their ways, and abjure countless errors, now thatphilosophy has discovered that there are no classes? Can youtell them, with a straight face, to follow philosophical argumentwherever it may lead? If they challenge your credentials, will youboast of philosophy’s other great discoveries: that motion isimpossible, that a Being than which no greater can be conceived cannotbe conceived not to exist, that it is unthinkable that anything existsoutside the mind, that time is unreal, that no theory has ever beenmade at all probable by evidence (but on the other hand that anempirically adequate ideal theory cannot possibly be false), that itis a wide-open scientific question whether anyone has ever believedanything, and so on, and on,ad nauseum? Not me! (1991a: 59)

And yet Lewis’s positive theory here is somewhat revisionary. Itdoesn’t revise the truth value of any mathematical claim, but itdoes revise the understanding of them. Is even this too much revisionto make on philosophical grounds? Perhaps not, but it is worryingenough for Lewis to conclude merely that the theory he proposes seemsbetter than the alternatives, not that there is a compelling positivecase for its truth.

7.2 Philosophy of Language

Lewis’s major contribution to formal semantics was his theory ofcounterfactual conditionals. But there were several othercontributions that he made, both on specific topics in formalsemantics, and on the role of semantic theory.

In “Adverbs of Quantification” (1975a), Lewis notesseveral difficulties in translating sentences involving“usually”, “frequently”, “rarely”or related adverbs into first-order logic or some similar formalsystem. Lewis’s solution to the puzzles raised involves twoformal advances. First, he treats the adverbs asunselectivequantifiers, binding all free variables in their scope. Thesecond advance concerns the if-clauses in sentences likeUsually,if a team plays well, they win. It is difficult for variousreasons to take the structure of this sentence to involve a quantifierover a compound sentence with a conditional connective. Lewis’ssecond advance is to say that these if-clauses are simply domainrestrictors. The ‘if’ is no more a sentential connectivethan the ‘and’ inNew York is between Boston andWashington. Instead, the if-clause restricts what things thequantifier denoted by ‘usually’ ranges over.

This paper is not widely read by philosophers, but it has been veryinfluential among linguists, especially semanticists. Indeed, itsuptake by semanticists has made it the fourth most cited paper ofLewis’s onGoogle Scholar. His most cited paper on Google Scholar is also in philosophy oflanguage; it is “Scorekeeping in a Language Game”(1979f).

That paper is about conversational dynamics. Lewis develops anextended analogy between the role of context in a conversation and therole of score in a baseball game. One central role of the score is tokeep a record of what has already happened. In that way, score isinfluenced by what happens on the field, or in the conversation. Butthe causal influence runs in the other way as well. Some events on thefield are influenced by the score. You’re only out after thethird strike, for example. Similarly, Lewis holds thatcontext (or the conversational score) can influence, or even bepartially constitutive of, what happens in the conversation. If I say“None of the cats are afraid of Barney”, which catsI’ve managed to talk about depends on which cats areconversationally salient. And in saying this, I’ve made Barneysalient, so the score changes in that respect. That change matters;now I can denote Barney by “he”.

Lewis argues that this model can make sense of a number of otherwisepuzzling features of language. One notable example of this involvesquantification. Most quantifiers we use do not range over the entireuniverse. We quantify only over a restricted range. Lewis says that itis the salient objects. He also says that this happens not just whenwe explicitly quantify, but also when we use terms that have aquantificational analysis. He mentions in passing that“knows” might be one such term.

This idea is developed more fully in “Elusive Knowledge”(1996b). Lewis argues thatS knows that p is true iffS is in a position to rule outall possibilities inwhichp is false. But when we sayS knows that p, wedon’t mean to quantify over all possibilities there are, onlyover the salient possibilities. The big advantage of Lewis’sapproach is that it lets him explain the appeal of scepticism. Whenthe sceptic starts talking about fantastic possibilities of error, shemakes those possibilities salient. Since we can’t rule them out,when we’re talking to the sceptic we can’t say we knowvery much. But since those possibilities aren’t usually salient,we are usually correct in our knowledge-ascriptions. So Lewis lets thesceptic win any debate they are in, without conceding that ordinaryknowledge-ascriptions are false.

The kind of position Lewis defends here, which came to be known ascontextualism, has been a central focus of inquiry in epistemology for the lastfifteen years. “Elusive Knowledge”, along with papers suchas Cohen (1986) and DeRose (1995) founded this research program.

7.3 Bayesian Philosophy

This subsection is largely about two pairs of papers:“Probabilities of Conditionals and ConditionalProbabilities” (1976b) and its sequel (1986h), and “Desireas Belief” (1988b) and its sequel (1996a). The papers have morein common than merely having a common naming convention.(They’re not even Lewis’s only sequels; “LucasAgainst Mechanism” (1969b) also has a sequel (1979d).) In bothcases Lewis aims to defend orthodoxBayesian epistemology against some challenges. And in both cases the argument turns onprinciples to do with updating. Lewis was throughout his career aBayesian; he frequently said that the ideal epistemic agent was aBayesian conditionaliser and expected utility maximiser. And hedefended this position with some gusto.

