\documentclass{article}
\usepackage{amssymb}
\usepackage[round, authoryear]{natbib}
\usepackage{color}
\linespread{1.3} %% double-spacing
\title{What is the Grounding Problem?}
\author{Louis deRosset\\{}\small{}[forthcoming in \emph{Philosophical Studies}]}
\date{\today}

\newcounter{sent}

\newenvironment{sentence}[0]{\addtocounter{sent}{1} \\ \vspace{4 pt} \\
  \begin{tabular}{lp{.8\textwidth}} (\arabic{sent}) & }{\\
  \end{tabular}\\ \vspace{4 pt} \\} 


\begin{document}
  \maketitle 
  
  The centerpieces of our discussion are a lump of clay and a statue,
  Lumpl and Goliath, respectively.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {This case, originally described in \citep{Gibbard:1975}, is a
  standard in the literature on material constitution.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} According to the standard story, which we will
  assume is correct, Lumpl and Goliath are created and destroyed at
  the same times, and are to be found in exactly the same locations
  throughout the period when both exist.  In a word, our centerpieces
  are \emph{coincident}.  How many centerpieces does our discussion
  have?  Philosophers don't agree: \emph{monists} claim that Lumpl and
  Goliath are identical; \emph{pluralists} deny that they
  are.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {For example, \citep{Baker:1997}, \citep{Fine:2003},
  \citep{Johnston:1992}, and \citep{Wiggins:1980} are pluralists,
  while \citep{Olson:2001} and \citep{Wasserman:2002} are monists.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} Pluralists argue for the distinctness of Lumpl and
  Goliath by noting that Lumpl has properties that Goliath lacks: it
  seems evident that Lumpl could survive being squashed into a ball,
  and that Goliath could not.  For the sake of brevity, I will adopt
  the barbarism ``squivable'' to stand for this property: a thing is
  squivable iff it can survive being squashed into a ball.  The
  pluralist argues that Lumpl and Goliath are distinct because Lumpl
  is squivable and Goliath is not.  Monists argue for their position
  on similarly compelling intuitive grounds: if Lumpl and Goliath are
  sitting in the center of our table, it seems evident that there is
  only one thing there.
  
  Our aim is not, however, to settle the dispute between monism and
  pluralism.  Our focus instead will be on a particular objection
  which monists urge against pluralists.  Here is a rough statement of
  the objection:
  \begin{quote}
    Lumpl and Goliath are made of all the same quarks and leptons.
    They share all of their spatiotemporal properties and relations.
    They are subject to all of the same physical pushes and pulls; any
    kick or wiggle administered to Lumpl is also administered to
    Goliath and vice versa.  Suppose that pluralism is correct, and so
    Lumpl and Goliath have different modal properties.  There seems to
    be nothing that could explain their having different modal
    properties.  It is natural to ask, for instance, what it is in
    virtue of which Lumpl is squivable, and Goliath not.  The
    pluralist can give no satisfactory answer.
  \end{quote}
  The objection is supposed to favor monism over pluralism because the
  demand for explaining the modal differences between Lumpl and
  Goliath goes away if one accepts, with the monist, that there are no
  modal differences to explain.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {Denying that there are modal differences to explain lands the
  monist with an explanatory task of his own: explain away the
  apparent modal differences between Lumpl and Goliath.  Assessing
  monist explanations (\emph{e.g.} those propounded in
  \citep{Wasserman:2002}, \citep{Gibbard:1975} and \citep{Lewis:1986})
  is beyond the scope of this discussion.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} The objection is called the Grounding
  Problem:\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {This label is introduced by \citep{Bennett:2004}.  The problem
  itself has been presented by many authors and in many forms.  See
  esp. \citep{Olson:2001}, \citep{Sider:2008}, and
  \citep{Zimmerman:1995}.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} the pluralist is alleged to be unable to explain,
  and so ground, the differences she claims between Lumpl and Goliath.
  
  % \linespread{1}\footnote
  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % {So-characterized, the Grounding Problem is emphatically not that
  % the pluralist can explain the differences she alleges, but the
  % monist's theory is better because, \emph{e.g.} it is simpler, more
  % elegant, or has a more economical ontology.  The Grounding Problem
  % is that the pluralist can't give an explanation in the first place.
  % Thus, the application of Occam's Razor and its cousins to the
  % dispute is a matter for another discussion.\label{fn:OckhamsRazor}}
  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % \linespread{1.3}
  
  This paper explores the question of whether there really is any such
  problem.  For the purposes of this paper, specifying a Grounding
  Problem involves specifying a legitimate explanatory task that
  there's good reason to think the pluralist can't meet.  Thus two
  conditions must be met by a specification of an explanatory task in
  order for it to pose a Grounding Problem: the task must be both
  \emph{legitimate} and \emph{problematic} for the pluralist.  
  
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %{An \emph{explanatory task} is given by its explanandum, together
  %with constraints on an appropriate explanation.  The two constraints
  %we impose throughout on any proposed explanation are: (i)
  %consistency with pluralist views regarding the differences between
  %Lumpl and Goliath; and (ii) plausibility (\emph{modulo} whatever
  %implausibilities may attach to the core claims of pluralism).  An
  %explanatory task is \emph{legitimate} if the pluralist's inability
  %to supply the requisite explanation would provide a reason to reject
  %her view.  What we are wondering, in effect, is whether there are
  %any differences between Lumpl and Goliath that someone who cleaves
  %to the core tenets of pluralism cannot explain, and where her
  %inability to provide this explanation provides a reason to reject
  %her view.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %\linespread{1.3}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
  It turns out to be more difficult than one might have hoped or
  feared to meet both conditions simultaneously.  Commentators have
  suggested many different specifications, but all of them that
  present clearly legitimate explanatory tasks seem also to leave the
  pluralist a way to provide the necessary explanation.  Matters are
  not quite so simple for specifications whose legitimacy is
  questionable.  But the pluralist has some overlooked resources even
  in these cases.  The arguments for these claims occupy the first
  three sections.
  
  Even if no extant attempt to specify a Grounding Problem succeeds,
  we might still worry that there is a Grounding Problem lurking out
  there somewhere, awaiting specification.  \S4 provides a reason to
  think that the pluralist is able to meet any Grounding Problems that
  may arise.  The pluralist distinguishes between Lumpl and Goliath;
  just about everyone distinguishes between a material object and the
  region of space (or spacetime) it occupies.  \S4 outlines some tight
  analogies between the the pluralist's view and the common-sense idea
  that a material object is distinct from the spatial (or
  spatiotemporal) region it occupies.  I argue that the pluralist can
  exploit this analogy to provide a reason for optimism about the
  prospects of meeting any Grounding Problem that may arise.  Thus,
  there is reason to suspect that there is no legitimate explanatory
  task which the pluralist ultimately cannot meet.  I conclude in \S5
  by drawing some morals from our discussion for some recent pluralist
  attempts to address the Grounding Problem.
  
  Before diving in, I'll briefly sketch some details of the pluralist
  position.  The pluralist holds that Lumpl and Goliath are distinct,
  though they stand in an intimate relation: Lumpl \emph{constitutes}
  Goliath.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {\citep{Baker:1997}, \citep{Johnston:1992}.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} The relation is asymmetric and irreflexive, so
  Goliath does not constitute Lumpl and Lumpl does not constitute
  itself.  Though Lumpl and Goliath differ with respect to their
  squivability and constitution relations, they also share many
  properties, including their spatiotemporal properties, which quarks
  and leptons make them up at a given time, their
  mass,\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {There are problems explaining, \emph{e.g.}, why the doubling of
  mass-instantiations in the region jointly occupied by Lumpl and
  Goliath does not result in a doubling of the mass to be found in
  that region; see \citep[pp. 87-8]{Zimmerman:1995} for an explanation
  of a problem of this sort.  But these problems are distinct from the
  Grounding Problem, and so will not be discussed here.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} which kicks and wiggles they received, \emph{etc.}
  Not every pluralist would agree with every particular of this
  sketch, and there is room for large differences over how to fill in
  the details.  We nevertheless have a rough and ready
  characterization of a recognizably pluralist view against which to
  test specifications of the Grounding Problem.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {This characterization is neutral on the question of whether Lumpl
    and Goliath have all the same parts.  This is because prominent
    pluralists claim that Goliath has parts that Lumpl does not
    \citep[p. 181]{Baker:2000}, \citep{Fine:1999},
    \citep{Koslicki:2008}.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3}
  
  \begin{section} {Supervenience}
    \label{sec:Supervenience}
    Some commentators have charged that pluralists must deny the
    supervenience of modal facts on non-modal facts.  This is supposed
    to indicate a Grounding Problem since it is plausibly assumed that
    explanation requires supervenience of some sort.  If the charge is
    correct, the pluralist cannot give a satisfactory explanation,
    \emph{e.g.}, of Lumpl's squivability.  But the charge is not
    correct.  The pluralist can secure the supervenience of such modal
    facts as Lumpl's squivability on the non-modal
    facts.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The fact that supervenience \emph{per se} presents no problem is
    noted by several commentators, including \citep{Bennett:2004},
    \citep{Olson:2001}, and \citep{Zimmerman:1995}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Supervenience claims are available to the
    pluralist in part because there are several different particular
    supervenience relations; and many of those supervenience relations
    can easily be affirmed by the pluralist to hold between modal and
    non-modal facts.  So, for instance, the pluralist can easily claim
    that the modal weakly globally supervenes on the non-modal: any
    possible world that is indiscernible from this world with respect
    to such non-modal facts as which quarks and leptons are where will
    have a lump of clay that is squivable, and a coincident statue
    that is not.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The pluralist can also affirm less familiar supervenience
    relations, including what \citep[p. 88]{Zimmerman:1995} and
    \citep{Rea:1997} call \emph{coincidents-friendly supervenience}:
    for any worlds $w_1$ and $w_2$ and objects $x$ and $y$, if the
    parts of $x$ compose something in $w_1$ that has exactly the same
    non-modal properties as something that the parts of $y$ compose in
    $w_2$, then the parts of y compose something that has in $w_2$
    exactly the same modal properties as something that the parts of
    $x$ compose in $w_1$.\label{fn:co-friendly}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    Supervenience is cheap because there are very weak kinds on the
    market.  Global supervenience is much weaker, for instance, than
    strong supervenience.  And often monists object that the kinds of
    supervenience that are consistent with pluralism are not strong
    enough: explaining Lumpl's squivability requires stronger stuff
    than mere global supervenience.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This objection is forcefully pressed by \citep{Olson:2001}, who
    presses the same worry regarding coincidents-friendly
    supervenience, broached in n. \ref{fn:co-friendly}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But supervenience is also cheap for another
    reason: on standard conceptions of supervenience, a supervenience
    claim by itself does not impose any further interesting
    explanatory requirement on the relation between the subvening and
    supervening facts.  In particular, contingent $A$-facts (or
    properties) may supervene on contingent $B$-facts (or properties)
    and not vice versa, without the $A$-facts obtaining in virtue of,
    or being explained by, the $B$-facts.
    
