\documentclass{article} %
\newcommand{\vars}[3][x]{\ensuremath{#1_{#2}, \dots, #1_{#3}}}
\usepackage{amssymb}
\usepackage{endnotes}
\usepackage[round, authoryear]{natbib}
\linespread{1.3} %% double-spacing
\title{Possible Worlds I: Modal Realism}
%\author{Louis deRosset}

\begin{document}
  \maketitle
  
  % \begin{abstract}
  %   It is difficult to wander far in contemporary metaphysics without
  %   bumping into talk of possible worlds.  And reference to possible
  %   worlds is not confined to metaphysics.  It can be found in
  %   contemporary epistemology and ethics, and has even found its way
  %   into linguistics and decision theory.  But what are those possible
  %   worlds, the entities to which theorists in these disciplines all
  %   appeal?  This paper sets out and evaluates a leading contemporary
  %   theory of possible worlds, David Lewis's Modal Realism.  I note
  %   two competing ambitions for a theory of possible worlds: that it
  %   be reductive and user-friendly.  I then outline Modal Realism and
  %   consider objections to the effect that it cannot satisfy these
  %   ambitions.  I conclude that there is some reason to believe that
  %   Modal Realism is not reductive and overwhelming reason to believe
  %   that it is not user-friendly.
  % \end{abstract}

  It is difficult to wander far in contemporary metaphysics without
  bumping into talk of possible worlds.  And reference to possible
  worlds is not confined to metaphysics.  It can be found in
  contemporary epistemology and ethics, and has even found its way
  into linguistics and decision theory.  But what are those possible
  worlds, the entities to which theorists in these disciplines all
  appeal?
    
  Call any attempt to answer this question a \emph{theory of possible
    worlds}.  This paper sets out and evaluates a leading contemporary
  theory of possible worlds.  The view's principal proponent is David
  Lewis, and his label for it is `Modal Realism,' which I will
  abbreviate `MR.'\linespread{1}\endnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {Plantinga \citeyearpar{Plantinga:1987} argues that labelling
    Lewis's view ``Modal Realism'' is inappropriate.  The label has
    nevertheless stuck.  I use the abbreviation `MR' in order to avoid
    terminological controversy.  Lewis is not the only defender of MR.
    Others include \citep{Bricker:2001, Bricker:2006, Bricker:2008}
    and \citep{McDaniel:2004, McDaniel:2006}.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} The view accepts the following systematic
  correspondence between certain modal facts and facts regarding the
  existence of possible worlds:
  \begin{description}
    \item[(SC)]  it is possible that $\phi$ iff there is a $w$ such
      that $w$ is a possible world and `$\phi$' is true at $w$. 
  \end{description}    
  Lewis proposes MR, in part, as an attempt to specify the nature of
  the possible worlds whose existence is required by (SC)'s instances.
  
  This paper outlines Lewis's view and discusses some main lines of
  objection.  I will start by noting two competing ambitions for a
  theory of possible worlds (\S\ref{sec:ambitionz}): that a theory of
  possible worlds be \emph{reductive} and \emph{user-friendly}.  I
  will then outline Lewis's version of MR (\S\ref{sec:exposition}),
  and consider objections on the grounds that MR is not reductive
  (\S\ref{sec:noRedxn}) and not user-friendly
  (\S\ref{sec:userHostile}).
  
  % I will first attempt to articulate two different and competing
  % ambitions one might have for a theory of possible worlds (\S1).  I
  % will then turn to the consideration of the five leading views
  % (\S\S2-6).  
  
  \begin{section}{Two Ambitions for a Theory of Possible Worlds}
    \label{sec:ambitionz}
    There are at least two ambitions one might have for a theory of
    possible worlds.  A principal ambition motivating Lewis is to
    advance the metaphysics of modality by giving a theory of the
    nature of modality, the meaning of modal discourse, or the
    analysis of modal concepts in terms of possible worlds.  Lewis has
    argued that (SC) provides the means to reduce modal facts, terms,
    or concepts to non-modal facts, terms or
    concepts.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Lewis argues that possible worlds are needed to provide analyses
    of more than just possibility, necessity and contingency.  Of
    particular interest is Lewis's argument that possible worlds are
    required for the analysis of certain philosophically crucial
    supervenience notions; see \citep[pp. 13-17]{Lewis:1986}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} On this view, the possibility that Bush have lost
    the 2000 electoral vote is reduced to, or analyzed as, the
    existence of a possible world at which ``Bush lost the 2000
    electoral vote'' is true.  Reductive proposals along these lines
    would be one means of specifying the nature of necessity.
    