The conditionals papers concern a position that was gaining popularitybefore Lewis showed it was untenable. The position in question startswith the idea that a speaker can properly sayProbably,if p,q if and only if their subjective probabilityofq givenp is high. And the position then offersan explanation of this purported fact. The English word‘if’ is a binary connective which forms a sentence to bewritten asp →q, and it is true in virtue ofthe meaning of this connective thatPr(q |p) = Pr(p →q). So, assuming‘probably’ means something like subjective probabilityProbably,if p,q means that the subjectiveprobability ofp →q, and, assuming the agentis coherent, that is true just in case the subjective probability ofq givenp is high.

Lewis doubted several aspects of this story. He briefly notes in“Adverbs of Quantification” that he didn’t think the‘if’ inProbably,if p,q is abinary connective. But the more telling objection was his proof thatthere could not be a connective → such that for allp,q,Pr(q |p) =Pr(p →q). Lewis first argued for thisin (1976b), and showed how to weaken some of the assumptions of theargument in (1986h). The effect of Lewis’s position was toessentially end the hope of analysing English ‘if’ interms of a binary connective with these probabilistic properties.

The desire papers (1988a, 1996b) are also about the Humean view thatmotivation requires both a belief and a desire. Lewis aims to attackthe anti-Humean position that some beliefs, in particular beliefs thata certain thing is good, can play the functional roles of both beliefsand desires. He argues that this is not, in general, possible. And theargument is that beliefs and desires update in different ways. Or, atleast, that anyone who updates their beliefs by conditionalisation andupdates their valuation functions in a plausible way, will not be ableto preserve a perfect correlation between their desire for aproposition being true and their belief in that proposition’sgoodness.

Both of these papers rely on the idea that conditionalisation is agood way to update beliefs. Neither, by the way, rely on the idea thatconditionalisation is the only rational way to update beliefs; thearguments go through given merely the permissibility ofconditionalising. Many Bayesians hold something stronger, namely thatconditionalisation isthe way to update beliefs. One widelyused argument in favour of this position is a so-called ‘DutchBook’ argument. This argument shows that if you plan to followany strategy for revising beliefs other than conditionalisation, andyou do follow that strategy, then someone who knows the strategy thatyou’re going to follow can produce a series of bets that willseem favourable to you when each is offered, but which willcollectively lead to a sure loss. It is also true that if you doupdate by conditionalisation, there is no similar Dutch Book that canbe made, but Lewis did not prove this. (It is Theorem V in Skyrms(1987).) The Dutch Book argument for conditionalisation was introducedto the literature by Paul Teller (1976), who credited it to Lewis.Lewis’s own version of the argument did not appear until 1999,inPapers in Metaphysics and Epistemology, under the title“Why Conditionalize?” (1999b). This was something he hadwritten as a course handout in 1972, and which had been very widelycirculated, and, via Teller’s paper, very influential on thedevelopment of Bayesian epistemology.

Lewis was an early proponent of one of the two major views about theSleeping Beauty puzzle, which is nicely described in Sorensen2009:

Sleeping Beauty is an ideal reasoner who knows she will be given asleeping pill that induces limited amnesia. She knows that after shefalls asleep a coin will be flipped. If it lands heads, she will beawakened on Monday and asked: “What is the probability that thecoin landed heads?”. She will not be informed which day it is.If the coin lands tails, she will be awaken on both Monday and onTuesday and asked the same question each time. The amnesia insuresthat, if awakened on Tuesday she will not remember being woken onMonday. What will her answer be to the questions?

The puzzle was introduced to the philosophical community by Adam Elga(2000), who argued that when Beauty woke up, her credence in Headsshould be¹⁄₃. Lewis argued that thecorrect answer was¹⁄₂. The core of hisargument was that before Beauty went to sleep, her credence in Headsshould be¹⁄₂. That was agreed on allsides. Moreover, nothing happened that surprised Beauty. Indeed,everything happened exactly as she expected it would. Lewis arguedthat “Only new relevant evidence, centred or uncentred, producesa change in credence” (2001c: 174), and that Beauty got no newevidence. This idea has featured heavily in subsequent work defendingthe¹⁄₂ answer to the Sleeping Beautypuzzle.

The Sleeping Beauty puzzle is important for another reason. As thequote above indicates, the puzzle is usually set up in terms of setsof centered worlds, following the work of Lewis we described insection 4.5. The work generated by the puzzle has been one of thereasons that that work, in particular (1979b), has received a largeamount of attention in recent years.

7.4 Philosophy of Religion

In “Anselm and Actuality” (1970a), Lewis tries to give asgood a formulation of theontological argument as can be made in modal realist terms. This is a good framework fordiscussing the ontological argument, since on one interpretation, theargument rests crucially on cross-world comparisons of greatness andthe modal realist can make sense of that kind of talk better thanviews that reject possible objects. Lewis argues that the principle“A being than which nothing greater can be conceived ispossible” is crucially ambiguous. One kind of reading is thatthe imagined being’s greatness in its world is greater than thegreatness of any other being in that being’s world. That may betrue, but it doesn’t imply that the being actually exists.Another kind of reading focusses on the imagined being’sgreatness in this world. It says that there (actually) is a beingwhose actual greatness is greater than the greatness of any possiblebeing. That entails the conclusion, but is not plausibly true. Thebroader conclusion here, that the ontological argument derives itspersuasive force from an equivocation, is one that has been widelyadopted since Lewis’s paper.

