## 1. Lewis's Life and Influence



As we've already seen, part of Lewis's significance came
from the breadth of subject matter on which he made major
contributions. It is hard to think of a philosopher since Hume who has
contributed so much to so many fields. And in all of these cases,
Lewis's contributions involved defending, or in many cases
articulating, a big picture theory of the subject matter, as well as
an account of how the details worked. Because of all his work on the
details of various subjects, his writings were a font of ideas even
for those who didn't agree with the bigger picture. And he was
almost invariably clear about which details were relevant only to his
particular big picture, and which were relevant to anyone who worked
on the subject.



Lewis was born in Oberlin, Ohio in 1941, to two academics. He was an
undergraduate 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 was
tutored by Iris Murdoch. He returned to Swarthmore as a philosophy
major, and never looked back. He studied at Harvard for his Ph.D.,
writing a dissertation under the supervision of W. V. O. Quine that
became his first book, *Convention*. In 1966 he was hired at
UCLA, where he worked until 1970, when he moved to Princeton. He
remained at Princeton until his death in 2001. While at Harvard he met
his wife Stephanie. They remained married throughout Lewis's
life, jointly attended numerous conferences, and co-authored three
papers. Lewis visited Australia in 1971, 1975, every year from 1979 to
1999, and again shortly before his death in 2001.



Lewis was a Fellow of the American Academy of Arts and Sciences, a
Corresponding Fellow of the British Academy, and an Honorary Fellow of
the Australian Academy of the Humanities. He received honorary
doctorates from the University of Melbourne, the University of York in
England, and Cambridge University. His Erdos number was 3.



Lewis published four books: *Convention* (1969a),
*Counterfactuals* (1973a), *On the Plurality of Worlds*
(1986a) and *Parts of Classes* (1991a). His numerous papers
have been largely collected in five volumes: *Philosophical Papers
Vol. I* (1983a), *Philosophical Papers Vol. II* (1986b),
*Papers in Philosophical Logic* (1998a), *Papers in
Metaphysics and Epistemology* (1999a) and *Papers in Social
Philosophy* (2000a). This entry starts with a discussion of
Lewis's first two books, then looks at his contributions to
philosophy of mind. Sections 5 and 6 are on his metaphysics, looking
in turn at Humean Supervenience and modal realism. Section 7 looks
very briefly at some of the many works that aren't been covered
in the previous five categories.


## 2. Convention



David Lewis's first book was *Convention* (1969a; note
that all citations are to works by David Lewis, unless explicitly
stated otherwise). It was based on his Harvard Ph. D. thesis, and
published in 1969. The book was an extended argument that language
could be entirely grounded in convention. There is a simple argument
that 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 to
*Convention*, Quine appears to express some sympathy for this
argument.) Lewis's response is to deny that conventions require
anything like an agreement. Rather, on his view, conventions are
regularities in action that solve co-ordination problems. We can
stumble into such a regularity without ever agreeing to do so. And
such a regularity can persist simply because it is in everyone's
best interest that it persist.


### 2.1 Analysis of Convention



Lewis viewed conventions as solutions to co-ordination problems (see
Section 3.2 of the entry on
 convention).
 His thinking about these problems was heavily influenced by Thomas
Schelling's work on co-operative games in *The Strategy of
Conflict* (Schelling 1960). Many of the key ideas in Lewis's
book come from game theory.



The simplest cases in which conventions arise are ones where we are
repeatedly playing a game that is purely co-operative, i.e. the
payoffs to each agent are the same, and there are multiple equilibria.
In such a case, we may well hope for the equilibrium to persist. At
the very least, we will prefer the persistence of the equilibrium to
any one person deviating from it. And we will have this preference
even if we would prefer, all things considered, to be in some other
equilibrium state. In such a case, there may well be a practice of
continuing to play one's part in the equilibrium that has been
reached. This is a regularity in action--it involves making moves
in the repeated game. Given that everyone else is following the
regularity, each agent has a reason to follow the regularity;
otherwise it wouldn't be an equilibrium. But if other agents
acted differently, agents would not be interested in following the
regularity, since there are alternative equilibria. Because these
three conditions are met, Lewis argued that the practice is really a
convention, even if there was never any explicit agreement to continue
it.



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



Instead of focussing on repeated co-ordination problems, Lewis just
focussed on repeated situations which collectively constitute a
co-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 may
be that the costs of performing some kind of action differ on
different occasions, so the formal game will be different, but the
differences are small enough that it makes sense to have a common
practice. And Lewis does not require that there be identity of
interests. In *Convention* he does require that there be large
overlap of interests, but this requirement does not do much work, and
is abandoned in later writing. With those requirements weakened, we
get the following definition of convention.



> 
> A regularity *R* in the behaviour of members of a population
> *P* when they are agents in a recurrent situation *S* is
> a *convention* if and only if it is true that, and it is common
> knowledge in *P* that, in almost any instance of *S*
> among members of *P*,
> 
> 1. almost everyone conforms to *R*;
> 2. almost everyone expects everyone else to conform to
> *R*;
> 3. almost everyone has approximately the same preferences regarding
> all possible combinations of actions;
> 4. almost everyone prefers that any one more conform to *R*,
> on condition that almost everyone conform to *R*;
> 5. almost everyone would prefer that any one more conform to
> *R*', on condition that almost everyone conform to
> *R*',
> 
> 
> 
> where *R*' is some possible regularity in the behaviour
> of members of *P* in *S*, such that almost no one in
> almost any instance of *S* among members of *P* could
> conform to both *R*' and to *R*. (Lewis 1969:
> 78)
> 
> 
> 



This is clearly a vague definition, with many 'almost's
scattered throughout. But Lewis, characteristically, thought this was
a feature not a bug of the view. Our intuitive notion of a convention
is vague, and any analysis of it should capture the vagueness. The
idea that analyses of imprecise folk concepts should be imprecise
recurs throughout Lewis's career.



The notion of 'common knowledge' that Lewis is working
with here is not the standard modern notion. Lewis does not require
that everyone know that everyone know etc., that all of these
conditions hold. Rather, when Lewis says that it is common knowledge
that *p*, he means that everyone has a reason to believe that
*p*, and everyone has a reason to believe everyone has a reason
to believe that *p*, and everyone has a reason to believe that
everyone has a reason to believe everyone has a reason to believe that
*p*, and so on. That people act on these reasons, or are known
to act on these reasons, to form beliefs is unnecessary. And that the
beliefs people would get if they acted on their reasons are true is
also not part of the view. Hence it is necessary to specify truth as
well as common belief in the definition.



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


### 2.2 Conventions of Language



In the final chapter of *Convention*, Lewis gives his theory of
what it is for a community to speak a language (see the section on
conventional theories of meaning in the entry on
 convention),
 i.e., for a community to have adopted one language as their language
by convention. Lewis individuates languages largely by the truth
conditions they assign to sentences. And his account of truth
conditions is given in terms of possible worlds. So the truth
condition of an indicative sentence is the set of possible worlds in
which it is true. Somewhat more abnormally, Lewis takes the truth
condition for an imperative to be the set of possible worlds in which
the imperative is obeyed. (The account of language in
*Convention* covers many different moods, but we will focus
here on the account of indicatives.)



The focus on truth conditions is not because Lewis thinks truth
conditions are all that there are to languages. He acknowledges that
languages also have 'grammars'. A grammar, in
Lewis's sense, is a lexicon (i.e. a set of elementary
constituents, along with their interpretation), a generative component
(i.e. rules for combining constituents into larger constituents), and
a representing component (i.e. rules for verbally expressing
constituents). Lewis's preferred interpretations are functions
from possible worlds to extensions. So we can sensibly talk about the
meaning of a non-sentential constituent of the language, but these
meanings are derived from the truth conditions of sentences, rather
than determining the meanings of sentences. That's because, as
we'll see, what the conventions of language establish in the
first instance are truth conditions for entire messages, i.e.,
sentences.



Given this understanding of what a language is, Lewis goes on to say
what it is for a population to speak a language. One natural approach
would be to say that speakers and hearers face a co-ordination
problem, and settling on one language to communicate in would be a
solution to that problem. When Lewis is analysing signalling, that is
the approach he takes. But he doesn't think it will work for
language in general. The reason is that he takes conventions to be
regularities in action, and it is hard to say in general what actions
are taken by hearers.



So instead Lewis says that a population *P* speaks a language
*L* if and only if there is a convention of speaking truthfully
in *L* that persists amongst *P*. The parties to the
co-ordination problem (and the convention that solves it) are the
different people who want to communicate in *P*. They solve
their problem by speaking truthfully (on the whole) in *L*.



It might be wondered whether it could really be a convention to speak
truthfully in *L*. After all, there is no obvious alternative
to speaking truthfully. As Lewis points out, however, there are many
natural alternatives to speaking truthfully in *L*; we could
speak truthfully in *L*' instead. The existence of
alternative languages makes our use of *L* conventional. And
the convention can be established, and persist, without anyone
agreeing to it.


### 2.3 Later Revisions



In "Languages and Language" (1975b), Lewis makes two major
revisions to the picture presented in *Convention*. He changes
the account of what a convention is, and he changes the account of
just what convention must obtain in order for a population to speak a
language.



There are two changes to the account of convention. First, Lewis now
says that conventions may be regularities in action and belief, rather
than just in action. Second, he weakens the third condition, which was
approximate 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 conformity
requires action, or an epistemic reason, when convention requires
belief.



In *Convention*, the conventions that sustained language were
regularities amongst speakers. As we noted, it would be more natural
to say that the conventions solved co-ordination problems between
speakers of a language and their hearers. That is what the new account
of what it is for a population to speak a language does. The
population *P* speaks the language *L* iff there are
conventions of truthfulness and trust in *L*. Speakers are
truthful in *L* if and only if they only utter sentences they
believe are true sentences of *L*. Hearers are trusting in
*L* if and only if they take the sentences they hear to be
(generally) true sentences of *L*.



The old account took linguistic conventions to be grounded in
co-ordination between speakers generally. We each communicate in
English because we think we'll be understood that way given
everyone else communicates that way, and we want to be understood. In
the new account there is still this kind of many-way co-ordination
between all the speakers of a language, but the most basic kind of
co-ordination is a two-way co-ordination between individual speakers,
who want to be understood, and hearers, who want to understand. This
seems like a more natural starting point. The new account also makes
it possible for someone to be part of a population that uses a
language even if they don't say anything because they
don't have anything to say. As long as they are trusting in
*L*, they are part of the population that conforms to the
linguistic regularity.



John Hawthorne (1990) argued that Lewis's account cannot explain
the intuitive meaning of very long sentences. While not accepting all
of Hawthorne's reasons as to why very long sentences are a
problem, in "Meaning Without Use: Reply to Hawthorne"
(1992a) Lewis agreed that such sentences pose a problem to his view.
To see the problem, let *L* be the function from each sentence
of English to its intuitive truth condition, and let *L*\* be
the restriction of that function to sentences that aren't very
long. Arguably we do not trust speakers who utter very long sentences
to have uttered truths, under the ordinary English interpretation of
their sentences. We think, as Lewis said, that such speakers are
"trying to win a bet or set a record, or feigning madness or
raving for real, or doing it to annoy, or filibustering, or making an
experiment to test the limits of what it is humanly possible to say
and mean." (Lewis 1992a: 108) That means that while there may be
a convention of truthfulness and trust in *L*\*, there is no
convention of trust in *L* in its full generality. So the
"Languages and Language" theory implies that we speak
*L*\*, not *L*, which is wrong.