    (SC) and associated claims hold out the hope of providing
    reductions only if the notion \emph{being a possible world} is
    given a non-modal explanation.  The other notions deployed on the
    right-hand side of (SC) seem suitably non-modal.  The quantifier
    `there is a $w$' doesn't seem modal.  And the notion of truth at a
    possible world seems to be no more modal than the notion of
    residence in an urban locality.  Whether instances of the
    right-hand side of (SC) provide matter for a reduction of
    possibility claims seems then to turn on whether the notion
    \emph{being a possible world} can be given a non-modal gloss.
    Thus, if our theoretical aim is reduction, we'll need to provide
    an explanation in non-modal terms of the notion of a
    \emph{possible world} (and of the correlative notion of
    \emph{truth at a possible world}).  Let's call a theory of
    possible worlds \emph{reductive} if it serves the ambition of
    reducing possibilities to non-modal terms by providing a non-modal
    characterization of the nature of possible worlds.
  
    Providing a reductive theory of possible worlds is only one of the
    tasks to which possible worlds have been put.  A second ambition
    for a theory of possible worlds is to explain their nature in such
    a way as to illustrate and underwrite their fitness as tools for
    \emph{end-users} in fields far removed from the metaphysics of
    modality, the semantics of modal discourse, or the analysis of
    modal concepts.  I have already noted that possible worlds are
    also used as a tool in a wide variety of other philosophical (and
    not-so-philosophical) projects.  For instance, a conspicuous and
    seminal use of possible worlds is as a basis for a variety of
    semantic theories; Lewis himself is an enthusiastic participant in
    these theoretical endeavors.  Many authors have defended the
    identification of propositions -- the contents of thought and
    assertoric speech -- with collections of possible worlds.  The
    idea here is that conveying information involves ruling some
    possibilities out and others in.  We can represent the information
    conveyed as the collection of maximal possibilities -- possible
    worlds -- which are ruled in.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {A seminal explanation may be found in \citep{Stalnaker:1978}.
    Lewis \citeyearpar{Lewis:1979} argues that a slightly more
    sophisticated construction using possible worlds as raw materials
    is required to handle indexicals.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Stalnaker \citeyearpar{Stalnaker:1968} and Lewis
    \citeyearpar{Lewis:1973} have also proposed analyses of
    counterfactuals in terms of possible worlds.  Another example is
    Stalnaker's suggestion that the progress of a conversation aimed
    at information exchange should be modeled using possible worlds.
    Though each of these proposals faces problems, they are all going
    concerns in contemporary semantics.  A quick glance at lots of
    other fields, including epistemology, ethics, decision theory, and
    linguistics, would tell a similar story.
    
    Let's call a theory of possible worlds suitable for satisfying
    this second ambition \emph{user-friendly}, and a theory
    \emph{user-hostile} insofar as it fails to be user-friendly.  A
    user-friendly theory of possible worlds would underwrite their
    fitness as tools for theorizing across a wide variety of fields.
    There are a number of ways in which a theory of possible worlds
    might be user-hostile.  Most obviously, a theory could be
    incoherent, or imply some contradiction or manifest absurdity.
    But good old-fashioned implausibility also counts against
    user-friendliness.  As Lewis argues,\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[p. 135]{Lewis:1986}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} we can't avail ourselves of a given theory of
    possible worlds if we can't bring ourselves to believe what the
    theory says.
    
    It is difficult to serve two masters.  As we shall see, MR in
    Lewis's hands appears on its face to be a reductive theory of
    possible worlds.  I will note objections to the claim the MR
    really is reductive.  Though, in my view, these objections
    ultimately succeed, the question of whether MR is really reductive
    is vexed.  On the other hand, it is easy to see that it is not
    user-friendly.
  \end{section}
  
  \begin{section}{Parallel Spacetimes}
    \label{sec:exposition}
    Lewis's development of MR is influential despite the fact that no
    one other than Lewis seems to accept it in its
    entirety.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Other defenders of MR (see \citep{Bricker:2001, Bricker:2006,
        Bricker:2008} and \citep{McDaniel:2004, McDaniel:2006}) depart
      from Lewis's own views at crucial places.  See the cited papers
      for details.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Lewis's theory holds that $x$ is a possible world
    iff $x$ is a world.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {I think this is a useful way to think of the view; I do not claim
      that Lewis himself thought of his view in this way, though the
      discussion in \citep[\S4.1]{Lewis:1973} and the title of
      \citep{Lewis:1986} are suggestive.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} According to Lewis's theory, there are many
    worlds.  Each of those worlds is a cosmos, a thing of the same
    kind as the cosmos in which we all live, move, and have our being.
    Our cosmos comprises an entire spacetime and all its contents.
    Other cosmoses similarly comprise entire spacetimes and all of their
    contents.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {More cautiously, other cosmoses comprise either entire spacetimes
      or entities analogous to spacetimes; see
      \citep[pp. 75-6]{Lewis:1986} for this wrinkle.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Our cosmos, the actual world, is just one cosmos
    among many, coexisting with the others.  There are also many
    individuals in this array of spacetimes.  Some of those
    individuals are in our spacetime; most are not.  The things of one
    spacetime stand in no spatial or temporal relations to the things
    of another, nor is there causal interaction between spacetimes;
    different spacetimes are causally and spatiotemporally isolated
    from one another.  Indeed, Lewis thinks that the cosmoses are
    individuated by their spatiotemporal isolation.  If a thing in a
    cosmos $x$ bears spatial or temporal relations to a thing in a
    cosmos $y$, then $x$ and $y$ are on that account the same
    cosmos.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[pp. 1-2, 69-81]{Lewis:1986}. }
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} 
      