In “Evil for Freedom’s Sake” (1993b), Lewis reflectsat length on thefree will defence to theproblem of evil. Lewis argues that for the defence to work, God must make quitedifferent trade-offs between freedom and welfare than we are usuallydisposed to make, and our understanding of what freedom consists in,and what divine foreknowledge consists in, must be different to whatthey currently are.

In “Do We Believe in Penal Substitution?” (1997a), Lewisnotes that we only sometimes accept that one person can be properlypunished for another’s misdeeds. He uses this to raise aninteresting difficulty for the Christian idea that Christ died for oursins, suggesting this may not be a form of penal substitution that isnormally acceptable.

In “Divine Evil” (2007), Lewis suggests that proponents ofthe problem of evil should not focus on what God fails to prevent, buton what God does. In orthodox forms of theism, particularlyChristianity and Islam, God is presented as perpetrating great evilagainst sinners of various stripes in the form of extreme punishmentsin the afterlife. Lewis suggests that a God that does would be so evilthat we should not only reject Him, but we may regard those whoendorse the divine punishments as themselves somewhat culpable fordivine evil. (The published version of this paper was composed byPhillip Kitcher after Lewis’s death from notes Lewis made, andconversations Kitcher had with Lewis.)

7.5 Ethics

Lewis is obviously not as well known for his work in ethics as for hiswork in other areas of philosophy. It was something of a surprise whenone of the volumes of his collected papers was calledPapers inEthics and Social Philosophy (2000a). On the other hand, theexistence of this volume indicates that there is a large body of workthat Lewis put together in moral philosophy, very broadly construed.There is very little secondary literature on Lewis’s ethics.I’m drawing heavily here on chapter 8 of Nolan (2005), andKeller (2015).

As Nolan suggests, the least inaccurate summary of Lewis’sethical positions is that he was avirtue ethicist. Indeed, a focus on virtue, as opposed to consequences, plays a rolein his defence of modal realism, as we saw in section 6.4. Nolan alsonotes that this position is somewhat surprising. Most philosophers whoaccept views related to Lewis’s about psychology anddecision-making (in particular, who accept a Humean story aboutbeliefs and desires being the basis for motivation, and who acceptsome or other version of expected utility maximisation as the basisfor rational decision) have broadly consequentialist positions. Butnot Lewis.

Lewis was also avalue pluralist (1984a, 1989b, 1993b). Indeed, this was part of his objection toconsequentialism. He rejected the idea that there was one summaryjudgment we could make about the moral value of a person. In“Reply to McMichael” (1978a) he complains about theutilitarian assumption that “any sort or amount of evil can beneutralized, as if it had never been, by enough countervailing good—and that the balancing evil and good may be entirelyunrelated” (1978a: 85).

In meta-ethics, Lewis defended a variety ofsubjectivism (1989b). Like many subjectivists, Lewis held that something isvaluable for us if and only if we would value it under idealcircumstances. And he held, following Frankfurt (1971), that valuingsomething is simply desiring to desire it. What is distinctive aboutLewis’s position is his view about what ideal circumstances are.He thinks they are circumstances of “full imaginativeacquaintance”. This has some interesting consequences. Inparticular, it allows Lewis to say that different goods have differentconditions of full imaginative acquaintance. It might, he suggests, beimpossible to properly imagine instantiating several different valuesat once. And that in turn lets him argue that his value pluralism isconsistent with this kind of subjectivism, in a way that it might notbe consistent with other varieties of subjectivism.

Lewis also wrote several more papers in applied ethics. In twointeresting papers ontolerance (1989a, 1989d), he suggests that one reason for being tolerant, andespecially of being tolerant of speech we disapprove of, comes fromgame-theoretic considerations. In particular, he thinks our motivationfor tolerance comes from forming a ‘tacit treaty’ withthose with differing views. If we agree not to press our numericalsuperiority to repress them when we are in the majority, they will dothe same. So tolerating opposing views may be an optimal strategy foranyone who isn’t sure that they will be in the majorityindefinitely. In these works it is easy to see the legacies ofLewis’s early work on philosophical lessons to be drawn fromgame theory, and especially from the work of Thomas Schelling.

7.6 Applied Metaphysics

There’s much more that could be said about Lewis’scontributions to philosophy, but we’ll end with a discussion oftwo wonderful pieces of applied metaphysics.

In “The Paradoxes of Time Travel” (1976d), Lewis discussesthe many complicated philosophical issues abouttime travel. He discussestemporal parts, personal identity, causation and causal loops, free will, and thecomplications arising from our many different modal concepts. In somecases he uses the canvas provided to illustrate his own take on themetaphysical issues that arise. But in some cases he notes that theproblems that arise are problems for everyone.