    Consider facts about the size and shape of a certain table.  For
    instance, there is the fact that it is more than 1 centimeter
    high, it is not spherical, \emph{etc.}  Call facts of this kind
    the \emph{table-facts}.  Now just pick a contingent fact $P$ from
    outside this realm.  For instance, let $P$ be the fact that there
    is at least one person in the same room as the table.  Consider
    the kind of fact obtained by conjoining $P$ with all of the
    table-facts in turn.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {I write here of conjoining facts; a somewhat more careful
    characterization of the conjunctive facts is that they are those
    facts which can be reported in any given situation by conjoining a
    contingent sentence $P$ with a sentence reporting a table-fact if
    $P$ is true; and conjoining $\neg{}P$ with a sentence reporting a
    table-fact if $P$ is not true.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.6} You get such facts as that $P$ and the table is
    more than one centimeter high, $P$ and the table is not spherical,
    \emph{etc.}  Call facts of this kind the \emph{conjunctive facts}.
    The table-facts supervene on the conjunctive facts, in the sense
    that situations cannot differ with respect to the table-facts
    without also differing with respect to the conjunctive facts.  The
    converse does not hold.  Since $P$ is contingent, situations can
    differ with respect to the conjunctive facts without differing
    with respect to the table-facts.  Consider, for instance, the
    situation now and the situation yesterday at noon, when no one was
    in the same room as the table.  Assuming that the table's size and
    shape has remained the same, the table-facts are the same in both
    situations, while the conjunctive facts differ.  It follows that
    the table-facts supervene on the conjunctive facts, and not vice
    versa.  The table-facts do not, however, obtain in virtue of the
    conjunctive facts.  If there is any explanatory relation here,
    it's partial, and it's going the other way.  Because the
    determination of the table-facts by the conjunctive facts is
    purely a matter of logic, this example can be adapted to fit any
    supervenience relation discussed in the literature, including
    strong local supervenience.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[p. 344]{Bennett:2004} notes that some forms of
    supervenience need not indicate any explanatory relation at all.
    The argument we are discussing shows that her conclusion is too
    cautious.  No form of supervenience in the literature need
    indicate that the supervening properties are to be explained even
    in part in terms of the subvening properties.  Does this mean that
    no form of supervenience has any further interesting upshot?  I
    don't know.  One could, of course, specify a relation that evaded
    the argument, and call it ``supervenience.''  Most simply, one
    could simply add an explanatory requirement, that the supervening
    properties obtain in virtue of the subvening properties.  Even if
    the result is still a supervenience relation, the argument from a
    failure of this sort of supervenience to an explanatory failure
    would be obviously circular.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    Supervenience is so cheap that it is very easy to come by.  It
    should be no surprise, then, that the pluralist need not content
    herself with weak forms of supervenience.  She can with perfect
    consistency claim that such modal properties as squivability
    strongly supervene on non-modal properties.  Pluralism is
    compatible, that is, with the claim that, whenever $x$ and $y$ are
    individuals of possible worlds $w_x$ and $w_y$ respectively, and
    the non-modal properties that $x$ has in $w_x$ are the same as the
    non-modal properties that $y$ has in $w_y$, then the modal
    properties that $x$ has in $w_x$ are the same as the modal
    properties that $y$ has in $w_y$.  This might seem surprising:
    Lumpl and Goliath, it seems, share non-modal properties in the
    actual world, but the pluralist claims that Lumpl is squivable and
    Goliath not.
    
    This initial impression is wrong, for two reasons.  First, a
    pluralist may plausibly appeal to certain non-modal properties to
    discern Lumpl from Goliath.  Goliath, for example, is badly made,
    though Lumpl is flawless.  Goliath is Romanesque; not so
    Lumpl.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[p. 206]{Fine:2003}.  Monists have rather a lot to say
    against the pluralist's argument for her position, including both
    the version which appeals to alleged modal differences,
    \citep[\S4.5]{Lewis:1986} and the version which appeals to the
    sort of non-modal differences under discussion here
    \citep{King:2006}.  Since our aim is not to settle the
    pluralism-monism debate, I don't want to dwell on the relative
    strengths of the pluralist's arguments here.  The present point is
    that if we assume that the pluralist's claims about which things
    have which properties are correct, then she can secure the strong
    supervenience of modal properties on non-modal properties.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} So the pluralist can deny, with some
    plausibility, that Lumpl and Goliath have the same non-modal
    properties in the actual world.
    
    Second, even if the pluralist does not appeal to such non-modal
    differences, there are further non-modal differences to which she
    is committed.  Pluralism claims that Goliath and Lumpl differ in
    what I will call their \emph{identity properties}: Goliath, unlike
    Lumpl, is identical to Goliath; and Goliath, unlike Lumpl, is not
    identical to Lumpl.  Given these non-modal differences between
    Lumpl and Goliath, no counter-example to the alleged strong
    supervenience of the modal on the non-modal is available.  This is
    important: the pluralist can with perfect consistency maintain
    that any possible individuals which differ modally also differ
    non-modally.  Since identity properties are part of the non-modal
    subvenience base, the pluralist is obliged to assert that Lumpl
    and Goliath differ non-modally.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {If identity properties turn out, contrary to appearances, to be
      modal properties, then the claim that modal properties strongly
      supervene on non-modal properties is implausible, quite
      independently of the pluralism-monism dispute.  This is a
      corollary of the argument from the possibility of qualitative
      twins in \S\ref{sec:IdDiffs} below.  The idea in effect is that
      it is possible that there be distinct individuals which are
      indistinguishable except in terms of identity facts regarding
      the spatiotemporal regions they occupy or the microphysical
      particles they comprise.  Thanks to Mark Moyer and David
      Christensen for discussion on this point.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}  One might complain that the identity differences
    the pluralist is obliged to accept are not explanatorily
    relevant.  We will consider this question in \S\ref{sec:IdDiffs}
    below.  The important point for present purposes is that this
    complaint abandons the charge that the pluralist must reject
    the supervenience of the modal on the non-modal.
    
    It is important to note that defending pluralism by appeal to such
    identity facts does not beg the question against monism.
    \emph{Arguing} for pluralism by appealing to identity facts would
    beg the question.  But identity facts are fair game when assessing
    which claims the pluralist's theory can explain.  If the charge is
    that her theory cannot fulfill some explanatory task, then it is
    legitimate for her to appeal to claims that centrally characterize
    that theory to provide the requisite explanations.  The claims
    concerning identity differences between Lumpl and Goliath
    centrally characterize pluralism; it is legitimate for the
    pluralist to appeal to these claims to rebut an alleged Grounding
    Problem.
    
    There are, of course, some supervenience claims that the pluralist
    must deny: most simply, she must deny the weak supervenience (and
    hence the strong supervenience) of the properties that Goliath and
    Lumpl do not share on the properties that they do share.  For
    instance, she must deny that, for any world $w$, any two
    individuals in $w$ which are indiscernible with respect to
    microphysical constituents are indiscernible with respect to
    squivability.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The argument of this section shows that supervenience by itself
    does not suffice for any interesting explanatory relation.  But
    the converse claim, that explanatory relations require
    supervenience, is very plausible.  The pluralist must deny that
    the properties Lumpl and Goliath do not share supervene on the
    properties they do.  We would have a Grounding Problem, then, if
    it were legitimate to demand that we explain the disparate
    features of Lumpl and Goliath in terms of their shared features.
    The arguments of \S\ref{sec:IdDiffs} below are designed to show
    that this explanatory demand is illegitimate.  If those arguments
    succeed, then the denial of such supervenience claims does not
    indicate a Grounding Problem.  For critical discussion of
    pluralism on the grounds that it denies such supervenience claims,
    see \citep{Olson:2001} and \citep{Rea:1997}.  Both Olson and Rea
    concentrate their criticisms on a different alleged case of
    coincidence, between human thinkers and their constituters.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But every view according to which there are
    distinct things that share some properties must deny some such
    supervenience claim.  In the absence of some independent
    motivation for such supervenience claims, their denial by itself
    is not a source of difficulty for the pluralist view.
    
    Because of the cheapness of even very strong forms of
    supervenience, the pluralist has no problem accommodating
    plausible supervenience claims.  But by this very token,
    accommodating even very strong supervenience claims does not meet
    the challenge posed by the Grounding Problem.  The Grounding
    Problem is an explanatory problem: the pluralist is alleged to be
    unable to explain the differences between Lumpl and
    Goliath.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {See \citep{Bennett:2004}, \citep{Olson:2001}, \citep{Rea:1997},
    \citep{Wasserman:2002}, \citep{Zimmerman:1995} for a sample of
    characterizations of the Grounding Problem that emphasize
    explanation.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Since supervenience does not automatically track
    explanatory relations, establishing the consistency of pluralism
    with supervenience does not resolve the underlying difficulty.
    Securing the consistency of pluralism with plausible supervenience
    claims is at best a necessary condition for avoiding the Grounding
    Problem.
  \end{section}
  
  \begin{section}{Explaining Modal Differences}
    Let's set aside supervenience and focus instead on the task of
    explaining the differences between Lumpl and Goliath.  In order to
    see how pluralism fares, we need to know what, exactly, requires
    explanation.  Our rough statement of the Grounding Problem
    suggests two sorts of candidates for the explanandum.  First,
    there is the fact that Lumpl and Goliath have different modal
    properties.  This suggests the following explanatory task presents
    a Grounding Problem:
    \begin{description}
      \item[ET1] Explain the fact that Lumpl and Goliath are modally
        discernible in terms of their other properties
    \end{description}
    Second, there are the further facts that illustrate this
    difference, \emph{e.g.}, that Lumpl is squivable and Goliath is
    not.  Call the first sort of candidate the \emph{mere modal
    difference} between Lumpl and Goliath.  Call the second sort of
    candidate the \emph{substantive modal differences} between Lumpl
    and Goliath.  Explaining the substantive modal differences between
    them involves separately explaining their respective modal
    features: specifying, for instance, those features of Lumpl in
    virtue of which it is squivable, and those features of Goliath in
    virtue of which it is not.  Thus, if we are to explain the
    substantive modal differences between Lumpl and Goliath, our
    explanatory task is:
    \begin{description}
      \item[ET2] Explain Lumpl and Goliath's disparate modal features
      in other terms.
    \end{description}
    We have, then, two different explanatory tasks on the table.
    