    No individual is in more than one spacetime on Lewis's view.  This
    point comports with his conception of a possible world as a
    spatiotemporally isolated cosmos.  Perhaps ordinary individuals
    like Bush can be scattered, having non-contiguous parts that are
    at some spatiotemporal distance from one another.  But surely they
    cannot have parts that bear \emph{no spatiotemporal relations
      whatsoever} to one another.  So an ordinary individual like Bush
    cannot be in two entirely separate, disjoint
    spacetimes.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\cite{McDaniel:2004, McDaniel:2006} describes a view that
      attempts to reconcile the idea that possible worlds are worlds
      with the idea that a single individual is in more than one
      spacetime.  The view accepts that Bush does not have parts in
      disjoint spacetimes, claiming instead that Bush is wholly
      located in disjoint spacetimes.  I will not here pursue in
      detail the interesting vicissitudes of McDaniel's view, but see
      n. \ref{fn:overlap}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    Lewis introduces a new relation to accompany his newly-discovered
    cosmoses.  There are \emph{counterpart} relations among the
    individuals of different spacetimes, founded in relations of
    similarity among them.  Roughly, an entity $x$ in one spacetime is
    a counterpart of an entity $y$ in another spacetime iff $x$
    resembles $y$ to a sufficient degree, and no other individual in
    $x$'s spacetime resembles $y$ more closely than $x$
    does.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This explanation of the counterpart relation follows the
    treatment in \citep{Lewis:1968}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Closeness of resemblance and sufficiency of
    degree of resemblance are apparently non-modal notions.  Thus,
    counterpart relations are ultimately explained in terms of
    similarity in non-modal respects, without reference to necessity
    or possibility.  They provide suitable raw material, then, for a
    proposal to reduce modal claims to a non-modal
    basis.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[p. 88]{Lewis:1986}.  Lewis's discussion of the counterpart
    relation is extremely complicated, and the rough gloss I have
    given does not really do it justice.  The important point for
    present purposes is that the counterpart relation is explained
    solely in terms of similarity in non-modal respects, without
    reference to necessity or possibility.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    MR appears to provide a basis for using possible worlds to reduce
    possibilities.  Lewis completes the proposed reduction by pairing
    modal claims with proposed analyses in non-modal terms.  Lewis's
    theory separates modal claims into two kinds.  The truth of the
    first kind, the \emph{de re} modal claims, turns on the
    possibilities for particular individuals.  The truth, for
    instance, of `Bush might have lost the 2000 electoral vote' turns
    on what's possible for Bush.  Lewis relies on counterparts to
    analyze \emph{de re} claims.  His analysis of the claim at hand
    is: there is a counterpart of Bush, an inhabitant of some cosmos
    or other, who lost.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[pp. 12-3]{Lewis:1986}.  Corresponding to each pairing of a
      claim of the form `it is possible that $\phi$' with a non-modal
      analysis is an account of what's required for $\phi$ to be true
      at a cosmos.  The truth of claims concerning particular
      individuals at a given cosmos is given by the properties of
      those individuals' counterparts (if there are any) in that
      cosmos.  In this case, `Bush lost the 2000 electoral vote' is
      true at a cosmos $w$ iff Bush has a counterpart in $w$ who lost
      a counterpart in $w$ of the 2000 electoral vote.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} This claim is no more modal than the claim that
    there is an opponent of Bush, an inhabitant of some state or
    other, who lost the vote.  Modal claims of the second kind, the
    \emph{de dicto} modal claims, do not turn on the possibilities for
    any particular individual.  The truth, for example, of `there
    might have been purple penguins' does not turn on how any
    particular individual might have been, but rather on the possible
    truth of a general claim to the effect that there are some purple
    penguins.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {See \citep{Plantinga:2003} for an introduction to the distinction
      between modality \emph{de dicto} and \emph{de re}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Lewis's analysis of \emph{de dicto} claims does
    not appeal to counterparts.  In the case at hand, Lewis's analysis
    is: there is a cosmos which includes some purple
    penguins.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[pp. 12-3]{Lewis:1986}.  Again, Lewis gives us an account
      of what's required for a generalization like `there are purple
      penguins' to be true at a cosmos; the generalization is true at
      a cosmos just in case the cosmos contains some purple penguins.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} This claim seems no more modal than the claim
    that there is a state whose inhabitants include some wealthy
    surfers.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep{Lewis:1968} provides a general scheme for pairing any
    possibility claim in English with a non-modal analysis in terms of
    worlds, individuals, and counterparts.  This scheme is repudiated,
    however, at \citep[pp. 12-3]{Lewis:1986}.  Lewis would still
    endorse the analyses offered for the uncontroversial cases in the
    main text.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
  \end{section}

