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\title{Grounding Explanations}
\author{Louis deRosset}
\date{\today}

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% TODO:

% (1) Suggestion about analogue for (BECAUSE) for grounding entities.

% (2) objection (Nickel): deflationism inconsistent with there being general
%     prins. that govern explanation

% (3) Move upward necessitation down to last sxn, and soften the
%     conclusion to ``IF up. nec. is a req., then BECAUSE passes'' [DONE]

% (4) Expand on motivating consid's for positive view: including the
%     fact that whatever else needs to be part of the story needn't
%     impugn the completeness of the proferred explanation. [DONE]

% (5) Objection (Dasgupta): PvQ b/c P and ~~P b/c P get the same
%     explanation?  Absurd!

% (6) Objection (Fine): The truth in general of instances of (BECAUSE)
%     needs to be made intelligible. [DONE]

% (7) Objection (Schwartzkopf): the reason (TRUTH) looks good isn't
%     deflationism; it's the appeal of P is true b/c P + transitivity.

% (8) Objection (Schaffer, Trogdon): Some restriction on (LINK) is
%     necessary. [DONE]

\begin{document}
  \maketitle 
  
  \linespread{1}
  \begin{abstract}
    \noindent A compelling idea holds that reality has a layered
    structure.  We often disagree about what inhabits the bottom layer
    (or even if there is one), but we agree that higher up we find
    chemical, biological, geological, psychological, sociological,
    economic, \etc, entities: molecules, human beings, diamonds,
    mental states, cities, interest rates, and so on.  How is this
    intuitive talk of a layered structure of entities to be
    understood?  Traditionally, philosophers have proposed to
    understand layered structure in terms of either reduction or
    supervenience.  But these traditional views face well-known
    problems.  A plausible alternative is that layered structure is to
    be explicated by appeal to explanations of a certain sort, termed
    \emph{grounding explanations}.  Grounding explanations tell us
    what obtains in virtue of what.  Unfortunately, the use of
    grounding explanations to articulate the layered conception faces
    a problem, which I call \emph{the collapse}.  The collapse turns
    on the question of how to ground the facts stated by the
    explanations themselves.  In this paper I make a suggestion about
    how to ground explanations that avoids the collapse.  Briefly, the
    suggestion is that the fact stated by a grounding explanation is
    grounded in its \emph{explanans}.  
  \end{abstract}
  \linespread{1.3}
  
  Consider some facts: water contains hydrogen, my colleague's cat is
  alive, diamond is harder than granite, I prefer oatmeal to brussels
  sprouts, Shanghai is the most populous Asian city, interest rates
  are low.  These chemical, biological, geological, psychological,
  sociological, and economic facts all appear to rest on further
  facts.  Facts involving cities, \eg, the fact that Shanghai is the
  most populous Asian city, are not rock-bottom: city facts depend on
  and are determined by facts about where people live, how they act,
  and what their attitudes are.  These facts might on occasion be hard
  to discover or state, given the number of people involved and the
  trouble we have saying exactly which actions and attitudes do the
  relevant work.  But we shouldn't let the difficulty of the details
  distract us from the original, compelling idea: city facts rest on
  other facts, including facts about human beings; facts about human
  beings rest on other facts, including facts about organs, cells, and
  genes; these facts in turn rest on chemical facts; and so it goes,
  at least for a while.  Reality comes in layers.  We often disagree
  about what there is at the bottom, or even if there is a
  bottom.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {For variety of views about which facts are fundamental, see
    \citep{Schaffer:2010, Schaffer:2009}, \citep{Papineau:2008},
    \citep{Lewis:1994}. For an exploration of the view that there are
    no fundamental facts, see \citep{Schaffer:2003}.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} But we agree that higher up we find facts
  involving a diverse array of entities,\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {Here and throughout, I am using ``entity'' as a catch-all term
    covering individuals, properties, kinds, tropes, states, events,
    processes, \etc{} I assume that facts are specifiable by an
    expression of the form `the fact that $\phi$'.  A fact
    \emph{involves} all of the entities mentioned in its
    specification.  For instance, the fact that Obama is president
    involves both Obama and \emph{being president}.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} including chemical, biological, geological,
  psychological, sociological, and economic entities; molecules, human
  beings, diamonds, mental states, cities, and interest rates all
  occupy higher layers.  The nature and existence of the entities in
  the higher layers are determined by, dependent upon, and derivative
  of the more fundamental facts and entities we find lower down.
  
  How is this intuitive talk of layered structure to be understood?
  One option is to cash out layering in terms of reduction: the upper
  layers -- the chemical, biological, geological, \etc -- are all
  reducible to lower layers.  Another option is to rely instead on
  supervenience: upper layers asymmetrically supervene on lower
  layers.  These options face a number of
  problems.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {See, \eg, \citep{Fodor:1974} and \citep{Putnam:1967} for classic
    statements of problems with using reduction to articulate the idea
    of layered structure.  See \citep{Fine:1994},
    \citep{Horgan:1993},\citep{Trogdon:2009}, \citep{Wilson:2005}, and
    \citep[\S1]{deRosset:forthcoming} for critiques of the proposal to
    explain layered structure in terms of
    supervenience.\label{fn:AltsBad}}
  % [REDACTED]
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} Some thinkers have recently advanced a third
  option, linked to a certain kind of explanation.  On this third
  option, upper layers are \emph{grounded in} what goes on below.
  
  This suggestion threatens to wrap a mystery in an enigma.
  \emph{Grounding} is supposed to be the notion needed to explain the
  compelling but elusive idea that reality has a layered structure.
  What, then, is grounding?  These thinkers link grounding to
  explanations of a certain kind.  Philosophers and scientists are
  fond of asking for explanations of this kind: ``In virtue of what is
  murder wrong?''  ``In virtue of what am I justified in believing
  that I have hands?''  ``What makes gravity such a weak force?''
  Each question sets the stage for a more or less familiar ongoing
  research program.  Each question calls for an explanation.  It is
  plausible to think that the correct and complete answer, if there is
  one, to each question gives us a picture of the structure of a small
  slice of reality.  For instance, if physicists manage to figure out
  what makes gravity so weak in comparison to the electromagnetic,
  weak, and strong nuclear interactions, then we will know which facts
  ground this striking fact.  If the investigation reveals a rich
  theory offering an explanation for the existence and important
  properties of gravity, then we will have discovered that the
  entities to which the theory appeals are what grounds gravity.  This
  merits calling the explanations in question \emph{grounding
    explanations}.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {Plausibility requires that grounding explanations and causal
    explanations are not to be identified.  First, what makes gravity
    weak or murder wrong is almost certainly not going to be something
    which causes gravity to be weak or murder to be wrong.  Second,
    the fact that explosions are caused by detonators does not warrant
    the conclusion that detonators occupy a more fundamental level
    than explosions.  I am agnostic on whether there are any causal
    explanations that do double duty as grounding explanations.  The
    point for present purposes is that grounding explanations are not,
    or not just, causal explanations.  In what follows I will use
    ``because'', ``explain'', and ``explanation'' narrowly to target
    grounding explanations.\label{fn:restrict}}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} Grounding explanations indicate grounding relations
  among entities.
  
  Proponents of grounding claim that that notion --- and the layered
  structure it reveals --- is the key to understanding certain
  traditionally recognized metaphysical investigations.  Grounding is
  useful for helping us characterize and pursue investigations
  concerning realism and anti-realism in various domains
  \citep{Fine:2001}.  Grounding provides a way of making sense of
  interesting kinds of metaphysical dependence \citep{Correia:2008}.
  It provides a way of articulating a sensible form of nominalism
  about properties \citep{Melia:2005}.  It is the notion needed to
  characterize physicalism \citep{Schaffer:2009, Schaffer:2003}.  It
  provides a way of reconciling a sparse inventory of fundamental
  entities with the rich ontological commitments of the special
  sciences \citep{Armstrong:1997}, \citep{Cameron:2008},
  \citep{Schaffer:2007, Schaffer:2009, Schaffer:2010}.  In short a, or
  perhaps the, central concern of metaphysics is saying what grounds
  what, thereby limning the structure of reality.
  
  Nice work, if we can get it.  But grounding will serve these
  purposes only if it can vindicate the layered conception of reality.
  For instance, grounding can be used to characterize physicalism only
  if it is \emph{prima facie} plausible to think that \emph{pro tanto}
  non-physical entities, \eg, my preference for oatmeal, do not occupy
  the fundamental layer.  Unfortunately the use of grounding to
  articulate the layered conception faces a problem, which I will call
  \emph{the collapse}:\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {The causal source of this label for the argument is Nathan Salmon's
    \citeyearpar{Salmon:2005} use of it to label a completely different
    phenomenon in another context.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} the problem, briefly, is that if we take grounding
  relations to be the fundamental basis of layered structure, then the
  layers collapse into one: every entity turns out to occupy the
  fundamental layer.\linespread{1}\footnote
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  {The problem is pressed in \citep[\S7.2]{Sider:forthcoming}.}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \linespread{1.3} The collapse emerges when we consider the question
  of how to ground the facts stated by the explanations themselves.  I
  will suggest a way of grounding explanations that avoids the
  problem.  Briefly, the suggestion is that the fact stated by a
  grounding explanation is grounded in its \emph{explanans}.
  
  Here's the plan.  \S1 lays out a simple-minded way of using
  grounding explanations to articulate the intuitive conception of
  layered structure.  I also differentiate this approach to
  articulating the idea of layered structure from a more traditional
  one centering on reduction.  \S2 shows how the commitments
  articulated in \S1 lead to the collapse, when paired with the claim
  that grounding explanations are fundamental.  In \S3, I advance my
  proposal for grounding those explanations, and thereby avoiding the
  collapse.  \S4 outlines and criticizes an alternative proposal for
  avoiding the collapse implicit in some of the the extant iterature,
  and \S5 discusses objections.
  
  \begin{section}{Grounding, Fundamentality, and
      Necessitation}\label{sec:setup} 
    
    How, exactly, does grounding reveal layered structure?  We can get
    an answer to this question by exploring in fuller detail the link
    between grounding and grounding explanations.  Some proponents of
    grounding hold that one entity may ground another, even though
    they are from disparate ontological categories.  Consider some
    examples of plausible grounding claims: the fact that snow is
    white grounds the fact that snow is either white or red; Obama,
    the man in full, grounds the fact that Obama exists; Obama grounds
    his singleton; the property \emph{being white} grounds \emph{being
      white or square}; England grounds (in part) the property of
    \emph{being queen of England}; Brutus grounds (in part) Brutus's
    stabbing of Ceasar.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The idea that grounding links entities of disparate sorts is
      explicit in Schaffer; see esp. \citep[pp. 345-6]{Schaffer:2010c}
      for more examples.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} These are plausible grounding claims asserting
    fact-fact, object-fact, object-object, property-property,
    object-property, and object-event relations, respectively.  The
    examples could be multiplied.  Though plausible, each of these
    grounding claims may turn out to fail.  If so, however, it won't
    be due to some prior constraint on grounding relations that rules
    them out.
    