Lewis's solution to this puzzle relies on his theory of natural
properties, described below in Section 4.6. He argues that some
grammars (in the above sense of grammar) are more natural than others.
By default, we speak a language with a natural grammar. Since
*L* has a natural grammar, and *L*\* doesn't, other
things being equal, we should be interpreted as speaking *L*
rather than *L*\*. 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 in *L* in
the vast majority of verbal interactions, and there is no other
language with a natural grammar in which there is a convention of
truthfulness and truth, then the theory will hold, correctly, that we
do speak *L*.


## 3. Counterfactuals



David Lewis's second book was *Counterfactuals* (1973a).
Counterfactual conditionals were important to Lewis for several
reasons. Most obviously, they are a distinctive part of natural
language and it is philosophically interesting to figure out how they
work. But counterfactuals would play a large role in Lewis's
metaphysics. Many of Lewis's attempted reductions of nomic or
mental concepts would be either directly in terms of counterfactuals,
or in terms of concepts (such as causation) that he in turn defined in
terms of counterfactuals. And the analysis of counterfactuals, which
uses possible worlds, would in turn provide motivation for believing
in possible worlds. We will look at these two metaphysical motivations
in more detail in section 4, where we discuss the relationship between
counterfactuals and laws, causation and other high-level concepts, and
in section 5, where we discuss the motivations for Lewis's modal
metaphysics.


### 3.1 Background



To the extent that there was a mid-century orthodoxy about
counterfactual conditionals, it was given by the proposal in Nelson
Goodman (1955). Goodman proposed that counterfactual conditionals were
a particular variety of strict conditional. To a first approximation,
If it were the case that *p*, it would be the case that
*q* (hereafter *p* #- *q*) is true
just in case Necessarily, either *p* is false or *q* is
true, i.e. #(*p* [?] *q*). Goodman realised that
this wouldn't work if the modal 'necessarily' was
interpreted unrestrictedly. He first suggested that we needed to
restrict attention to those possibilities where all facts
'co-tenable' with *p* were true. More formally, if
S is the conjunction of all the co-tenable facts, then *p*
#- *q* is true if and only if #((*p*
[?] S) [?] *q*).



Lewis argued that this could not be the correct set of truth
conditions for *p* #- *q* in general. His
argument was that strict conditionals were in a certain sense
indefeasible. If a strict conditional is true, then adding more
conjuncts to the antecedent cannot make it false. But intuitively,
adding conjuncts to the antecedent of a counterfactual can change it
from being true to false. Indeed, intuitively we can have long
sequences of counterfactuals of ever increasing strength in the
antecedent, but with the same consequent, that alternate in truth
value. 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 to
> electoral fraud, he will be the next mayor.
> 
> 
> 
> (3.3) If Smith gets the most votes, but is disqualified due to
> electoral fraud, then launches a military coup that overtakes the city
> government, he will be the next mayor.
> 
> 
> 
> (3.4) If Smith gets the most votes, but is disqualified due to
> electoral fraud, then launches a military coup that overtakes the city
> government, but dies during the coup, he will be the next mayor.
> 
> 
> 



If we are to regard *p* #- *q* as true if and
only if #((*p* [?] S) [?] *q*), then the S
must vary for different values of *p*. More seriously, we have
to say something about *how* S varies with variation in
*p*. Goodman's own attempts to resolve this problem had
generally been regarded as unsuccessful, for reasons discussed in
Bennett (1984). So a new solution was needed.


### 3.2 Analysis



The basic idea behind the alternative analysis was similar to that
proposed by Robert Stalnaker (1968). Let's say that an
*A*-world is simply a possible world where *A* is true.
Stalnaker had proposed that *p* #- *q* was
true just in case the most similar *p*-world to the actual
world is also a *q*-world. Lewis offered a nice graphic way of
thinking about this. He proposed that we think of similarity between
worlds as a kind of metric, with the worlds arranged in some
large-dimensional space, and more similar worlds being closer to each
other than more dissimilar worlds. Then Stalnaker's idea is that
the closest *p*-world has to be a *q*-world for
*p* #- *q* to be true. Lewis considered
several ways of filling out the details of this proposal, three of
which will be significant here.



First, he rejected Stalnaker's presupposition that there is a
most similar *p*-world to actuality. He thought there might be
many worlds which are equally similar to actuality, with no
*p*-world being more similar. Using the metric analogy
suggested above, these worlds all fall on a common
'sphere' of worlds, where the centre of this sphere is the
actual world. In such a case, Lewis held that *p* #-
*q* is true if and only if all the *p*-worlds on this
sphere are *q*-worlds. One immediate consequence of this is
that Conditional Excluded Middle, i.e., (*p* #-
*q*) [?] (*p* #- ~*q*) is not a
theorem of counterfactual logic for Lewis, as it was for
Stalnaker.



Second, he rejected the idea that there must even be a sphere of
closest *p*-worlds. There might, he thought, be closer and
closer *p*-worlds without limit. He called the assumption that
there was a sphere of closest worlds the "Limit
Assumption", and noted that we could do without it. The new
truth conditions are that *p* #- *q* is true
at *w* if and only if there is a *p* [?]
*q*-world closer to *w* than any *p* [?]
!*q*-world, or that there is no *p* world.



Third, he considered dropping the assumption that w is closer to
itself than any other world, or even the assumption that w is among
the worlds that are closest to it. When we think in terms of
similarity (or indeed of metrics) these assumptions seem perfectly
natural, but some philosophers have held that they have bad proof
theoretic consequences. Given the truth conditions Lewis adopts, the
assumption that w is closer to itself than any other world is
equivalent to the claim that *p* [?] *q* entails
*p* #- *q*, and the assumption that w is
among the worlds that are closest to it is equivalent to the claim
that *p* #- *q* and *p* entail
*q*. The first of these entailments in particular has been
thought to be implausible. But Lewis ultimately decided to endorse it,
in large part because of the semantic model he was using. When we
don't think about entailments, and instead simply ask ourselves
whether 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 the
book Lewis offers an axiomatisation of the counterfactual logic he
prefers (see Table 6 in Section 3.3 of the entry
 logic of conditionals),
 as well as axiomatisations for several other logics that make
different choices about some of the assumptions we've discussed
here. And he has proofs that these axiomatisations are sound and
complete with respect to the described semantics.



He also notes that his preferred counterfactual logic invalidates
several familiar implications involving conditionals. We already
mentioned that strengthening the antecedent, the implication of
(*p* [?] *r*) #- *q* by *p*
#- *q*, is invalid on Lewis's theory, and gave
some natural language examples that suggest that it should be invalid.
Lewis also shows that contraposition, the implication of ~*q*
#- ~*p* by *p* #- *q*, and
conditional syllogism, the implication of *p* #-
*r* by *p* #- *q* and *q*
#- *r*, are invalid on his model, and gives
arguments that they should be considered invalid.


### 3.3 Similarity



In *Counterfactuals*, Lewis does not say a lot about similarity
of worlds. He has some short arguments that we can make sense of the
notion of two worlds being similar. And he notes that on different
occasions we may wish to use different notions of similarity,
suggesting a kind of context dependency of counterfactuals. But the
notion 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 a
> nuclear war.
> 



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



In "Counterfactual Dependence and Time's Arrow"
(1979c), Lewis responded by saying more about the notion of
similarity. In particular, he offered an algorithm for determining
similarity in standard contexts. He still held that the particular
measure of similarity in use on an occasion is context-sensitive, so
there is no one true measure of similarity. Nevertheless there is, he
thought, a default measure that we use unless there is a reason to
avoid it. Here is how Lewis expressed this default measure.


1. It is of the first importance to avoid big, widespread, diverse
violations of law.
2. It is of the second importance to maximize the spatio-temporal
region throughout which perfect match of particular fact
prevails.
3. It is of the third importance to avoid even small, localized,
simple violations of law.
4. It is of little or no importance to secure approximate similarity
of particular fact, even in matters that concern us greatly. (Lewis
1979c: 47-8)



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



One way to see the effects of Lewis's ordering is to work
through its implication for an important class of cases. When the
antecedent of a counterfactual is about the occurrence or
non-occurrence of a particular event *E* at time *t*,
the effect of these rules is to say that the nearest worlds are the
worlds where the following claims all hold, with *t*\* being as
late as possible.


* There is an exact match of particular fact with actuality up to
*t*\*.
* There is a small, localized law violation at *t*\*.
* There is exact conformity to the laws of actuality after
*t*\*.
* The antecedent is true.



So we find a point just before *t* where we can make the
antecedent true by making a small law violation, and let the laws take
over from there. There is something intuitively plausible about this
way of viewing counterfactuals; often we do aim to talk about what
would have happened if things had gone on in accordance with the laws,
given a starting point slightly different from the one that actually
obtained.



Jonathan Bennett (2003) notes that when the antecedent of a
conditional is not about a particular event, Lewis's conditions
provide the wrong results. For instance, if the antecedent is of the
form *If one of these events had not happened*, then
Lewis's rules say that the nearest world where the antecedent is
true is always the world where the most recent such event did not
happen. But this does not seem to provide intuitively correct truth
conditions for such conditionals. This need not bother Lewis's
larger project. For one thing, Lewis was not committed to there being
a uniform similarity metric for all counterfactuals. Lewis could say
that his default metric was only meant to apply to cases where the
antecedent was about the happening or non-happening of a particular
event at a particular time, and it wouldn't have seriously
undermined his larger project. Indeed, as we'll see in Section
5.2 below, the counterfactuals he was most interested in, and for
which these criteria of similarity were devised, did have antecedents
concerning specific events.


## 4. Philosophy of Mind



In "Reduction of Mind" (1994b), David Lewis separates his
contributions to philosophy of mind into two broad categories. The
first category is his reductionist metaphysics. From his first
published philosophy paper, "An Argument for the Identity
Theory" (1966a), Lewis defended a version of the mind-brain
identity theory (see the entry on the
 identity theory of mind).
 As he makes clear in "Reduction of Mind", this became an
important part of his global reductionism. We'll look at his
metaphysics of mind in sections 4.1-4.3.



The second category is his theory of mental content. Following Donald
Davidson in broad outlines, Lewis held that the contents of a
person's mental states are those contents that 'fit'
the typical causal profile of the state. For example, a state
isn't constituted by the combination of a
desire for some end plus a belief that waving will bring about that
end, unless it typically causes waving. In this
respect Lewis's views resembled
 interpretationist
 theories of beliefs. But he differed from other interpretationists in
several ways. We will focus here on two of them. Lewis held that
mental contents are typically *properties*, not
*propositions*. And he held that a theory of mental content
requires an *inegalitarian* theory of properties. We'll
look 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 sense
of science. On the one hand, they thought that all meaningful talk was
ultimately talk about observables. On the other hand, they respected
science enough to deny that talk of unobservables was meaningless. The
solution was to 'locate' the unobservables in the
observation language; in other words, to find a way to reduce talk of
unobservables to talk about observables.



Lewis didn't think much of the broader positivist project, but
he was happy to take over some of their technical advances in solving
this location problem. Lewis noted that this formal project, the
project of trying to define theoretical terms in an already understood
language, was independent of the particular use we make of it. All
that really matters is that we have some terms introduced by a new
theory, and that the new theory is introduced in a language that is
generally understood. In any such case it is an interesting question
whether we can extract the denotation of an introduced term from the
theory used to introduce it.