    The first explanatory task, (ET1), requires explaining the mere
    modal difference between Lumpl and Goliath.  This task is pretty
    easy for the pluralist.  In virtue of what do Lumpl and Goliath
    have different modal properties?  Pluralism requires that the mere
    modal difference between Lumpl and Goliath is partly explained by
    the fact that they are distinct.  Any numerically distinct
    individuals will differ modally.  One way to see this is to apply
    the necessity of identity: in virtue of having the property
    \emph{being identical to Goliath}, Goliath has a modal property
    which Lumpl lacks, namely \emph{being necessarily identical to
    Goliath}.  But even skeptics about the necessity of
    identity\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Gibbard himself, who came up the the Lumpl-Goliath example, uses
    it to push such skepticism \citep{Gibbard:1975}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} should admit that differences in identity
    properties explain why Lumpl and Goliath have different modal
    properties.  For even a skeptic about the necessity of identity
    should admit that Goliath, but not Lumpl, has the modal property
    \emph{being necessarily actually identical to Goliath} if it has
    the non-modal property \emph{being Goliath}.  The mere modal
    difference between Lumpl and Goliath may also be explained by
    other differences between them.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Any explanation of the substantive modal differences between
    Lumpl and Goliath will also explain their mere modal difference.
    Thus, the sortal strategy discussed below provides an example of
    another, complementary explanation of the mere modal difference.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But this particular explanation of their mere
    modal difference is obligatory for a pluralist.
    
    At this point, the monist might legitimately complain that we have
    been taking it too easy on pluralism.  The existence of a mere
    modal difference between Lumpl and Goliath is secured if one has
    any old modal property that the other lacks.  If the pluralist
    gets to take her pick of discerning modal property to explain,
    then she can easily explain the mere modal difference in terms of
    differences in identity properties.  But the monist intends to set
    the bar higher.  The pluralist is not entitled to pick some
    particular modal difference and explain that.  She must explain
    all of the particular modal differences that there actually are.
    Some of these, like the difference with respect to \emph{being
    necessarily identical to Goliath}, will be easy for her.  But
    other differences, like Lumpl's squivability and Goliath's
    unsquivability, require explanation too. (ET2), not (ET1), is what
    gives rise to the Grounding Problem.  The substantive modal
    differences between Lumpl and Goliath present the pluralist a more
    difficult challenge.
    
    There is a standard pluralist explanation of what it is in virtue
    of which Lumpl is squivable and Goliath is
    not.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {See, \emph{e.g.}, discussion at \citep{Wiggins:1980},
    \citep{Bennett:2004}, and \citep{Moyer:unpublished}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Goliath is unsquivable, the explanation goes, in
    virtue of being a statue, and not a lump of clay.  Lumpl is
    squivable in virtue of being a lump of clay, and not a
    statue.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Some pluralists (\emph{e.g.} \citep{Baker:1997}) accept that
    there is a sense in which Lumpl is a statue.  But its being a
    statue in this sense depends on it constituting something which is
    a statue.  Thus, Lumpl's statuehood is derivative.  Obviously, it
    is Goliath's non-derivative statuehood that is doing the
    explanatory work in the text.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} More generally, these apparently non-modal
    differences between Lumpl and Goliath are supposed to explain a
    wide variety of modal differences between them.  The general
    strategy is to explain the modal differences between coincident
    objects by reference to sortal differences between them.  Call
    this invocation of sortal differences to explain further
    differences the \emph{sortal strategy}.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Technically, we should distinguish the sortal strategy from a
    stronger view, which we might call the \emph{pure sortal
    strategy}, which adds to the application of the sortal strategy
    the claim that the disparate sortal features of Lumpl and Goliath
    are primitive.  The arguments in the main text apply to both
    views.\label{fn:pure}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    By now the sortal strategy is old hat.  I want, however, to dwell
    on one difficulty that is sometimes overlooked: the explanation of
    substantive modal differences in terms of sortals is incomplete.
    Consider Goliath's unsquivability.  The proposed explanation for
    this feature is that Goliath is a statue.  This explanation is
    obviously incomplete.  It is easy to imagine an artist creating a
    sculpture in some Space Age material which ``remembers'' its
    shape.  You can squash this statue, \emph{Gumby}, into a ball, and
    a swift kick will restore it.  In fact, we may imagine that
    periodic squashing is just what the sculptor had in mind.  Thus,
    something can be a statue and still be squivable.  Giving a full
    explanation of Goliath's unsquivability will therefore require
    more resources than its mere statuehood.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The example of Gumby might suggest that Goliath could survive
      squashing.  Suppose it is possible that the laws that actually
      regulate the Space Age material also govern clay.  Suppose too
      that it is possible to make Goliath in such a case.  Then
      Goliath itself might survive squashing, just as Gumby does.  But
      if we put the issue instead in terms of the natural or
      nomological impossibility of Goliath's surviving squashing,
      there would still be a modal difference between Lumpl and
      Goliath, and our discussion would be otherwise unaffected.
      Thanks to David Christensen for suggesting the need for this
      clarification.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    Monists do not dwell on the sketchiness of the proffered
    explanation, however, perhaps because they assume that the
    apparent gaps in the explanation can be filled.  Goliath's
    statuehood won't by itself ground its unsquivability.  But its
    being a statue produced in the circumstances at hand will do the
    trick.  Goliath is made of ordinary clay, not any Space Age
    material.  Goliath's sculptor did not foresee or intend
    squivability for it.  Certainly more needs to be said.  But it is
    generally assumed that some such further features of the case,
    added to the sortal difference, will complete the explanation in
    question.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {One might even insist that \emph{statue} is just shorthand for
    the \emph{real} sort at the heart of the explanation, which is
    much more difficult to state because it incorporates the relevant
    features of the circumstances.  One might claim, for instance,
    that the sort at hand is \emph{statue made of clay}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    A more standard monist objection to the sortal strategy is to
    argue that the sortal differences themselves require explanation.
    I will call this kind of response \emph{respecification}.  The
    original challenge was to explain the substantive modal
    differences between Lumpl and Goliath.  The sortal strategy
    proposes to meet this challenge.  But, the monist objects, the
    sortal strategy is not an adequate solution to the Grounding
    Problem, because the sortal differences stand in similar need of
    explanation.  Thus, the course of the dialectic has revealed that
    the specification of the Grounding Problem by (ET2) is at best
    incomplete.  A better specification, also requiring the
    explanation of Lumpl and Goliath's disparate sortal features, is
    needed.
    
    It is important to emphasize that respecification is sometimes the
    right move.  Suppose someone challenges me to explain why a
    certain draught puts people to sleep.  I explain that it puts
    people to sleep because it has a dormitive virtue.  It seems
    legitimate to complain that no great advance has been made: the
    dormitive virtue itself requires explanation.
    
    Why think the monist's respecification of the Grounding Problem is
    legitimate?  It seems to me that some motivation for this
    respecification is provided by the plausible thought that Goliath
    is a statue partly in virtue, \emph{e.g.}, of the arrangement of
    its material parts, the cultural milieu in which it was produced,
    \emph{etc.}  This can't, of course, be the whole explanation of
    Goliath's statuehood for a pluralist, since Lumpl has precisely
    these features and is not a statue.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This remark does not imply that, pluralism aside, it is plausible
    to claim that the proffered features provide a complete
    explanation of Goliath's statuehood.  I only mean to emphasize
    that the features in question won't distinguish Lumpl from
    Goliath, and so won't explain sortal differences between them.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Thus, we ordinarily presume that Goliath's
    statuehood is explicable in other terms.
    
    It is not obvious that this motivation for the respecification at
    hand succeeds.  A sortal strategist might urge that we are here
    confusing modally necessary conditions for Goliath's statuehood
    with the features in virtue of which it is a statue.  It is
    plausible to hold that Goliath could not have been a statue unless
    its parts were arranged more or less as they actually are by the
    efforts of an artist or artists.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Some commentators motivate the respecification in question by in effect
    assuming that the supervenience of statuehood on certain other
    features implies that statuehood is explained in terms of those
    features.  Since the sortal strategy denies that Goliath's being a
    statue has an explanation, accepting this assumption lands the
    sortal strategist with the implausible view that it is possible
    that there be something made just as Goliath was, but no statue is
    thereby produced.  See, for instance, an argument suggested at
    \citep[p. 87]{Zimmerman:1995}.  The argument of
    \S\ref{sec:Supervenience} shows that the assumption should not be
    accepted, so this motivation fails.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But, the sortal strategist might argue, these
    necessary conditions do not explain that in virtue of which
    Goliath is a statue, since Goliath's statuehood is explanatorily
    basic.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This argument is available only to a pure sortal strategist, in
    the terminology of n. \ref{fn:pure}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    The debate over the legitimacy of the proposed respecification is
    murky.  Let's just assume that it is legitimate.  The formulation
    of the Grounding Problem by means of (ET2) is at best incomplete.
    The problem, according to the respecification, is not (or not
    just) to explain the substantive modal differences between Lumpl
    and Goliath.  The problem is to explain both the sortal
    differences and the substantive modal differences by reference to
    some further difference between them.  Thus, explaining Lumpl and
    Goliath's disparate modal features in terms of their disparate
    sortal features does not adequately discharge the explanatory
    burden.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep{Bennett:2004} appreciates this point, and coins the phrase
    ``sortalish differences'' to cover both kinds of differences.  She
    uses this terminology to characterize the Grounding Problem as the
    problem of explaining the sortalish differences between Lumpl and
    Goliath. }
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} A more complete specification of the explanatory
    task that gives rise to a Grounding Problem is:
    \begin{description}
      \item[ET3] Explain Lumpl and Goliath's disparate modal and
        sortal features in other terms.
    \end{description}
    Since Lumpl's relevant sortal feature is \emph{being a lump of
    clay} and Goliath's is \emph{being a statue}, ``other terms''
    rules out use of modal features, statuehood, or lumphood in the
    explanation.
    
    Our discussion of the sortal strategy and respecification shows
    that the Grounding Problem is not adequately characterized as a
    problem the pluralist has explaining just the modal differences,
    substantive or not, between Lumpl and Goliath.  There is no reason
    to think that a pluralist has any trouble explaining the disparate
    modal features of Lumpl and Goliath, so long as she is allowed to
    appeal to the various non-modal differences she claims to find.
    We have in view a number of observations which point towards this
    conclusion: (i) as we've just seen, the invocation of apparently
    non-modal sortal features to explain modal features is taken by
    the monist not to have answered the underlying explanatory
    challenge; (ii) pluralists may appeal to such non-modal
    differences as \emph{being Romanesque} to discern Lumpl and
    Goliath; and, (iii) pluralists are committed to there being
    non-modal differences between Lumpl and Goliath, with regard to
    identity properties.
    