    So, grounding plausibly links a disparate assortment of entities
    in a wide variety of cases.  What ties all of these cases
    together?  One common thread is that the entities that ground $e$
    are supposed to be the entities in virtue of which $e$
    exists\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {It's a little unnatural to say that entities of some sorts, \eg,
      events and facts, exist.  ``Exist'' as I use it here may be
      taken to stand in for the appropriate correlative locution
      appropriate to a given entity $e$: ``\emph{occur}'' for an
      event, ``\emph{obtain}'' for a fact, and similarly for other
      sorts of entities.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} and has the nature it does.  As Schaffer puts the
    point,
    \begin{quote}
      [Grounding is] the metaphysical notion on which one entity
      depends on another for its nature and existence. [...]  This is
      the notion that Plato famously invokes in the \emph{Euthyphro}
      dilemma, asking `Is what is holy holy because the gods approve
      it, or do they approve it because it is holy?'... , and the
      notion that Aristotle codifies as \emph{priority in
        nature}.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {\citep[p. 345]{Schaffer:2010c}.  Schaffer's terminology
        differs from mine in this passage, where he speaks of
        ``priority'' instead of ``grounding.''}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
    \end{quote}
    Consider, for example, the case of Socrates and his singleton.
    Socrates's existence and features explain the existence and
    features of his singleton, and not vice versa.  For instance, the
    singleton exists because Socrates does, and the singleton contains
    a snub-nosed man because Socrates is a snub-nosed man.  More
    generally, there is a systematic link between grounding, which may
    relate entities of any sort, and explanation, which canonically
    relates facts:
    \begin{description}
      \item[LINK] $e_1, \dots, e_n$ are the entities that ground
        entity $e$ only if $e$'s existence and features are all
        explicable solely by reference to the existence and features
        of $e_1, \dots, e_n$.
    \end{description}
    
    \textbf{LINK} helps us show how grounding can be used to explicate
    the idea of layered structure.  The thought is that grounding
    explanations give us a way of making clear the idea that
    \emph{facts} are organized into layers; and then \textbf{LINK}
    enables us to read the layered structure of \emph{entities} off of
    the layered structure of facts.  The biological \emph{entities},
    for instance, are the entities characteristically involved in the
    biological \emph{facts}.  Those entities occupy a higher layer
    than the chemical entities only if the biological facts are
    explained by the chemical facts.
    
    Grounding explanations provide us with both relative and absolute
    notions of fundamentality.  Let's start with notions of
    fundamentality for facts.  The relative notion first: one fact is
    \emph{more fundamental} than another iff the one explains the
    other, but not vice versa.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Why do we need the ``not vice versa?'' For all we have said,
      there may be facts which are \emph{self-explainers}: ``because''
      is an anti-symmetric connective.  This would reconcile the idea
      that there is a most fundamental level with a traditional
      commitment to a principle of sufficient reason
      \citep{DellaRocca:2010}.} % TODO:  FIX REFERENCE!!!!
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} For instance, Barack Obama's children carry some
    of his genes partly in virtue of the biochemical fact that certain
    DNA molecules bear certain causal and structural relations to one
    another.  Thus, the fact involving Obama's genes is less
    fundamental than the biochemical fact.  Relative fundamentality is
    asymmetric and transitive, and thus induces a partial ordering on
    facts.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This result assumes the standard view that grounding explanation
      is anti-symmetric and transitive.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Given a relative notion, we can also define an
    absolute notion of fundamentality: a fact is \emph{fundamental}
    iff it is not explained by any other fact.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {It is typically assumed that there are some fundamental facts,
      though this assumption has been questioned; see
      \citep{Schaffer:2003}.  The collapse relies on a premise which
      implies that there are fundamental facts; see
      \S\ref{sec:collapse} below.  The solution I explore in
      \S\ref{sec:positiveView} does not rely on any such assumption.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} A \emph{derivative fact} is a fact that is not
    fundamental, \ie, a fact which is explained by some other facts.
    
    We can also specify notions of relative and absolute
    fundamentality for entities of other ontological categories using
    the notion of grounding.  An entity is \emph{less fundamental}
    than the entities that ground it.  It is standardly claimed that
    grounding is asymmetric and transitive, so relative fundamentality
    induces a partial order on entities.  An entity is
    \emph{fundamental} iff it is not grounded by any other entities,
    and \emph{derivative} otherwise.
    
    On this picture, the grounding relations among entities are
    reflected in the layered structure of grounding explanations.
    According to \textbf{LINK}, for instance, if Obama's genes are
    less fundamental than certain DNA molecules, then the facts
    involving Obama's genes will all be explicable in terms of those
    recognizably chemical entities.  If this pattern is repeated for
    the genes of all living things, then it is plausible to hold that
    genes in general are less fundamental than the molecules that
    ground them.  This is the sense in which genes occupy a higher
    ``layer'' than molecules.
    
    The systematic correspondence asserted by \textbf{LINK} between
    grounding and explanation implies a similar correspondence between
    fact- and entity-fundamentality:
    \begin{description}
      \item[CORR] An entity $e$ is fundamental if $e$'s existence or
        its possession of some feature is fundamental.
    \end{description}
    Here is the argument that \textbf{LINK} implies \textbf{CORR}.
    Suppose that $e$'s existence or its possession of some feature is
    fundamental.  Assume for \emph{reductio} that $e$ is derivative,
    and so grounded in other entities.  If $e$ is grounded, then the
    application of \textbf{LINK} implies that $e$'s existence and its
    possession of each of its features are derivative, contradicting
    our supposition.  QED.
    
    Arguments aside, \textbf{CORR} is an intuitively plausible result.
    The fundamental facts are those facts in virtue of which all other
    facts obtain.  \textbf{CORR} says that, if one were to detail all
    and only the fundamental facts, then one would mention only
    fundamental entities: derivative entities aren't part of the
    fundamental story of the world.
    
    % \linespread{1}\footnote
    % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % {Recall that some entities $e_1, \dots, e_n$ ground an entity $e$
    %   only if $e$'s existence and features are all explicable by
    %   reference to $e_1, \dots, e_n$.  Thus, if some fact involving
    %   $e$ is fundamental, then $e$ is not grounded by any other
    %   entities, and $e$ itself is fundamental.}
    % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % \linespread{1.3} 
    
    The idea of layered structure has historically been associated
    with the ambition to provide reductions of theories of entities in
    higher layers to theories of entities in lower
    layers.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep{OppenheimPutnam:1958}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But grounding does not require reduction, so the
    idea of layered structure is independent of these historically
    important reductive claims.  I assume that reduction of the
    relevant sort requires modal equivalence: if a fact $P$ is
    reducible to a fact $Q$, then it is necessary that $P$ iff
    $Q$.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This assumption is widely shared, though it is rejected, at least
      in the unqualified form I use here, in
      \citep{Lewis:1994b}.\nocite{Lewis:1999}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Paradigm cases of grounding explanations indicate
    that grounding is weaker than reduction, so long as this
    assumption is true.  For instance, it is plausible to think that
    Al and Beth and have an average height of 5'6'' in virtue of the
    fact that Al's height is 5'4'' and Beth's is 5'8''.  But Al and
    Beth's average height is not reducible to their having those
    specific heights, since they could have had different heights that
    nevertheless average to 5'6''.  Plausibly, there is a reduction of
    average height in the offing, but that should not distract us from
    the conceptual point: one fact can be explicable by another
    without being reducible to it.  A similar result holds for
    properties.  It is plausible to require that $F$-ness is reducible
    to $G$-ness only if necessarily every $F$ is a $G$ and vice versa.
    Presumably all of the actual rectilinear material objects are so
    in virtue of being composed of particles in a rectilinear
    arrangement.  And this is so even if it turns out to be possible
    for there to be rectilinear material objects made of non-quantized
    matter.  So, in the actual world, the distribution of the property
    \emph{being rectilinear} is explained by appeal to arrangements of
    particles, even if it turns out that those arrangments of
    particles are not modally necessary for \emph{being rectilinear}
    to be instantiated.
    
    In general, the layered structure given by grounding explanations,
    unlike the layered structure given by reductions, is consistent
    with the phenomenon known as \emph{multiple realizability}.  A
    fact $P$ can be explained by a fact $Q$, even if it is possible
    that something other than $Q$ explain $P$, and $Q$ not obtain at
    all.  Similar results hold for properties and entities of other
    categories: the explanation of the existence and features of an
    entity $e$ by the existence and features of some entities $e_1,
    \dots, e_n$ does not entail the impossibility $e$'s existing and
    having those features in the absence of $e_1, \dots, e_n$.
    
    In short, an explanatory relation can hold, even if the
    \emph{explanans} is not necessitated by the \emph{explanandum}.
    An immediate upshot is that providing a grounding explanation for
    a fact does not require providing necessary and sufficient
    conditions for that fact to obtain.  Likewise, explaining the
    instantiation of a property in a certain thing or the occurrence
    of an event at a certain time does not hang on our ability to
    frame necessary and sufficient conditions for the instantiation of
    the property or the occurrence of the event.  Thus, grounding
    relations among entities may obtain even when the more fundamental
    entities are no part of any reduction or analysis of the grounded
    entities.
  \end{section}
  
  \begin{section} {The Collapse}\label{sec:collapse}
    If grounding explanations are to vindicate the layered conception,
    then facts involving properties and objects that, on that
    conception, inhabit higher layers cannot turn out to be
    fundamental.  For instance, on the layered conception, high-level
    properties like cityhood are supposed to be derivative.  But
    suppose that some facts involving cityhood, \eg,
    \begin{example}
      \text{Beijing is a city.}
    \end{example}
    were fundamental.  The application of \textbf{CORR} would yield
    the fundamentality of cityhood.  Since Beijing's cityhood would
    not then be grounded by any other facts or entities, there would
    be no reasonable sense in which the structure of grounding
    relations would show that Beijing, cityhood, or Beijing's cityhood
    are determined by, dependent upon, or derivative of more basic
    facts and entities.  There would be no reasonable sense in which
    the explanations one might offer of facts involving Beijing or
    cityhood warrant the claim that they belong at a higher layer
    than, say, people, neurons, carbon atoms, electrons, quarks, \etc
    
    Undoubtedly, our intuitive and relatively crude appreciation of
    layered structure is wrong in some cases.  So perhaps we would be
    wrong to insist in advance that cityhood inhabits a
    non-fundamental layer.  It would be fatal for the proposal to
    understand layered structure in terms of grounding, however, if it
    turned out that \emph{every} individual and property somehow
    figured into a complete specification of the fundamental facts.
    Then grounding explanations might reveal an interesting structure
    among \emph{facts}: some facts get explained in terms of others.
    But they wouldn't reveal any interesting structure among
    individuals or properties: all individuals and all properties
    belong at the fundamental level.  The erstwhile layered structure
    would collapse into a single, all-encompassing fundamental layer.
    Sider \citeyearpar[\S\S7.2, 8.2.1]{Sider:forthcoming} argues, in
    effect, that our proposal to use grounding to understand layered
    structure has this fatal flaw.  The fundamentality of the
    grounding facts themselves entails that all individuals and all
    properties inhabit the fundamental level; a complete specification
    of the fundamental facts would mention every individual and every
    property.
    