“Holes” (Lewis and Lewis 1970) was co-written withStephanie Lewis. In it they discuss, in dialog form, some of themetaphysical issues that holes generate. One of the characters, Argle,wants to eliminate holes from his ontology, and the paper goes overwhat costs must be met to make this form ofnominalism work. The other character, Bargle, pushes Argle to clarify hiscommitments, and in doing so draws out many details of the nominalistframework. The case is of some interest in itself, but it is also, asthe authors note at the end, a useful case-study in the kind of movesnominalists can make in eliminating unwanted ontology, and the costsof those moves.

Each paper can be, and indeed often has been, used for introducingcomplicated metaphysical issues to students. The papers are, like manyof Lewis’s papers, widely anthologised. They are both excellentillustrations of the fact that, as well as being a wonderfulphilosopher, Lewis was one of the best philosophical writers of histime.

Bibliography

Primary Literature

1966a, “An Argument for the Identity Theory,”Journal of Philosophy, 63: 17–25.
1966b, “Percepts and Color Mosaics in VisualExperience,”Philosophical Review, 75:357–368.
1966 (with Jane S. Richardson), “Scriven on HumanUnpredictability,”Philosophical Studies, 17:69–74.
1968, “Counterpart Theory and Quantified Modal Logic,”Journal of Philosophy, 65: 113–126.
1968 (with Wilfrid Hodges), “Finitude and Infinitude in theAtomic Calculus of Individuals,”Noûs, 2:405–410.
1969a,Convention: A Philosophical Study, Cambridge, MA:Harvard University Press.
1969b, “Lucas against Mechanism,”Philosophy,44: 231–233.
1969c, “Policing the Aufbau,”PhilosophicalStudies, 20: 13–17.
1969d, Review of Capitan and Merrill (eds.),Art, Mind, andReligion,Journal of Philosophy, 66: 22–27.
1970a, “Anselm and Actuality,”Noûs, 4:175–188.
1970b, “General Semantics,”Synthese, 22:18–67.
1970c, “How to Define Theoretical Terms,”Journalof Philosophy, 67: 427–446.
1970d, “Nominalistic Set Theory,”Noûs,4: 225–240.
1970 (with Stephanie R. Lewis), “Holes,”Australasian Journal of Philosophy, 48: 206–212.
1971a, “Analog and Digital,”Noûs, 5:321–327.
1971b, “Completeness and Decidability of Three Logics ofCounterfactual Conditionals,”Theoria, 37:74–85.
1971c, “Counterparts of Persons and Their Bodies,”Journal of Philosophy, 68: 203–211.
1971d, “Immodest Inductive Methods,”Philosophy ofScience, 38: 54–63.
1972a, “Psychophysical and TheoreticalIdentifications,”Australasian Journal of Philosophy,50: 249–258.
1972b, “Utilitarianism and Truthfulness,”Australasian Journal of Philosophy, 50: 17–19.
1973a,Counterfactuals, Oxford: Blackwell Publishers andCambridge, MA: Harvard University Press, 1973, Reprinted withrevisions, 1986.
1973b, “Causation,”Journal of Philosophy,70: 556–567.
1973c, “Counterfactuals and Comparative Possibility,”Journal of Philosophical Logic, 2: 418–446.
1973d, “Lingue e lingua,”Versus, 4:2–21.
1974a, “Tensions,” in Milton K. Munitz and Peter K.Unger (eds.),Semantics and Philosophy, New York: New YorkUniversity Press, pp. 49–61.
1974b, “Intensional Logics Without Iterative Axioms,”Journal of Philosophical Logic, 3: 457–466.
1974c, “Radical Interpretation,”Synthese,23: 331–344.
1974d, “Semantic Analyses for Dyadic Deontic Logic,”in Sören Stenlund (ed.),Logical Theory and SemanticAnalysis: Essays Dedicated to Stig Kanger on His FiftiethBirthday, Dordrecht: Reidel, pp. 1–14.
1974e, “Spielman and Lewis on Inductive Immodesty,”Philosophy of Science, 41: 84–85.
1975a, “Adverbs of Quantification,” in Edward L.Keenan (ed.),Formal Semantics of Natural Language,Cambridge: Cambridge University Press, pp. 3–15.
1975b, “Languages and Language,” in Keith Gunderson(ed.),Minnesota Studies in the Philosophy of Science, VolumeVII, Minneapolis: University of Minnesota Press, pp. 3–35.
1975 (with Stephanie R. Lewis), Review of Olson and Paul,Contemporary Philosophy in Scandinavia,Theoria, 41:39–60.
1976a, “Convention: Reply to Jamieson,”CanadianJournal of Philosophy, 6: 113–120.
1976b, “Probabilities of Conditionals and ConditionalProbabilities,”Philosophical Review, 85:297–315.
1976c, “Survival and Identity,” in Amélie O.Rorty (ed.),The Identities of Persons, Berkeley: Universityof California Press, pp. 17–40.
1976d, “The Paradoxes of Time Travel,”AmericanPhilosophical Quarterly, 13: 145–152.
1977a, “Possible-World Semantics for Counterfactual Logics:A Rejoinder,”Journal of Philosophical Logic, 6:359–363.
1978a, “Reply to McMichael,”Analysis, 38:85–86.
1978b, “Truth in Fiction,”American PhilosophicalQuarterly, 15: 37–46.
1979a, “A Problem about Permission,” in E. Saarinenet al. (eds.),Essays in Honour of Jaakko Hintikka,Dordrecht: Reidel, pp. 163–175.
1979b, “AttitudesDe Dicto andDeSe,”Philosophical Review, 88: 513–543.