The term-introducing theory could be a scientific theory, such as the
theory that introduces terms like 'electron', and the
language of the theory could be observation language. Or, more
interestingly, the term-introducing theory could be folk psychology,
and the language of the theory could be the language of physics. If we
have a tool for deriving the denotations of terms introduced by a
theory, and we have a way of treating
 folk 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's
important early work on the metaphysics of mind was concerned with
systematising 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 are
important 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 new
name *t*, Lewis says that *t* denotes the *x*
such that T[*x*], where T[*x*] is the sentence we get by
(a) converting T to a single sentence, perhaps a single long
conjunction, and (b) replacing all occurrences of *t* with the
variable *x*. That is, if there is a unique *x* such
that T[*x*], *t* denotes it, and *t* is
denotationless otherwise. (Note that it isn't
*meaningless*, but it is *denotationless*.)



The simplest case is not fully general in a few respects. First,
theories often introduce many terms simultaneously, not just one. So
the theory might introduce new terms *t*1,
*t*2, ..., *tn*. No problem,
we can just quantify over *n*-tuples, where *n* is the
number of new terms introduced. So instead of looking at
[?]1*x* T[*x*], where [?]1
means 'exists a unique' and *x* is an individual
variable, we look at [?]1**x**
T[**x**], where **x** is a variable that
ranges over *n*-tuples, and T[**x**] is the
sentence you get by replacing *t*1 with the first
member of **x**, *t*2 with the second
member of **x**, ..., and *tn*
with the *n*th member of **x**.
Although this is philosophically very important, for simplicity
I'll focus here on the case where a single theoretical term is
to 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 we
can quantify over them. Lewis's response, at least in the early
papers, is to say we can always *replace* them with names that
amount to the same thing. So if T says that all *F*s are
*G*s, and we are interested in the term 'G', then
we'll rewrite T so that it now says *G*ness is a property
of all *F*s. In the early papers, Lewis says that this is a
harmless restatement of T, but this isn't correct. Indeed, in
later papers such as "Void and Object" (2004d) and
"Tensing the Copula" (2002a) Lewis notes that some
predicates don't correspond to properties or relations. There is
no property of being non-self-instantiating, for instance, though we
can predicate that of many things. In those cases the rewriting will
not be possible. But in many cases, we can rewrite T, and then we can
quantify into it.



The procedure here is often called Ramsification, or Ramseyfication.
(Both spellings have occurred in print. The first is in the title of
Braddon-Mitchell and Nola (1997), the second in the title of Melia and
Saatsi (2006).) The effect of the procedure is that if we had a theory
T which was largely expressed in the language O, except for a few
terms *t*1, *t*2, ...,
*tn*, then we end up with a theory expressed
entirely in the O-language, but which, says Lewis, has much the same
content. Moreover, if the converted theory is true, then the T-terms
can be defined as the substitutends that make the converted sentence
true. This could be used as a way of eliminating theoretical terms
from an observation language, if O is the observation language. Or it
could be a way of understanding theoretical terms in terms of natural
language, if O is the old language we had before the theory was
developed.



In cases where there is a unique *x* such that T[*x*],
Lewis says that *t* denotes that *x*. What if there are
many such *x*? Lewis's official view in the early papers
is that in such a case *t* does not have a denotation. In
"Reduction of Mind", Lewis retracted this, and said that
in such a case *t* is indeterminate between the many values. In
"Naming the Colours" he partially retracts the retraction,
and says that *t* is indeterminate if the different values of
*x* are sufficiently similar, and lacks a denotation
otherwise.



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



As it stands, the formal theory does not have the resources to make
this distinction. But this is easy to fix. Just replace the theory T
with a theory T\*, which is a long disjunction of various important
conjuncts of T. So if T consisted of three claims,
*p*1 *p*2 and
*p*3, and it is close enough to true if two of them
are true, then T\* would be the disjunction (*p*1
[?] *p*2) [?] (*p*1 [?]
*p*3) [?] (*p*2 [?]
*p*3). Lewis endorses this method in
"Psychophysical and Theoretical Identifications" The
disjuncts are propositions that are true in states that would count as
close enough to the world as described by T that T's terms
denote. Note that in a real-world case, some parts of T will be more
important than others, so we won't be able to just 'count
the conjuncts'. Still, we should be able to generate a plausible
T\* from T. And the rule in general is that we apply the above strategy
to 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 to
argue for the mind-brain identity theory, in "An Argument for
the Identity Theory". Lewis claims in this paper that his
argument does not rely on parsimony considerations. The orthodox
argument for the identity theory at the time, as in e.g. J. J. C.
Smart (1959), turned on parsimony. The identity theory and dualism
explain the same data, but the dualist explanation involves more
ontology than the identity theory explanation. So the identity theory
is preferable. Lewis says that this abductive step is unnecessary. (He
even evinces concern that it is unsound.) Lewis offers instead an
argument from the causal efficacy of experience. The argument is
something like the following. (I've given the argument that
pains are physical, a similar argument can be given for any other kind
of experience.)


1. Pains are the kind of thing that typically have such-and-such
physical causes and such-and-such physical effects, where the
'such-and-such's are filled in by our folk theory of
pain.
2. Since the physical is causally closed, the things that have
such-and-such physical causes and such-and-such physical effects are
themselves physical.
3. So, pains are physical.



The first premise is analytically true; it follows from the way we
define theoretical terms. The second premise is something we learn
from modern physics. (It isn't clear, by the way, that we can
avoid Smart's parsimony argument if we really want to argue for
premise 2.) So the conclusion is contingent, since modern physics is
contingent, but it is well-grounded. Indeed, if we change the second
premise a little, drawing on neurology rather than physics, we can
draw a stronger conclusion, one that Lewis draws in
"Psychophysical and Theoretical Identifications".


1. Pains are the kind of thing that typically have such-and-such
physical causes and such-and-such physical effects, where the
'such-and-such's are filled in by our folk theory of
pain.
2. Neural state N is the state that has such-and-such physical causes
and such-and-such physical effects.
3. So, pains are instances of neural state N.



So, at least in the second argument, Lewis is defending a kind of
identity theory. Pains just are instances of neural states. I'll
finish up this survey of Lewis's metaphysics of mind with a look
at two complications to this theory.


### 4.3 Madmen and Martians



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



The simplest way to account for madmen would be to simply identify
pain with a neural state. So Lewis's identity theory is
well-placed to deal with them. But there is a complication. Not every
creature in the universe who is in pain has the same neural states as
us. It is at least possible that there are creatures in which some
silicon state S plays the pain role. That is, the creatures are averse
to 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 any
such creature a Martian. A simple identification of pain with neural
state N will stipulate that there couldn't be any Martians. That
would be a bad stipulation to make.



The possibility of madmen pushes us away from a simple functional
definition of pain. Some creatures have pains that do not play the
pain role. The possibility of Martians pushes us away from a purely
neural definition of pains. Some creatures have pains that are not
like our neural pain states. Indeed, some of them might have pains
without having any neural states at all. Lewis's way of
threading this needle is to say that pains, like all mental states,
are defined for kinds of creatures. Pains in humans are certain neural
states. They are the neural states that (typically, in humans) have
the functional role that we associate with pain. In other kinds of
creatures 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 contents
that best make sense of the state. As he sometimes puts it, they are
the contents that 'fit' the state. Part of what it is to
fit a state is to rationalise the behavior that the state typically
causes. So constraints of rationality, especially concerning what
actions are rational given that one is in a mental state, are
partially constitutive of mental content.



Put this broadly, Lewis's position is indebted to Donald
Davidson's work, and Lewis frequently acknowledges the debt. But
Lewis differs from Davidson in several respects. I'll briefly
mention four of them here, then look at two substantial changes in the
next two sections. (The primary sources for the discussion in this
section are "Radical Interpretation" (1974c) and
especially its appendices in *Philosophical Papers: Volume I*
(1983a), and "Reduction of Mind".)



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



Second, Lewis does not give a particularly special place to the
subject's verbal behaviour in considering which content fits. In
particular, we don't first ask what assignment of contents to
their words best makes sense of their verbal behavior, and then say
that the central aspect of fit for mental states involves dispositions
to produce words with the same contents as belief states. Rather,
Lewis follows Grice (among others) in taking mental content to be
metaphysically primary, and linguistic content to be determined by
mental states (see the section on meaning in the entry on
 Grice).



Third, Lewis believes in
 narrow content.
 Indeed, there is a sense in which he thinks narrow content is
primary. He holds that
 Swampman
 has contentful states, thereby disagreeing with Davidson (among
others). And he thinks that we share many beliefs (most clearly
metalinguistic beliefs) with denizens of
 Twin Earth.



Finally, Lewis's theory of mental content, like his theory of
mind in general, is anti-individualistic. What matters is the
functional role that a state typically has in creatures of a certain
kind, not what role it has in this creature. So there might be a
madman who does not attempt to get what they desire. A pure
functionalist may say that such a person has no desires, since
desires, by definition, are states that agents attempt to satisfy.
Lewis says that as long as this state typically leads to
satisfaction-attempts in creatures of this kind, it is a desire.
Indeed, if a state typically leads to attempts to get *X*, it
is a desire for *X*, even if little about the role the state
plays in this particular agent would suggest it is a desire for
*X*.


### 4.5 *De Se* Content



Some of our beliefs and desires are about specific individuals. I
might, for instance, believe that BW is a crook and desire that he be
punished. 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 be
punished. If I know that I am BW, then I should not have all of those
beliefs and desires. But I might be ignorant of this. In some
circumstances (e.g., amnesia, or receiving deceptive information about
your identity) it is no sign of irrationality to not know who you are.
And if you don't know you are *X*, you may ascribe
different properties to yourself and to *X*.



Lewis's way of handling this problem was exceedingly simple. His
original version of interpretationism had it that belief-states were
ultimately probability distributions over possible worlds, and
desire-states were ultimately utility functions, again defined over
possible worlds. In "Attitude *De Dicto* and *De
Se*" (1979b), he argued that this isn't correct.
Beliefs and desires are, at the end of the day, probability and
utility functions. (Or at least they are approximations to those
functions.) 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 the
language of possible worlds. The standard view is that propositions
are (or at least determine) sets of possible worlds, and that the
content of a belief is a proposition. To believe something then is to
locate yourself within a class of possible worlds; to believe that you
inhabit one of the worlds at which the proposition is true.
Lewis's view is that properties are (or at least determine) sets
of possible individuals, and that the content of a belief is a
property. To believe something then is to locate yourself within a
class of possible individuals; to believe that you are one of the
individuals with the property. More simply, beliefs are the
self-ascriptions of properties.



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



Lewis's suggestion about how to think of self-locating mental
states has recently been very influential in a variety of areas. Adam
Elga (2001, 2004) has extensively investigated the consequences of
Lewis's approach for decision theory. Andy Egan (2007) has
developed a novel form of semantic relativism using Lewis's
approach as a model. Daniel Nolan (2007) has recently argued that
Lewis's approach is less plausible for desire than for belief,
and Robert Stalnaker (2008) argues that the view makes the wrong
judgments about sameness and difference of belief across agents and
times.


### 4.6 Natural Properties



One classic problem for interpretationism is that our dispositions
massively underdetermine contents. I believe that (healthy) grass is
green. But for some interpretations of
 'grue',
 ascribing to me the belief that grass is grue will fit my
dispositions just as well. As Lewis points out towards the end of
"New Work For a Theory of Universals" (1983e), if we are
allowed to change the interpretations of my beliefs and desires at the
same time, the fit can be made even better. This looks like a problem
for interpretationism.



The problem is of course quite familiar. In different guises it is
 Goodman's grue/green problem,
 Kripkenstein's plus/quus problem, Quine's
 gavagai
 problem, and
 Putnam's puzzle
 of the brain in a vat with true beliefs (Goodman 1955, Wittgenstein
1953, Kripke 1982, Quine 1960, Putnam 1981). One way or another it has
to be solved.



