## 1. Monisms


### 1.1 Many monisms



There are many monisms. What they share is that they attribute
oneness. Where they differ is in what they attribute oneness to
(*the target*), and how they count (*the unit*). So
strictly speaking there is only *monism* *relative to a
target and unit*, where monism for target \(t\) counted by
unit \(u\) is the view that \(t\) counted by \(u\) is
one.



Monisms are correlative with *pluralisms* and
*nihilisms*. Where the monist for target \(t\) counted by
unit \(u\) holds that \(t\) counted by \(u\) is one,
her pluralist counterpart holds that \(t\) counted by \(u\)
is many, and her nihilist counterpart holds that \(t\) counted by
\(u\) is none. Among pluralists it is sometimes useful to single
out the dualist: the dualist for \(t\) and \(u\) holds that
\(t\) counted by \(u\) is two



To illustrate these various doctrines for various targets and units,
let the target \(t\_1 =\) concrete objects, and let the
unit \(u\_1 =\) highest type. To be a monist for
\(t\_1\) counted by \(u\_1\) is to hold
that concrete objects fall under one highest type. The materialist,
idealist, and neutral monist are all monists of this sort
(*substance monism*). They all agree that concrete objects fall
under one highest type, disagreeing only over whether the one highest
type is material, mental, or something deeper.



To be a pluralist for \(t\_1\) counted by
\(u\_1\) is to hold that concrete objects fall under
more than one highest type. The Cartesian dualist is a pluralist of
this sort (*substance dualism*). She holds that concrete
objects fall under two highest types: the material (with the primary
attribute of extension), and the mental (with the primary attribute of
thought).



To be a nihilist for \(t\_1\) counted by
\(u\_1\) is to hold that concrete objects fall under no
highest type. The bundle theorist who is an eliminativist about
concrete objects is a nihilist of this sort (*substance
nihilism*). She rejects the target: she thinks that there are no
concrete objects to
 count.[1]
 One who accepts concrete objects but rejects the relevant notion of
"highest" type would also be a nihilist for
\(t\_1\) counted by \(u\_1\). She rejects
the unit: she thinks that this is no way to count.



As a second illustration, let the target \(t\_2 =\)
properties. The monist for \(t\_1\) counted by
\(u\_1\) (the substance monist, e.g., the materialist)
might still be a pluralist for \(t\_2\) counted by
\(u\_1\) (for properties counted by highest type). For
instance, she might hold that there are two highest types of property,
physical and mental, inhering in one and the same type of substance
(*property dualism*). Or she might be a nihilist for
\(t\_2\) counted by \(u\_1\), by being an
eliminative nominalist about properties and thereby rejecting the
target. (These examples show the need to relativize monism to a
target.)



As a third illustration, let the unit \(u\_2 =\) individual token. The
monist for \(t\_1\) counted by \(u\_1\) (the substance monist, e.g., the
materialist) might still be a pluralist for \(t\_1\) counted by \(u\_2\)
(for concrete objects counted by tokens). For instance, she might hold
that there exist many concrete object tokens (*existence
pluralism*), while maintaining that these are all material
objects. Likewise the pluralist for \(t\_1\) counted by \(u\_1\) might
be a monist for \(t\_1\) counted by \(u\_2\). For instance, she might
hold that there is only the one "world-person" with two
highest types of property, physical and mental. (These examples show
the need to relativize monism to a unit.)



Monism, along with pluralism and nihilism, must therefore be
relativized to both a target and a unit. The underlying reason for
this double relativity is that these are theses of numerical
predication ('...is one/many/none'), and all
numerical predication is doubly relative in this way: for a target
(what is to be counted), and by a unit (how it is to be counted). This
is one way to understand the moral of Frege's (1884: 59)
insight: 



> 
> 
> While looking at one and the same external phenomenon, I can say with
> equal truth both 'It is a copse' and 'It is five
> trees,' or both 'Here are four companies' and
> 'Here are 500 men.'
> 
> 
> 



The "external phenomenon" is the target, and
"copse" and "tree" (or "companies"
and "men") serve as potential
 units.[2]


### 1.2 Important examples



I now mention some of the more interesting target-unit pairs, leading
to a list of some of the more interesting monisms. To begin with, on
perhaps the most general level, one may target the categories
themselves, and consider whether the schedule of categories has
various sorts of unity. There are at least two interesting sorts of
unity to consider: (i) the number of categories (including
subcategories), and (ii) the number of highest categories (excluding
subcategories).