1979c, “Counterfactual Dependence and Time’sArrow,”Noûs, 13: 455–476.
1979d, “Lucas Against Mechanism II,”CanadianJournal of Philosophy, 9: 373–376.
1979e, “Prisoners’ Dilemma is a NewcombProblem,”Philosophy and Public Affairs, 8:235–240.
1979f, “Scorekeeping in a Language Game,”Journalof Philosophical Logic, 8: 339–359.
1980a, “A Subjectivist’s Guide to ObjectiveChance,” in Richard C. Jeffrey (ed.),Studies in InductiveLogic and Probability, Volume II, Berkeley: University ofCalifornia Press, pp. 263–293.
1980b, “Index, Context, and Content,” in Stig Kangerand Sven Öhman (eds.),Philosophy and Grammar,Dordrecht: Reidel, pp. 79–100.
1980c, “Mad Pain and Martian Pain,” in Ned Block(ed.),Readings in Philosophy of Psychology, Volume I,Cambridge, MA: Harvard University Press, pp. 216–32.
1980d, “Veridical Hallucination and ProstheticVision,”Australasian Journal of Philosophy, 58:239–249.
1981a, “Are We Free to Break the Laws?,”Theoria, 47: 113–121.
1981b, “Causal Decision Theory,”AustralasianJournal of Philosophy, 59: 5–30.
1981c, “Ordering Semantics and Premise Semantics forCounterfactuals,”Journal of Philosophical Logic, 10:217–234.
1981d, “What Puzzling Pierre Does Not Believe,”Australasian Journal of Philosophy, 59: 283–289.
1981e, “Why Ain’cha Rich?,”Noûs,15: 377–380.
1982a, “‘Whether’ Report,” in Tom Pauli(ed.),320311: Philosophical Essays Dedicated to LennartÅqvist on his Fiftieth Birthday, Uppsala: University ofUppsala Press, pp. 194–206.
1982b, “Censored Vision,” Written under the name“Bruce LeCatt,”,Australasian Journal ofPhilosophy, 60: 158–162.
1982c, “Logic for Equivocators,”Noûs,16: 431–441.
1983a,Philosophical Papers, Volume I, Oxford: OxfordUniversity Press.
1983b, “Extrinsic Properties,”PhilosophicalStudies, 44: 197–200.
1983c, “Individuation by Acquaintance and byStipulation,”Philosophical Review, 92:3–32.
1983d, “Levi Against U-Maximization,”Journal ofPhilosophy, 80: 531-534.
1983e, “New Work For a Theory of Universals,”Australasian Journal of Philosophy, 61: 343–377.
1984a, “Devil’s Bargains and the Real World,” inDouglas MacLean (ed.),The Security Gamble: Deterrence in theNuclear Age, Totowa, NJ: Rowman and Allenheld, pp.141–154.
1984b, “Putnam’s Paradox,”AustralasianJournal of Philosophy, 62: 221–236.
1986a,On the Plurality of Worlds, Oxford: BlackwellPublishers.
1986b,Philosophical Papers, Volume II, Oxford: OxfordUniversity Press.
1986c, “A Comment on Armstrong and Forrest,”Australasian Journal of Philosophy, 64: 92–93.
1986d, “Against Structural Universals,”Australasian Journal of Philosophy, 64: 25–46.
1986e, “Buy Like a MADman, Use Like a NUT”QQ6: 5–8.
1986f, “Causal Explanation” in Lewis 1986b, pp.214–240.
1986g, “Events” in Lewis 1986b, pp.241–269.
1986h, “Probabilities of Conditionals and ConditionalProbabilities II,”Philosophical Review, 95:581–589.
1987, “The Punishment that Leaves Something toChance,”Proceedings of the Russellian Society,University of Sydney, 12: 81–97.
1988a, “Ayer’s First Empiricist Criterion of Meaning:Why Does it Fail?,”Analysis, 48: 1–3.
1988b, “Desire as Belief,”Mind, 97:323–332.
1988c, “Rearrangement of Particles: Reply to Lowe,”Analysis, 48: 65–72.
1988d, “Relevant Implication,”Theoria, 54:162–174.
1988e, “Statements Partly About Observation,”Philosophical Papers, 17: 1–31.
1988f, “The Trap’s Dilemma,”AustralasianJournal of Philosophy, 66: 220–223.
1988g, “Vague identity: Evans misunderstood,”Analysis, 48: 128–130.
1988h, “What Experience Teaches,”Proceedings ofthe Russellian Society, University of Sydney, 13:29–57.
1989a, “Academic Appointments: Why Ignore the Advantage ofBeing Right?,” inOrmond Papers, Ormond College,University of Melbourne. Reprinted in Lewis 2000a, pp.187–200.
1989b, “Dispositional Theories of Value,”Proceedings of the Aristotelian Society, Supplementary Volume63: 113–137.
1989c, “Finite Counterforce,” in Henry Shue (ed.),Nuclear Deterrence and Moral Restraint, Cambridge: CambridgeUniversity Press, pp. 51–114.
1989d, “Mill and Milquetoast,”AustralasianJournal of Philosophy, 67: 152–171.
1989e, Review of John Bigelow,The Reality of Numbers,Australasian Journal of Philosophy, 67: 487–489.
1990, “Noneism or Allism?,”Mind, 99:23–31.
1991,Parts of Classes, Oxford: BlackwellPublishers.
1992a, “Meaning Without Use: Reply to Hawthorne,”Australasian Journal of Philosophy, 70: 106–110.
1992b, Critical Notice of Armstrong,A Combinatorial Theory ofPossibility,Australasian Journal of Philosophy, 70:211–224.
1993a, “Counterpart Theory, Quantified Modal Logic, andExtra Argument Places,”Analysis, 53: 69–71.
1993b, “Evil for Freedom’s Sake?,”Philosophical Papers, 22: 149–172.