    Here's the argument.  Assume that a given property, say, cityhood,
    is derivative.  Then there is a fact $\psi$ such that
    \begin{example}
      Beijing is a city because
      $\psi$\label{sent1}\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Here and below, I am sloppy about use and mention where there
        is no threat of confusion.  Also, I indulge the harmless
        simplifying assumption that explanations always have a single
        \emph{explanans} $\psi$.  Perhaps there are cases in which
        there are ineliminably a plurality of facts $\psi_1, \dots,
        \psi_n$, that explain some fact $\phi$.  If so, the arguments
        of this paper could be modified, with some loss of simplicity,
        to accommodate pluralities of \emph{explanans}.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
    \end{example}
    is true.  (\ref{sent1}) states a grounding explanation; call the
    sort of fact reported by (\ref{sent1}) a \emph{grounding fact}.
    Grounding facts are the fundamental basis of layered structure.
    So, presumably, grounding facts are fundamental.  But
    (\ref{sent1}) itself states a fact involving cityhood.  Since
    cityhood is derivative only if no fact involving cityhood is
    fundamental, cityhood is not derivative.  But our choice of
    cityhood was arbitrary: the argument would work equally well with
    any instantiated chemical, biological, geological, psychological,
    sociological, or economic property.  Similar remarks apply to
    other sorts of entities.  So, all such entities are fundamental;
    everything that supposedly inhabits upper layers has turned out to
    be fundamental. This argument is \emph{the collapse}.
    
    The argument shows that the following claims are jointly
    inconsistent:
    \begin{description}
      \item[D1] Beijing is a city;
      \item[D2] Cityhood is derivative;
      \item[FUND] Grounding facts are fundamental;
      \item[FACTS] Cityhood is derivative only if no fact involving
        cityhood is fundamental.
    \end{description}
    \textbf{D1}, \textbf{D2}, and \textbf{FACTS} together imply that
    some claim of the form (\ref{sent1}) is true.  Since (\ref{sent1})
    states a grounding fact, application of \textbf{FUND} yields the
    fundamentality of that fact.  But then \textbf{FACTS} implies that
    cityhood is not derivative.  Contradiction.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The collapse threatens the idea that there is a layered structure
      of \emph{entities}.  A similar puzzle can be put for the claim
      that there is a layered structure of \emph{facts}.  As with the
      collapse, the key insight is that if a fact reported by a true
      instance of (\ref{sent1}) is itself fundamental, then the fact
      that Beijing is a city will be mentioned in any full
      specification of the fundamental facts.  See
      \citep{deRosset:2010} for discussion of a different argument
      that every \emph{entity} is fundamental; that argument does not
      generalize to threaten the idea that there is a layered
      structure of facts.} % [REDACTED]
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    What gives rise to the collapse is that grounding is supposed to
    be the relation that connects the less fundamental to the more
    fundamental, and, ultimately, the fundamental to the derivative.
    If grounding relations are not themselves grounded, then these
    relations between the fundamental and the supposedly derivative
    are among the fundamental facts.  So, the erstwhile derivative
    entities will figure into a full specification of the fundamental
    facts.  In order to make Beijing a city God must not only arrange
    people in the relevant way, He must also set up the grounding
    relations connecting the people and their arrangement to Beijing's
    cityhood.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {This theological metaphor, on which what's fundamental is given
      by what God would have to do to create the world and its
      contents, runs through the literature on grounding.  See,
      \emph{e.g.}, \citep[p. 351]{Schaffer:2009}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But then cityhood turns out to be fundamental.
    It will get mentioned in any complete specification of the
    fundamental facts.  It plays an ineliminable role in the
    fundamental story of the world.

    If we are to use grounding to explicate the intuitive idea of
    layered structure, then one of the claims among \textbf{D1},
    \textbf{D2}, \textbf{FUND}, and \textbf{FACTS} must go.  Which
    one?  For expository purposes, I will assume that \textbf{D1} and
    \textbf{D2} are data, not properly to be rejected.  The specific
    claims \textbf{D1} and \textbf{D2} are, as I have already
    indicated, negotiable.  The point for present purposes is that
    analogues of \textbf{D1} and \textbf{D2} are available with
    respect to every fact involving ostensibly higher-level entities.
    Rejecting the conjunction of such analogues in a given case means
    either denying the putative fact, or admitting the fundamentality
    of the entities it involves.  If we do this in every case, then we
    end up with a view on which all the facts that remain involve only
    fundamental entities.  That's tantamount to collapse.  Thus,
    avoiding the collapse requires accepting the analogues of
    \textbf{D1} and \textbf{D2} in \emph{some} cases.  I'm assuming
    for expository purposes that Beijing's cityhood is one of those
    cases.  That leaves a proponent of the layered conception a choice
    between rejecting \textbf{FUND} and rejecting \textbf{FACTS}.
    
    % FN: no reification of facts is really required
    
    One might think the obvious right response is to reject
    \textbf{FACTS}, which holds the derivativeness of a property,
    cityhood, hostage to the fundamentality of facts involving that
    property.  The truth of a claim like (\ref{sent1}) requires that
    cityhood have a certain feature, the feature that any property $F$
    has if it satisfies the relevant instance of
    \begin{example}
      \text{Beijing is $F$ because $\psi$}.
    \end{example}
    Since possession of that feature is not further explicable, it
    turns out that cityhood's having this feature cannot be explained
    solely by reference to other entities.  Thus, \textbf{FACTS} is an
    upshot of the correspondence \textbf{CORR} between fundamentality
    for facts and fundamentality for the entities they involve.  I
    have argued that \textbf{CORR} is a consequence of
    \begin{description}
      \item[LINK] $e_1, \dots, e_n$ are the entities that ground
        entity $e$ only if $e$'s existence and features are all
        explicable solely by reference to the existence and features
        of $e_1, \dots, e_n$,
    \end{description}
    which we can use to explicate the idea of layered structure.
    
    Perhaps, however, the threat posed by the collapse indicates that
    the way I have used grounding to explicate the idea of layered
    structure is too simple-minded.  A critic might suggest, for
    instance, that \textbf{LINK} is too strong: it requires that a
    derivative entity $e$'s existence and \emph{all} of its features
    be explicable in terms of the existence and features of the
    entities that ground it.  Perhaps we should require only that
    $e$'s existence and \emph{intrinsic} features be explicable by
    reference to those entities.  If \emph{having Beijing as an
      instance because $\psi$} is not an intrinsic feature of
    cityhood, then the weaker requirement does not lead to the
    collapse.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Thanks to Jonathan Schaffer and Kelly Trogdon for independently
      suggesting the need to explore the prospects for weakening
      \textbf{LINK} to avoid the collapse.}
    % [PHILOSOPHER1] and [PHILOSOPHER2]
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} 
    
    The question of whether the explanatory properties involved in
    grounding facts are intrinsic features is difficult.  Fortunately,
    we can duck that difficult question, since the proposed
    replacement for \textbf{LINK} is too weak.  Consider a view on
    which the facts concerning Beijing's intrinsic features are
    completely explicable solely by reference to facts about people,
    but some of its extrinsic properties, including its location, are
    not.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Here I assume that the location of a city is an extrinsic
      property.  This assumption is supported by the fact that
      locations need not be shared among duplicate cities, and thus
      location meets Lewis's test for extrinsicality; see
      \citep[pp. 355ff.]{Lewis:1983}.  It is also supported by
      intuition: a city may change its location without any intrinsic
      change whatsoever.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Nothing in this view forecloses the hypothesis
    that certain facts involving people would be explicable in part by
    appeal to Beijing's features.  Suppose, for instance, that Hu
    Jintao is one of the people whose existence and features explain
    Beijing's population, but that just now he is more than 20 miles
    away from Beijing.  Then the fact that Hu is more than 20 miles
    away from Beijing is, plausibly, explicable in part by appeal to
    Beijing's location; the explanation I have in mind holds that Hu
    is more than 20 miles away from Beijing in virtue of the fact that
    Hu is located at $L_1$, Beijing is located at $L_2$, and $L_1$ and
    $L_2$ are more than 20 miles apart.  So, the view we are
    discussing holds that some facts involving Beijing are explicable
    by appeal to facts involving people, but it also allows that some
    facts involving people are explicable by appeal to facts involving
    Beijing.  For this reason, it is not a view which vindicates the
    claim that certain people are the entities that ground Beijing,
    and it is not a view on which Beijing occupies a higher layer than
    people.  The moral in this case is clear: we should require that
    Beijing's location be explicable by appeal to the entities which
    ground it, even though location is extrinsic.  More generally,
    restricting \textbf{LINK} to intrinsic features does not yield a
    principle that is strong enough on its own to explicate the
    intuitive idea of a layered structure of entities.
    
    There is a lot of middle ground between \textbf{LINK} and its
    restriction to intrinsic features.  Perhaps a subtler explication
    of the idea of layered structure can exploit that ground.  I am
    pessimistic about the prospects for such an explication, but let's
    suppose this pessimism is unwarranted, and we manage to come up
    with a qualified version of \textbf{LINK} that may plausibly be
    used to explicate the idea of layered structure.  Then
    \textbf{LINK} could be safely rejected.  But, strictly speaking,
    the full-strength of \textbf{LINK} is not required for the
    collapse.  The collapse requires only the weaker claim
    \begin{description}
    \item[CORR] An entity $e$ is fundamental if $e$'s existence or
      its possession of some feature is fundamental.
    \end{description}
    of which \textbf{FACTS} is a contraposed instance.  \textbf{LINK}
    offers some support for \textbf{CORR}, but, I have argued,
    \textbf{CORR} is in any case independently plausible.  So, it
    seems to me that \textbf{CORR} should be a commitment of any view
    which attempts to account for layered structure by appeal to
    grounding explanations.  \textbf{CORR} is a natural upshot of the
    idea that grounding structure is revealed by grounding
    explanations, which say what obtains in virtue of what.  The idea
    is that the fundamental entities are the entities that must be
    mentioned in a complete specification of that in virtue of which
    all else obtains.  Insofar as the relevant instance of
    (\ref{sent1}) is fundamental, cityhood will be mentioned in any
    such specification.  Abandoning \textbf{FACTS}, then, is
    tantamount to abandoning the attempt to explain layered structure
    by means of grounding explanations.  For this reason I prefer to
    explore responses to the objection that leave \textbf{FACTS}
    alone.
    