As to the first sort of unity concerning the number of categories,
some posit a categorical distinction between *object* and
*property*, thereby recognizing a pluralism of at least two
categories. But others would prefer the elegant monistic picture of a
"one category ontology": for instance, some trope
theorists and property-only theorists claim a property-only schedule,
or a schedule that effaces the object/property distinction (Williams
1953; Campbell 1990; Paul 2013); and eliminative nominalists claim an
object-only schedule (Rodriguez-Pereyra 2002).



As to the second sort of unity concerning the number of highest
categories, those who are pluralists about the number of categories
still may (or may not) posit one highest category--a *summum
genus*, such as *entity* or *being*--under
which all the entities in the lower categories fall. Spinoza
(*Ethics* IV pref., II: 207), for instance, is a pluralist
about the categories but a monist about the highest categories,
positing a categorical divide between *substance* and
*mode* but unifying both under *being*: 



> 
> 
> We are accustomed to refer all individuals in nature to one genus
> which is called the most general, that is, to the notion of Being,
> which embraces absolutely all the individuals in nature.
> 
> 
> 



While Aristotle is a pluralist about both the categories and the
highest categories, denying that there is any higher category above
his *substance*, *quantity*, *quality*,
 etc.[3]



Moving down from the level of the categories themselves, one may
target a particular type of entity, and consider whether that type has
various sorts of unity. Of special interest to the discussion to come
is the concrete material realm as a target. For this target there are
at least four interesting sorts of unity to consider: (i) the number
of types (including subtypes), (ii) the number of highest types
(excluding subtypes), (iii) the number of tokens (including derivative
tokens), and (iv) the number of basic tokens (excluding derivative
tokens). The neutral monist (as per above) is a pluralist about the
number of types, but a monist about the number of highest types. On
her view there are material and mental types, but both fall under a
higher neutral type from which the material and the mental are
derivative. The priority monist (as per above) may well be a pluralist
about the number of tokens, but is a monist about the number of basic
tokens. On this view there are many concrete objects other than the
one fundamental whole, but these other objects are all
"shards": derivative fragments of the One.



The abstract realm is another interesting target. For this target it
is not obvious that there is a sensible type/token
 distinction.[4]
 So only two of the four natural count policies for concrete objects
seem applicable: (i) the number of abstract objects (including
derivative ones), and (ii) the number of basic abstract objects
(excluding derivative ones). So consider the hierarchy of pure set
theoretic objects. One might very naturally be a pluralist about the
number of pure set-theoretic abstracta that exist, but a monist about
the number of basic set-theoretic abstracta, insofar as one holds that
the entire transfinite hierarchy is founded upon a single element: the
empty set. Those who reject abstract objects altogether will obviously
be nihilists on either count policy (c.f. Goodman and Quine 1947).



In general, for any target that supports a type/token
distinction--perhaps for any concrete target--it seems that
there will be at least the four natural count policies as seen with
concrete objects. While for any target that does not support a
type/token distinction--perhaps for any abstract target--it
seems that there will only be the two natural count policies as seen
with abstract objects. To further illustrate these patterns: with
concrete events, one might count by types, highest types, tokens, or
basic tokens. While with abstract Platonic universals, one might count
the number of forms, or the number of basic forms. For example, Plato
is a pluralist about the number of forms, but a monist about the
number of basic forms, maintaining that they are all sustained by the
form of the
 good.[5]



Moving down from targets that concern a particular type of entity, one
might also target a particular token entity, and consider whether it
has various sorts of unity. A dizzying variety of natural count
policies present themselves. A particular concrete object might, for
instance, be counted by (i) the number of its parts, (ii) the number
of its atomic parts, (iii) the number of its maximally continuous
parts, (iv) the number of its functionally integrated parts, or (v)
the number of its qualitatively homogeneous parts. So if one considers
a chess set, one might count it functionally as 1 (1 chess set), by
its connected parts as 33 (32 pieces and 1 board), by its homogeneous
parts as 96 (32 pieces plus 64 squares), by its atomic parts as
bazillions of particles, and by its parts as
\(2^n -1\), where \(n\) is the number of its
atomic
 parts.[6]
 Obviously many other count policies are available. It is not clear
that there is more to be said of a systematic nature about natural
count policies for various particular entities.



There is one count policy of some metaphysical interest worth
mentioning, which is to count by the number of individuals
(self-identicals) present. Thus one might say, for a given target,
that there are exactly three individuals involved. Restricting our
domain of quantification to the target, this would be to uphold the
formula:



> 
> 
> \(\exists x\exists y\exists z(x\ne y \amp x\ne z \amp y\ne z \amp \forall v(v=x \vee v=y \vee v=z))\)
> 
> 
> 



Unless one thinks that identity itself is a relative notion (Geach
1962), or that there is some other problem with this formalism, this
formula represents a perfectly legitimate count policy. My point is
that it is not the only legitimate count policy. It is perfectly
legitimate to count the copse as one, without denying the presence of
the five trees, or identifying them.