    These observations help the pluralist in one way, and hinder her
    in another.  They help because they demonstrate that the
    pluralist's view is that Lumpl and Goliath are non-modally
    discernible; thus, she has various non-modal differences available
    to explain the modal differences she alleges.  They hinder because
    she may now be required to provide more explanations: it may be
    legitimate to respecify the Grounding Problem to require
    explanations of these non-modal differences, in addition to the
    explanations of modal differences the pluralist was already asked
    to supply.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {See, \emph{e.g.}, the discussion of the Grounding Problem in
    \citep{Olson:2001}, where it is called ``the Indiscernibility
    Problem.''  Most of the explanatory tasks considered by Olson
    involve non-modal explananda.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} One thing, however, is clear: the Grounding
    Problem simply doesn't turn on the demand to explain modal facts
    in non-modal terms.  Perhaps respecification is legitimate, so
    that the Grounding Problem turns on (ET3), but that is a further
    matter.
    
    %Turbellarian worm:  Planarian Regeneration, Bronsted QH499.B7 1969
    
  \end{section}
  
  \begin{section} {Identity Differences}
    \label{sec:IdDiffs}
    Suppose that the monist respecifies the Grounding Problem to
    require the pluralist to meet (ET3), explaining at one swoop both
    substantive modal differences and sortal differences between Lumpl
    and Goliath.  At this point, many commentators argue that the
    pluralist cannot fulfill (ET3); her best recourse is thus to argue
    that respecification is illegitimate in this
    case.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {See, for instance, \citep{Wiggins:1980}, \citep{Bennett:2004},
    and \citep{Moyer:unpublished}; each provides reasons to believe
    that no explanation of the relevant properties is required.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} According to this pluralist line, some among
    Goliath and Lumpl's modal and sortal properties must be primitive
    if pluralism is to prevail.  This is a matter of significant
    controversy.  It is not clear whether (ET3) is legitimate.  I will
    not, however, try to adjudicate the dispute, since the pluralist
    has resources to meet the challenge, even on the assumption that
    (ET3) poses a legitimate explanatory task.  The pluralist has an
    alternative to insisting on the illegitimacy of (ET3).
    
    \begin{subsection}{Identity-Based Explanations}
      To illustrate the kind of response I have in mind, assume that
      respecification is legitimate.  The pluralist must explain why
      Goliath is a statue but Lumpl is not.  The pluralist still has
      the identity differences between Lumpl and Goliath at her
      disposal.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {There are also the constitution differences between them.  I
      set those aside because of the complications attending the
      characterization the constitution relation.  But whatever the
      pluralist can do with identity differences, she can do with
      identity differences plus constitution differences, so long as
      constitution is characterized non-modally.  I will be suggesting
      that the identity differences suffice on their own to give the
      pluralist the resources to meet (ET3).}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      In virtue of what is Goliath a statue?  If any explanation is
      possible for the pluralist, it will surely involve certain
      circumstances under which Goliath was brought into existence,
      and in which it exists over the course of its career.  Indeed,
      our respecification of the Grounding Problem is motivated by the
      intuitively plausible observation that it is partly in virtue of
      such circumstances that Goliath is a statue.  These
      circumstances may include the arrangement of the matter that
      makes up Goliath, the manner in which it was created, and the
      intentions with which it was made.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Here, I assume that the artist had no intentions at or before
      the time of creation regarding Goliath, in virtue of which
      Goliath is a statue.  It is not obvious that this assumption is
      true.  If it turns out to be false, then we could recapitulate
      the monism-pluralism dispute with a case involving something
      humbler than a statue.  Consider, for instance, a ball bearing
      stamped out by a machine.  A pluralist would distinguish the
      ball bearing from the lump of alloy constituting it.  We may
      further suppose that no one ever thought about this particular
      ball bearing, so no one has any intentions regarding it.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} They undoubtedly involve much more.  Let's use
      `$C$' to abbreviate a statement of the circumstances in
      question.  $C$ cannot be the whole explanation of Goliath's
      statuehood according to the pluralist, since Lumpl, a
      non-statue, was also brought into existence and had its career
      under exactly the same circumstances.
      
      Here's where the identity differences between Lumpl and Goliath
      can be used.  It is plausible for the pluralist to suggest that
      Goliath is a statue (rather than a lump of clay) in virtue of
      both $C$ and its identity properties.  Most of the explanatory
      work is done by $C$: $C$ will explain why Goliath is either a
      statue or a lump of clay rather than, say, a window.  But it
      won't explain why Goliath is a statue, since the putative
      explanation would presumably also apply to Lumpl.  But the only
      extra ingredient needed to explain why Goliath is a statue is
      its identity properties.  So part of what makes Goliath a statue
      is the arrangement of its parts; but another part of what makes
      Goliath a statue is its being the individual that it is.
      Similar comments apply to explaining Lumpl's sort.  The reason
      in turn why Goliath's sort differs from Lumpl's is that
      Goliath's identity properties differ from Lumpl's.  Once the
      pluralist has an explanation of the disparate sortal features of
      Lumpl and Goliath, she can give the explanations of their
      substantive modal differences made available by the sortal
      strategy.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Thus, this response to respecification provides an example of
      an application of the sortal strategy that is not a pure sortal
      strategy in the sense of n. \ref{fn:pure}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Ultimately, according to the view we are
      exploring, both the sortal and modal differences between Lumpl
      and Goliath are grounded in their identity differences.  Call
      such an explanation \emph{identity-based}.
      
      A familiar Aristotelian position\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {\citep{Wiggins:1980}, \citep{Fine:1999}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} has it that the identity of an individual is
      explained (at least in part) by its sort.  Goliath, for
      instance, is the individual that it is partly in virtue of being
      a statue.  The less familiar, identity-based, position claims
      the converse explanatory relation: Goliath is a statue partly in
      virtue of being the individual that it is.  Identity explains
      sort, not the other way around.  Goliath and Lumpl have the
      sorts they do in virtue of their respective identity properties.
      Thus, even if it is legitimate to respecify the Grounding
      Problem to require the pluralist to meet (ET3), the pluralist
      can avail herself of this identity-based explanation of sortal
      differences.
      
      % Garthoff: identity-based explanation = insisting sort is
      % fundamental.
    \end{subsection}
    
    \begin{subsection}{Three Virtues}
      The identity-based explanation of Goliath's statuehood and
      unsquivability has three considerable virtues.  First, it can
      easily accommodate the motivation for respecification.  Recall
      that requiring the pluralist to meet (ET3) is motivated by the
      idea that Goliath is a statue partly in virtue of certain
      features it shares with Lumpl, including, \emph{e.g.}, the
      arrangement of its material parts.  On the identity-based
      strategy, this idea is correct.  But the resulting explanation
      is incomplete on the pluralist's view, for it won't
      differentiate Goliath from the non-statue Lumpl.  According to
      the identity-based explanation, the missing ingredient is
      Goliath's identity properties.  Taking Lumpl and Goliath's
      sortal properties as primitive, on the other hand, obviously
      rules out the explicability of those properties in other terms.
      
      % Drawback:  plausibly no epistemic explanation
      
      % There is one potential drawback to providing an identity-based
      % explanation of sortal facts.  The resulting explanation may not
      % afford the sort of insight into the fact explained that one might
      % have hoped for.  One longs to be told what it is \emph{about
      % Goliath} (in addition to $C$) that makes it a statue.  The
      % identity-based explanation at hand appears to allow no answer,
      % other than ``just the fact that it is Goliath''.  If this answer
      % is deemed unhelpful, it's not obvious that there is any helpful
      % answer that this strategy can provide.\linespread{1}\footnote
      % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % {There is one further answer available to the pluralist, if she
      % opted instead to advert to the constitution differences between
      % Lumpl and Goliath.  She could say that, ultimately, what makes
      % Goliath a statue is the fact that $C$ plus the fact that it is the
      % constitutee in the region in question, rather than the
      % constitutor.  How helpful this answer turns out to be depends on
      % how the technical notion of constitution is explained.}
      % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % \linespread{1.3} The explanatory connection between \emph{being
      % Goliath} and \emph{being a statue} is primitive; there is no
      % further explanation of why the former feature engenders the latter
      % (under $C$).  Thus we may feel cheated of the insight we might
      % have hoped to gain.
      % 
      % I sympathize with those who long for more insight than the
      % identity-based explanation provides.  It is not clear, however,
      % how serious a difficulty the proposal faces on this count.  We
      % have been assuming that the demand for grounding -- for an answer
      % to ``in virtue of'' questions -- is sometimes legitimate and can
      % sometimes be met.  If it weren't, then there would be no Grounding
      % Problem, since the pluralist would be no worse off than anyone
      % else so far as explanations go.  It seems, though, that every such
      % explanation is going to involve primitive explanatory connections
      % between facts.\linespread{1}\footnote
      % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % {As I am using the term here, there is a \emph{primitive}
      % explanatory connection between $P$ and $Q$ iff $P$ explains $Q$,
      % but no helpful answer to the question, ``What is it about $P$ that
      % explains $Q$?'' is possible.}
      % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % \linespread{1.3} Take the explanation provided by the sortal
      % strategy of Goliath's unsquivability in terms its statuehood plus
      % $C$.  I also sympathize with those who long for more insight into
      % Goliath's unsquivability than is provided by $C$ plus statuehood.
      % What is it about Goliath's statuehood under circumstances $C$, one
      % wants to know, that makes for unsquivability?
      % 
      % The sortal strategist can provide answers that seem helpful at
      % first blush.  He might appeal, for instance, to further sortals
      % that Goliath falls under, or specify the conditions that accompany
      % Goliath's statuehood.  Suppose, to illustrate, he adverts to the
      % claim that Goliath is a work of art whose form is a part, in some
      % sense to be explained, of its very existence.  
      % 
      % Let's set aside concerns about the import or plausibility of the
      % proffered explanans.  Primitive explanatory connections are still
      % needed.  The sortal strategist may ultimately only appeal to
      % non-modal features of Goliath in order to explain its
      % unsquivability, since (ET3) requires explanation of all of
      % Goliath's modal features.  To put it tendentiously, these will be
      % facts about how Goliath and its surroundings happen to be.  In the
      % case at hand, these facts include that a certain form happens as a
      % matter of fact to be part of Goliath's existence.  But what's to
      % be explained is the impossibility of Goliath's surviving
      % squashing.  It's easy to see, given Goliath's non-modal features,
      % why it does not in fact survive being squashed into a ball.  By
      % hypothesis, Goliath is not squashed into a ball; its actual
      % survival of such an operation is not in question.  The
      % impossibility, however, is a further matter, a matter not just of
      % what happens to be the case, but of what had to be the case.  In
      % explaining Goliath's unsquivability, the sortal strategist may
      % pile up a bunch of facts that seem relevant on the non-modal side
      % of the ledger.  At some point, however, a connection between these
      % non-modal features and the modal feature in question must be
      % asserted.  That connection will be primitive.  One longs to know
      % what it is about how Goliath happens to be that makes surviving a
      % squash an impossibility.\linespread{1}\footnote
      % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % {The sortal strategist might at this point advert to \emph{a
      % priori} connections between Goliath's statuehood and
      % unsquivability.  The idea is that \emph{a priori} connections
      % yield the kind of insight we require of explanations.  But there
      % are at least two reasons for caution.  First, as the example of
      % Gumby shows, the simplest general claim that springs to mind,
      % ``Anything which is a statue is unsquivable'' is not even true,
      % much less \emph{a priori}.  Appropriate revisions will dig into
      % the messy details of the possibilities for statues made in clay.
      % Such details will depend on the \emph{a posteriori} modal
      % differences between clay and the Space Age material that Gumby
      % comprises.  Thus, the more complicated claim that is true will
      % have at best a dubious title to being \emph{a priori}.  Second,
      % the mere presence of an \emph{a priori} connection does not by
      % itself yield the kind of insight we require of explanations.
      % Mathematical proofs reveal \emph{a priori} connections.  But not
      % all such proofs are explanatory, in part because some of them do
      % not yield the sort of insight we require of explanations.}
      % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      % \linespread{1.3} The point is not that primitive explanatory
      % connections are generally unacceptable, so any explanation is
      % bound to fail.  The point is that primitive explanatory
      % connections are inevitable, so any successful explanation is bound
      % to have them.  Neither the identity-based explanation nor the
      % sortal strategy are exceptions.
      % 
      % The explanatory task (ET3) requires, among other things, that
      % Goliath's modal features generally obtain in virtue of other
      % facts.  Thus, monists will also encounter primitive explanatory
      % connections when it comes time to explain whatever modal features
      % they think obtain in the region occupied by Lumpl and Goliath.
      % Their explanations will involve primitive explanatory connections
      % between the non-modal and the modal.  It is not clear that the
      % presence of primitive explanatory connections provides a reason to
      % reject any of these explanations.  The point here is just that the
      % identity-based explanation is no worse off for appealing to
      % primitive explanatory connections.
      