  \begin{section}{Is MR Reductive?}
    \label{sec:noRedxn}
    Lewis's version of MR avoids any obvious modal component in its
    explanation of the notion \emph{being a possible world}.  For
    this reason, it seems to provide a reductive theory of possible
    worlds.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {There are worries, however, about how well MR captures
      certain epistemological motivations for reduction.  One
      rough-and-ready epistemological motivation for reducing modal
      facts to non-modal facts is that our standard techniques for
      gathering evidence about, \emph{e.g.}, Bush only provide
      information about how he is; our observational and perceptual
      evidence gives us no information about how he might have been
      (other than the trivial information we glean by observing how he
      is).  Similarly, our observational and perceptual evidence gives
      us no information concerning unactualized \emph{de dicto}
      possibilities, like the possibility that there be purple
      penguins.  How, then, can we know about unactualized
      possibilities?  If we can reduce unactualized possibilities to
      non-modal matters of fact, then we can know about the former in
      the same way we know about the latter.  But Lewis-style
      reductions just reintroduce the problem.  Unactualized
      possibilities for Lewis turn on facts concerning how matters are
      in spacetimes which we do not observe or perceive.  See
      \citep[p. 87]{Lewis:1973} and \citep[\S2.4,
        pp. 108--15]{Lewis:1986} for some responses to such
      epistemological objections.  Lewis's response in effect is to
      reject the claim that our standard techniques for gathering
      evidence about Bush or penguins exhaust our techniques for
      gathering such evidence.\label{fn:epist}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Critics have charged, however, that things are
    not as they seem, and that MR is not really reductive, because the
    attempted reduction it proposes is inadequate.  We will examine
    two objections on this score.
    
    \begin{subsection} {Relevance}
      The first objection is that goings-on in places spatiotemporally
      isolated from this spacetime have no bearing on the question of
      what might have been the case here.  For instance, the loss of
      some electoral vote by someone else in a different spacetime,
      bearing no spatiotemporal relations to Bush at all, is
      irrelevant to whether Bush might have lost the electoral vote
      here in 2000.  It is implausible to hold that the victories of
      other individuals in other elections in other spacetimes has
      anything to do with the fact that Bush might have lost here.
      The point is reinforced by a comparison to elections in other
      places in the spacetime which we all inhabit.  The losses of
      other individuals in other elections in other countries has
      nothing to do with the possibility of a Bush loss
      here.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {The loss of someone else elsewhere might provide
        \emph{evidence} that Bush might have lost.  But this is not
        the sort of relevance at issue.  According to Lewis's version
        of MR, part of what it is for Bush to be a possible loser is
        that someone elsewhere who resembles Bush is a loser in fact.
        The objection at hand holds that such constitutional claims
        require more than just evidential relevance.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Thus, according to this objection, even if we
      accept the ontology of MR -- even if we accept the existence of
      a varied lot of parallel spacetimes and their inhabitants -- the
      bearing of that ontology on the modal facts is dubious.
      
      We ordinarily expect the relevance of a proposed reductive
      explanation to what it purportedly explains to be manifest.  The
      relevance of reducer to reduced is a hallmark of successful
      reductions.  Consider, for instance, the analysis of certain
      facts about the density of water in terms of facts about
      configurations of hydrogen and oxygen atoms.  Assuming the
      chemist's ontology is correct, the relevance of facts about
      hydrogen and oxygen atoms to the density properties of water is
      manifest.  The bits of water which exhibit the properties are
      composed of hydrogen and oxygen atoms; those atoms are the loci
      of mass in the water; and so facts about how close these atoms
      get to one another are intimately involved in how dense the
      water is.  The chemist's theory has a built-in relevance to the
      density facts it is supposed to explain.  To give a name to this
      sort of phenomenon, the chemist's reductive explanation of the
      density facts regarding water has the \emph{relevance effect}.
      The problem with Lewis's proposed reduction is that it does not
      have the relevance effect.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Philosophers who have offered this objection from relevance
        include \citep[p.119]{vanInwagen:1985},
        \citep[p. 209]{Plantinga:1987}, and \citep{Cameron:2007}.  It
        might be what Kripke had in mind by the so-called ``Humphrey
        objection'' \citep[p. 45n]{Kripke:1980}.  It's difficult to
        tell, since the passage in question is just a joke; the
        underlying objection is left inexplicit.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      Lewis himself dismisses the objection from
      relevance,\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {\citep[p. 98]{Lewis:1986}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} asserting that his proposed analysis provides
      the sort of relevance he needs.  For instance, the theory claims
      that part of what it is for Bush to be a possible loser is for
      someone resembling Bush to have lost elsewhere.  The losses of
      others elsewhere are relevant to Bush's possible loss according
      to the theory because they help constitute it; that's just what
      the theory says.  But, as our chemical example shows, the
      relevance effect is not achieved by fiat.  This is a reason to
      think that the proposed reduction fails.
      