1993c, “Many, But Almost One,” in Keith Campbell, JohnBacon, and Lloyd Reinhardt (eds.),Ontology, Causality and Mind:Essays on the Philosophy of D. M. Armstrong, Cambridge: CambridgeUniversity Press, pp. 23–38.
1993d, “Mathematics is Megethology,”PhilosophiaMathematica, 3: 3–23.
1994a, “Humean Supervenience Debugged,”Mind,103: 473–490.
1994b, “Reduction of Mind,” in Samuel Guttenplan(ed.),A Companion to Philosophy of Mind, Oxford: BlackwellPublishers, pp. 412–431.
1995a, “Ern Malley’s Namesake,”Quadrant, 39: 14–15.
1995b, “Should a Materialist Believe in Qualia?,”Australasian Journal of Philosophy, 73: 140–144.
1996a, “Desire as Belief II,”Mind, 105:303–313.
1996b, “Elusive Knowledge,”Australasian Journalof Philosophy, 74: 549–567.
1996c, “Maudlin and Modal Mystery,”AustralasianJournal of Philosophy, 74: 683–684.
1996d, “Illusory Innocence?” review of Peter Unger,Living High and Letting Die,Eureka Street, 6, No.10 December 1996: 35–36.
1996 (with Stephanie R. Lewis), Review of R. Casati and A. Varzi,Holes,Philosophical Review, 105: 77–79.
1997a, “Do We Believe in Penal Substitution?,”Philosophical Papers, 26: 203–209.
1997b, “Finkish Dispositions,”PhilosophicalQuarterly, 47: 143–58.
1998a,Papers in Philosophical Logic, Cambridge:Cambridge University Press.
1997c, “Naming the Colours,”Australasian Journalof Philosophy, 75: 325–342.
1998b, “A World of Truthmakers?” review of D. M.Armstrong,A World of States of Affairs, published under anincorrect title inTimes Literary Supplement, 4950, 13February 1998: 30.
1998 (with Rae Langton), “Defining‘Intrinsic’,”Philosophy and PhenomenologicalResearch, 58: 333–345.
1999a,Papers in Metaphysics and Epistemology, Cambridge:Cambridge University Press.
1999b, “Why Conditionalize?,” Written in 1972 as acourse handout, but not published until 1999 in Lewis 1999a.
1999c, “Zimmerman and the Spinning Sphere,”Australasian Journal of Philosophy, 77: 209–212.
2000a,Papers in Ethics and Social Philosophy, Cambridge:Cambridge University Press.
2000b, “Causation as Influence” abridged version,Journal of Philosophy, 97: 182–197.
2001a, “Forget About the ‘Correspondence Theory ofTruth’,”Analysis, 61: 275–280.
2001b, “Redefining ‘Intrinsic’,”Philosophy and Phenomenological Research, 63:381–398.
2001c, “Sleeping Beauty: Reply to Elga,”Analysis, 61: 171–176.
2001d, “Truthmaking and Difference-Making,”Noûs, 35: 602-615.
2001 (with Rae Langton), “Marshall and Parsons on‘Intrinsic’” Rae Langton, co-author,Philosophyand Phenomenological Research, 63: 353–355.
2002a, “Tensing the Copula,”Mind, 111:1–14.
2002b, “Tharp’s Third Theorem,”Analysis, 62: 95–97.
2003a, “Rights to Rights,”Theoria, 69:160–165.
2003b, “Things qua Truthmakers,” in HallvardLillehammer and Gonzalo Rodriguez-Pereyra (eds.),RealMetaphysics: Essays in Honour of D. H. Mellor, London: Routledge,pp. 25–38.
2003 (with Gideon Rosen), “Postscript to ‘Things quaTruthmakers’: Negative Existentials,”, in HallvardLillehammer and Gonzalo Rodriguez-Pereyra (eds.),RealMetaphysics: Essays in Honour of D. H. Mellor, London: Routledge,pp. 39–42.
2004a, “Causation as Influence” unabridged version, inJohn Collins, Ned Hall, and L.A. Paul (eds.),Causation andCounterfactuals, Cambridge, MA: MIT Press, pp. 75–106.
2004b, “How Many Lives has Schrödinger’sCat?,”Australasian Journal of Philosophy, 82:3–22.
2004c, “Tensed Quantifiers,” in Dean Zimmerman (ed.),Oxford Studies in Metaphysics, Volume 1, Oxford: OxfordUniversity Press, pp. 3–14.
2004d, “Void and Object,” in John Collins, Ned Hall,and L.A. Paul (eds.),Causation and Counterfactuals,Cambridge, MA: MIT Press, pp. 277–290.
2004e, “Letters to Priest and Beall,” in GrahamPriest, J. C. Beall and Bradley Armour-Garb (eds.),The Law ofNon-Contradiction, Oxford: Oxford University Press, pp.176–177.
2005, “Quasi-Realism is Fictionalism” in Mark Calderon(ed.),Fictionalism in Metaphysics, Oxford: Clarendon Press,pp. 314–321.
2007, “Divine Evil” in Louise Anthony (ed.),Philosophers Without Gods, Oxford: Oxford University Press,pp. 231–242.
2009, “Ramseyan Humility” in David Braddon-Mitchelland Robert Nola (eds.),Conceptual Analysis and PhilosophicalNaturalism, Cambridge, MA: MIT Press, pp. 203–222.
2015a, “Counterparts of States of Affairs” in BarryLoewer and Jonathan Schaffer (eds.),A Companion to DavidLewis, New York: Wiley Blackwell, pp. 15-17.
2015b, “Reply to Dana Scott, “Is There Life on OtherPossible Worlds”” in Barry Loewer and Jonathan Schaffer(eds.),A Companion to David Lewis, New York: WileyBlackwell, pp. 18-21.
2020a,Philosophical Letters of David K. Lewis, volume 1:Causation, Modality, Ontology, edited by Helen Beebee and A. R.J. Fisher, Oxford: Oxford University Press.
2020b,Philosophical Letters of David K. Lewis, volume 2:Mind, Language, Epistemology, edited by Helen Beebee and A. R. J.Fisher, Oxford: Oxford University Press.