      % Two Advantages:
      
      % (1) criterion of adequacy: Nec(x=Goliath & C ==> Statue(x))
      
      The second virtue of the identity-based explanation is that it
      is projectible, since it plausibly provides a modally sufficient
      condition for statuehood.  Given pluralism, it is very plausible
      to maintain that, as a matter of necessity, anything identical
      to Goliath and created under circumstances $C$ is an unsquivable
      statue.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Notice that this claim does not imply that Goliath is
      necessarily a statue.  Many find the latter claim quite
      plausible.  But even those who doubt it (see \emph{e.g.}
      \citep[p. 347]{Olson:2001} for some related doubts) should
      accede to the claim in the main text, at least in the absence of
      any scepticism about the meaningfulness or truth of \emph{de re}
      modal claims generally.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} As a matter of necessity, nothing so created
      that is either squivable or a non-statue is the very same
      individual as Goliath.  Similarly, as a matter of necessity,
      anything identical to Lumpl and created under $C$ is a squivable
      lump of clay.  So the proposed explanations plausibly provide
      modally sufficient conditions for Lumpl and Goliath's disparate
      modal and sortal features.
      
      % (2) respecification illegit.
      
      The third significant virtue of identity-based explanations is
      that they are proof against further respecification of the
      Grounding Problem.  Suppose we respecify, replacing (ET3) with
      \begin{description}
        \item[ET4] Explain Lumpl and Goliath's disparate modal,
          sortal, and identity features in other terms.
      \end{description}    
      This explanatory demand, I will argue, is illegitimate.  Notice
      first that (ET4) admits of two different interpretations,
      depending on what's required for an explanation in ``other
      terms''.  On the one hand, explaining Goliath's identity
      properties in ``other terms'' might require explaining them in
      purely qualitative terms.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {In accord with general usage, I mean by ``qualitative terms'' a
        specification of the facts in question which makes no mention
        of any particular individual, and so no particular quark,
        lepton, spacetime region, physical push or pull, \emph{etc.}.
        Such a specification does not involve the identity properties
        of any particular thing.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Alternatively, we might more liberally allow an
      explanation of Goliath and Lumpl's disparate identity properties
      in terms of the identity properties of other things, like the
      identity properties of quarks and leptons or spacetime regions.
      Thus, there are two different explanatory challenges that might
      be posed:
      \begin{description}
        \item[ET4.1] Explain Lumpl and Goliath's disparate modal,
          sortal, and identity features in other, qualitative terms.
        \item[ET4.2] Explain Lumpl and Goliath's disparate modal,
          sortal, and identity features in other terms, whether
          qualitative or not.
      \end{description}
      So we really have two different respecifications, one more
      demanding than the other.
      
      Explanatory task (ET4.1), the stronger demand to explain the
      identity facts at hand in purely qualitative terms, is
      illegitimate.  One cannot generally explain the identity facts
      of a thing in terms of a qualitative specification of the
      arrangement of its quarks and leptons, its spatiotemporal
      relations to other things, the physical pushes and pulls to
      which it is subjected, and so on.  It is plausible to think that
      distinct things could share qualitatively specified quark and
      lepton arrangements and the rest.  Consider, for instance,
      Lewis's \citeyearpar[p. 157]{Lewis:1986} example of a world of
      eternal recurrence, where the qualitatively specified history of
      each epoch is exactly the same as the preceding epoch.  The
      first postmaster general of one epoch has all the same
      qualitatively specified quark and lepton arrangements,
      \emph{etc.}, as the first postmaster general of the next epoch,
      even though they are distinct.  This fact is quite independent
      of the debate between monists and pluralists.  Even if Lumpl is
      Goliath, Lumpl (\emph{i.e.} Goliath) could have distinct
      duplicates.  So no proposed explanation of identity properties
      in terms of the properties shared by Lumpl and Goliath provides
      modally sufficient conditions for identity properties.
      Explaining identity facts in terms of the qualitatively
      specifiable properties that Lumpl and Goliath share cannot be
      done even by the monist, and so cannot legitimately be demanded
      of the pluralist.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {A monist might appeal to the Principle of the Identity of
        Indiscernibles (see \citep{Black:1952} for discussion) to
        argue that the alleged examples of qualitatively indiscernible
        but distinct individuals are impossible.  If so, then
        explanatory task (ET4.1) may present a Grounding Problem.  But
        proponents of the Grounding Problem certainly don't argue for
        the Identity of Indiscernibles in their presentation of the
        problem, and the possibility of cases of distinct qualitative
        duplicates are powerfully plausible.  Nevertheless, a full
        consideration of the merits of arguments for the Identity of
        Indiscernibles is beyond the scope of this paper.  Readers who
        endorse it may take the arguments of this section as revealing
        a new application for arguments for the Identity of
        Indiscernibles: such an argument removes an impediment to
        posing a Grounding Problem.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      But suppose the respecification of the explanatory task is the
      more modest (ET4.2), allowing the use of some identity facts in
      the explanation, just not the identity properties of Lumpl or
      Goliath.  This respecification allows appeal to facts about the
      identities of the quarks and leptons that Lumpl and Goliath
      share, for instance, or the particular location in space and
      time that they occupy.
      
      The argument against the legitimacy of the stronger explanatory
      demand (ET4.1) does not apply as readily to the more modest
      (ET4.2).  Uncontroversial examples of distinct things that share
      qualitative properties and relations always involve their having
      numerically distinct parts, or inhabiting different times and
      places, and the like.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {In accord with general usage, I use ``qualitative property
      (relation)'' for any property (relation) which has a qualitative
      specification, \emph{i.e.}, a specification that requires no
      mention of any particular individual.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} In our example the first postmaster general of
      one epoch is not spatiotemporally coincident with the first
      postmaster general of the next epoch.  So if we let identity
      properties of the microphysical particles and spacetime regions
      in as part of the pluralist's explanatory resources, it is not
      as obvious that the explanatory task we set is illegitimate.
      
      At this point, the pluralist might argue for the illegitimacy of
      the modest respecification (ET4.2) by claiming that the addition
      of identity facts regarding spacetime regions, quarks, and
      leptons still won't suffice to explain the identity properties
      of macroscopic things.  She might argue, for instance, for a
      radical haecceitist position, according to which there are no
      interesting modally sufficient conditions for being a particular
      individual: someone could have had exactly your life and career,
      been descended from the same people, been made of the same
      quarks and leptons as you were, and yet have been distinct from
      you.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Guy Rohrbaugh and I broached such a view, under the label ``the
        bare identities view'' in \citep{RohrAnddeR:2004} and
        \citep{RohrAnddeR:2006}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      %I broach it (and provide some motivation) in [CITE!]
      %``PossWorlds''.  I confess that I have a great deal of sympathy
      %for the view, even though I don't insist on it in the main text.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} If she could make her case, then no one could
      explain identity facts in the manner required by the modest
      respecification.  The demand to explain identity facts in other
      terms would be illegitimate, quite independently of any
      antecedent commitment to monism or pluralism.
      