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



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



Natural properties will play a major role for Lewis. We've
already seen one place where it turns out they are needed; namely, in
saying what it is for two worlds to have an 'exact match'
of spatiotemporal regions. What Lewis means by that is that the
regions are intrinsic duplicates. And the way he analyses intrinsic
duplication in (1983e) is that two things are duplicates if they have
the same intrinsic properties. We will see many other uses of natural
properties as we go along, particularly in the discussion of Humean
supervenience in section 5.



But as Lewis (1983e) makes clear, natural properties play many more
roles in his larger philosophy, including in the theory of
rationality, the theory of mental content, the theory of linguistic
content, and the theory of laws. It is rational to have a belief with
a more natural rather than a less natural content. If two different
assignments of beliefs and desires would make equally good sense of an
agent's dispositions, the more natural assignment is the correct
one. If two different interpretations of the words of a public
language would make equally good sense of speakers' practices,
the more natural interpretation is the correct one. And laws are
simple generalisations, where simplicity is defined in part in terms
of naturalness.



There is some scholarly dispute about the relationship between the
four theses set out in the last four sentences of the preceding
paragraph. Williams (2007) argues that the thesis about laws is
explanatorily prior to some of the theses about rationality and
content. Sider (2001) argues that the third thesis is a standalone
part of Lewis's theory. Schwarz (2014), however, argues that it
isn't even a part of Lewis's theory. Weatherson (2003)
endorses Sider's view, but later Weatherson (2013) endorses
Schwarz's critique of Sider's interpretation, while
arguing that a qualified version of the third thesis can nevertheless
be derived from the first two. (A version of Schwarz's paper had
been in circulation since 2006, so it well precedes Weatherson's
2013 paper, despite the slightly later publication date.)
Janssen-Lauret and MacBride (2020) respond to Schwarz, arguing that
evidence from Lewis's recently available correspondence supports
the view that Lewis took naturalness to play a central role in
determining the reference of individual words.



This topic, natural properties, was one of very few topics where Lewis
had a serious change of view over the course of his career. Of course,
Lewis changed the details of many of his views, in response to
criticism and further thought. But the idea that some properties could
be natural, could make for objective similarity, in ways that most
sets of possibilia do not, is notably absent from his writings before
"New Work". Indeed, as late as "Individuation by
Acquaintance and by Stipulation" (1983c), he was rather
dismissive of the idea. But natural properties came to play central
roles in his metaphysics and, as we see here, his theory of mind. As
Lewis notes in "New Work", much of the impetus for his
change of view came from discussions with D. M. Armstrong, and from
the arguments in favour of universals that Armstrong presented in his
(1978).


## 5. Humean Supervenience



Many of David Lewis's papers in metaphysics were devoted to
setting out, and defending, a doctrine he called "Humean
Supervenience". Here is Lewis's succinct statement of the
view.



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



The doctrine can be factored into two distinct theses. The first is
the thesis that, in John Bigelow's words, "truth
supervenes on being". That is, all the truths about a world
 supervene
 on the distribution of perfectly natural properties and relations in
that world. The second is the thesis that the perfectly natural
properties and relations in this world are
 intrinsic properties
 of point-sized objects, and spatiotemporal relations. Lewis held that
the first of these was necessary and a priori. (See, for instance,
"Parts of Classes" (1991a), "Reduction of
Mind", "Truthmaking and Difference-making" (2001d).)
The second is contingently true if true at all. Indeed, modern physics
suggests that it is not true (Maudlin 2007: Ch. 2). Lewis was aware of
this. His aim in defending Humean supervenience was to defend, as he
put it, its "tenability" (1986a: xi). We will return at
the end of this section to the question of why he might have wanted to
do this. For now, we will focus on how he went about this project.



The primary challenge to Humean supervenience comes from those who
hold that providing a subvenient basis for all the truths of this
world requires more than intrinsic properties of point-sized objects
and spatiotemporal relations. Some of these challenges come from
theorists who think best physics will need non-spatiotemporal
relations in order to explain
 Bell's Theorem.
 But more commonly it comes from those who think that grounding the
modal, the nomic or the mental requires adding properties and
relations to any Humean mosaic constructed from properties found in
fundamental physics. (I'm using 'mental' here to
cover all the properties that Lewis considered mental, broadly
construed. This includes contents, since Lewis thought content was
grounded in mental content, and value, since he thought values were
grounded in idealised desires. So it's a fairly broad category,
and there is a lot that isn't obviously reducible to fundamental
physics. As we'll see, Lewis attempts to reduce it all
step-by-step.)



We've discussed in the previous section how Lewis aimed to
reduce the mental to the nomic. (Or at least much of it; we'll
return to the question of value in section 7.5.) We'll discuss
in the next section his distinctive modal metaphysics. In this section
we'll look at how he attempted to locate the nomic in the Humean
mosaic. Lewis's aim was to show that nomic properties and
relations could be located in the Humean mosaic by locating them as
precisely and as explicitly as he could. So the location project
revealed a lot about these nomic features. We'll spend the next
two subsections looking at the two important parts of this project.
Notably, they are two parts where Lewis refined his views several
times on the details of the location.


### 5.1 Laws and Chances



Lewis's reductionist project starts with
 laws of nature.
 Building on some scattered remarks by Ramsey and Mill, Lewis proposed
a version of the 'best-system' theory of laws of nature.
There is no paper devoted to this view, but it is discussed in section
3.3 of *Counterfactuals*, in "New Work For a Theory of
Universals", 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 truths
are simple, e.g. the truth that this table is brown. Some truths are
strong; they tell us a lot about the world. For example, the
conjunction of every truth in this Encyclopedia rules out a large
chunk of modal space. Typically, these are exclusive categories;
simple truths are not strong, and strong truths are not simple. But
there are some exceptions. The truth that any two objects are
attracted to one another, with a force proportional to the product of
their masses and inversely proportional to the distance between them,
is relatively simple, but also quite strong in that it tells us a lot
about 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 view
of laws. It is collections of truths, not individual truths, that are
measured and compared for simplicity and strength. And it is not every
truth in the winning collection (or best system), but only the
generalisations within it, that are laws. So even if the best system
includes particular facts about the Big Bang or its immediate
aftermath, e.g. that the early universe was a low entropy state, those
facts are not laws on Lewis's view.



In "New Work For a Theory of Universals", Lewis notes
another restriction that is needed. If we measure the simplicity of
some truths by the length of their statement in an arbitrarily chosen
language, then any truth at all can be made simple. Let *Fx* be
true if and only if *x* is in a world where every truth in this
Encyclopedia is true. Then *Everything is F* is simply
stateable in a language containing *F*, and is presumably
strong. So *Everything is F* will be a law. But this kind of
construction would clearly trivialise the theory of laws.
Lewis's solution is to say that we measure the simplicity of a
claim by how easily stateable it is in a language where all predicates
denote *perfectly natural* properties. He notes that this move
requires that the natural properties are specified prior to specifying
the laws, which means that we can't reductively specify
naturalness in terms of laws. (In any case, since Lewis holds that
laws are contingent (1986a: 91) but which properties are natural is
not contingent (1986a: 60n), this approach would not be open to
Lewis.)



In "Humean Supervenience Debugged", Lewis notes how to
extend this theory to indeterministic worlds. Some laws don't
say what will happen, but what will have a chance of happening. If the
chances of events could be determined antecedently to the laws being
determined, we could let facts about chances be treated more or less
like any other fact for the purposes of our 'competition'.
But, as we'll see, Lewis doesn't think the prospects for
doing this are very promising. So instead he aims to reduce laws and
chances simultaneously to distributions of properties.



Instead of ranking collections of truths by two measures, strength and
simplicity, we will rank them by three, strength, simplicity and fit.
A collection of truths that entails that what does happen has (at
earlier times) a higher chance of happening has better fit than a
collection that entails that what happens had a lower chance of
happening. The laws are those generalisations in the collection of
truths that do the best by these three measures of strength,
simplicity and fit. The collection will entail various
'history-to-chance' conditionals. These are conditionals
of the form *If Ht then Pt(A) = x*, where
*Ht* is a proposition about the history of the world
to *t*, and *Pt* is the function from
propositions to their chance at *t*. The chance of *A*
at *t* in *w* is *x* if and only if there is some
such conditional *If Ht then Pt(A) = x*,
where *Ht* is the history of *w* to
*t*.



The position that I've sketched here is the position that Lewis
says that he originally was drawn towards in 1975, and that he
endorsed in print in 1994. (The dates are from his own description of
the evolution of his views in (1994a).) But in between, in both
(1980a) and Postscript C to its reprinting in (1986b), he rejected
this position because he thought it conflicted with a non-negotiable
conceptual truth about chance. This truth was what he called the
"Principal Principle".



The Principal Principle says that a rational agent conforms their
credences to the chances. More precisely, it says the following is
true. Assume we have a number *x*, proposition *A*, time
*t*, rational agent whose evidence is entirely about times up
to and including *t*, and a proposition *E* that (a) is
about times up to and including *t* and (b) entails that the
chance of *A* at *t* is *x*. In any such case,
the agent's credence in *A* given *E* is
*x*.



An agent who knows what happens after *t* need not be guided by
chances at *t*. If I've seen the coin land heads, that
its chance of landing heads was 0.5 at some earlier time is no reason
to have my credence in heads be 0.5. Conversely, if all I know is that
the chance is 0.5, that's no reason for my conditional credence
in heads to be 0.5 conditional on anything at all. Conditional on it
landing heads, my credence in heads is 1, for instance. But given
these two restrictions, the Principal Principle seems like a good
constraint. Lewis calls evidence about times after *t*
'inadmissible', which lets us give a slightly more concise
summary of what the Principal Principle says. For agents with no
inadmissible evidence, the rational credence in *A*,
conditional on the chance of *A* being *x*, combined
with any admissible evidence, is *x*.



The problem Lewis faced in the 1980s papers is that the best systems
account of chance makes the Principal Principle either useless or
false. Here is a somewhat stylised example. (I make no claims about
the physical plausibility of this setup; more plausible examples would
be more complicated, but would make much the same point.) Let
*t* be some time before any particle has decayed. Let
*A* be the proposition that every radioactive particle will
decay before it reaches its actual half-life. At *t*,
*A* has a positive chance of occurring. Indeed, its chance is 1
in 2*n*, where *n* is the number of
radioactive particles in the world. (Assume, again for the sake of our
stylised example, that *n* is finite.) But if *A*
occurred, the best system of the world would be different from how it
actually is. It would improve fit, for instance, to say that the
chance of decay within the actual half-life would be 1. So someone who
knows that the chance of *A* is 1 in 2*n*
knows that *A* won't happen.



Lewis called *A* an 'undermining' future; it has a
chance of happening, but if it happens the chances are different. The
problem with underminers is that they conflict with the Principal
Principle. Someone who knows the chance of *A* should, by the
Principal Principle, have credence 1 in 2*n* that
*A* will happen. But given the chance of *A*, it is
possible to deduce ~*A*, and hence have credence in *A*.
This looks like an inconsistency, so like any principle that implies a
contradiction, the Principal Principle must be false. The most obvious
way out is to say that information about the chance of *A* is
inadmissible, since it reveals something about the future, namely that
*A* doesn't occur. But to say that chances are
inadmissible is to make the Principal Principle useless. So given the
best systems theory of laws and chances, the Principal Principle is
either false or useless. Since the Principal Principle is neither
false nor useless, Lewis concluded in these 1980s papers that the best
systems theory of laws and chances was false.