    % three-category views (Johnston, Fine) reject \textbf{FUND}
  \end{section}
  
  \begin{section}{Grounding Explanations}\label{sec:positiveView}
    I have suggested that those who wish to use grounding explanations
    to explicate layered structure should avoid the collapse by
    denying \textbf{FUND}.  I have further suggested that one should
    not deny \textbf{FUND} while affirming that grounding facts do not
    obtain in virtue of any further facts.  The best way to avoid the
    collapse, I think, is to grasp the nettle, and say how grounding
    facts are themselves to be grounded.  The history of attempts to
    explicate grounding in other terms is not encouraging.  In
    particular, the attempt to recruit supervenience to play the role
    of grounding faces serious objections.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Lewis \cite[p. 358]{Lewis:1983} makes this suggestion in passing;
      For criticism, see works cited in n. \ref{fn:AltsBad}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} The lesson this history teaches is that we should
    make no attempt to provide either a conceptual or a metaphysical
    analysis that provides necessary and sufficient conditions for
    grounding.  Proponents of grounding have taken this lesson to
    heart.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\citep[p. 21]{Fine:2001}, \citep[pp. 375--77]{Schaffer:2009}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} But one lesson of our efforts in
    \S\ref{sec:setup} to distinguish grounding explanations from
    reductions is that grounding explanations do not require necessary
    and sufficient conditions.  This opens the door to a view on which
    grounding facts can themselves be grounded, even in the absence of
    an analysis or reduction of the grounding relation.
    
    Some informal reflections motivate just such a view.  Suppose that
    a claim of the form
    \begin{example}\label{sent2}
      $\phi$ because $\psi$
    \end{example}
    is true.  It is plausible to think that a true explanation
    must be backed by an argument from \emph{explanans} to
    \emph{explanandum}.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Most prominently, this presumption is enshrined in the
      deductive-nomological account of explanation
      \citep{HempelOppenheim:1948}.  I am not, however, signing on to
      the deductive-nomological account in detail; in particular, I
      assume neither that the arguments in question are
      \emph{deductive}, nor that they are \emph{nomological} -- laws
      need play no special role.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Call such an argument an \emph{explanatory
      story}.  On this presumption (\ref{sent2})'s truth requires that
    there is an explanatory story that one could in principle tell,
    that starts with $\psi$ and ends with $\phi$.  We can represent
    the form of this explanatory story by
    \begin{equation}\label{sent11}
      \begin{tabular}{|c|}\hline
      $\qquad\qquad\psi\qquad\qquad$\\$\chi_1$\\$\chi_2$\\$\dots$\\So, $\phi$\\\hline
      \end{tabular}
    \end{equation}
    , where the $\chi$'s stand in for ancillary material that may be
    necessary for making the \emph{explanandum} intelligible (given
    the \emph{explanans}) to one's audience.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {A limiting case of an explanatory story of the form represented
      by (\ref{sent11}) is a case in which there is no such ancillary
      material, and so no $\chi$'s at all.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}  For example, if the explanatory claim in
    question is
    \begin{example}\label{sent13}
      It is either chilly or windy because it is chilly
    \end{example}
    then the ancillary information might include the observation that
    the \emph{explanans} is a disjunction, a review of the truth table
    for disjunction, or a reference to a rule of disjunction
    introduction.
    
    If the explanatory story represented by (\ref{sent11}) is
    successful, it issues in the conclusion that (\ref{sent2}) is
    true.  Thus, (\ref{sent11}) is an initial segment of a further
    argument, which has the form
    \begin{equation}\label{sent12}
      \begin{tabular}{|c|}\hline
      \qquad$\psi$\qquad\qquad\\$\chi_1$\\$\chi_2$\\\dots\\So,
      $\phi$\\$\chi^\prime_1$\\$\chi^\prime_2$\\\dots\\So, $\phi$
      because $\psi$\\\hline
    \end{tabular}
    \end{equation}
    Assuming that (\ref{sent11}) is a successful explanatory story
    issuing in the conclusion (\ref{sent2}), (\ref{sent12}) is a good
    (presumably non-deductive) argument.  My suggestion is that this
    argument \emph{is also an explanatory story}.  Consider again an
    explanation of the form
    \begin{equation*}
      \tag{\ref{sent1}}\text{Beijing is a city because $\psi$}
    \end{equation*}
    where $\psi$ is a fact concerning the locations, activities, and
    attitudes of certain people.  If that explanation is correct, then
    one could in principle start by laying out the facts involving
    people, trace how those facts make it the case that Beijing is a
    city, and conclude by noting (\ref{sent1}).  But then that very
    same story seems to answer the question of what makes it the case
    that the grounding fact reported by (\ref{sent1}) obtains.  One
    could, as before, start by laying out the facts involving people,
    trace how those facts make it the case the Beijing is a city, note
    (\ref{sent1})'s truth, and conclude by noting
    \begin{equation}
      \label{sent4}\text{(Beijing is a city because $\psi$) because $\psi$}.
    \end{equation}
    In general, the suggestion is that every instance of the following
    schema is true:
    \begin{description}
      \item[BECAUSE] $\phi$ because $\psi\Longrightarrow (\phi$ because
        $\psi)$ because $\psi$.\linespread{1}\footnote
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        {Notice that the \emph{prima facie} plausibility of
          \textbf{BECAUSE} depends on my artificially narrow use of
          ``because'' to indicate grounding explanation; see
          n. \ref{fn:restrict}.  For instance, if pressing the
          detonator \emph{causally explains} the explosion, then it
          would not be plausible to claim that pressing the detonator
          causally explains \emph{the fact that pressing the detonator
            caused the explosion}.}
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        \linespread{1.3}
    \end{description}
    
    The informal reflections that motivate \textbf{BECAUSE} can hardly
    be taken to be decisive.  But adoption of \textbf{BECAUSE} has two
    important advantages.  The first advantage, conspicuous in the
    present context, is that adopting \textbf{BECAUSE} allows us to
    evade the collapse.  Recall that the collapse depended on the
    claim
    \begin{description}
      \item[FUND] Grounding facts are fundamental.
    \end{description}
    If we adopt \textbf{BECAUSE}, then \textbf{FUND} turns out to be
    false.  The trouble concerned the allegation that an explanation
    of the form
    \begin{equation*}
      \tag{\ref{sent1}}\text{Beijing is a city because $\psi$}
    \end{equation*}
    is fundamental.  But \textbf{BECAUSE} implies that (\ref{sent1})
    is not fundamental; it obtains in virtue of $\psi$.  So long as
    $\psi$ is cityhood-free, we needn't mention cityhood to give a
    complete description of that in virtue of which all else obtains.
    
    In fact, barring any reduction of grounding facts,
    \textbf{BECAUSE} is well-nigh inevitable if we wish to avoid the
    collapse while accepting the idea that layered structure is to be
    explicated by appeal to explanatory fundamentality, in the sense
    of \S\ref{sec:setup}.  An explication of this sort, I have argued,
    is best defended by denying \textbf{FUND}, which says that
    grounding facts are fundamental.  Suppose for illustration that
    Beijing's cityhood is explained by some fundamental fact $\psi$.
    Consider the question of how to ground
    \begin{equation*}
      \tag{\ref{sent1}}\text{Beijing is a city because $\psi$.}
    \end{equation*}
    Explaining (\ref{sent1}) requires explaining the relationship
    between Beijing's cityhood and $\psi$.  There are, in principle,
    only four ways to go: (\emph{i}) appeal to both of the relata,
    (\emph{ii}) appeal only to Beijing's cityhood; (\emph{iii}) appeal
    to some fact involving neither $\psi$ nor Beijing's cityhood; or
    (\emph{iv}) appeal only to $\psi$.  Appealing to both relata or to
    Beijing's cityhood alone doesn't avoid the collapse.  Appealing to
    Beijing's cityhood alone is also a clear non-starter, as, it seems
    to me, is appealing to some fact involving neither $\psi$ nor
    Beijing's cityhood.  The best salient alternative, then, is to
    appeal to $\psi$ alone.  That, in effect, is what \textbf{BECAUSE}
    does.       
    
    The second advantage of adopting \textbf{BECAUSE} is a little
    subtler.  Recall that grounding explanations are consistent with
    multiple realizability.  Thus, an explanation of the form
    \begin{equation*}
      \tag{\ref{sent2}}\text{$\phi$ because $\psi$}
    \end{equation*}
    does not entail what we might call \emph{downward necessitation}:
    \begin{equation}
      \square(\phi\Rightarrow\psi)\qquad.\label{sent9}
    \end{equation}
    Several authors have suggested, however, that the converse
    necessitation relation is required if the explanation is complete:
    if a fact $P$ is completely explained by $Q$, then it is
    impossible that $Q$ obtain and $P$ not obtain.  This requirement
    is plausible.  Suppose I suggest that a certain lump of coal has
    the mass it does in virtue of the fact that it is made of a
    certain number $n$ of carbon atoms.  The fact that those atoms
    could be replaced by different isotopes of carbon to give the lump
    a different mass indicates that this cannot be the whole story:
    the fact that the lump is made of $n$ carbon atoms explains its
    mass only against the background of the facts detailing the
    relative proportions of relevant carbon isotopes.  In general, an
    explanation has modal force: it's supposed to indicate what
    \emph{makes} the \emph{explanans} obtain.  If it is possible for
    the \emph{explanandum} to obtain while the \emph{explanans} does
    not, then the \emph{explanandum} does not make the
    \emph{explanans} obtain, and so the explanation fails.  Something
    similar holds for properties and entities of other categories: if
    an entity $e$'s existence and features are explained by appeal to
    entities $e_1, \dots, e_n$, then it is impossible that $e_1,
    \dots, e_n$ exist and have the features they do and yet $e$ fail
    to exist or have some of its actual features.  In summary, it is
    plausible to impose a requirement of \emph{upward necessitation}
    on claims of the form (\ref{sent2}):\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {The reflections in the main text are meant to be suggestive, but
      don't conclusively support a requirement of upward
      necessitation.  In particular, there are ways of spelling out
      the notion of \emph{making something the case} that are weaker
      than necessitation.  Contemporary discussions of causation may
      be construed as sketching the outlines of such a notion; see
      \citep{Woodward:2008} for discussion.  Such a requirement is
      assumed by many; see, \eg, \citep[p. 118]{Rosen:2010}.  But it
      is disputed by some, including Stephan Leuenberger (personal
      communication) and \cite[pp. 320-1]{Schaffer:2010b}.  We can
      accommodate doubts about upward necessitation by casting the
      argument of the next paragraph as showing that \emph{if} there
      is a requirement of upward necessitation, then the explanations
      required by \textbf{BECAUSE} meet it.  In fact, I don't believe
      these doubts should be accommodated.  See \citep{deRosset:2010}
      for a more serious argument in favor of a requirement of upward
      necessitation.  Thanks to Stephan Leuenberger and Jonathan
      Schaffer for discussion.
      % [REDACTED]
      % [PHILOSOPHER1] and [PHILOSOPHER2]
    }
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} if such an explanation is complete, it entails
    \begin{equation}
      \square(\psi\Rightarrow\phi)\qquad.\label{sent10}
    \end{equation}
    