      But she does not need to make a case for this sort of radical
      haecceitism.  She can simply insist that, if it is legitimate to
      take some identity facts as basic, then there is no reason not
      to take the identity facts she claims for Goliath and Lumpl as
      basic.  What's good enough for quarks and leptons is good enough
      for statues and lumps.  At the very least, the monist who
      proposes the modest respecification (ET4.2) faces a challenge:
      he needs to say why we may take identity facts regarding
      microphysical entities or spacetime regions as primitive, but
      may not extend the same courtesy to things that are made up of
      microphysical entities or occupy spacetime regions.  The
      difficulty of the monist's position here can perhaps be better
      appreciated by noting the unattractiveness of the analogous
      position with respect to statuehood.  According to the analogous
      position, Goliath's statuehood cannot be taken as explanatorily
      fundamental, though some other instances of statuehood --
      Gumby's perhaps -- may.  This is an unattractive
      position.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {There may be special cases in which the identity facts
      involving a certain thing are explicable in other terms.
      Perhaps the most compelling case is the claim that the identity
      facts regarding sets obtain in virtue of their membership
      relations.  But these special cases provide no reason to demand
      the explicability in general of identity facts, nor do they
      provide any reason to demand the explicability of identity facts
      involving statues or lumps of clay, while taking identity facts
      involving spacetime regions and microphysical entities as
      explanatorily basic.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Without a principled reason to exclude the
      identity properties of Lumpl and Goliath, the modest
      respecification of the Grounding Problem is
      illegitimate.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Some commentators have suggested that relying on an
        identity-based explanation of the disparate sortal and modal
        features of Lumpl and Goliath is tantamount to insisting that
        those features are primitive.  The course of our discussion
        shows that the suggestion is incorrect.  I have argued that
        identity-based explanations are immune to respecification;
        whatever one thinks of the merits of this argument, it is
        quite different from arguments that are advanced in favor of
        primitive sortal and modal properties (see
        \citep{Wiggins:1980}, \citep{Bennett:2004}, and
        \citep{Moyer:unpublished}).  Also, I have argued that
        identity-based explanations provide the pluralist a way of
        accommodating the intuition that \emph{statuehood} is not
        primitive.  Obviously, a view on which \emph{statuehood} is
        primitive cannot accommodate this intuition; it must explain
        it away.  Thanks to Jonathan Garthoff.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      It is useful, perhaps, to recall that the pluralist begs no
      questions against the monist in taking the identity properties
      of Lumpl and Goliath as primitive.  Insofar as the Grounding
      Problem involves an explanatory challenge for the pluralist's
      theory, she's entitled to deploy the full ontological resources
      of that theory to meet the challenge.  It is legitimate for
      anyone, pluralist or not, to take some identity claims as
      primitive, inexplicable in other terms.  It seems, then,
      legitimate for the pluralist to take the identity claims
      peculiar to her position as primitive.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {One might argue that the monist's demand for the explicability
      of the pluralist's identity claims is based on simplicity
      considerations: the pluralist must take certain identity claims
      as primitive; since the monist does not think that those claims
      are true, he takes fewer identity claims as primitive.  Set
      aside for the moment how to make clear the idea that there are
      ``fewer'' primitive identity facts in the monist's theory.  This
      simplicity argument is tantamount to favoring monism because it
      has a sparser ontology than pluralism.  I take such
      simplicity-based arguments to be distinct from the Grounding
      Problem, and so beyond the scope of our discussion.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
    \end{subsection}
    
    \begin{subsection} {Objections}
      Perhaps, despite these advantages, identity-based explanations
      have problems which merit their
      rejection.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {The following discussion of the problems faced by
      identity-based explanations owes a great deal to conversation
      and correspondence with Kit Fine.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} For instance, one might worry that
      identity-based explanations don't generalize in the way that we
      would ordinarily expect.  A good explanation of why Goliath is a
      statue should also provide fodder for explaining why other
      things under relevantly similar circumstances are statues.  But
      an explanation which appeals to an identity property like
      \emph{being identical to Goliath} won't apply to anything else.
      We have, then, a proposal to explain Goliath's statuehood which
      can't, even in principle, serve to explain the sortal features
      of any other statue, even if the statue in question is in
      exactly similar circumstances $C$.  In this sense, the
      explanation is \emph{sui generis}.  But, the objection goes,
      this is intolerable.  So Goliath's identity properties simply
      aren't fit to explain its statuehood.
      
      It's true, I think, that we ordinarily expect the explanation of
      a certain feature of a given individual to generalize; an
      explanation is adequate only if it is possible in principle to
      generalize it to explain the possession of the same features
      under similar circumstances by a different individual.  For
      instance, if Lumpl and Goliath were created in a world of
      eternal recurrence, we should expect the explanation of
      Goliath's statuehood to generalize to cover the relevant statues
      of other epochs.  Fortunately, there is a way to generalize the
      identity-based explanation to apply to other things.
      
      To illustrate the kind of generalization in the offing, let's
      leave for the moment the question of how to explain Goliath's
      statuehood.  Consider instead the question, in virtue of what
      does the pair set \{Socrates, Plato\} have the identity
      properties it does?  In virtue of what, for instance, does it
      have the property \emph{being identical to \{Socrates, Plato\}}?
      A plausible answer says that this set has the identity
      properties it does because it has the membership properties it
      does.  In particular, the set has its identity properties in
      virtue of having Socrates, Plato, and nothing else as its
      members.  One might complain that this explanation won't
      generalize in the way we ordinarily expect, since the
      \emph{explanandum} is not a feature of any other thing.  But
      there is a very natural generalization available; we just have
      to generalize over the property being explained: every set has
      the identity properties it does because it has the membership
      properties it does.  This seems to be the most natural
      generalization of the explanatory strategy proposed for the
      identity properties of \{Socrates, Plato\}, and this general
      explanatory claim seems quite plausible.
      
      But now something similar is in the offing when identity
      properties show up in the \emph{explanans}.  We just have to
      generalize over the property doing the explaining.  A rough
      statement of the generalization of our identity-based
      explanation of Goliath's statuehood would be: every statue has
      the sortal properties it does partly partly in virtue of its
      identity properties.  So identity-based explanations generalize
      after all, just as explanations for the identity properties of
      sets do.
      
      This response also illustrates a general strategy for assessing
      the soundness in principle of identity-based explanations.  In
      assessing a particular charge against identity-based
      explanations, see whether an analogous charge applies to
      independently plausible explanations of identity properties.
      The individuation of sets by their membership properties
      provides a plausible test case.  Adapt whatever response fits in
      the case of the individuation of sets to the case of the
      identity-based explanation.  Rinse and repeat.
      
      Another charge against identity-based explanations is that it is
      implausible to think that Goliath has such qualitative
      properties as statuehood and squivability in virtue of
      non-qualitative properties like \emph{being Goliath}.  The
      charge relies on the idea that qualitative properties are
      explicable only in terms of other qualitative properties.
      
      The case of explanations of the features of sets provides a
      useful test case for this charge as well.  The pair set
      \{Socrates, Plato\} has the qualitative property \emph{having
      exactly two members}.  But it is very plausible to hold that it
      has this property in virtue of having exactly Socrates and Plato
      as members.  Thus, we have a plausible explanation of a
      qualitative feature in non-qualitative terms.  The general
      injunction against explanations of qualitative features in
      non-qualitative terms seems to fail in many cases.  A proponent
      of the identity-based explanation argues that explaining
      Goliath's statuehood and squivability provides another
      counter-example.
      
      I have been arguing that there is no reason to think that an
      identity-based explanation of Goliath and Lumpl's disparate
      modal and sortal properties is inadequate. Suppose, however,
      that I am completely wrong on this score: ultimately, no
      identity-based explanation is adequate.  Our discussion of
      identity-based explanations still has an important upshot.  It
      is not legitimate to demand that we explain all of the alleged
      differences between Lumpl and Goliath in terms of the sorts of
      properties they share.  For instance, it is not legitimate to
      require the pluralist to explain all of the properties of Lumpl,
      including Lumpl's identity properties, in terms of its
      microphysical properties.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {This challenge is suggested by the discussion in
      \citep{Olson:2001}.  Olson also urges that the pluralist must
      explain Lumpl's sort in terms of its microphysical properties
      and relations \citep[p. 345]{Olson:2001}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Thus, the claim that all of the differences
      between Lumpl and Goliath must obtain in virtue of microphysics
      should not convince us.  This certainly does not show that the
      pluralist is out of the woods; it only shows that no Grounding
      Problem is specified by demanding generically that we explain
      all of Lumpl and Goliath's disparate features in terms of the
      microphysical features they share.
    \end{subsection}
    
    Let's take stock of the state of our discussion.  We have two
    proposals for explaining some of the differences between Lumpl and
    Goliath in terms of other such differences.  The sortal strategy
    recommends that the substantive modal differences between Lumpl
    and Goliath be explained in terms of their sortal differences
    together with surrounding circumstances.  There is no reason to
    think it can't meet (ET2).  If no explanatory demand stronger than
    (ET2) is legitimate, then the pluralist can use the sortal
    strategy to meet every legitimate explanatory task.  Suppose it is
    legitimate to respecify the Grounding Problem by adding the
    disparate sortal features of Lumpl and Goliath to those facts
    requiring explanation.  We would thereby replace (ET2) with (ET3)
    in our specification of a Grounding Problem.  We have a sketch of
    an explanation which takes the identity differences between them
    as basic.  There seems to be no reason to conclude that an
    identity-based explanation cannot meet the explanatory challenge
    posed by (ET3).  Thus, if no explanatory demand stronger than
    (ET3) is legitimate, then the pluralist can use identity-based
    explanations to meet every legitimate explanatory task.  But no
    explanatory demand stronger than (ET3) is legitimate.  In
    particular, respecifying the Grounding Problem again to demand a
    further explanation of Lumpl and GOliath's identity differences is
    not legitimate.  In any case, it is illegitimate to demand an
    explanation of all of the differences between Lumpl and Goliath in
    terms of the properties they share.  Thus, we have not yet found a
    legitimate explanatory task that we have some reason to think the
    pluralist cannot meet.  So far, no satisfactory specification of a
    Grounding Problem has turned up.
  \end{section}
  
  \begin{section}{Another Case of Coincidence}        
    I want to close by suggesting a reason for thinking that no
    satisfactory specification of the Grounding Problem will
    ultimately merit the rejection of pluralism; we have some reason
    to think that the pluralist can meet any legitimate explanatory
    demand she faces.  The argument involves an analogy with another
    metaphysical dispute, also involving spatiotemporal coincidence.
    Consider half of Max Black's \citep[p. 156]{Black:1952} famous
    thought experiment: a perfectly homogeneous material sphere $S$,
    which always has and always will occupy a certain region of space
    $R$.  \emph{Cartesians} claim that $S$ and $R$ are numerically
    identical;\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Cartesianism is inspired by Descartes's doctrine that the essence
      of body is extension; see the \emph{Principles}, I, 53,
      \citep[pp. 210--1]{Descartes}.  I leave the question of what
      Descartes's actual position was or would have been to more
      qualified commentators.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}\emph{Lockeans} claim that $S$ and $R$ are
    numerically distinct.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Lockeanism is so-called because of Locke's rejection of
      Descartes's claim that the essence of body is extension in
      bk. II, ch. 4 of the \emph{Essay}, entitled ``Of Solidity''
      \citep{Locke}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    There are tight analogies between the Lockean position and the
    pluralist position.  The pluralist position is that the entities
    in question are distinct, but are nevertheless intimately related
    by \emph{constitution}: Lumpl constitutes Goliath, but not vice
    versa.  The Lockean position replaces constitution with another
    relation.  Lockeanism holds that the sphere $S$ and the region $R$
    are distinct, but nevertheless intimately related by
    \emph{occupation}: $S$ occupies $R$ and not vice versa.  Both
    pluralists and Lockeans might appeal to modal properties to
    discern the relevant entities: pluralists to the fact that Lumpl
    is squivable and Goliath not, and Lockeans to the fact that $S$ is
    necessarily spatiotemporally coincident with a material object and
    $R$ not.  But both positions might instead appeal to non-modal
    differences.  We have already mentioned pluralist appeals to such
    apparently non-modal facts as that Goliath is Romanesque and Lumpl
    not.  The Lockean might similarly argue that $S$ has mass, while
    $R$ does not.  Both Lockeans and pluralists should admit that the
    entities in question also share lots of properties.  Both
    positions maintain that distinct entities share spatiotemporal
    properties and relations.  Lumpl and Goliath share a little more
    than $S$ and $R$, however, including quarks and leptons, physical
    pushes and wiggles, and mass.
    