The problem with this was that it wasn't clear what could
replace the best systems theory. Lewis floated two approaches in the
postscripts to the reprinting of (1980a), one based on primitive
chances, and the other based on history-to-chance conditionals being
necessary. But neither seemed metaphysically plausible, and although
each was consistent with the Principal Principle, they made it either
mysterious (in the first case) or implausible (in the second). A
better response, as set out in "Humean Supervenience
Debugged", was to qualify the Principal Principle. Lewis said
that what was really true was the "New Principle". His
proposal was based on ideas developed by Ned Hall (1994) and Michael
Thau (1994).



We'll explain the New Principle by starting with a special case
of the old Principle. Let *T* be the 'theory of
chance' for the world, the conjunction of all history-to-chance
conditionals. And let *H* be the history of the world to
*t*. Assuming *T* is admissible, the old Principal
Principle says that the credence in *A* given *H* [?]
*T* should be the chance of *A* at *t*. The New
Principle says that the credence in *A* given *H* [?]
*T* should be the chance of *A* given *T* at
*t*. That is, where *C* is the agent's credence
function, and *P* is the chance function, and the agent has no
inadmissible evidence, it should be that *C*(*A* |
*H* [?] *T*) = *P*(*A* | *T*).
This compares to the old principle, which held that
*C*(*A* | *H* [?] *T*) =
*P*(*A*).



That's the special case of the New Principle for an agent with
no inadmissible evidence. The general case follows from this special
case. In general, assuming the agent has no inadmissible evidence, the
rational credence in *A* given *E* is the expected
value, given *E*, of the chance of *A* given *H*
[?] *T*. That is, where *C* is the agent's
credence function, and *P* is the chance function, it should be
the sum across all possible combinations of *H* and *T*
of *C*(*H* [?] *T* |
*E*)*P*(*A* | *H* [?] *T*).



The New Principle is, Lewis argues, consistent with the best systems
theory of laws and chances. Lewis had originally thought that any
specification of chance had to be consistent with the Principal
Principle. But in later works he argued that the New Principle was a
close enough approximation to the Principal Principle that a theory of
chances consistent with it was close enough to our pre-theoretic
notion of chance to deserve the name. So he could, and did, happily
endorse the best systems theory of laws and chance.


### 5.2 Causation



In "Causation" (1973b), Lewis put forward an analysis of
 causation in terms of counterfactual dependence.
 The idea was that event *B* was counterfactually dependent on
event *A* if and only if the counterfactual *Had A not
occurred, B would not have occurred* was true. Then event
*C* causes event *E* if and only if there is a chain
*C*, *D*1, ..., *D*n,
*E* such that each member in the chain (except *C*) is
counterfactually 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 many
thought unavoidable for a counterfactual theory of causation, namely
the problem of pre-empting causes. Imagine that Suzy throws a rock,
the rock hits a window and the window shatters. Suzy's throw
caused the window to shatter. But there is a backup
thrower--Billy. Had Suzy not thrown, Billy would have thrown
another rock and broken the window. So the window breaking is not
counterfactually dependent on Suzy's throw. Lewis's
solution was to posit an event of the rock flying towards the window.
Had Suzy not thrown, the rock would not have been flying towards the
window. And had the rock not been flying towards the window, the
window would have not shattered. Lewis's thought here is that it
is Suzy's throwing that causes Billy to not throw; once she has
thrown Billy is out of the picture and the window's shattering
depends only on what Suzy's rock does. So we avoid this problem
of pre-empters.



Much of the argumentation in "Causation" concerns the
superiority of the counterfactual analysis to deductive-nomological
theories. These arguments were so successful that from a contemporary
perspective they seem somewhat quaint. There are so few supporters of
deductive-nomological theories in contemporary metaphysics that a
modern paper would not spend nearly so much time on them.



After "Causation" the focus, at least of those interested
in reductive theories, moved to counterfactual theories. And it became
clear that Lewis had a bit of work left to do. He needed to say more
about the details of the notion of counterfactual dependence. He did
this in "Counterfactual Dependence and Time's Arrow"
(1979c), as discussed in section 2. He needed to say more about the
nature of events. In "Events" (1986g) he said that they
were natural properties of regions of space-time. (At this stage he
assumed that events were the relata of the causal relation. This
assumption is criticised by L. A. Paul (2000), and in (2004d) Lewis
drops it.) And prodded by Jaegwon Kim (1973), he needed to add that
*A* and *B* had to be wholly distinct events for
*B* to counterfactually depend on *A*. The alternative
would be to say that an event's happening is caused by any
essential part of the event, which is absurd.



But the biggest problem concerned what became known as "late
pre-emption". In the rock throwing example above, we assumed
that Billy decided not to throw when he saw Suzy throwing. But we can
imagine a variant of the case where Billy waits to see whether
Suzy's rock hits, and only then decides not to throw. In such a
case, it is the window's shattering, not anything prior to this,
that causes Billy not to throw. That means that there is no event
between Suzy's throw and the window's shattering on which
the shattering is counterfactually dependent.



Lewis addressed this issue in "Redundant Causation", one
of the six postscripts to the reprinting of "Causation" in
(1986b). He started by introducing a new concept: quasi-dependence.
*B* quasi-depends on *A* if and only if there is a
process starting with *A*\*, and ending with *B*\* , and
*B*\* counterfactually depends on *A*\*, and the process
from *A*\* to *B*\* is an intrinsic duplicate of the
process from *A* to B, and the laws governing the process from
*A*\* to *B*\* (i.e. the laws of the world in which
*A*\* and *B*\* happen) are the same as the laws governing
the process from *A* to *B*. In short, quasi-dependence
is the relation you get if you start with dependence, then add all of
the duplicates of dependent processes. Causation is then the ancestral
of quasi-dependence. Although the window's shattering does not
depend on Suzy's throw, it does quasi-depend on it. That's
because there is a world, with the same laws, with a duplicate of
Suzy's throw, but Billy determined not to throw, and in that
world the window shatters in just the same way, and depends on
Suzy's throw.



Eventually, Lewis became unsatisfied with the quasi-dependence based
theory. In "Causation as Influence" (2000a, 2004a) he set
out several reasons for being unhappy with it, and a new theory to
supersede it.



One argument against it is that it makes causation intrinsic to the
pair *C* and *E*, but some cases, especially cases of
*double prevention*, show that causation is extrinsic. Double
prevention occurs when an event, call it *C*, prevents
something that would have prevented *E* from happening.
Intuitively, these are cases of causation. Indeed, when we look at the
details we find that many everyday cases of causation have this
pattern. But that *C* causes *E* does not depend on the
intrinsic natures of *C* and *E*. Rather, it depends on
there being some threat to *E*, a threat that *C*
prevents, and the existence of threats is typically extrinsic to
events.



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



Lewis's alternative theory relied on changing the definition of
counterfactual dependence. The theory in "Causation" was
based on what he came to call 'whether-whether'
dependence. What's crucial is that *whether* *B*
happens depends counterfactually on *whether* *A*
happens. The new theory was based on what we might call
'how-how' dependence. Lewis says that *B* depends
on *A* if there are large families of counterfactuals of the
form *If *A* had happened in this way, then *B* would
have happened in that way*, and the ways in which *B* would
happen are systematically dependent on the ways in which *A*
happens. How much *A* influences *B* depends on how big
this family is, how much variation there is in the way *B*
changes, and how systematic the influence of *A* on *B*
is. He then defines causation as the ancestral of this notion of
counterfactual dependence.



On this new theory, causation is a degree concept, rather than an
'all-or-nothing' concept, since counterfactual dependence
comes in degrees. Sometimes Lewis says we properly ignore small
amounts of causation. For instance, the location of nearby parked cars
influences the smashing of a window by a rock in virtue of small
gravitational effects of the cars on the flight of the rock. But
it's very little influence, and we properly ignore it most of
the time.



There are two other notable features of "Causation as
Influence". It contains Lewis's most comprehensive defence
of the transitivity of causation. This principle was central to
Lewis's theory of causation from the earliest days, but had come
under sustained attack over the years. And the paper has a brief
attack on non-Humean theories that take causation to be a primitive.
Lewis says that these theories can't explain the variety of
causal relations that we perceive and can think about. These passages
mark an interesting change in what Lewis took to be the primary
alternatives to his counterfactuals based reductionism. In 1973 the
opponents were other kinds of reductionists; in 2000 they were the
non-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 clear
in "Finkish Dispositions" (1997b), the reduction is not as
simple as it might have seemed. Perception is reduced to dispositions
and causes. (See, for instance, "Veridical Hallucination and
Prosthetic Vision" (1980d).) We discussed the reduction of
mental content to dispositions and causes in section 4. And we
discussed the reduction of linguistic content to mental content in
section 1. Values are reduced to mental states in "Dispositional
Theories of Value" (1989b).



But we might worry about the very foundation of the project. We
started with the assumption that our subvenient base consists of
intrinsic properties of point-sized objects and spatiotemporal
relations. But Bell's inequality suggests that modern physics
requires, as primitive, other relations between objects. (Or it
requires intrinsic properties of dispersed objects.) So Humean
supervenience fails in this world.



Lewis's response is somewhat disarming. Writing in 1986, part of
his response is scepticism about the state of quantum mechanics.
(There is notably less scepticism in "How Many Lives Has
Schrodinger's Cat" (2004b).) But the larger part of
his response is to suggest that scientific challenges to Humean
supervenience are outside his responsibility.



> 
> Really, what I uphold is not so much the truth of Humean supervenience
> as the *tenability* of it. If physics itself were to teach me
> that it is false, I wouldn't grieve ... What I want to fight are
> *philosophical* arguments against Humean supervenience. When
> philosophers claim that one or another common-place feature of the
> world cannot supervene on the arrangement of qualities, I make it my
> business to resist. Being a commonsensical fellow (except where
> unactualized possible worlds are concerned) I will seldom deny that
> the features in question exist. I grant their existence, and do my
> best to show how they can, after all, supervene on the arrangement of
> qualities. (1986b: xi)
> 



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



Recall that we said that Humean supervenience is a conjunction of
several theses. One of these is a thesis about which perfectly natural
properties are instantiated in this world, namely local ones. That
thesis is threatened by modern physics. But the rest of the package,
arguably, is not. In particular, the thesis that all facts supervene
on the distribution of perfectly natural properties and relations does
not appear to be threatened. (Though see Maudlin (2007: Ch. 2) for a
dissenting view.) Nor is the thesis that perfectly natural properties
and relations satisfy a principle of recombination threatened by
modern physics. The rough idea of the principle of recombination is
that any distribution of perfectly natural properties is possible.
This thesis is Lewis's version of the Humean principle that
there are no necessary connections between distinct existences, and
Lewis is determined to preserve as strong a version of it as he
can.



Although physics does not seem to challenge these two theses, several
philosophers do challenge them on distinctively philosophical grounds.
Some of them suggest that the nomic, the intensional, or the normative
do not supervene on the distribution of perfectly natural properties.
Others suggest that the nomic,
 intentional,
 or normative properties are perfectly natural, and as a consequence
perfectly natural properties are not freely recombinable. The
philosophical arguments in favour of such positions rarely turn on the
precise constitution of the Humean's preferred subvenient base.
If Lewis can show that such arguments fail in the setting of classical
physics, then he'll have refuted all of the arguments against
Humean superveience that don't rely on the details of modern
physics. In practice that means he'll have refuted many, though
not quite all, of the objections to Humean supervenience.