    
    The second advantage of adopting \textbf{BECAUSE} is that, given that an
    explanation of the form 
    \begin{equation*}
      \tag{\ref{sent2}}\text{$\phi$ because $\psi$}
    \end{equation*}
    meets the requirement of upward necessitation, the explanations
    for grounding facts required by \textbf{BECAUSE} appear to as
    well.  Suppose that an explanation of the form (\ref{sent2}) is
    true.  Application of \textbf{BECAUSE} yields
    \begin{equation}
      (\phi \text{ because } \psi) \text{ because } \psi.\label{sent5}
    \end{equation}
    Upward necessitation requires that, if (\ref{sent5}) is complete,
    then its \emph{explanans} $\psi$ necessitates its
    \emph{explanandum} (\ref{sent2}).  Assume that (\ref{sent5}) is
    complete.  (\ref{sent2}) will also be
    complete.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Here I assume that if (\ref{sent5}) is a complete explanation,
      then so is (\ref{sent2}).  Any incompleteness in (\ref{sent2})
      indicates that the explanation of $\phi$ by $\psi$ is only
      partial: $\psi$ is only a part of the totality of facts which
      explain $\phi$, and so only explains $\phi$ against the
      background of certain further facts.  Thus, any full
      specification of the facts in virtue of which $\psi$ (partially)
      explains $\phi$ needs to include those further facts.  In short,
      an incompleteness in (\ref{sent2}) implies an incompleteness in
      (\ref{sent5}).}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} The application of upward necessitation to
    (\ref{sent2}) guarantees that
    \begin{equation*}
      \tag{\ref{sent10}}\square(\psi\Rightarrow\phi)
    \end{equation*}
    is true.  The only way for (\ref{sent5}) to fail the requirement
    of upward necessitation is for
    \begin{equation}
      \square(\psi\Rightarrow(\phi \text{ because } \psi))
    \end{equation}
    to be false.  That, in turn, would require that it be possible for
    $\psi$ to obtain but not ground $\phi$.  Given the necessitation
    of $\phi$ by $\psi$, it must be possible that $\phi$ and $\psi$
    both obtain, and yet $\phi$ not obtain in virtue of $\psi$.  In
    focal cases of grounding explanations, there is no such
    possibility.  For instance, given that Al and Beth's heights
    average 5'6'' because Al is 5'4'' and Beth is 5'8'', it is not
    possible for Al and Beth to have those respective heights, and yet
    for their height to average 5'6'' in virtue of some other
    circumstances.  Likewise, given that a certain material object is
    rectilinear in virtue of being exhaustively composed of particles
    in a rectilinear arrangement, it is not possible for that object
    to be rectilinear and exhaustively composed of particles in that
    arrangement, and yet for there to be no explanatory relation
    between those facts.
    
    It should be noted that a related necessitation claim may fail.
    Perhaps there are causes in which $\psi$ is actually a complete
    explanation of $\phi$, and yet it is possible that $\psi$ obtain
    and not be a \emph{complete} explanation of $\phi$.  It is
    plausible, for instance, to think that (\emph{i}) a certain
    yellow, rectilnear material object is \emph{either red or
      rectilinear} in virtue of being composed of particles in a
    rectilinear arrangement; furthermore, (\emph{ii}) the
    compositional fact completely explains the thing's being either
    red or rectilinear; but (\emph{iii}) it is possible that it be
    \emph{either red or rectilinear} in virtue of being \emph{both}
    red \emph{and} composed of particles in a rectilinear arrangment;
    and so (\emph{iv}) it is possible that its being either red or
    rectilinear is explained, but not \emph{completely} explained, by
    the arrangement of its composing particles.  The conjunction of
    all of the claims (\emph{i})-(\emph{iv}) is consistent with
    \textbf{BECAUSE}.
    
    The second advantage, then, of adopting \textbf{BECAUSE} is that
    it provides a way of explaining grounding facts that appears to
    meet the requirement of upward necessitation.
    
    \textbf{BECAUSE} does not provide the means to ground every fact
    we might express using ``because'', even on my artifically narrow
    use of the term to indicate grounding
    explanation.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {See n. \ref{fn:restrict}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Suppose, for instance, that $\psi$ and $\chi$
    explain Beijing's and Shanghai's cityhood, respectively.  Then
    \begin{example}
      $\neg$($\psi$ because $\chi$).
    \end{example}
    is plausible.  \textbf{BECAUSE} does not tell us how to ground
    such a fact.  More generally, \textbf{BECAUSE} gives no hint about
    how to ground negations of explanatory claims.  Recall that
    fundamentality for a fact $\phi$ boils down to there being no
    explainer for $\phi$.  So, \textbf{BECAUSE} gives us no hint as to
    how to ground facts concerning what's
    fundamental.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {\textbf{BECAUSE} does, however, point the way to explaining the
      \emph{non}-fundamentality of Beijing's being a city.  Given the
      framework sketched in \S\ref{sec:setup}, the non-fundamentality
      of Beijing's being a city comes to there being some explainer
      for that fact.  According to \textbf{BECAUSE}, the fact $\psi$
      that explains Beijing's cityhood also explains a certain
      grounding fact: to wit, that $\psi$ explains Beijing's cityhood.
      It is plausible to think that \emph{some fact or other} explains
      Beijing's cityhood in virtue of $\psi$'s doing so.  Thus,
      ultimately, the fact that explains Beijing's cityhood is also
      the fact in virtue of which Beijing's cityhood is
      derivative. \label{fn:explaining_derivativeness}}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Thus, embracing \textbf{BECAUSE} is consistent
    with thinking that \emph{some} facts involving grounding are
    themselves fundamental.  But the collapse does not involve any of
    those facts.
  \end{section}
  
  \begin{section}{Trialism}
    The response to the collapse that I have urged denies
    \textbf{FUND} by suggesting how the grounding facts may themselves
    be grounded.  There is, however, a different response implicit in
    some of the extant literature.  I have been working with a
    characterization of fundamentality on which facts (and entities)
    divide exhaustively into the fundamental and the derivative.  The
    idea is illustrated by the simple picture in
    fig. \ref{fig:simple}.
    \begin{figure}
      \begin{tabular}{|c|}
        \hline
        \includegraphics[scale=0.8]{picturez/slide1.jpg}\\
        \hline
      \end{tabular} 
      \caption{The simple picture}
      \label{fig:simple}
    \end{figure}
    Some theorists suggest that we should instead divide facts into
    three categories: the grounding facts, the basic facts, and the
    generated facts.  Grounding facts are, as we have already seen,
    the facts about what grounds what; \emph{basic facts} are not
    themselves grounding facts, but, together with the grounding
    facts, they generate the full, rich array of facts; and the rest
    are the \emph{generated facts}.  Suppose, for instance, that
    Beijing is a city in virtue of the locations, actions, and
    attitudes of certain human beings (and ignore for the moment that
    the relevant facts involving human beings are themselves further
    explicable).  The relevant facts involving those human beings are
    a basis that, together with the grounding fact that Beijing is a
    city in virtue of those facts, yield the generated fact that
    Beijing is a city.  On this view, which I'll call \emph{trialism},
    all basic facts are fundamental: they do not obtain in virtue of
    any further facts.  But the converse is not guaranteed: some
    fundamental facts -- in particular, those fundamental facts
    concerning what grounds what -- may fail to be basic.  Thus,
    according to trialism, we need to distinguish two different kinds
    of fundamental fact: the basic facts and the fundamental grounding
    facts.  Our simple picture needs to be complicated a little, as
    illustrated in fig. \ref{fig:trialism}.
    \begin{figure}
      \begin{tabular}{|c|}
        \hline
        \includegraphics[scale=0.75]{picturez/slide2.jpg}\\
        \hline
      \end{tabular} 
      \caption{The trialist picture.}
      \label{fig:trialism}
    \end{figure}
    If we wish to generalize from facts to entities, the generated
    entities are given by the basic entities, together with
    generators.  Consider, for instance, a certain bunch of
    marbles.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Thanks to Mark Moyer for suggesting this example.% [PHILOSOPHER]
    }
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} It is plausible to think that the bunch of
    marbles is grounded in its constituent marbles.  Then those
    marbles and their standing in the \emph{bunched} relation provide
    a basis that, together with the generator provided by the
    grounding relation, yields the bunch of marbles as a generated
    entity.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {A thoroughgoing exposition of trialism would include a more
      satisfactory characterization of the tripartite distinctions
      among facts and entities.  Here I sketch only as much as is
      necessary to outline and schematically assess the trialist
      defense against the collapse.  For more complete treatments, see
      \citep{Fine:1991}, \citep{Johnston:2006}, and
      \citep{Schaffer:2009}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
    
    % \begin{figure}[h]
    %   \centering
    %   \xymatrix@1@C=20pt{
    %     &&&&&&&\\
    %     &&&&&&&\\
    %     && {\ellipse(12,16){}} & *!/r
    %     0.45cm/{}\ar@{=>}[rrr]_*+!/l 8pt/{EXPLAIN} & & & *!/l 0.3cm/{} &
    %     {\ellipse(12,16){}} \\
    %     &&&&&&\\
    %     && *!/d 1cm/\txt{\it{}fundamental\\\it{}facts} & &&&& *!/d 1cm/\txt{\it{}derivative\\\it{}facts}
    %   }
    % \end{figure}    \\
    
      
    Given trialism's tripartite division of facts, the objector
    suggests that the notion of a \emph{basic} fact should replace the
    notion of \emph{fundamental} fact in our explication of layered
    structure.  Likewise, the notion of a \emph{generated} fact should
    replace the notion of a \emph{derivative} fact.  A fact $f$ is
    \emph{more basic} than $g$ iff $f$ explains $g$ and not vice
    versa.  Grounding facts will thus be excluded from the basicness
    ordering, except insofar as they themselves serve as
    \emph{explanans} or \emph{explananda}.  Consider again a grounding
    fact of the form
    \begin{equation*}
      \tag{\ref{sent1}}\text{Beijing is a city because $\psi$.}
    \end{equation*}
    That grounding fact is neither more nor less basic than Beijing's
    cityhood, supposing it neither explains nor is explained by that
    fact.  This basicness ordering can be used to explicate layered
    structure.  If facts involving genes are quite generally less
    basic than facts about molecules, so that every gene fact obtains
    in virtue of some molecule fact, but not vice versa, then it is
    plausible to think that the genes inhabit a higher layer than the
    molecules.  The basic entities, which inhabit the lowest layer,
    will then be just those entities involved in the basic
    facts.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {My uses of the words ``basic'', ``generated'', ``fundamental'',
      and ``derivative'' are stipulative and artificial: I aim to mark
      different notions with different vocabulary.  This
      terminological choice is not intended to track any pre-theoretic
      distinction one might discern, \eg, between the near-synonyms
      ``basic'' and ``fundamental''.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} If we adopt the trialist's proposal, then the
    collapse will have to be recast using the trialist's favored
    notions.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {For the record, if we fail to recast the collapse, insisting that
      the trialist choose between \textbf{FUND} and \textbf{FACTS},
      the trialist may reject \textbf{FACTS}, claiming that cityhood's
      involvement in fundamental facts does not impugn its status as
      derivative, so long as those fundamental facts are grounding
      facts.  Alternatively, the trialist may reject \textbf{D2}, the
      claim that cityhood is derivative, in the sense of
      \S\ref{sec:setup}.  (Clearly these alternatives are not
      exclusive: the trialist may reject both claims.) Rejecting
      \textbf{D2} is tantamount to accepting the collapse in its
      original form; the trialist may take its lesson to be that
      fundamentality, in the sense of \S\ref{sec:setup}, is the wrong
      notion for explicating the idea of layered structure.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} The result of recasting yields, as the two key
    claims:
    \begin{description}
    \item[FUND${}^*$] Grounding facts are basic;
    \item[FACTS${}^*$] Cityhood is generated only if no fact involving
      cityhood is basic.
    \end{description}
    Trialism requires the rejection of \textbf{FUND${}^*$}, and so
    escapes the collapse.  Grounding facts are not basic; they are not
    generated either; instead, they belong to their own, third
    category.  Thus, cityhood's involvement in grounding facts does
    not count against its being generated.
    