      But not all successful reductions have the relevance effect on
      first inspection.  Some successful reductions achieve relevance
      by what one might call ``fit'': accepting the reductive proposal
      for a certain phenomenon yields a theory which predicts and
      explains its central features.  Consider, for instance, the
      reduction of temperature in thermodynamic systems to the mean
      kinetic energy of their molecules.  Even if one is convinced
      that a thermodynamic system contains molecules, there is no
      reason on the face of the matter to think that the system's
      temperature has anything to do with how those molecules are
      moving.  The mean kinetic energy of molecules does not have
      built-in relevance to the temperature of the system.  But by
      accepting the identification of the temperature of a
      thermodynamic system with the mean kinetic energy of its
      molecules, together with some ancillary assumptions, we can
      derive the ideal gas law from Newtonian mechanics.  An
      empirically observed feature of gases is that they (roughly)
      obey the ideal gas law.  So the proposed reduction achieves
      relevance by fit.
      
      In the present case, MR could achieve relevance if we had a
      theory of the nature and extent of the cosmoses that, together
      with the proposed pairings of possibility claims with
      counterpart-theoretic analyses, exactly predicted what was
      possible.  In fact, Lewis attempts to do just this.  The next
      objection is that Lewis's attempt fails.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Lewis explores a view \citep{Lewis:1983} which appears to
        sidestep the relevance objection, by claiming that individuals
        like Bush are trans-spatial: they have proper parts in
        different spacetimes.  Bush, for instance, has a winning part
        in the actual world, but a losing part in some other
        spacetime.  Where MR speaks of the many counterparts of Bush,
        the new view will speak of his many spatiotemporally isolated
        parts.  Lewis calls such individuals ``modal continuants.''
        This view appears to evade the relevance objection because the
        features of Bush's parts are manifestly relevant to how Bush
        might have been: since Bush's skin is pale, he is pale, and so
        might have been.  The view Lewis explores, without endorsing,
        has it that being a possible loser will succumb to a similar
        treatment.  Kris McDaniel \citeyearpar{McDaniel:2004} defends
        another version of MR which appears at first glance to
        sidestep the relevance objection.  The view McDaniel explores
        holds that ordinary individuals like Bush don't just have
        parts in other spacetimes, but are \emph{wholly} present in
        different spacetimes.  Versions of the relevance argument can
        be resurrected for both of these variant views, however, by
        focusing on a different possibility claim.  If Bush turns out
        to be present (either in part or in whole) in other
        spacetimes, we can still ask after the possibilities for
        spatiotemporal regions of the actual world containing him.
        For instance, any spacetime region which in fact contained his
        victory might have contained a Gore victory instead.
        Presumably at least one of those spacetime regions is not
        present -- either in part or in whole -- in other
        spacetimes.\label{fn:overlap}}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
    \end{subsection}
    