    It seems to me that the Lockean position is evidently the correct
    position.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Though Lockeanism is the consensus view, there are significant
      dissenters.  For instance, \citep[p. 17]{Quine:1981},
      \citep[p. 76n.]{Lewis:1986}, and \citep[p. 110]{Sider:2001}
      suggest in passing some reasons to prefer the Cartesian view.  A
      sustained defense is offered in \citep{Schaffer:2009}, where it
      is called \emph{supersubstantivalism}.  Thanks to Jonathan
      Schaffer for pointing me towards contemporary defenses of
      Cartesianism.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} In the spirit of the Grounding Problem, we might
    wonder what grounds the myriad modal and non-modal differences
    between sphere $S$ and region $R$.  In virtue of what, for
    instance, might $R$ have existed without being coincident with
    (and so occupied by) any material object?  And in virtue of what
    must $S$ have been coincident with some material object?  I can
    imagine two different plausible answers to this question, similar
    to the two sorts of answers I have given the pluralist to the
    coordinate questions.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {A third response to the question is to reject the presupposition
    that the relevant properties have an explanation in terms of some
    further features of $S$ and $R$, respectively.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} First, the Lockean might adopt a sortal
    strategy. The fundamental difference is a difference of sort: the
    sphere is a material object, in virtue of which it is necessarily
    coincident with a material object; the region, by contrast, is a
    region of space, by virtue of which it might have been empty of
    material objects.  Perhaps it is legitimate at this point for a
    Cartesian opponent to press the point by respecifying the original
    explanatory task to demand that we also explain the sortal
    differences.  If the Cartesian's respecification is legitimate,
    the Lockean might then adopt an identity-based explanation,
    arguing that $R$ is a region of space in virtue of being the very
    individual that it is; and similarly for $S$'s materiality.  Or
    perhaps some entirely different response is warranted.
    
    However the dialectic goes, it does not seem that there is any
    legitimate explanatory demand that we have reason to think the
    Lockean cannot meet, and so no analogue of the Grounding Problem
    for the Lockean.  Thus, we are presented with a challenge for any
    attempt to specify the Grounding Problem: any explanatory demand
    that merits the rejection of pluralism must be such that the
    analogous demand does not merit the rejection of Lockeanism.  If
    the sortal strategy or the identity-based explanation does all
    the necessary explanatory work for the Lockean, we need some
    reason for thinking that it cannot do all the necessary
    explanatory work for the pluralist.  If some further, hitherto
    unknown explanation does all the necessary explanatory work for
    the Lockean, then we need some reason for thinking that no
    analogous explanation will do all the necessary work for the
    pluralist.
    
    I suspect that some will reject the analogy between pluralism and
    Lockeanism, on the grounds that we have missed a crucial element
    of the original puzzle regarding the relation between Lumpl and
    Goliath.  The reason why pluralism gives rise to a Grounding
    Problem is that Lumpl and Goliath are coincident \emph{material
    objects}.  Though there is not generally any need to explain
    differences between coincident individuals, there is when they are
    material objects.  The problem arises, in other words, not just
    because Lumpl and Goliath are spatiotemporally coincident, but
    because they are spatiotemporally coincident \emph{material
    objects}.  The case of the sphere $S$ and region $R$ is different.
    There is no need to explain the differences between $S$ and $R$
    because they are not both material objects.  There's no special
    problem about there being differences between spatially coincident
    individuals unless they are both material
    objects.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {And maybe there is no special problem about differences among
    spatially coincident material objects, unless they share material
    parts.  In this connection, see Sider's case of two objects made
    out of stuffs that interpenetrate without reacting
    \citep[p. 141]{Sider:2001}.  The objects are spatiotemporally
    coincident, but we needn't think that claiming they are distinct
    or differ modally or sortally raises any analogue of the Grounding
    Problem.  The differences between them may be explained in part by
    the different kinds of matter that compose them.  Some
    commentators \citep{Moyer:unpublished} take the Grounding Problem
    to arise when coincident objects share all of their parts.  Others
    \citep{Olson:2001} take it to arise when they share all of their
    microphysical parts.\label{fn:sharingParts}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    This avenue of resistance to the analogy, however, essentially
    concedes the point.  Indeed, it seemingly involves an application
    of the sortal strategy to the case of $S$ and $R$.  It isn't quite
    the sortal strategy.  The crucial claim is that a certain
    difference of sort indicates that all legitimate explanatory
    demands can be met in some way or other.  The relevant sort in
    question is \emph{material object}.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {If any of the qualifications of n. \ref{fn:sharingParts} are
    adopted, then the relevant sort will have to be narrower.  For
    instance, if we accept Sider's case of interpenetrable kinds of
    matter at face value, our sort might be \emph{being a material
    object made entirely of atoms}, on the assumption that matter made
    entirely of atoms is not interpenetrable in a way that allows for
    exact spatiotemporal coincidence.  }
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} No particular explanatory strategy is required,
    and thus the sort \emph{material object} need play no particular
    explanatory role.  Still, this way of resisting the analogy
    succeeds only if any legitimate demand to explain the sortal and
    modal differences between distinct but coincident individuals can
    be met if one of them is a material object and the other is not.
    The analogous claim in the case of Lumpl and Goliath takes the
    relevant sort to be, say, \emph{statue}: any legitimate demand to
    explain the sortal and modal differences between numerically
    distinct but coincident individuals can be met if one of them is a
    statue and the other is not.  This response is warranted on both
    the sortal strategy and the identity-based
    explanation.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The response may be warranted for slightly different reasons
    however.  On an identity-based explanation, the argument for this
    response is that the sortal differences imply that Lumpl and
    Goliath differ in their identity properties, and all legitimate
    explanatory demands are met by appeal to identity differences.  If
    we insist instead that the sortal features are fundamental, then
    the argument is obvious: all legitimate demands for explanation
    are met by appeal to sortal differences; and all demands to
    explain the basic sorts are illegitimate.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Unless we have some reason to think that this
    kind of response fails for the sort \emph{statue} but succeeds for
    the sort \emph{material object}, we've got no reason to think that
    there is any problem meeting a legitimate explanatory demand in
    one case but not the other.
    
    Another way of resisting the analogy is suggested by the focus of
    much of the literature on the fact that Lumpl and Goliath share
    material parts.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Thanks to Dean Zimmerman for suggesting this response.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Let's say that a \emph{complete decomposition
    into material parts} of a thing $x$ is a set of proper material
    parts of $x$ none of whose members overlap, and such that every
    material part of $x$ overlaps with at least one
    member.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This explanation of ``complete decomposition'' closely follows
    the definition given at \citep[p. 62]{Zimmerman:1995}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} For instance, the set of atoms contained by Lumpl
    is a complete decomposition of it into material parts.  It is
    plausible to hold that a Grounding Problem arises only when the
    the objects in question share a complete decomposition into
    material parts.  For brevity, we may say that a pair of objects
    are \emph{materially coincident} when they share a complete
    decomposition into material parts.  By hypothesis, Lumpl and
    Goliath are made of the same quarks and leptons, and so the same
    atoms.  They are materially coincident.  But the same cannot be
    said for the sphere $S$ and the region $R$ on the Lockean view.
    $R$ has no material parts, and so has no complete decomposition
    into material parts.  The problem arises, in other words, not
    because Lumpl and Goliath are spatiotemporally coincident, but
    because they are \emph{materially} coincident.  That's why,
    according to this response, there is a Grounding Problem for the
    pluralist, but none for the Lockean.
    
    As before, I think this way of resisting the analogy essentially
    concedes the point.  Once again, the response is tantamount to
    leveraging a difference of sort to ground a difference in the
    legitimacy of explanatory demands.  This is perhaps easiest to see
    if we focus on the pair of individuals in question in each case.
    The pair $\langle \mathrm{Lumpl}, \mathrm{Goliath} \rangle$
    belongs to the sort \emph{materially coincident pair}.  The pair
    $\langle S, R \rangle$ does not.  According to the response, all
    legitimate explanatory demands can be met in the second case but
    not in the first because of this difference in
    sort.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {If the appeal to pair sortals is considered too artificial, we
    could always put the point in terms of collective attributions of
    sort to pluralities of individuals, as in, ``Gossie and Gertie are
    best friends,'' or ``$\mathcal{A}$ and $\mathcal{B}$ are disjoint
    sets.''  The relevant collective attribution would be, ``Lumpl and
    Goliath are materially coincident objects.''}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But now there is an obviously analogous claim
    available to the pluralist: no Grounding Problem arises for pairs
    of the sort \emph{lump-statue pair}.  Since $\langle
    \mathrm{Lumpl}, \mathrm{Goliath} \rangle$ are a lump-statue pair,
    this claim would get pluralism off the hook.  As before, this
    response is warranted on both the sortal strategy and the
    identity-based explanation.  Unless we have some reason to think
    that this kind of response fails for lump-statue pairs but
    succeeds for materially coincident pairs, we've got no reason to
    think that there is any problem meeting a legitimate explanatory
    demand in one case but not the other.
    
    Indeed, the discussion makes clear that appeal to different sorts
    of pairs is going to be essential to driving a wedge between
    Lockeanism and pluralism.  Any disanalogy between the two cases
    will involve claiming that a certain difference in sort between
    $\langle S, R \rangle$ and $\langle \mathrm{Lumpl},
    \mathrm{Goliath} \rangle$ explains why no explanatory difficulty
    analogous to a Grounding Problem arises for the Lockean.  Anyone
    who proposes a Grounding Problem thus faces a challenge: show why
    the Lockean's sortal difference gets her off the hook, while the
    pluralist's sortal difference does not.
    