Putting this together, here is a list of some of the more interesting
examples of monistic doctrines mentioned above:


* *Genus monism*: target: categories; unit: highest type
(the doctrine that there is a highest category; e.g., being)
* *Substance monism*: target: concreta; unit: highest type
(the doctrine that all concreta are of a common type; e.g.,
materialism)
* *Property monism*: target: properties; unit: highest type
(the doctrine that all properties are of a common type; e.g., physical
properties)
* *Existence monism*: target: concreta; unit: tokens (the
doctrine that there is exactly one concretum)
* *Priority monism*: target: concreta; unit: basic tokens
(the doctrine that there is exactly one fundamental concretum)



This list is not intended to be exhaustive, but just to indicate a
handful of the more interesting monisms, and classify them with
respect to their associated target and
 unit.[7]



Most of these five monisms are independent, though there are the
following logical relations. Pluralism about the number of basic
tokens for some concrete category entails pluralism about the
respective number of tokens. In the other direction, both monism and
nihilism about the number of tokens for some concrete category entails
a corresponding monism or nihilism about the respective number of
basic tokens. Further, nihilism about the number of highest types for
any concrete category entails nihilism about the number of tokens (and
thus the number of basic tokens) for that category.



Thus with *existence monism* and *priority monism* (the
main foci of what follows), one finds the following logical relations:
existence monism entails priority monism, and priority pluralism
entails existence pluralism. But otherwise the views are independent.
So for instance, one might be an existence pluralist but a priority
monist. This would be to maintain that many things exist (not just the
world, but also persons, furniture, particles, and whatnot), but that
the whole world is basic. The *partialia* are merely dependent
fragments. It may be that this is the view that most historical
monists have held, and that especially deserves serious
 attention.[8]


## 2. Existence Monism


### 2.1 Overview



Existence monism targets concrete objects and counts by individual
token. It holds that exactly one concrete object token exists (the
One). It represents an interesting and historically important form of
monism, albeit one which is widely regarded as deeply implausible.
Consider any two concrete individuals, such as you and I. The
existence monist must either deny that at least one of us exists, or
deny that at least one of us is a concrete object, or hold that we are
identical. This is hard to swallow. (It is important to distinguish
existence monism from priority monism, which does not have this
implausible implication.)



Historically, existence monism may have been defended by Parmenides,
Melissus, Spinoza, and Bradley, though in each case the claim is
 controversial.[9]
 Among contemporary philosophers, Horgan and Potrc are probably
the leading, and perhaps the only, existence
 monists.[10]
 Thus Horgan and Potrc (2000: 249; c.f. 2008: 8) advance the
following ontological and semantical theses:


* There really is just one concrete particular, viz., the whole
universe (the *blobject*).
* The blobject has enormous spatiotemporal structural complexity,
and enormous local variability--even though it does not have any
genuine parts.
* Numerous statements employing posits of common sense and science
are true, even though nothing in the world answers directly to these
posits.
* Truth, for such statements, is *indirect* language-world
correspondence.



Note that existence monism should not be confused with the formula:
\(\exists x\forall y(x=y)\). That is
the logician's formula for expressing the claim that exactly one
entity exists. The existence monist is making a much weaker (and
slightly more plausible) claim. She can allow that many abstract
entities exist, she can allow that many spatiotemporal points exist
(assuming that she does not follow the *supersubstantivalist*
in identifying objects with regions), and she can allow that many
property tokens exist (assuming she does not follow the *bundle
theorist* in identifying objects with compresent property tokens),
as long as she maintains that only one concrete object token
 exists.[11]



In order to properly characterize existence monism, one should first
introduce a predicate '\(C\)' that denotes the property
of being a concrete object. (The notion of being a concrete object is
natural and useful, so this should be clear enough to work with.) Then
one can introduce the formula:



> 
> 
> *Existence monism*: \(\exists x(Cx \amp \forall y(Cy \rightarrow x=y))\)
> 
> 
> 



The corresponding logical formulae for existence pluralism and
nihilism then run:



> 
> 
> *Existence pluralism*: \(\exists x\exists y
> (Cx \amp Cy \amp x\ne y)\)
> 
> 
> 
> *Existence nihilism*: \({\sim}\exists xCx\)
> 
> 
> 



It is not built into the formulation of *Existence monism* that
the one concretum has any particular nature. It might be my nose or
your left foot. It might be material (realist) or mental (idealist) or
neutral. Idealist and neutral forms of existence monism may or may not
identify the One with some sort of divinity. Materialist and neutral
forms of existence monism typically identify the One with the whole
cosmos (Horgan and Potrc's "blobject"). Using
'\(u\)' as a dedicated constant for the cosmos, which
may be defined mereologically as the sum of all concreta, one thus
reaches:



> 
> 
> *Existence monism (cosmic)*:
> \(\exists !xCx \amp Cu\)
> 
> 
> 



This says that there is exactly one concretum, namely the cosmos.