    \begin{subsection}{Plenitude}
      MR needs to achieve relevance by fit if the reduction it
      proposes is to succeed.  Fit can be achieved only by
      supplementing the view with some claims that guarantee that
      there is a possible world of the right sort to ground every
      possibility.  Following Lewis, I will call the cosmoses
      \emph{plenitudinous} if every possibility is backed by a cosmos
      of the right sort.  MR needs supplementation with principles
      that imply that the cosmoses are plenitudinous.  Adding all of the
      instances of the left-to-right direction of (SC)
      \begin{description}
      \item[(SC)${}^\Rightarrow$] If it is possible that $\phi$,
        then there is a $w$ such that $w$ is a possible world and
        `$\phi$' is true at $w$
      \end{description}
      might do the trick, if the consequent is analyzed along the
      lines Lewis proposes.  But if the modal idiom in the antecedent
      of (SC)${}^\Rightarrow$ is left unanalyzed, then there is a
      residuum of primitive modality: we achieve fit but lose the
      reduction.  If, on the other hand, we apply the possible worlds
      analysis of ``possible'' endorsed by MR, we get the triviality
      \begin{description}
        \item[(USELESS)] If there is a $w$ such that $w$ is a possible
          world and `$\phi$' is true at $w$, then there is a $w$ such
          that $w$ is a possible world and `$\phi$' is true at $w$.
      \end{description}
      As the label indicates, (USELESS) won't help secure a fit
      between what's possible and what cosmoses there are.  Instances of
      (USELESS) are tautologies, trivially satisfied by any theory of
      possible worlds.  (USELESS) won't help us sift those theories
      which exactly predict what's possible from those which do
      not.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {This abbreviated discussion of the merits of supplementing MR
        by adding (SC)${}^\Rightarrow$ or (USELESS) follows and
        simplifies the discussion at \citep[pp. 86--7]{Lewis:1986}}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      A new idea is needed to secure the fit between the possibilities
      and the cosmoses without indulging in primitive modality.  Lewis
      proposes a \emph{principle of recombination}.  The guiding idea
      is the Humean thought that anything can coexist with anything:
      possibilities can be combined at will, \emph{modulo} spatial
      re-arrangements to make sure that everything fits together.  For
      instance, if there could be a nine-foot-tall man and there could
      be a purple elephant, then a nine-foot-tall man and a purple
      elephant could coexist, so long perhaps as they occupied
      different spatiotemporal regions.  In Lewis's hands, this
      principle takes the following form:
      \begin{description}
      \item[(RECOMBO)] If $x_1$ is an individual in a spacetime $w_1$,
        $x_2$ is an individual in a spacetime $w_2$, \dots, then there
        is a spacetime $w^\forall$ containing any number (including 0) of
        duplicates of $x_1$ and any number (including 0) of
        duplicates of $x_2$, and \dots, size and shape
        permitting.\linespread{1}\endnote
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        {\citep[pp. 87--90]{Lewis:1986}.}
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        \linespread{1.3}
      \end{description}
      
      (RECOMBO) is not strong enough to achieve the fit that reduction
      requires.  To the best of my knowledge, no one has ever had skin
      which had the lime-green color of Oz's Wicked Witch of the West.
      (Philosophy concerns the underlying nature of things -- makeup
      doesn't count.)  Bush might have had skin of that color.  But
      duplicate Bush and the rest of us human beings as many or as few
      times as you like, and you will never come up with a person with
      skin that is exactly the right color.  If Bush, the rest of us
      human beings, and our duplicates are the only things that there
      happen to be that are sufficiently person-like, then Lewis's
      recombination principles can be satisfied without supplying a
      counterpart for Bush with skin of the right color.  But neither
      (RECOMBO) nor any other postulate of Lewis's version of MR
      requires that there be anything sufficiently person-like other
      than us and our duplicates.
      
      Lewis might hope to get a green-skinned counterpart of Bush out
      of (RECOMBO) by ``pushing down'' to the microscopic level.
      Perhaps it may be held that recombination (and rearrangement) of
      Bush's cells and some duplicates of frog cells require there to
      be a spacetime in which the frog cells form a skin which fits over
      the cells constituting Bush's body without its skin.  Or again,
      perhaps if we push down to the level of atoms, they can be
      recombined and rearranged so that atoms with green
      reflectance-profiles are clustered around the outside of what
      otherwise would be an atom-for-atom duplicate of
      Bush.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Notice that we need to do some rearrangement of duplicates at
        the microscopic level to get the right sort of counterparts,
        so, strictly speaking, (RECOMBO) requires supplementation; see
        \citep{DiversMelia:2002}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} But ``pushing down'' does not really help,
      since the problem will just reappear at the microscopic level.
      Suppose there are no particles that have exactly the mass of two
      electrons, and otherwise have the features of protons.
      According to the Humean intuitions that back (RECOMBO), it is
      possible that there be such things.  But (RECOMBO) will not
      secure their existence.
      
      Lewis's recombination principles seem not to guarantee that
      there are cosmoses of the right sort to back every possibility.
      Lewis himself acknowledges that ``\dots our principle of
      recombination falls short of capturing all the plenitude of
      possibilities.''\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {See \citep[p. 92]{Lewis:1986}.  (RECOMBO) relies on recombining
        duplicate individuals to achieve plenitude.  Armstrong
        proposes to replace (RECOMBO) with a principle that relies
        instead on recombining properties.  Sider
        \citeyearpar{Sider:2005} gives a sophisticated battery of
        objections to Armstrong's proposal.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      MR does not achieve relevance by fit, and so still seems not to
      deliver a reduction of modality to non-modal terms.  Further,
      notice that in embracing the Humean recombination principle,
      Lewis has incurred a substantial modal commitment.  (RECOMBO)
      settles the dispute over whether laws of nature are
      necessary.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {As Lewis writes, ``Another use of my principle is to settle --
        or as opponents might say, beg -- the question of whether laws
        of nature are strictly necessary.''
        \citeyearpar[p. 91]{Lewis:1986} See \citep{Shoemaker:1980} for a
        defense of the view that laws of nature are necessary.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Assuming it's a law that no electron swerves
      without being subjected to some force, (RECOMBO) guarantees the
      existence of a spacetime with one swerving electron and 0 forces.
      This makes Lewis's view less user-friendly than it was without
      (RECOMBO), since it holds end-users' theories of possible worlds
      hostage to the controversial Humean modal metaphysics encoded in
      (RECOMBO).  
      