Cited Secondary Literature

Adams, Robert, 1974, “Theories of Actuality”Noûs, 8: 211–231.
Armstrong, D. M., 1978,Universals and ScientificRealism, Cambridge: Cambridge University Press.
Bennett, Jonathan, 1984, “Counterfactuals and TemporalDirection”Philosophical Review, 93: 57–91.
Bennett, Jonathan, 2003,A Philosophical Guide toConditionals, Oxford: Oxford University Press.
Braddon-Mitchell, David and Robert Nola, 1997,“Ramsification and Glymour’s Counterexample”Analysis, 57: 167–169.
Cohen, Stewart, 1986, “Knowledge and Context”,TheJournal of Philosophy, 83: 574–583.
Davies, Martin, 1981,Meaning, Quantification, Necessity:Themes in Philosophical Logic, London: Routledge.
Elga, Adam, 2000, “Self-Locating Belief and the SleepingBeauty Problem,”Analysis 60: 143–147.
DeRose, Keith, 1995, “Solving the Skeptical Problem”,The Philosophical Review, 104(1), 1–52.
–––, 2004, “Defeating Dr. Evil withSelf-Locating Belief,”Philosophy and PhenomenologicalResearch, 69: 383–396.
Egan, Andy, 2007, “Epistemic modals, relativism andassertion,”Philosophical Studies, 133:1–22.
Fine, Kit, 1975, “Critical Notice ofCounterfactuals,”Mind, 84:451–458.
Forrest, Peter, 1982, “Occam’s Razor and PossibleWorlds”Monist, 65: 456–464.
––– and D. M. Armstrong, 1984, “AnArgument Against David Lewis’ Theory of Possible Worlds,”Australasian Journal of Philosophy, 62: 164–8.
Frankfurt, Harry, 1971, “Freedom of the Will and the Conceptof a Person,”Journal of Philosophy, 68:5–20.
Goodman, Nelson, 1955,Fact, Fiction and Forecast,Cambridge, MA: Harvard University Press.
Hall, Ned, 1994, “Correcting the Guide to ObjectiveChance”,Mind 103: 505–518.
Hawthorne, John, 1990, “A Note on Languages andLanguage,”Australasian Journal of Philosophy, 68:116–118.
Hájek, Alan, 2008, “David Lewis,” inTheNew Dictionary of Scientific Biography, ed. Noretta Koertke, NewYork: Scribners.
Jackson, Frank, 1998,From Metaphysics to Ethics, Oxford:Oxford University Press.
Janssen-Lauret, Frederique and Fraser MacBride, 2020,“Lewis’s Global Descriptivism and ReferenceMagnetism,”Australasian Journal of Philosophy, 98:192–198.
Keller, Simon, 2015, “David Lewis’s Social andPolitical Philosophy”, in Barry Loewer and Jonathan Schaffer(eds.),A Companion to David Lewis, New York: WileyBlackwell, pp. 549-561.
Kim, Jaegwon, 1973, “Causes and Counterfactuals,”Journal of Philosophy, 70: 570–572.
Kripke, Saul, 1982,Wittgenstein on Rules and PrivateLanguage, Oxford: Blackwell.
Lewis, Stephanie, 2015, “Intellectual Biography of DavidLewis (1941-2001): Early Influences”, in Barry Loewer andJonathan Schaffer (eds.),A Companion to David Lewis, NewYork: Wiley Blackwell, pp. 1-14.
Melia, Joseph, 1992, “A Note on Lewis’sOntology”,Analysis, 52: 191–192.
Melia, Joseph and Juha Saatsi, 2006, “ Ramseyfication andTheoretical Content”,British Journal for the Philosophy ofScience, 57: 561–585.
Nolan, Daniel, 2005,David Lewis, Chesham: AcumenPublishing.
–––, 2007, “Selfless Desires”,Philosophy and Phenomenological Research, 73:665–679.
Paul, L. A., 2000, “Aspect Causation,”Journal ofPhilosophy, 97: 235–256.
Plantinga, Alvin, 1974,The Nature of Necessity, Oxford:Oxford University Press.
Putnam, Hillary, 1981,Reason, Truth and History,Cambridge: Cambridge University Press.
Quine, Willard van Orman, 1960,Word and Object,Cambridge, MA: MIT Press.