    The trialist defense requires that we accord special treatment to
    grounding facts in our explication of the idea of layered
    structure.  Suppose we accept the tripartite divisions of facts
    and entities.  Then there is by implication a distinction between
    two sorts of fundamental facts: the grounding facts and the rest.
    The grounding facts don't get the label ``basic'', but they still
    must be mentioned if we are to completely specify that in virtue
    of which all of the rich panoply of facts obtain.  One of the key
    intuitions backing the idea of layered structure is that cityhood,
    along with a lot of other entities, need not be mentioned in order
    to give a complete specification of fundamental reality.  The
    trialist defense has it that the mention of cityhood (along with
    all of the other entities) in grounding facts does not count
    against this idea.  Somehow a specification of fundamental reality
    can be complete without mentioning grounding facts.
    
    There are two problems with this idea.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Sider appears to concur; see \citep[\S8.2.1]{Sider:forthcoming}.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} First, the grounding facts are, after all,
    \emph{facts}, and they are, on the trialist defense, facts that
    cannot be explained by appeal to further facts.  So a
    specification of fundamental reality that leaves out the grounding
    facts leaves out some of the facts.  This seems on its face a
    reason to think that such a specification is incomplete.  The
    problem, to summarize, is that \emph{any full specification of the
      basic facts that leaves the grounding facts out is intuitively
      incomplete}.  Second, there seems to be no reason to grant
    grounding facts special treatment when we determine which entities
    are fundamental.  Other facts, like
    \begin{example}
      \text{Beijing is a less populous city than Shanghai}
    \end{example}
    would, if they appeared in a complete specification of fundamental
    reality, count against the idea that cityhood is derivative.  So
    \emph{the trialist defense needs to justify the special treatment
      given to grounding facts}.
     
    
    A trialist might motivate special treatment for grounding facts by
    appeal to a natural analogy between grounding and
    causation.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Thanks to Shamik Dasgupta and Jonathan Schaffer for offering this
      suggestion.}% [PHILOSOPHER1] and [PHILOSOPHER2]
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3} Grounding relations, like causal relations, are
    relations of determination and dependence.  Like causal relations,
    grounding relations are accompanied by explanations that trace the
    direction of determination and dependence.  The trialist picture
    yields a further point of similarity: both grounding and causal
    explanations have a tripartite structure.  We have already noted
    the trialist's three-fold distinction among basic facts, generated
    facts, and grounding facts.  In the case of causation, there are
    (\emph{i}) the \emph{causes}, (\emph{ii}) the \emph{effects}, and
    (\emph{iii}) the \emph{causal mediators}, which, depending on
    one's view of the metaphysics of causation, may be the laws,
    enabling conditions, counterfactual dependence relations, the
    causal relation itself, \emph{etc.}  It is a mistake, the trialist
    notes, to demand an answer to the question, ``What caused the
    mediator?''  in every case.  Suppose, for instance, that the
    causal relation between the striking of the match and its ignition
    is mediated by a law which says, roughly, that matches ignite when
    struck.  It would be a mistake to ask what caused the law itself
    to obtain.  The law is not a cause; it is not an effect either; it
    is a third kind of thing.  The trialist paints a picture on which
    grounding shares a tripartite structure with causation.  The
    trialist may exploit this similarity of structure to argue for
    special treatment for grounding facts.  The idea is that, just as
    it is a mistake to ask what causes the law that matches ignite
    when struck, so it is a mistake to ask what grounds the fact that
    $\psi$ grounds Beijing's cityhood.  Just as causal mediators need
    not themselves be part of the causal order, so the grounding facts
    need not themselves be part of the fundamentality order.
    
    This analogy with causation does not support the claim that
    grounding facts are not part of the fundamentality order.  Or,
    more accurately, it equally motivates the contrary claim, that
    grounding facts are part of the fundamentality order.  This is
    because, while it does often seem mistaken to ask what
    \emph{causes} a given causal mediator, it is not mistaken at all
    to ask what \emph{grounds} it.  Almost no one has written about
    what causes causal laws because that seems like a bad question;
    barrels of ink have been spilled in disputes about what grounds
    causal laws because that is a very good question.  We may
    therefore exploit the similarity of structure between causation
    and grounding to argue that grounding facts should not receive
    special treatment: just as it is clearly in order to ask what
    grounds the law that matches ignite when struck, so it is clearly
    in order to ask what grounds the fact that $\psi$ grounds
    Beijing's cityhood.  Grounding facts are part of the
    fundamentality order, just like causal mediators.  The trialist
    has noted that one way of generalizing from the case of causation
    suggests granting special treatment to grounding facts.  But
    another, equally appropriate way of generalizing suggests instead
    that grounding facts should not be granted special treatment.
    Thus, the trialist's analogy between causation and grounding does
    not ultimately justify granting grounding facts the sort of
    special treatment required by the trialist defense.
    
    Perhaps, however, a justification could be mounted along the
    following lines: grounding is needed to explicate the idea of
    layered structure, and is theoretically very fruitful; if the
    price of these theoretical fruits is special treatment for
    grounding facts, then that price is well worth paying.  The
    assumption here is that the trialist defense provides the only
    plausible way of avoiding the collapse.  I have argued, however,
    that this assumption is false: we can avoid collapse at a cheaper
    price by endorsing \textbf{BECAUSE}.  A trialist might urge, in
    response, that \textbf{BECAUSE} has its own problems: it faces
    objections independently of any antecedent commitment to trialism.
    Let's now consider some of these objections.
  \end{section}

  
  \begin{section}{Objections}
    \begin{subsection}{Regress}
      It might be thought that \textbf{BECAUSE} implies a problematic
      infinite regress.  Suppose again that we have a true explanation
      of the form
      \begin{equation*}
        \tag{\ref{sent1}}\text{Beijing is a city because $\psi$}.
      \end{equation*}
      Then applications of \textbf{BECAUSE} yield a series of explanatory
      claims:
      \begin{description}
      \item
        \begin{tabular}{|l|}\hline
          (Beijing is a city because $\psi$) because $\psi$\\ ((Beijing is
          a city because $\psi$) because $\psi$) because
          $\psi$\\ (((Beijing is a city because $\psi$) because $\psi$)
          because $\psi$) because $\psi$\\ \dots\\\hline
        \end{tabular}
      \end{description}
      This series is infinite, but there is no regress, or at least no
      problematic regress.  According to \textbf{BECAUSE}, each fact
      in the series is grounded; all are grounded in the same fact,
      $\psi$.  So explanations for every item in the series are
      anchored in a single fact.  There is nothing more problematic in
      such a series of \emph{explananda} than there is in the sensible
      idea that $\psi$ also grounds every fact in the series
      \begin{description}
      \item 
        \begin{tabular}{|l|}\hline
          $(\psi\vee\phi_1)$\\
          $((\psi\vee\phi_1)\vee\phi_2)$\\
          $(((\psi\vee\phi_1)\vee\phi_2))\vee\phi_3)$\\
          \dots\\\hline
        \end{tabular}
      \end{description}
      where $\phi_1, \phi_2, \dots$ are pairwise distinct,
      contingently false claims, \eg, ``I am 1 cm taller than LeBron
      James'', ``I am 2 cm taller than LeBron James'', \etc
      
      Another worry about \textbf{BECAUSE} is not so easily dismissed.
      The worry is that the explanations of grounding facts provided
      by instances of \textbf{BECAUSE} are all inadequate or
      incomplete.  Suppose again that some fact $\psi$ explains
      Beijing's cityhood.  Then $\psi$ and the fact that Beijing is a
      city are related in a rare and special way: there is an
      explanatory tie between them.  The fact $\psi$ is not related in
      this way to just any old fact.  Thus, the mere assertion of the
      fact $\psi$ fails to account for the rare and special relation
      obtaining between $\psi$ and Beijing's cityhood and marked by
      our use of ``because.''  To account for that relation we need to
      say more than just that one of the relata obtains.  
      
      Why think that $\psi$ fails to account for the explanatory
      relation between $\psi$ and Beijing's cityhood?  Three reasons
      spring to mind.  The rest of this section will be devoted to
      discussing each reason in turn.
    