A broader reason for Lewis to care about Humean supervenience comes
from looking at his overall approach to metaphysics. When faced with
something metaphysically problematic, say
 free will,
 there are three broad approaches. Some philosophers will argue that
free will can't be located in a scientific world-view, so it
should be eliminated. Call these 'the eliminativists'.
Some philosophers will agree that free will can't be located in
the scientific world-view, so that's a reason to expand our
metaphysical picture to include free will, perhaps as a new primitive.
Call these 'the expansionists'. And some philosophers will
reject the common assumption of an incompatibility. Instead they will
argue that we can have free will without believing in anything that
isn't in the scientific picture. Call these 'the
compatibilists'.



As the above quote makes clear, Lewis was a compatibilist about most
questions in metaphysics. He certainly was one about free will.
("Are We Free to Break the Laws?" (1981a).) And he was a
compatibilist 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 and
Actuality" (1970a), "Divine Evil" (2007)). And in
some sense he was an expansionist about modality. Lewis may have
contested this; he thought introducing more worlds did not increase
the number of kinds of things in our ontology, because we are already
committed to there being at least one world. As Melia (1992: 192)
points out though, the inhabitants of those worlds include all kinds
of things not found in, or reducible to, fundamental physics. They
include spirits, gods, trolls and every other consistent beast
imaginable. So at least when it came to what there is, as opposed to
what there actually is, Lewis's ontology was rather
expansionist.



For all that, Lewis's default attitude was to accept that much
of our common-sense thinking about the nomic, the intentional and the
normative was correct, and that this was perfectly compatible with
this world containing nothing more than is found in science, indeed
than is found in fundamental physics.



Compatibilists should solve what Frank Jackson calls 'the
location problem' (Jackson 1998). If you think that there are,
say, beliefs, and you think that having beliefs in one's
metaphysics doesn't commit you to having anything in your
ontology beyond fundamental physics, then you should, as Jackson puts
it, be able to *locate* beliefs in the world described by
fundamental physics. More generally, for whatever you accept, you
should be able to locate it in the picture of the world you
accept.



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



What Lewis's defence of Humean supervenience gives us is a
recipe for locating the nomic, intentional and normative properties in
a physical world. And it is a recipe that uses remarkably few
ingredients; just intrinsic properties of point-sized objects, and
spatio-temporal relations. It is likely that ideal physics will have
more in it than that. For instance, it might have entanglement
relations, as are needed to explain Bell's inequality. But it is
unlikely to have less. And the more there is in fundamental physics,
the *easier* it is to solve the location problem, because the
would-be locator has more resources to work with.



The upshot of all this is that a philosophical defence of Humean
supervenience, especially a defence like Lewis's that shows us
explicitly how to locate various folk properties in classical physics,
is likely to show us how to locate those properties in more up-to-date
physics. So Lewis's defence of Humean supervenience then
generalises into a defence of the compatibility of large swathes of
folk theory with ideal physics. And the defence is consistent with the
realist principle that truth supervenes on being, and with the Humean
denial 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 diverse
contributions to philosophy. But there is one thesis with which he is
associated above all others: modal realism. Lewis held that this world
was just one among many like it. A proposition, *p* is possibly
true if and only if *p* 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 like
*You are happy* to be true in another world is not for you to
be happy in that world; you aren't in that world. Rather, it is
for your *counterpart* to be happy in that world.



Lewis wrote about modal realism in many places. As early as
*Counterfactuals* he wrote this famous passage.



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



And Lewis used counterpart theory throughout his career to resolve
metaphysical puzzles in fields stretching from
 personal identity
 ("Counterparts of Persons and Their Bodies" (1971c)) to
 truthmaker theory
 ("Things qua Truthmakers" (2003b)). Indeed, Lewis's
original statement of counterpart theory is in one of his first
published metaphysics papers ("Counterpart Theory and Quantified
Modal Logic" (1968)).



But the canonical statement and defence of both modal realism and
counterpart theory is in *On the Plurality of Worlds* (1986a),
the book that grew out of his 1984 John Locke lectures. This section
will follow the structure of that book.



The little 'argument by paraphrase' from
*Counterfactuals* is a long way from an argument for
Lewis's form of modal realism. For one thing, the argument
relies on taking a folksy paraphrase as metaphysically revealing;
perhaps we would be better off treating this as just a careless manner
of speaking. For another, the folksy paraphrase Lewis uses isn't
obviously innocuous; like many other abstraction principles it could
be hiding a contradiction. And the argument does little to show that
other possible worlds are concreta; talking of them as ways things
could be makes them sound like properties, which are arguably
abstracta if they exist at all. The first three chapters of
*Plurality* address these three issues. The fourth chapter is
an 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 from *Counterfactuals* that I quoted seems
deeply unQuinean. Rather than saying that possible worlds exist
because they are quantified over in the best paraphrase of our
theories, Lewis says they exist because they are quantified over in
just one
 paraphrase
 of our theories. To be sure, he says this is a permissible
paraphrase. On the other hand, there is vanishingly little defence of
its permissibility.



In the first chapter of *Plurality* Lewis takes a much more
orthodox Quinean line. He argues, at great length, that the best
version of many philosophical theories requires quantification over
possibilities. In traditional terms, he offers an extended
 indispensability argument
 for unactualised possibilities. But traditional terms are perhaps
misleading here. Lewis does not say that possibilities are absolutely
indispensable, only that they make our philosophical theories so much
better that we have sufficient reason to accept them.



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


* **Modality**: Traditional treatments of modal talk in
terms of operators face several difficulties. They can't, at
least without significant cost, properly analyse talk about contingent
existence, or talk about modal comparatives, or modal supervenience
theses. All of these are easy to understand in terms of quantification
across 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't
real.
* **Content**: Lewis argues, in part following
Stalnaker (1984), that our best theory of mental and verbal content
analyses content in terms of sets of possibilities. This, in turn,
requires that the possibilities exist.
* **Properties**: We often appear to quantify over
properties. The modal realist can take properties to be sets of
possibilia, and take such quantification at face value. In his
discussion of properties here, Lewis expands upon his theory of
natural properties that he introduced in "New Work for a Theory
of Universals", and that we discussed in section 3.



After arguing that we are best off in all these areas of philosophy if
we accept unactualised possibilities, Lewis spends the rest of chapter
1 saying what possible worlds are on his view. He isn't yet
arguing for this way of thinking about possible worlds; that will come
in chapter 3. For now he is just describing what he takes to be the
best theory of possible worlds. He holds that possible worlds are
isolated; no part of one is spatio-temporally related to any other
world. Indeed, he holds that lack of spatio-temporal relation (or
something like it) is what marks individuals as being in different
worlds. So his theory has the somewhat odd consequence that there
could not have been two parts of the world that aren't
spatio-temporally connected. He holds that worlds are concrete, though
spelling out just what the abstract/concrete distinction comes to in
this context isn't a trivial task. And he holds that worlds are
plenitudinous, there are enough of them to do the work needed for an
analysis of modality. This requires at least that they satisfy a
principle of recombination. But since it is possible that things are
different in kind to anything that actually exists, plenitude implies
that there are worlds that can't be made by simply putting parts
of this world together. (Alastair Wilson (forthcoming) has a good survey of
the complicated relationship between plenitude and recombination.)


### 6.2 Paradox in Paradise?



Chapter 2 deals with several objections to modal realism. Some of
these objections claim that modal realism leads to paradox. Other
objections claim that it undermines our ordinary practice. We will
look at two examples of each.



Peter Forrest and D. M. Armstrong (1984) argue that modal realism
leads to problems given the principle of recombination. An
unrestricted principle of recombination says that for any things that
could exist, there is a world in which there is a duplicate of all of
them. Forrest and Armstrong apply the principle by taking the things
to be the different possible worlds. A world containing a duplicate of
all the worlds would, they show, be bigger than any world. But by the
principle it would also be a world. Contradiction. Lewis' reply
is to deny the unrestricted version of the principle. He insists that
there is independent reason to qualify the principle to those things
whose size and shape permits them to be fit into a single world.
Without an unrestricted principle of recombination, there is no way to
create the large world that's at the heart of Forrest and
Armstrong'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 version
presented by Martin Davies (1981: 262). On Lewis's theory, every
set of worlds is a proposition. For any proposition, says Kaplan, that
proposition might be the only proposition being thought by a person at
location *l* at time *t*. So for each proposition, there
is a world where it (alone) is thought by a person at location
*l* at time *t*. That means there is a one-one
correspondence between the sets of worlds and a subset of the worlds.
Contradiction. Lewis's reply is to deny that every proposition
can be thought. He claims that functionalism about belief, plus the
requirement that beliefs latch onto relatively natural properties,
mean that most propositions cannot be thought, and this blocks the
paradox.



Peter Forrest (1982) argues that modal realism leads to inductive
scepticism. According to modal realism, there are other thinkers very
much like us who are deceived by their surroundings. Given this, we
should doubt our inductive inferences. Lewis's reply is that
modal realism does not make inductive challenges any worse than they
were 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 might
focus the mind on them, and hence make us less confident, but does not
seem to change the inference's justificatory status.
Lewis's argument seems hard to dispute here. Given the mutually
agreed upon fact that the inference could fail, it's hard to see
what epistemological cost is incurred by agreeing that it does fail
for someone kind of like the inferrer in a distant possible world.



Robert Adams (1974) argues that modal realism leads to surprising
results in moral philosophy. The modal realist says that the way
things are, in the broadest possible sense, is not a contingent
matter, since we can't change the nature of the pluriverse.
Hence we cannot do anything about it. So if moral requirements flow
from a requirement to improve the way things are, in this broadest
possible sense, then there are no moral requirements. Lewis rejects
the antecedent of this conditional as something that only an extreme
utilitarian could accept. What is crucial about morality is that
*we* not do evil. Even if their actions won't make a
difference to the nature of the pluriverse, a virtuous agent will not
want to, for instance, cause suffering. By rejecting the view that in
our moral deliberations we should care about everyone, possible and
actual, equally, Lewis avoids the problem.


### 6.3 Paradise on the Cheap?



In chapter 3 Lewis looks at the alternatives to his kind of modal
realism. He takes himself to have established that we need to have
possible worlds of some kind in our ontology, but not that these
possible worlds must be concrete. In particular, they can be abstract,
or what he calls "ersatz" possible worlds. Lewis does not
have a single knock-down argument against all forms of ersatzism.
Instead he divides the space of possible ersatzist positions into
three, 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, and
the way they represent possibilities is something like the way that
language represents possibilities. In particular, they represent
possibilities without resembling possibilities, but instead in virtue
of structural features of the representation.



He levels three main objections to linguistic ersatzism. First, it
takes modality as a primitive, rather than reducing modality to
something simpler (like concrete possible worlds). Second, it
can't distinguish qualitatively similar individuals in other
possible worlds. Lewis argues that will mean that we can't
always quantify over possibilia, as we can in his theory. Third, it
can't allow as full a range of 'alien', i.e.
uninstantiated, natural properties as we would like. Sider (2002) has
replied that some of these challenges can be met, or at least reduced
in 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 "pictoral
ersatzism". This is the view that ersatz possible worlds are
representations, and the way they represent possibilities is something
like the way that pictures or models represent possibilities. That is,
they represent by being similar, in a crucial respect, to what they
are representing. The pictoral ersatzist, says Lewis, is caught in
something of a bind. If the representations are not detailed enough,
they will not give us enough possibilities to do the job that possible
worlds need to do. If they are detailed enough to do that job, and
they represent by resembling possibilities, then arguably they will
contain as much problematic ontology as Lewisian concrete possible
worlds. So they have the costs of Lewis's theory without any
obvious advantage.