      If the relevance and plenitude objections stick, MR does not
      provide an adequate starting point for a reduction of
      modality.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Divers and Melia \citeyearpar{DiversMelia:2002} argue that no
        principle of plenitude can achieve the fit needed to meet the
        constraint of reduction.  The presentation here differs from
        theirs in that they insist that achieving fit is a basic
        constraint on successful reduction, while I have argued that it
        flows instead from the need to achieve relevance by fit.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} There is reason to believe, then, that MR does
      not deliver an adequate reduction of modality to non-modal
      terms.
      \label{ssec:plenitude}
    \end{subsection}    

  \end{section}
  
  \begin{section}{Is MR User-Friendly?}
    \label{sec:userHostile}
    The question of whether MR's proposed reduction of modality
    succeeds is controversial.  A less controversial charge is that MR
    is user-hostile.  I will sketch three objections on this score.
    
    \begin{subsection}{Paradox}
      Some\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {See \citep{ForrestArmstrong:1984}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} have argued that Lewis's theory of possible
      worlds gives rise to paradox in conjunction with certain plausible
      principles.  They claim, for instance, that
      \begin{description}
      \item[(PARADOX)] For any non-empty collection $C$ of worlds,
        there is a single world which contains non-overlapping
        duplicates of the worlds in $C$.
      \end{description}
      is plausible.  Supposing there to be a collection of all possible
      worlds, (PARADOX) demands the existence of a \emph{maximal} world:
      a world containing non-overlapping duplicates of them all,
      including itself.  Suppose the maximal world has some cardinal
      number $k$ of electrons in it.  There are $2^k - 1$ non-empty
      subsets of those electrons.  (RECOMBO) implies that, for every
      such subset, there is a smaller world containing duplicates of
      exactly those electrons, and no other electrons.  Each of these
      $2^k - 1$ worlds contains an electron and has a duplicate as part
      of the maximal world.  So the maximal world contains at least $2^k
      - 1$ electrons, contradicting our supposition.  Lewis's response
      to this problem is to deny (PARADOX), on the grounds that a
      maximal world would require a spacetime larger than any possible
      spacetime.  According to Lewis, the plausibility of (PARADOX) is
      founded on the same Humean idea that underwrites his endorsement
      of (RECOMBO).  But, he argues, the resulting principle of
      recombination needs qualification: possibilities can only be
      recombined \emph{modulo} spatial re-arrangements to make sure that
      everything fits together.  This is why Lewis's statement of that
      idea, (RECOMBO), included the qualification ``size and shape
      permitting.''  According to Lewis, the argument shows that there
      is an upper bound on the possible size of a spacetime.  There
      isn't room in any possible spacetime to contain non-overlapping
      duplicates of every possible world; a maximal world is too large
      to fit into any possible spacetime.  Thus, (PARADOX) should be
      rejected: there is no maximal world.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {See \citep[\S2.2]{Lewis:1986}.  There are other responses
        available.  One could deny that there is a collection of all
        possible worlds.  Or one could deny that there is a cardinal
        number of electrons in a maximal world.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
    \end{subsection}
    
    \begin{subsection}{Actuality}
      \label{subsec:actual}
      Some of Lewis's early critics\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {See, for instance, \citep{Richards:1975} and
        \citep{Lycan:1979}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} hold that MR delivers implausible or incoherent
      results when it is applied to facts concerning actuality.  These
      theorists object to MR on the grounds that it requires there to
      be things that exist, but do not \emph{actually} exist; in
      addition to all the things that actually exist, Lewis's view
      seems to require that there are some things that don't,
      \emph{e.g.} purple penguins.  These theorists hold that it is
      implausible, or even incoherent, to suppose that there are any
      non-actual things.  Lewis counters\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {See, \emph{e.g.}, \citep[pp. 99-101]{Lewis:1986}.  See also
        \citep[\S9]{Lewis:1970}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} by showing how to make sense of the distinction
      between existence and actual existence.  He interprets
      ``actual'' and its cognates as indexical modifiers which, in a
      given context, apply to all and only those things in the same
      spacetime as the speaker.  Thus, no purple penguins actually
      exist, because no purple penguins exist in the spacetime jointly
      inhabited by you and me.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Bricker \citeyearpar{Bricker:2006, Bricker:2008} has argued
        that this makes the notion of actuality objectionably
        relational and derivative: black-and-white penguins are actual
        in virtue of being spatiotemporally related to me, the speaker
        in the present context.  According to Bricker, the notion of
        actuality is both categorical and absolute.  Bricker
        \citeyearpar{Bricker:2006, Bricker:2008} develops a version of
        MR on which actuality is both absolute and fundamental.  It is
        not clear, however, whether Bricker's proposal is an
        improvement on Lewis's, because (i) it is not obvious that
        actuality really is fundamental and absolute; and (ii)
        actuality seems to be a modal notion, so accepting it as
        fundamental means abjuring the goal of reducing modality by
        means of possible worlds.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
    \end{subsection}
    