    \end{subsection}
    
    \begin{subsection}{Connection}
      
      The first reason one might have for thinking that instances of
      \textbf{BECAUSE} fail to account for the explanatory relation
      between \emph{explanans} and \emph{explanandum} concerns the
      form that explanations of grounding facts must take, given our
      assumptions.  ``Surely,'' the objection goes, ``one cannot
      explain why $\psi$ explains Beijing's cityhood without drawing a
      connection between $\psi$ and Beijing's cityhood.  In order to
      explain why $\psi$ explains Beijing's cityhood, one would need
      to say something about \emph{Beijing} and \emph{cityhood}.
      Since there's no way to explain the explanatory relation between
      $\psi$ and Beijing's cityhood without mentioning the erstwhile
      derivative entities, the relevant instance of \textbf{BECAUSE}
      is false.''\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Thanks to Rob Rupert and Shamik Dasgupta for independently
        pressing the need to respond to this objection.}
      % [PHILOSOPHER1] and [PHILOSOPHER2]
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      The objector's core claim is:
      \begin{description}
      \item[CONNECTION] To explain a certain feature of Beijing's
        cityhood -- its being explained by $\psi$ -- one must appeal
        to facts which themselves involve Beijing and cityhood.
      \end{description}
      The first thing to note about the objection is that the problem
      is not peculiar to the explanation of grounding facts.  An
      entirely analogous objection can be put with respect to the
      putative explanation of ordinary facts involving Beijing.
      Consider Beijing's cityhood.  If \textbf{CONNECTION} is
      plausible, then so is the claim that one must mention Beijing
      and cityhood to explain Beijing's cityhood.  Without such a
      mention, it will be mysterious how the putative explanation of
      Beijing's cityhood is connected with \emph{Beijing} and
      \emph{cityhood}.  Thus, insofar as \textbf{CONNECTION} is
      plausible, so is
      \begin{description}
      \item[ANALOGUE] To explain a certain feature of Beijing -- its
        cityhood -- one must appeal to facts which themselves involve
        Beijing and cityhood.
      \end{description}
      Call this \emph{the connection problem} for explaining Beijing's
      features.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {I borrow the label from Jonathan Schaffer.}% (personal
                                                  % communication)
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      A constraint on an adequate solution to the connection problem
      for explaining Beijing's cityhood is that if we establish the
      requisite connection to Beijing by appeal to some fact involving
      Beijing or cityhood then that fact need not be among the
      \emph{explanantia} for Beijing's cityhood.  The proponent of
      \textbf{BECAUSE} has the resources to meet this constraint.
      Recall that we can represent the form of an explanatory story by
      \begin{equation*}
        \tag{\ref{sent11}}
        \begin{tabular}{|c|}\hline
          $\qquad\qquad\psi\qquad\qquad$\\$\chi_1$\\$\chi_2$\\$\dots$\\So, $\phi$\\\hline
        \end{tabular}
      \end{equation*}
      , where the $\chi$'s stand in for ancillary material.
      Importantly, this ancillary material needn't itself be reckoned
      to be part of the \emph{explanans}.  Suppose, for instance, that
      it is chilly but not windy.  Then
      \begin{equation*}
        \tag{\ref{sent13}}\text{It is either chilly or windy because it
          is chilly}
      \end{equation*}
      is both true and complete.  But, as we have seen, an explanatory
      story backing (\ref{sent13}) may mention certain general facts
      involving the nature of disjunction, appealing, perhaps, to an
      inference rule or truth table for `or'.  One shouldn't think of
      these appeals to general claims about disjunction as part of the
      complete specification of those facts in virtue of which it is
      either chilly or windy, however.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {I think it's tolerably clear that general claims about
        disjunction are not themselves part of any full specification
        of the facts in virtue of which it is either chilly or windy.
        But there is an argument for this conclusion, inspired by
        \citep{Carroll:1895}.  Suppose we appeal to the validity of an
        inference rule for disjunction introduction in giving the
        explanatory story backing (\ref{sent13}).  Then a more
        complete grounding explanation for (\ref{sent13}) is given by
        \begin{example}
          It is either chilly or windy because: it is chilly, and
          \emph{$\vee$-introduction} is valid.
        \end{example}
        This explanatory proposal will itself be backed by an
        explanatory story, which makes appeal, implicitly or not, to
        the validity of, say, \emph{modus ponens}.  By parity of
        reasoning, a more complete explanation is given by
        \begin{example}
          It is either chilly or windy because: it is chilly,
          \emph{$\vee$-introduction} is valid, and \emph{modus ponens}
          is valid.
        \end{example}
        But these explanatory proposals have gotten progressively less
        plausible.  (If the conditionals corresponding to the
        applications of the inference rules must also be included,
        then we get a Carroll-style regress.)  Clearly, the most
        plausible and least \emph{ad hoc} way to respond to this
        pseudo-problem is to deny the first step: the validity of
        disjunction introduction is no part of a complete
        specification of that in virtue of which it is either chilly
        or windy.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} 
      
      Thus, we need to distinguish the entities that \emph{must be
        mentioned in the explanatory story} from the entities
      \emph{involved in the \emph{explanans}}.  A proponent of the
      plausible idea that Beijing is a city in virtue of facts
      concerning the locations, attitudes and activities of certain
      people may accept \textbf{ANALOGUE}, and insist that the
      relevant facts involving erstwhile derivative entities must be
      mentioned in the explanatory story, but are not themselves part
      of the \emph{explanans}.
      
      A similar response can be mounted to solve the connection
      problem for explaining the fact that $\psi$ grounds Beijing's
      cityhood.  This shows, in effect, that \textbf{CONNECTION} is
      consistent with \textbf{BECAUSE}: we may appeal to facts
      involving derivative entities in the course of explaining the
      grounding fact even if the \emph{explanans} $\psi$ for the
      grounding fact involves none of those entities.  Thus, the
      objector's argument from \textbf{CONNECTION} to the falsity of
      an instance of \textbf{BECAUSE} is invalid as it stands.
      
      One last note.  The connection problem presents a challenge to
      the plausible suggestion that Beijing's cityhood may be
      explained by appeal to facts that do not involve Beijing.  For
      the same reasons, I have argued, it presents a challenge to the
      relevant instance of \textbf{BECAUSE}.  But it is not a
      challenge that turns on whether grounding facts are derivative
      or how to ground them if they are.  The connection problem is
      thus a more general (and potentially more serious) problem than
      the collapse.  \emph{A fortiori} it is a different problem from
      the collapse.  Since this paper's focus is the collapse, I set
      further discussion of the connection problem to the
      side.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {See \citep{deRosset:2010} for an extensive discussion of the
        connection problem.} % [REDACTED]
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
    \end{subsection}
    
    \begin{subsection}{Intelligibility}
      The connection problem apppeals to a constraint on the
      \emph{form} of an explanation of the fact that Beijing's
      cityhood is explained by $\psi$: mention must be made of the
      erstwhile derivative entities.  The second reason for thinking
      that $\psi$ fails to account for the explanatory tie between
      $\psi$ and Beijing's cityhood appeals instead to a constraint on
      an explanation's \emph{epistemological features}.  ``Any
      adequate explanation,'' the objector claims, ``must make its
      \emph{explanandum} intelligible, given the \emph{explanans}.
      Apply this constraint to the case of grounding facts.  Here what
      needs to be made intelligible is the rare and special
      explanatory relation holding between $\psi$ and Beijing's
      cityhood.  Merely citing $\psi$ itself does not make that
      connection intelligible.  Thus, the relevant instance of
      \textbf{BECAUSE} is false.''  Call this the
      \emph{intelligibility problem} for the explanation of Beijing's
      cityhood.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Thanks to Kit Fine for pressing the need to address the
        intelligibility problem.  We might discern a link between the
        intelligibility problem and the connection problem: the
        connection problem might be thought to arise because we will
        fail to make the Beijing's possession of its features
        intelligible to our audience unless we mention Beijing or the
        relevant feature.}%[PHILOSOPHER]
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
      A proponent of \textbf{BECAUSE} should respond to the
      intelligibility problem in the same way she responded to the
      connection problem.  The facts one must cite to render the
      explanatory relation between $\psi$ and Beijing's cityhood is
      merely ancillary material.  Indeed, the point of inserting
      ancillary material into the explanatory story is to deliver the
      relevant epistemic payoff -- intelligibility -- to one's
      audience.  In this respect, it is analogous to an appeal to
      inference rules in an explanatory story backing the proposal to
      explain a disjunctive fact by appeal to one of its disjuncts.
      Thus, in the course of offering the explanatory story that takes
      us from $\psi$ to
      \begin{equation*}
        \tag{\ref{sent1}}\text{Beijing is a city because $\psi$}.
      \end{equation*}
      we might cite certain claims concerning how the entities
      involved in $\psi$ are well-placed to be explainers for
      Beijing's cityhood.  We might, for instance, cite the fact that
      many of the people involved in $\psi$ reside in Beijing's
      location, and so their activities and actions are in the right
      place to explain Beijing's cityhood.  Perhaps these ancillary
      claims are needed to show how $\psi$ renders the grounding fact
      intelligible to one's audience.  But we should not infer that
      they are part of those facts in virtue of which the grounding
      fact (\ref{sent1}) obtains.  The objector's inference from the
      need to render (\ref{sent1}) intelligible to the falsity of
      instances of \textbf{BECAUSE} is invalid as it stands.
    \end{subsection}
    
    \begin{subsection}{Explanatoriness}
      The intelligibility problem alleges that the explanatory claims
      yielded by instances of \textbf{BECAUSE} are
      \emph{epistemically} inadequate.  The next objection focuses
      instead on a supposed \emph{metaphysical} inadequacy of those
      claims.  The worry is that grounding facts have a component that
      the explanations given by instances of \textbf{BECAUSE} fail to
      capture.  This extra component is what we might call the
      \emph{explanatoriness} of the relation between \emph{explanans}
      and \emph{explanandum}.  It's the explanatory \emph{oomph}
      imparted to Beijing's cityhood by whatever facts explain it.
      
      The problem may be approached by way of an analogy.  It is a
      fact that Elizabeth Windsor, the Queen of England, was born of
      certain parents.  A rough outline of the sort of facts relevant
      to grounding this fact might include facts concerning the
      production by her parents of certain gametes, the combination of
      those gametes, and her emergence through a normal process of
      gestation and birth.  These seem like the sort of facts in
      virtue of which Windsor was born of those parents.  But now
      suppose that it is a fact that Windsor was born of those parents
      as a matter of necessity.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Perhaps what's necessary is only that Windsor be born of
        certain parents \emph{if she exists}.  I suppress any such
        qualification here and below for the sake of exposition.}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} The facts which explain her (actually) being
      born of those parents clearly fail to explain her
      \emph{necessarily} being born of those parents.  That is, if
      Windsor is born of parents $p_1$ and $p_2$ in virtue of the fact
      that $P$, the explanatory proposal
      \begin{equation}
        \text{Windsor is necessarily born of $p_1$ and $p_2$ because
          $P$}\label{sent8}
      \end{equation}
      clearly fails.  
    
      It's obvious that what's missing from (\ref{sent8}) is precisely
      something that grounds the \emph{necessity} of Windsor's
      parentage.  Further, it just seems wrong to suggest that the
      further facts we must mention to account for this necessity are
      mere ancillary material that are no part of those facts in
      virtue of which the necessity obtains.  Finally, (\ref{sent8})
      clearly fails even if it passes the requirement of upward
      necessitation.  Suppose that the characteristic axiom schema of
      S4 is true, so that if it is necessary that Windsor be born of
      certain parents, then it is necessarily necessary that she be
      born of those parents. On this supposition, the explanatory
      proposal (\ref{sent8}) passes the requirement of upward
      necessitation.  Given that Windsor is necessarily born of
      certain parents, it is necessary that she necessarily be born of
      those parents.  Since it's impossible that the
      \emph{explanandum} be false, it's impossible that the proposed
      \emph{explanans} be true and the \emph{explanandum} false.  This
      gives us upward necessitation.  So what?  The explanatory
      proposal (\ref{sent8}) is clearly incomplete or inadequate
      anyway.
    