Schaffer, Jonathan, “Trumping Preemption,”Journalof Philosophy, 97: 165–181.
Schelling, Thomas, 1960,The Strategy of Conflict,Cambridge, MA: Harvard University Press.
Schwarz, Wolfgang, 2009,David Lewis: Metaphysik undAnalyse, Paderborn: Mentis-Verlag.
–––, 2014, “Against Magnetism,”Australasian Journal of Philosophy, 92: 17–36.
Skyrms, Brian, 1987, “Dynamic Coherence and ProbabilityKinematics,”Philosophy of Science, 54:1–20.
Sider, Theodore, 2001, “Criteria of Personal Identity andthe Limits of Conceptual Analysis,”PhilosophicalPerspectives, 15: 279–315.
–––, 2002, “The Ersatz Pluriverse,”Journal of Philosophy, 99: 279–315.
Smart, J. J. C., 1959 “Sensations and BrainProcesses,”Philosophical Review, 68:141–156.
Sorensen, Roy, 2009, “Epistemic Paradoxes,”TheStanford Encyclopedia of Philosophy (Spring 2009 Edition), EdwardN. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2009/entries/epistemic-paradoxes/>.
Stalnaker, Robert, 1968, “A Theory of Conditionals, ”in Nicholas Rescher (ed.),Studies in Logical Theory(American Philosophical Quarterly Monograph Series: Volume 2), Oxford:Blackwell, pp. 98–112.
–––, 1976, “Possible Worlds”Noûs, 10: 65–75.
–––, 1984,Inquiry, Cambridge, MA:Bradford Books.
–––, 2008,Our Knowledge of the InternalWorld, Oxford: Oxford University Press.
Teller, Paul, 1976, “Conditionalization, observation, andchange of preference” in: W. L. Harper and C. A. Hooker (eds.),Foundations of Probability Theory, Statistical Inference, andStatistical Theories of Science, vol. 1. Dordrecht: Reidel, pp.205–253.
Thau, Michael, 1994, “Undermining and Admissibility”,Mind, 103: 491–504.
Weatherson, Brian, 2003, “What Good areCounterexamples?”Philosophical Studies, 115:1–31.
–––, 2013, “The Role of Naturalness inLewis’s Theory of Meaning”Journal for the History ofAnalytical Philosophy, 1(10) [available online].
Williams, J. Robert G., 2007, “Eligibility andInscrutability,”Philosophical Review, 116:361–399.
Wilson, Alastair, forthcoming, “Plenitude and Recombination,”in Helen Beebee and Anthony Fisher (eds.),David Lewis:A Historical Perspective, Oxford: Oxford University Press.
Wittgenstein, Ludwig, 1953,Philosophical Investigations,Oxford: Blackwell.

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Acknowledgments

I’ve learned a lot over the years from talking aboutLewis’s philosophy with Wolfgang Schwarz. I trust his book(2009) is excellent on all these topics, but unfortunately it’sonly out in German so far, which I don’t read. But a lot ofimportant points are collected on hisblog, which is listed under other internet resources. This entry drawsheavily on Daniel Nolan’s excellent bookDavid Lewis(2005). Without that book, section 7.5 of this entry wouldn’texist, section 6.3 would be unintelligible, and every section would beworse. Much of the biographical information in the introduction istaken from Hájek (2008), supplemented by the information in theshort biography that written by Stephanie Lewis (2015). Many peoplehelpfully spotted typos and infelicities of expression in earlierversions of this entry. Thanks especially to Zachary Miller for manysuggested improvements and revisions. The bibliography is based inlarge part on a bibliography provided to me by Stephanie Lewis.

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