The final theory he considers is what he calls "magical
ersatzism". Unlike the previous two theories, this theory is
defined negatively. The magical ersatzist is defined by their denial
that possible worlds represent, or at least that they represent in
either of the two ways (linguistic and pictoral) that we are familiar
with. And Lewis's primary complaint is that this kind of theory
is mysterious, and that it could only seem attractive if it hides from
view the parts of the theory that are doing the philosophical work.
Lewis argues that as soon as we ask simple questions about the
relationship that holds between a possibility and actuality if that
possibility is actualised, such as whether this is an internal or
external relation, we find the magical ersatzist saying things that
are either implausible or mysterious.



It isn't clear just who is a magical ersatzist. Lewis wrote that
at the time he wrote *Plurality* no one explicitly endorsed
this theory. This was perhaps unfair to various *primitivists*
about modality, such as Adams (1974), Plantinga (1974) and Stalnaker
(1976). Given the negative definition of magical ersatzism, and given
the fact that primitivists do not think that possible worlds represent
possibilities via any familiar mechanism, it seems the primitivists
should count as magical ersatzists, or, as Lewis calls them,
"magicians". In any case, if magical ersatzism, in all its
varieties, is objectionably mysterious, that suggests ersatzism is in
trouble, and hence if we want the benefits of possible worlds, we have
to pay for them by accepting concrete possible worlds.


### 6.4 Counterparts or Double Lives?



The last chapter of *Plurality* changes tack somewhat. Instead
of focussing on different ways the world could be, Lewis's focus
becomes different ways things could be. The chapter defends, and
expands upon, Lewis's counterpart theory.



Counterpart theory was first introduced by Lewis in "Counterpart
Theory and Quantified Modal Logic" (1968) as a way of making
modal discourse extensional. Instead of worrying just what a name
inside the scope of a modal operator might mean, we translate the
language of quantified modal logic into a language without operators,
but with quantifiers over worlds and other non-actual individuals. So
instead of saying #*Fa*, we say
[?]*w*[?]*x* ((*Ww* [?] *Ixw*
[?] *Cxa*) [?] *Fx*). That is, for all *w*
and *x*, if *w* is a world, and *x* is in
*w*, and *x* is a counterpart of *a*, then
*Fx*. Or, more intuitively, all of *a*'s
counterparts are *F*. The paper shows how we can extend this
intuitive idea into a complete translation from the language of
quantfied modal logic to the language of counterpart theory. In
"Tensions" (1974a) Lewis retracts the claim that it is an
advantage of counterpart theory over quantified modal logic that it is
extensional rather than intensional, largely because he finds the
distinction between these two notions much more elusive than he had
thought. But he still thought counterpart theory had a lot of
advantages, and these were pressed in chapter 4.



The intuitive idea behind counterpart theory was that individuals, at
least ordinary individuals of the kind we regularly talk about, are
world-bound. That is, they exist in only one world. But they do not
have all of their properties essentially. We can truly say of a
non-contender, say Malloy, that he could have been a contender. In the
language of possible worlds, there is a possible world *w* such
that, according to it, Malloy is a contender. But what in turn does
this mean? Does it mean that Malloy himself is in *w*? Not
really, according to counterpart theory. Rather, a counterpart of
Malloy's is a contender in *w*. And Malloy himself has
the modal property *could have been a contender* in virtue of
having a counterpart in *w* who is a contender. This way of
thinking about modal properties of individuals has, claims Lewis, a
number of advantages.



For one thing, it avoids an odd kind of inconsistency. Malloy might
not only have been a contender, he might have been 6 inches taller. If
we think that is because there is a world in which Malloy himself is 6
inches taller, then it seems like we're saying that Malloy can
have two heights, his actual height and one 6 inches taller. And that
looks inconsistent. The obvious way out of this is to say that he
bears one height in relation to this world, and another to another
world. But that turns height from an intrinsic property into a
relation, and that seems like a mistake. Lewis thinks this problem,
what he dubs the 'problem of accidental intrinsics', is a
reason to deny that Malloy himself is in multiple worlds.



For another, it allows us a kind of inconstancy in our modal
predications. Could Malloy have been brought by a stork, or must he
have had the parents he actually had? In some moods we think one, in
other moods we think another. Lewis thinks that counterpart theory can
reflect our indecision. There is a world with someone brought by a
stork who has a life much like Malloy's. Is he one of
Malloy's counterparts? Well, he is according to some counterpart
relations, and not according to others. When one of the former
relations is contextually salient, it's true to say that Malloy
could have been brought by a stork. When more demanding counterpart
relations are salient, he isn't one of Malloy's
counterparts, and indeed all of Malloy's counterparts share his
parents. (More precisely, all of his counterparts have parents who are
counterparts of Malloy's actual parents.) In those contexts, it
is true to say that one's parentage is essential. Throughout his
career, Lewis uses this inconstancy of the counterpart relation to
resolve all manner of metaphysical puzzles, from puzzles about
personal identity (1971c) to puzzles about truthmakers (2003b). The
final section of *Plurality* is Lewis's most extended
argument that this variability of the counterpart relation is a
strength, not a weakness, of the theory.


## 7. Other Writings



Lewis wrote a lot that isn't covered by the broad categories
we've discussed so far. The point of this section is to provide
a sample of that material. It isn't close to being
comprehensive. It doesn't include his treatment of
 qualia
 in (1988h) and (1995b). It doesn't include his contributions to
 causal decision theory
 in (1979e) and (1981b). It goes very quickly over his many papers in
ethics. And it skips his contributions to debates about non-classical
logics, such as (1982c) and (1990). We've tried to restrict
attention to those areas where Lewis's contributions were
groundbreaking, influential, and set out a new positive theory.
Shockingly, there is a lot to cover that meets those constraints, and
is not included in the above survey of the major themes of his
philosophy.


### 7.1 Mathematics and Mereology



*Parts of Classes* (1991a) and "Mathematics is
Megethology" (1993d) consider the distinctive philosophical
problems raised by
 set theory.
 As Lewis notes, it is widely held that all of mathematics reduces to
set theory. But there is little consensus about what the metaphysics
of set theory is. Lewis puts forward two proposals that might,
collectively, help to clarify matters.



The first proposal is what he calls the *Main 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 are
proper classes, and hence not sets. And one set, the null set, has no
members, so is not a class. Individuals, for Lewis, are things without
members. Since the null set has no members, it is an individual. But
the overlap between the sets and the classes is large; most sets we
think about are classes.



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



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



One of the technical advances of (1991a) and (1993d) was that they
showed 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 of
the mereological atoms is an
 inaccessible cardinal),
 and given plural quantification, we can say exactly what constraints
a function must satisfy for it to do the work we want the singleton
function to do. (By 'the singleton function' I mean the
function that maps anything that has a singleton onto its singleton.
Since proper classes don't have singletons, and nor do fusions
of sets and objects, this will be a partial function.) Given that, we
can understand mathematical claims made in terms of sets/classes as
quantifications over singleton functions. That is, we can understand
any claim that would previous have used 'the' singleton
function as a claim of the form *for all s*:
...*s*...*s*..., where the terms
*s* go where we would previously have referred to
'the' singleton function. It is provable that this
translation won't introduce any inconsistency into mathematics
(since there are values for *s*), or any indeterminacy (since
the embedded sentence ...*s*...*s*... has
the same truth value for any eligible value for *s*).



Should we then adopt this structuralist account, and say that we have
removed the mysteries of mathematics? As noted above, Lewis is
uncharacteristically equivocal on this point, and seemed to change his
mind about whether structuralism was, all things considered, a good or
a bad deal. His equivocation comes from two sources. One worry is that
when we work through the details, some of the mysteries of set theory
seem to have been relocated rather than solved. For instance, if we
antecedently understood the singleton function, we might have thought
it could be used to explain why the set theoretic universe is so
large. Now we have to simply posit a very large universe. Another is
that the proposal is in some way revisionary, since it takes ordinary
mathematical talk to be surreptitiously quantificational. *Parts of
Classes* contains some famous invective directed against
philosophers who seek to overturn established science on philosophical
grounds.



> 
> I'm moved to laughter at the thought of how *presumptous*
> it would be to reject mathematics for philosophical reasons. How would
> *you* like the job of telling the mathematicians that they must
> change their ways, and abjure countless errors, now that
> *philosophy* has discovered that there are no classes? Can you
> tell them, with a straight face, to follow philosophical argument
> wherever it may lead? If they challenge your credentials, will you
> boast of philosophy's other great discoveries: that motion is
> impossible, that a Being than which no greater can be conceived cannot
> be conceived not to exist, that it is unthinkable that anything exists
> outside the mind, that time is unreal, that no theory has ever been
> made at all probable by evidence (but on the other hand that an
> empirically adequate ideal theory cannot possibly be false), that it
> is a wide-open scientific question whether anyone has ever believed
> anything, and so on, and on, *ad nauseum*? Not me! (1991a: 59)
> 



And yet Lewis's positive theory here is somewhat revisionary. It
doesn't revise the truth value of any mathematical claim, but it
does revise the understanding of them. Is even this too much revision
to make on philosophical grounds? Perhaps not, but it is worrying
enough for Lewis to conclude merely that the theory he proposes seems
better than the alternatives, not that there is a compelling positive
case for its truth.


### 7.2 Philosophy of Language



Lewis's major contribution to formal semantics was his theory of
counterfactual conditionals. But there were several other
contributions that he made, both on specific topics in formal
semantics, and on the role of semantic theory.



In "Adverbs of Quantification" (1975a), Lewis notes
several difficulties in translating sentences involving
"usually", "frequently", "rarely"
or related adverbs into first-order logic or some similar formal
system. Lewis's solution to the puzzles raised involves two
formal advances. First, he treats the adverbs as *unselective
quantifiers*, binding all free variables in their scope. The
second advance concerns the if-clauses in sentences like *Usually,
if a team plays well, they win*. It is difficult for various
reasons to take the structure of this sentence to involve a quantifier
over a compound sentence with a conditional connective. Lewis's
second advance is to say that these if-clauses are simply domain
restrictors. The 'if' is no more a sentential connective
than the 'and' in *New York is between Boston and
Washington*. Instead, the if-clause restricts what things the
quantifier denoted by 'usually' ranges over.



This paper is not widely read by philosophers, but it has been very
influential among linguists, especially semanticists. Indeed, its
uptake by semanticists has made it the fourth most cited paper of
Lewis's on
 Google Scholar.
 His most cited paper on Google Scholar is also in philosophy of
language; it is "Scorekeeping in a Language Game"
(1979f).



That paper is about conversational dynamics. Lewis develops an
extended analogy between the role of context in a conversation and the
role of score in a baseball game. One central role of the score is to
keep a record of what has already happened. In that way, score is
influenced by what happens on the field, or in the conversation. But
the causal influence runs in the other way as well. Some events on the
field are influenced by the score. You're only out after the
*third* strike, for example. Similarly, Lewis holds that
context (or the conversational score) can influence, or even be
partially constitutive of, what happens in the conversation. If I say
"None of the cats are afraid of Barney", which cats
I've managed to talk about depends on which cats are
conversationally salient. And in saying this, I've made Barney
salient, 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 otherwise
puzzling features of language. One notable example of this involves
quantification. Most quantifiers we use do not range over the entire
universe. We quantify only over a restricted range. Lewis says that it
is the salient objects. He also says that this happens not just when
we explicitly quantify, but also when we use terms that have a
quantificational analysis. He mentions in passing that
"knows" might be one such term.