      The analogous complaint in the case of \textbf{BECAUSE} is that
      the proposed explanations of grounding facts are incomplete or
      inadequate insofar as they are missing something that grounds
      the \emph{explanatoriness} of the relation between the facts in
      question.  Thus, given a fact $\psi$ in virtue of which Beijing
      is a city, \textbf{BECAUSE} yields
      \begin{equation}
        \text{(Beijing is a city because $\psi$) because
          $\psi$.}\label{sent6}
      \end{equation}
      $\psi$ may necessitate Beijing's being a city, and, as I have
      argued, it may even necessitate the explanatory relation between
      Beijing's being a city and $\psi$.  This would give us upward
      necessitation.  ``But,'' the objection goes, ``so what?  Mere
      necessitation is insufficient for there to be an explanatory
      relation between $\psi$ and Beijing's being a city.  The
      explanatory proposal (\ref{sent6}) is incomplete or inadequate:
      it fails to include any ground for the explanatory \emph{oomph}
      imparted by $\psi$ to Beijing's cityhood.''
    
      The complaint in the case of the alleged explanation of the
      necessity of Windsor's being born of her actual parents seems to
      me clearly correct.  Here is an analogue, for necessary truths
      $\phi$, of \textbf{BECAUSE}
      \begin{description}
      \item[NEC] $\phi$ because $\psi \Rightarrow \square\phi$ because
        $\psi$.
      \end{description}
      To see the analogy, note that we can understand \textbf{BECAUSE}
      as saying that when $\psi$ explains a derivative fact $\phi$,
      $\psi$ also explains a certain feature of $\phi$: to wit, its
      obtaining in virtue of $\psi$.  \textbf{NEC} may be understood
      similarly, as the claim that when $\psi$ explains a necessary
      truth $\phi$, it also explains a certain feature of $\phi$: its
      necessity.  \textbf{NEC} is a clear non-starter.  The objector
      is claiming that \textbf{BECAUSE} has an analogous problem.
      
      How should a proponent of \textbf{BECAUSE} respond?  The idea
      that animates the objection is
      \begin{description}
        \item[EXPLANATORINESS] There is a component --
          \emph{explanatoriness} -- of the explanatory relation
          between Beijing's cityhood and a fact $\psi$ in virtue of
          which it obtains that isn't captured by any explanation that
          appeals only to $\psi$ as \emph{explanans}.
      \end{description}
      This claim is pretty obscure.  Though the obscurity of the claim
      gives me pause, I propose to press on nonetheless.  Presumably
      there is a similar worry about the obscurity of the idea that
      there is a component -- necessity -- of the fact that Windsor is
      necessarily born of certain parents, but the charge against
      \textbf{NEC} is nonetheless compelling.  So, let's provisionally
      set aside the worry about the obscurity of
      \textbf{EXPLANATORINESS}.  It seems to me that the best strategy
      for responding to the objection is to deny that metaphysical
      claim, and embrace instead a deflationary view of grounding
      explanation.
    
      A deflationary view of grounding explanation would hold that
      there is nothing interesting or informative to say about the
      nature or constitution of \emph{explanatoriness} in general.
      The explanatory \emph{oomph} imparted by the facts that ground
      Beijing's cityhood is constituted by those very same facts.
      Likewise, the explanatory \emph{oomph} imparted by the very
      different facts that ground the weakness of gravity is
      constituted by those different facts.  There is no commonality
      in the nature of these instances of \emph{explanatoriness} that
      can helpfully be brought to bear when considering the merits of
      a proposed grounding explanation of the relevant grounding
      facts.  There is no extra component of the grounding fact
      \begin{equation*}
        \tag{\ref{sent1}}\text{Beijing is a city because $\psi$}.
      \end{equation*}
      that fails to be accounted for even after we have noted that
      $\psi$ obtains.  Thus, there is no helpful general account of
      the nature of \emph{explanatoriness}, as might be provided, \eg,
      by the deductive-nomological account
      \citep{HempelOppenheim:1948}.  The nature of grounding
      explanation is exhausted by the instances of \textbf{BECAUSE}.
    
      This deflationary point of view makes available the following
      response to the objection: the explanation of (\ref{sent1}) by
      appeal to $\psi$ does, after all, contain the ground for the
      \emph{explanatoriness} of the relation between $\psi$ and
      Beijing's being a city.  The ground for that explanatoriness is
      $\psi$ itself.  The explanation does not take the form of
      applying a helpful general account of the nature and
      constitution of \emph{explanatoriness} to the case at hand, and
      showing that $\psi$ fits the contours of that account.  For
      instance, it does not take the form of invoking the
      deductive-nomological account of explanation, and showing that
      $\psi$ fits.  But, according to the deflationary view, there is
      no such general account to be had, unless we think of the
      totality of instances of \textbf{BECAUSE} as providing the
      account.
    
      Once again, an analogy may help to make the response clearer.  A
      deflationist about truth endorses an analogue, for truths
      $\phi$, of \textbf{BECAUSE}:
      \begin{description}
      \item[TRUTH] $\phi$ because $\psi\Rightarrow$ (it is true that
        $\phi$) because $\psi$.\linespread{1}\footnote
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        {To see the analogy, recall that \textbf{BECAUSE} may be
          understood as saying that when $\psi$ explains a derivative
          fact $\phi$, $\psi$ also explains a certain feature of
          $\phi$: to wit, its obtaining in virtue of $\psi$.
          \textbf{TRUTH} may be understood similarly, as the claim
          that when $\psi$ explains a truth $\phi$, it also explains a
          certain feature of $\phi$: its truth.}
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        \linespread{1.3}
      \end{description}    
      Consider once again a grounding explanation of the form
      \begin{equation*}
        \tag{\ref{sent1}}\text{Beijing is a city because $\psi$}.
      \end{equation*}
      Application of \textbf{TRUTH} yields
      \begin{example}
        (It is true that Beijing is a city) because
        $\psi$.\label{sent7}
      \end{example}
      Imagine an objector who complains that (\ref{sent7}) is
      incomplete or inadequate, since it provides no grounds for the
      \emph{truthiness} of the proposition that Beijing is a city.  A
      deflationist about truth should reply that there is nothing
      interesting or informative to be said about the nature or
      constitution of \emph{truthiness} in general.  That nature is
      exhausted by the totality of instances of the
      schema\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {I am ignoring the fact that \textbf{E} in its full generality
        apparently leads to the liar paradox.}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      \begin{description}
      \item[E] $\langle\phi\rangle$ is true iff $\phi$
        \citep{Horwich:1990}
      \end{description}
      The \emph{truthiness} of the proposition that Beijing is a city
      is imparted by Beijing's being a city; likewise, the
      \emph{truthiness} of the proposition that telling lies is wrong
      is imparted by the wrongness of telling lies.  There is no
      commonality in the nature of these instances of
      \emph{truthiness} that can be brought to bear when considering
      the merits of a proposed grounding explanation of the relevant
      truth facts.  The instances of (E) say all there is to say about
      the nature of \emph{truthiness}.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {This deflationary view is in principle independent of various
        forms of \emph{disquotationalism} about truth.  A
        disquotationalist might hold that the sole function of truth
        predicates in natural language is disquotational, or that
        sentences of the form `it is true that $\phi$' are synonymous
        with $\phi$, \emph{etc.}  Thanks to Richard Heck.
        % [PHILOSOPHER]
      }
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3} Such a deflationist will hold that, insofar as
      there is any such thing as \emph{truthiness}, (\ref{sent6})
      provides grounds for the \emph{truthiness} of the proposition
      that Beijing is a city, and so is not incomplete or inadequate
      as the objector maintains.  I am suggesting, in effect, that
      \textbf{BECAUSE} be defended along similar lines.
      
      A deflationist about truth holds that, insofar as there is any
      such thing as \emph{truthiness}, it is accounted for in every
      case by appeal to instances of \textbf{E}; as the proponents of
      the deflationary conception sometimes put it, the instances of
      \textbf{E} ``exhaust the nature of truth.''  One might worry
      that this deflationary claim is so obscure that we have no
      reasonable grip on what it means. One might have a similar worry
      about the deflationary view of grounding explanation: we have no
      reasonable grip on the claim that, insofar as there is any such
      thing as \emph{explanatoriness}, it is accounted for in every
      case by the instances of \textbf{BECAUSE}.  I share these
      worries.  But, in the case of the deflationary defense of
      grounding, it is important to realize that the obscurity of the
      idea is a problem with the objection: the objection we are
      considering relies on \textbf{EXPLANATORINESS}; the deflationary
      response I have suggested is just the denial of that claim.
      Recall that, in discussing how to respond to the objection, we
      set aside the obscurity of \textbf{EXPLANATORINESS}.  The
      proposal to embrace deflationism thus only arises if the
      obscurity of the objector's claim is no barrier to a discussion
      of its merits.  So, either \textbf{EXPLANATORINESS} is
      objectionably obscure, or it isn't.  If it is, then we don't
      have an objection to \textbf{BECAUSE} that is clear.  If it
      isn't, then neither is its denial.  In neither case, I have
      argued, do we have an objection to \textbf{BECAUSE} that is both
      clear and well-motivated.\linespread{1}\footnote
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      {Thanks to Ted Sider and Robert Schwartzkopff for discussion.}
      % [PHILOSOPHER] and [PHILOSOPHER]
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \linespread{1.3}
      
    \end{subsection}
  \end{section}
  
  \begin{section}{Conclusion}
    
    Grounding explanations are ubiquitous in philosophy and the
    sciences.  They appear to provide a way of making sense of the
    intuitive conception of reality on which it has layered structure.
    The collapse threatens this way of making sense of layered
    structure.  I have suggested that the collapse may be avoided by
    denying that grounding explanations are fundamental, and I have
    urged \textbf{BECAUSE} as a proposal for grounding them.
    \textbf{BECAUSE} does not require that grounding explanation be
    analyzable in or reducible to other terms; it does not require
    that the notion of a grounding explanation be either conceptually
    or metaphysically derivative.  It meets the requirement of upward
    necessitation.  It does not require the trialist's otherwise
    unmotivated distinction between grounding facts and other
    explanatorilty fundamental facts.  It does not succumb to problems
    concerning regress, connection, intelligibility, or
    explanatoriness.  These considerations make a powerful case in its
    favor.\linespread{1}\footnote
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    {Versions of this paper were presented at ....  Thanks to .....}
    % { A version of this paper was presented at the ``Because'' II
    %   conference, jointly sponsored by the Eidos Centre for
    %   Metaphysics and the Phlox group, at the Humboldt Universit\"at
    %   zu Berlin and at the 2011 Western APA in San Diego, CA.  Thanks
    %   to Shamik Dasgupta, Kit Fine, Carrie Jenkins, Mark Moyer,
    %   Jonathon Schaffer, Benjamin Schnieder, Robert Schwartzkopff, Ted
    %   Sider, Alex Skiles, and Kelly Trogdon for comments and
    %   discussion.  }
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \linespread{1.3}
  \end{section}
  
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