    But there is another reason to think that the appeal to material
    coincidence doesn't drive the right wedge between the Lockean
    position and the pluralist position.  The monism-pluralism dispute
    can be put using a case in which the constituter and the
    constitutee are not materially coincident.  Some years ago,
    researchers used a scanning tunnelling microscope to arrange 35
    individual xenon atoms in a dot-matrix pattern so that they
    spelled ``IBM'' (see \citep{EiglerSchweitzer:1990} for a
    description and images).  It is pretty easy to imagine someone
    doing something similar with mereologically simple point
    particles;\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {If we can imagine ``extended simples'' -- individuals which have
      spatial extent but no proper parts, see \citep{Markosian:1998}
      -- then we might also imagine the arrangement of such into the
      relevant pattern.  Wasserman
      \citeyearpar[p. 696--7]{Wasserman:2004} suggests that, on the
      assumption that there could be extended simples, the dispute
      over pluralism could be set in a case in which a Goliath-sized
      statue is constituted by a single extended simple; in fact this
      is a consequence of the view defended in
      \citep{Markosian:1998}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} to get a case suitably similar to the
    Lumpl-Goliath case, let's assume that the researchers arranged for
    those mereological atoms to materialize in place, and for the
    entire sculpture to be annihilated some time later.  Now consider
    a part of the resulting sculpture: the lower right-hand tip of the
    ``M''.  Call this part of the sculpture \emph{Tip}.  Tip
    coincides, we assume, with a certain mereological atom (call it
    \emph{Adam}) for the entirety of its existence.  They share a
    great deal in common, including mass, spatiotemporal relations,
    and physical pushes and pulls.  It is nevertheless easy to imagine
    a pluralist arguing that Tip and Adam are distinct, on the grounds
    that they have different modal features: Tip is necessarily part
    of the sculpture,\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {As is customary in discussing necessary features of individuals,
    I am suppressing the qualifier ``if it exists'', which may be
    required in my sketch of the pluralist's argument in this case.
    But the discussion in the main text is unaffected by this
    wrinkle.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} so could not survive Adam's jumping out of the
    sculpture and whizzing off into space; but Adam could.  Tip and
    Adam do not materially coincide, since, by hypothesis, Adam has no
    proper material parts.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {It might be held that a Grounding Problem arises because Tip and
      Adam share parts after all: Tip is an improper part of itself,
      but a proper part of Adam.  This response requires a version of
      pluralism on which the constituter is a part of the constitutee;
      see, \emph{e.g.}, \citep{Fine:2008} and \citep{Koslicki:2008}.
      But, on this view, Tip has a complete decomposition into
      material parts, \emph{viz.}  $\{$Adam$\}$, but Adam has
      none. So, Adam and Tip still do not materially coincide, and we
      should expect no Grounding Problem.  Thanks to an anonymous
      referee for suggesting this response.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Thus, insisting that a Grounding Problem arises
    only in cases of material coincidence classifies the Tip-Adam and
    $S$-$R$ cases together; no Grounding Problem arises for the
    pluralist's view that Tip and Adam differ modally and
    sortally.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Thanks to E.J. Lowe for helpful discussion of this case.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} 
    
    Further, if there's no Grounding Problem in the case of Tip and
    Adam, it is plausible to think that there will be no Grounding
    Problem in the case of the entirety of the ``IBM'' sculpture and
    the grouping of atoms with which it coincides.  If one is a
    pluralist, it is plausible to think that the sculpture has parts
    which, like Tip, are specified in terms of their formal or
    representational properties.  These parts have, \emph{e.g.}, modal
    features that distinguish between the sculpture and the group of
    atoms.  Tip, for instance, is necessarily part of the sculpture
    but not necessarily part of the group of atoms.  We have
    available, then, an explanation of the modal and sortal features
    of the entire sculpture in terms of the modal and sortal features
    of certain of its parts.  The pluralist can plausibly claim,
    \emph{e.g.}, that the ``IBM'' sculpture is a sculpture partly in
    virtue of having parts which are necessarily part of a sculpture
    identical to it.  This is a feature that the group of atoms lacks.
    Even if, for instance, Tip is a part of that group of atoms, it
    isn't \emph{necessarily} a part of that group, since Tip can
    survive the annihilation and subsequent replacement of one of the
    atoms on the ``I'', but the group cannot.
    
    If no Grounding Problem arises for the pluralist with respect to
    the disparate modal and sortal features of Tip and Adam, then none
    should arise for the disparate modal and sortal features at any
    higher level.  But the monist-pluralist disputes in these cases
    seem just like the disputes in the case of Lumpl and Goliath.
    Indeed, for all we have said so far, the case of Lumpl and Goliath
    is exactly analogous: nothing in our description of the original
    centerpiece case ruled out an elaboration on which Goliath has a
    part that is specified in terms of its formal or representational
    features and coincident with a mereologically simple particle.
    The proposal to differentiate Lockeanism and pluralism by appeal
    to material coincidence won't do the trick.
    
    Perhaps, however, this result just indicates that our
    specification of the notion of material coincidence doesn't
    capture the idea in its full generality.  For, a monist might
    argue, Tip and Adam contain the same matter, even if they share no
    proper material parts.  If the contention that Tip and Adam
    contain the same matter is accepted, then they can be said to
    materially coincide in that sense.  This response involves
    distinguishing Tip -- a point particle -- from the matter it
    contains; Tip's matter is contained by both Tip and Adam, but Tip
    itself is contained by neither.  There are views which distinguish
    material individuals from the portions of stuff that make them up
    (see, \emph{e.g.}, \citep{Markosian:1998}); to my mind, these
    views lack plausibility when the material individual in question
    is a point-particle.  But even if we accept such a view, this
    response is tantamount to accepting a form of pluralism.  For a
    standard articulation of pluralism holds that some material
    individuals are distinct from their matter.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {For instance, \citep{Fine:2003} is entitled, ``The Non-Identity
      of a Material Thing and Its Matter;'' see also the discussion at
      p. 206.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Moreover, if it is claimed that distinguishing
    Tip from its matter is justified because Tip is an
    \emph{particle}, while its matter is just a \emph{portion of
      matter}, then the monist is once again relying on the idea that
    a difference of sort indicates that all legitimate explanatory
    demands can be met.
    
    The analogy between Lockeanism and pluralism provides some reason,
    then, to suspect that there is no legitimate explanatory demand
    that the pluralist will ultimately be unable to meet.  We have
    some reason to suspect that, if there turns out to be a Grounding
    Problem, the pluralist can solve it.
  \end{section}
  
  \begin{section} {What is the Grounding Problem?}
    We have gone looking for a specification of a Grounding Problem: a
    legitimate explanatory demand which we have some reason to think
    the pluralist cannot meet.  We have not found one.  In fact, the
    analogy between Lockeanism and pluralism provides some reason to
    suspect that there is no such explanatory task that cannot
    ultimately be met by the pluralist.  It is not exactly clear,
    then, what the Grounding Problem is.  Some philosophers exploring
    defenses of pluralism are pushed by the Grounding Problem to make
    extraordinary metaphysical claims.  Bennett
    \citeyearpar[pp. 354-5]{Bennett:2004}, for instance, suggests that
    the pluralist accept that there is an object coincident with Lumpl
    and Goliath for every possible combination of modal properties.
    There is an individual, for instance, which is squivable on
    Sundays and unsquivable otherwise.  This, Bennett holds, makes the
    claim that Goliath's modal features are primitive less
    ``mysterious and obfuscatory'' \citep[p. 355]{Bennett:2004};
    Bennett argues that the fact that all the possible modal profiles
    are instantiated where Goliath is obviates the need to explain
    what it is in virtue of which any one of the individuals there has
    its modal features.  According to Bennett's suggestion, there are
    approximately a bazillion things spatiotemporally coincident with
    Lumpl.  Moyer \citeyearpar{Moyer:unpublished} suggests that, for
    each sort instantiated in the region, there is an object which is
    essentially of that sort, so exactly as many distinct objects as
    sorts.  If sorts are fairly easy to come by, so that, for
    instance, \emph{undamaged statue} is a sort, and \emph{statue
      covered with pigeons} is another sort, then there will, again,
    be approximately a bazillion things on the scene.  Unlike
    Bennett's pluralist, Moyer's pluralist takes Goliath's statuehood,
    rather than its unsquivability, to be
    primitive.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {More accurately, Moyer's pluralist takes Goliath's
    \emph{essential} statuehood to be primitive, and explains its
    unsquivability on that basis.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Like Bennett, Moyer argues that the plenitude of
    objects satisfying different sorts makes the assertion of
    primitivity palatable.  Fine \citeyearpar{Fine:2008} and Koslicki
    \citeyearpar{Koslicki:2008} argue that the myriad differences
    between Goliath and Lumpl are explained by the fact that, though
    they have all the same material parts, they have different
    non-material parts.  Sider \citeyearpar{Sider:2008} suggests that
    the pluralist deny that individual things like Goliath really do
    have such modal properties as squivability.  Sider's pluralist
    avoids the Grounding Problem by denying that there are any
    substantive modal differences to explain.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Sider's pluralist maintains that there are modal differences
    between Lumpl and Goliath even though there are no non-relational
    modal properties that one of them has and the other does not.
    This requires (and gets) quite a bit of explanation from Sider.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    But, if the argument of this paper is correct, the Grounding
    Problem provides no reason for a pluralist to sign on to these
    controversial metaphysical claims.  There is no legitimate
    explanatory task which the pluralist cannot ultimately meet, even
    if she rejects all the metaphysical claims offered by Bennett,
    Koslicki, Moyer, Fine, and Sider.  It is much easier to be a
    pluralist than these champions of pluralism indicate.
    
    None of the preceding reflections provide anything like a thorough
    defense of pluralism.  Nor do any of them provide a solution to
    the Grounding Problem.  I hope to have provided reasons for
    thinking that there is really no problem to
    solve.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Versions of this paper were read at McGill University and at the
      ``Because'' conference at the Eidos Centre for Metaphysics at
      the University of Geneva, Switzerland.  Thanks to Bill Butchard,
      David Christensen, Kit Fine, Jonathan Garthoff, E.J. Lowe, Mark
      Moyer, Derk Pereboom, Zolt\'an Szab\'o, Dean Zimmerman, and an
      anonymous referee for comments on various drafts.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}

  \end{section}
  \linespread{1}  
  \bibliographystyle{plainnat}
  \bibliography{groundprob}      
\end{document}