This idea is developed more fully in "Elusive Knowledge"
(1996b). Lewis argues that *S knows that p* is true iff
*S* is in a position to rule out *all* possibilities in
which *p* is false. But when we say *S knows that p*, we
don't mean to quantify over all possibilities there are, only
over the salient possibilities. The big advantage of Lewis's
approach is that it lets him explain the appeal of scepticism. When
the sceptic starts talking about fantastic possibilities of error, she
makes those possibilities salient. Since we can't rule them out,
when we're talking to the sceptic we can't say we know
very much. But since those possibilities aren't usually salient,
we are usually correct in our knowledge-ascriptions. So Lewis lets the
sceptic win any debate they are in, without conceding that ordinary
knowledge-ascriptions are false.



The kind of position Lewis defends here, which came to be known as
 contextualism,
 has been a central focus of inquiry in epistemology for the last
fifteen years. "Elusive Knowledge", along with papers such
as 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 Conditional
Probabilities" (1976b) and its sequel (1986h), and "Desire
as Belief" (1988b) and its sequel (1996a). The papers have more
in common than merely having a common naming convention.
(They're not even Lewis's only sequels; "Lucas
Against Mechanism" (1969b) also has a sequel (1979d).) In both
cases Lewis aims to defend orthodox
 Bayesian epistemology
 against some challenges. And in both cases the argument turns on
principles to do with updating. Lewis was throughout his career a
Bayesian; he frequently said that the ideal epistemic agent was a
Bayesian conditionaliser and expected utility maximiser. And he
defended this position with some gusto.



The conditionals papers concern a position that was gaining popularity
before Lewis showed it was untenable. The position in question starts
with the idea that a speaker can properly say *Probably*,
*if p*, *q* if and only if their subjective probability
of *q* given *p* is high. And the position then offers
an explanation of this purported fact. The English word
'if' is a binary connective which forms a sentence to be
written as *p* - *q*, and it is true in virtue of
the meaning of this connective that *Pr*(*q* |
*p*) = Pr(*p* - *q*). So, assuming
'probably' means something like subjective probability
*Probably*, *if p*, *q* means that the subjective
probability of *p* - *q*, and, assuming the agent
is coherent, that is true just in case the subjective probability of
*q* given *p* is high.



Lewis doubted several aspects of this story. He briefly notes in
"Adverbs of Quantification" that he didn't think the
'if' in *Probably*, *if p*, *q* is a
binary connective. But the more telling objection was his proof that
there could not be a connective - such that for all *p*,
*q*, *Pr*(*q* | *p*) =
*Pr*(*p* - *q*). Lewis first argued for this
in (1976b), and showed how to weaken some of the assumptions of the
argument in (1986h). The effect of Lewis's position was to
essentially end the hope of analysing English 'if' in
terms of a binary connective with these probabilistic properties.



The desire papers (1988a, 1996b) are also about the Humean view that
motivation requires both a belief and a desire. Lewis aims to attack
the anti-Humean position that some beliefs, in particular beliefs that
a certain thing is good, can play the functional roles of both beliefs
and desires. He argues that this is not, in general, possible. And the
argument is that beliefs and desires update in different ways. Or, at
least, that anyone who updates their beliefs by conditionalisation and
updates their valuation functions in a plausible way, will not be able
to preserve a perfect correlation between their desire for a
proposition being true and their belief in that proposition's
goodness.



Both of these papers rely on the idea that conditionalisation is a
good way to update beliefs. Neither, by the way, rely on the idea that
conditionalisation is the only rational way to update beliefs; the
arguments go through given merely the permissibility of
conditionalising. Many Bayesians hold something stronger, namely that
conditionalisation is *the* way to update beliefs. One widely
used argument in favour of this position is a so-called 'Dutch
Book' argument. This argument shows that if you plan to follow
any strategy for revising beliefs other than conditionalisation, and
you do follow that strategy, then someone who knows the strategy that
you're going to follow can produce a series of bets that will
seem favourable to you when each is offered, but which will
collectively lead to a sure loss. It is also true that if you do
update by conditionalisation, there is no similar Dutch Book that can
be made, but Lewis did not prove this. (It is Theorem V in Skyrms
(1987).) The Dutch Book argument for conditionalisation was introduced
to the literature by Paul Teller (1976), who credited it to Lewis.
Lewis's own version of the argument did not appear until 1999,
in *Papers in Metaphysics and Epistemology*, under the title
"Why Conditionalize?" (1999b). This was something he had
written as a course handout in 1972, and which had been very widely
circulated, and, via Teller's paper, very influential on the
development of Bayesian epistemology.



Lewis was an early proponent of one of the two major views about the
Sleeping Beauty puzzle, which is nicely described in Sorensen
2009:



> 
> Sleeping Beauty is an ideal reasoner who knows she will be given a
> sleeping pill that induces limited amnesia. She knows that after she
> falls asleep a coin will be flipped. If it lands heads, she will be
> awakened on Monday and asked: "What is the probability that the
> coin landed heads?". She will not be informed which day it is.
> If the coin lands tails, she will be awaken on both Monday and on
> Tuesday and asked the same question each time. The amnesia insures
> that, if awakened on Tuesday she will not remember being woken on
> Monday. 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 Heads
should be 1/3. Lewis argued that the
correct answer was 1/2. The core of his
argument was that before Beauty went to sleep, her credence in Heads
should be 1/2. That was agreed on all
sides. Moreover, nothing happened that surprised Beauty. Indeed,
everything happened exactly as she expected it would. Lewis argued
that "Only new relevant evidence, centred or uncentred, produces
a change in credence" (2001c: 174), and that Beauty got no new
evidence. This idea has featured heavily in subsequent work defending
the 1/2 answer to the Sleeping Beauty
puzzle.



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



### 7.4 Philosophy of Religion



In "Anselm and Actuality" (1970a), Lewis tries to give as
good a formulation of the
 ontological argument
 as can be made in modal realist terms. This is a good framework for
discussing the ontological argument, since on one interpretation, the
argument rests crucially on cross-world comparisons of greatness and
the modal realist can make sense of that kind of talk better than
views that reject possible objects. Lewis argues that the principle
"A being than which nothing greater can be conceived is
possible" is crucially ambiguous. One kind of reading is that
the imagined being's greatness in its world is greater than the
greatness of any other being in that being's world. That may be
true, but it doesn't imply that the being actually exists.
Another kind of reading focusses on the imagined being's
greatness in this world. It says that there (actually) is a being
whose actual greatness is greater than the greatness of any possible
being. That entails the conclusion, but is not plausibly true. The
broader conclusion here, that the ontological argument derives its
persuasive force from an equivocation, is one that has been widely
adopted since Lewis's paper.



In "Evil for Freedom's Sake" (1993b), Lewis reflects
at length on the
 free will defence
 to the
 problem of evil.
 Lewis argues that for the defence to work, God must make quite
different trade-offs between freedom and welfare than we are usually
disposed to make, and our understanding of what freedom consists in,
and what divine foreknowledge consists in, must be different to what
they currently are.



In "Do We Believe in Penal Substitution?" (1997a), Lewis
notes that we only sometimes accept that one person can be properly
punished for another's misdeeds. He uses this to raise an
interesting difficulty for the Christian idea that Christ died for our
sins, suggesting this may not be a form of penal substitution that is
normally acceptable.



In "Divine Evil" (2007), Lewis suggests that proponents of
the problem of evil should not focus on what God fails to prevent, but
on what God does. In orthodox forms of theism, particularly
Christianity and Islam, God is presented as perpetrating great evil
against sinners of various stripes in the form of extreme punishments
in the afterlife. Lewis suggests that a God that does would be so evil
that we should not only reject Him, but we may regard those who
endorse the divine punishments as themselves somewhat culpable for
divine evil. (The published version of this paper was composed by
Phillip Kitcher after Lewis's death from notes Lewis made, and
conversations Kitcher had with Lewis.)


### 7.5 Ethics



Lewis is obviously not as well known for his work in ethics as for his
work in other areas of philosophy. It was something of a surprise when
one of the volumes of his collected papers was called *Papers in
Ethics and Social Philosophy* (2000a). On the other hand, the
existence of this volume indicates that there is a large body of work
that 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), and
Keller (2015).



As Nolan suggests, the least inaccurate summary of Lewis's
ethical positions is that he was a
 virtue ethicist.
 Indeed, a focus on virtue, as opposed to consequences, plays a role
in his defence of modal realism, as we saw in section 6.4. Nolan also
notes that this position is somewhat surprising. Most philosophers who
accept views related to Lewis's about psychology and
decision-making (in particular, who accept a Humean story about
beliefs and desires being the basis for motivation, and who accept
some or other version of expected utility maximisation as the basis
for rational decision) have broadly consequentialist positions. But
not Lewis.



Lewis was also a
 value pluralist
 (1984a, 1989b, 1993b). Indeed, this was part of his objection to
consequentialism. He rejected the idea that there was one summary
judgment we could make about the moral value of a person. In
"Reply to McMichael" (1978a) he complains about the
utilitarian assumption that "any sort or amount of evil can be
neutralized, as if it had never been, by enough countervailing good
--and that the balancing evil and good may be entirely
unrelated" (1978a: 85).



In meta-ethics, Lewis defended a variety of
 subjectivism
 (1989b). Like many subjectivists, Lewis held that something is
valuable for us if and only if we would value it under ideal
circumstances. And he held, following Frankfurt (1971), that valuing
something is simply desiring to desire it. What is distinctive about
Lewis's position is his view about what ideal circumstances are.
He thinks they are circumstances of "full imaginative
acquaintance". This has some interesting consequences. In
particular, it allows Lewis to say that different goods have different
conditions of full imaginative acquaintance. It might, he suggests, be
impossible to properly imagine instantiating several different values
at once. And that in turn lets him argue that his value pluralism is
consistent with this kind of subjectivism, in a way that it might not
be consistent with other varieties of subjectivism.



Lewis also wrote several more papers in applied ethics. In two
interesting papers on
 tolerance
 (1989a, 1989d), he suggests that one reason for being tolerant, and
especially of being tolerant of speech we disapprove of, comes from
game-theoretic considerations. In particular, he thinks our motivation
for tolerance comes from forming a 'tacit treaty' with
those with differing views. If we agree not to press our numerical
superiority to repress them when we are in the majority, they will do
the same. So tolerating opposing views may be an optimal strategy for
anyone who isn't sure that they will be in the majority
indefinitely. In these works it is easy to see the legacies of
Lewis's early work on philosophical lessons to be drawn from
game theory, and especially from the work of Thomas Schelling.


### 7.6 Applied Metaphysics



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



In "The Paradoxes of Time Travel" (1976d), Lewis discusses
the many complicated philosophical issues about
 time travel.
 He discusses
 temporal parts,
 personal identity, causation and causal loops, free will, and the
complications arising from our many different modal concepts. In some
cases he uses the canvas provided to illustrate his own take on the
metaphysical issues that arise. But in some cases he notes that the
problems that arise are problems for everyone.



"Holes" (Lewis and Lewis 1970) was co-written with
Stephanie Lewis. In it they discuss, in dialog form, some of the
metaphysical issues that holes generate. One of the characters, Argle,
wants to eliminate holes from his ontology, and the paper goes over
what costs must be met to make this form of
 nominalism
 work. The other character, Bargle, pushes Argle to clarify his
commitments, and in doing so draws out many details of the nominalist
framework. The case is of some interest in itself, but it is also, as
the authors note at the end, a useful case-study in the kind of moves
nominalists can make in eliminating unwanted ontology, and the costs
of those moves.



Each paper can be, and indeed often has been, used for introducing
complicated metaphysical issues to students. The papers are, like many
of Lewis's papers, widely anthologised. They are both excellent
illustrations of the fact that, as well as being a wonderful
philosopher, Lewis was one of the best philosophical writers of his
time.