    \begin{subsection}{Ontological Extravagance}
      Even though MR escapes paradox and incoherence, there is still a
      big strike against its user-friendliness.  It is ontologically
      extravagant.  According to MR, since it is possible that there
      be, \emph{e.g.}, flying pigs, there are flying pigs, albeit in
      other spacetimes.  This is certainly a claim we ordinarily would
      deny.  The examples of such violations of ontological modesty
      can be multiplied.
      
      Lewis was well-aware of these violations, and acknowledged that
      this was an objectionable feature of his theory of possible
      worlds.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {\citep[p. 135]{Lewis:1986}.  Lewis also attempts here to
        mitigate the ontological extravagance by arguing that our
        ordinary denial of the existence, \emph{e.g.} of flying pigs
        is consistent (when interpreted correctly in context) with MR.
        His response, in essence, is that when we say ``there are no
        flying pigs'', we ordinarily mean that there \emph{actually}
        are no flying pigs.  On Lewis's semantics for ``actual'' (see
        \S\ref{subsec:actual} above), a proponent of MR who
        acknowledges the possibility of flying pigs can comfortably
        deny that there \emph{actually} are any, \emph{i.e.}, that
        there are any in our cosmos.  See also the response to this
        problem at \citep[pp. 86-7]{Lewis:1973}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} He claimed, however, that other virtues of MR
      made it the most attractive alternative on balance.  In
      particular, the fact that MR facilitates the reduction of
      modality to non-modal terms was for Lewis a conspicuous
      virtue.
      
      The ontological extravagance of MR is a severe count against its
      user-friendliness.  Lewis ultimately concedes this objection.  He
      characterizes the issue between MR and competing alternatives as
      a dispute about the appropriate way to balance violations of
      ontological modesty and reduction.\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {\citeyearpar[p. 156]{Lewis:1986}}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Lewis holds that analyzing modality is worth
      the ontological extravagance of MR; reduction is more important
      than even this very severe form of user-hostility.  His
      opponents disagree.  One critic terms the ontological
      extravagance of MR ``an appalling
      violation.''\linespread{1}\endnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {\citep[p. 136]{Melia:2008}}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
    \end{subsection}
    
    There are other objections to the user-friendliness of Lewis's
    version of MR.\linespread{1}\endnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {For instance, Bricker \citeyearpar{Bricker:2001, Bricker:2008}
      objects to Lewis's view on the grounds that it requires that it
      be impossible that there should be disconnected spacetimes.
      Notice that Lewis's analysis of the \emph{de dicto} claim ``it
      is possible that there be two disconnected spacetimes'' is that
      there is a cosmos containing two disconnected spaces.  Since
      Lewis's version of MR says that cosmoses are individuated by their
      spatiotemporal isolation, there is no such cosmos on Lewis's
      view.  To be sure, this is another count against
      user-friendliness.  Further, it may be a reason to reject
      Lewis's version of MR if it turns out that there is independent
      reason to believe that disconnected spacetimes are possible.
      Lewis \citeyearpar[pp. 71-3]{Lewis:1986} bites the bullet here,
      arguing that it isn't really possible for there to be
      disconnected spacetimes, though some related claims are
      possible.  Bricker's version of MR addresses the problem by
      identifying possible worlds with mereological fusions of
      cosmoses.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} I have already noted, for example, that Lewis's
    embrace of (RECOMBO) is a strike against user-friendliness.  But
    Lewis's response to the apparent ontological extravagance of his
    view indicates that reduction weighs much more heavily with him
    than does user-friendliness.  It is not clear that any form of
    user-hostility short of incoherence would outweigh reduction in
    Lewis's estimation.
  \end{section}
  
  \begin{section}{Conclusion}
    The results of our brief and admittedly incomplete canvass have
    not been encouraging.  Lewis's view suffers from significant
    user-hostility.  It seems at first glance well-suited for reducing
    modality, but the proposed reduction faces problems.  Nevertheless,
    if one's paramount concern in developing a theory of possible
    worlds is to reduce modality, then some variant of Lewis's view
    seems worth pursuing.  In particular, the task of developing a
    theory of the nature and extent of the cosmoses that achieves
    relevance by fit is indicated.  If, on the other hand,
    user-friendliness has any significance at all, then the extensive
    respects in which MR is user-hostile motivate looking elsewhere.
  \end{section}
  
  
  
  \theendnotes
   \linespread{1}  
   \bibliographystyle{plainnat}
   \bibliography{PossWorlds}    
\end{document}