### 2.2 Arguments


#### 2.2.1 Moorean truisms



As mentioned, existence pluralism is widely embraced. This attitude
came to the fore in the early analytic revolt against the neo-Hegelian
monistic idealists, and has made all forms of "monism"
something of a taboo until recently (cf. Schaffer 2010b: SS1).
This pluralistic stance is fairly explicit in Moore's (1993:
166) declaration: "Here is one hand... and here is
another," and fully explicit in Russell's (1918 [1985]:
36) declaration:



> 
> 
> I share the common-sense belief that there are many separate things; I
> do not regard the apparent multiplicity of the world as consisting
> merely in phases and unreal divisions of a single indivisible
> Reality.
> 
> 
> 



Whether due wholly to argumentative force or at least partly to
historical contingencies, such declarations had the effect of ending
any interest in monism (even in forms of monism such as priority
monism that agree with Moorean truisms: SS3), for nearly one
hundred years. And so philosophical fashion swung from some form of
monism in the nineteenth century, to some form of pluralism in the
twentieth
 century.[12]



There are actually two distinct sources of evidence for existence
pluralism: *intuition* and *perception*. Where Russell
seems to be appealing to his "common-sense belief," Moore
seems to be appealing directly to the content of perception, as do
Hoffman and Rosenkrantz (1997: 78):



> 
> 
> Monism... is inconsistent with something that appears to be an
> evident datum of experience, namely, that there is a plurality of
> things. We shall assume that a plurality of material things exists,
> and hence that monism is false.
> 
> 
> 



So, barring a radical skepticism about both intuition and perception,
there seems to be strong *prima facie* evidence for existence
pluralism.



The argument may be formulated in various ways, but--for reasons
that will emerge below--one of the more interesting (and very
natural) formulations runs as follows:


1. It is intuitively obvious (/perceptually apparent) that there are
a plurality of concrete objects.



1 makes a claim about the status of a given proposition, *that
there are a plurality of concrete objects*. It says that this
proposition is intuitively obvious and/or perceptually apparent.


2. If it is intuitively obvious (/perceptually apparent) that there
are a plurality of concrete objects, then there is *prima
facie* reason to believe that there are a plurality of concrete
objects.



2 makes an epistemic claim about propositions that enjoy the status of
being intuitively obvious (/perceptually apparent). The epistemic
claim is that these propositions thereby enjoy *prima facie*
justification. The argument thus concludes:


3. There is *prima facie* reason to believe that there are a
plurality of concrete objects.



The argument is valid and the premises seem plausible. Of course the
conclusion is not existence pluralism, but rather the weaker claim
that there is *prima facie* reason to believe in existence
pluralism. But this leaves existence pluralism as the default view
barring any overriding arguments otherwise. This is exactly the way
Russell (1918 [1985]: 48) sees the dialectic:



> 
> 
> The empirical person would naturally say, there are many things. The
> monistic philosopher attempts to show that there are not. I should
> propose to refute his *a priori* arguments.
> 
> 
> 



How might the existence monist or nihilist reply? As a claim about the
content of intuition (/perception), 1 seems hard to question. And as a
claim about *prima facie* justification, 2 seems plausible as
well (albeit more theoretically loaded).



There is a fairly standard existence monist and nihilist reply to
arguments in the vicinity of 1-3, which involves attempts to
*paraphrase* claims of commonsense. For instance, when one
claims that there is a hand here, the existence monist might hold that
what is strictly the case is that the world is handish here. The
claims of commonsense could then be downgraded to being strictly false
but still explicable given the truth of the paraphrase, or as true but
only according to the 'tacit fiction' of decomposition,
which is the 'fiction' that the world decomposes into
proper parts.
 [13]



Other techniques besides paraphrase may be employed. For instance,
Horgan and Potrc (2000: 50-51) offer an *indirect
correspondence theory of truth*, declaring talk of a plurality of
discrete objects apt for tracking "lumps" and
"congealings" of the blobject, saying that "such
tracking would constitute an *indirect* kind of language/world
correspondence" which "would be a very plausible candidate
for *truth*" (2000: 50-1). Their idea is to posit a
contextually sensitive parameter in truth-evaluation, for
*directness of correspondence required*, so that Moorean
truisms can count as true in lax
 contexts.[14]
 Another option would be to offer a *truthmaker theory of
commitment*, claiming that truths commit one just to their
truthmakers, and that the truthmaker for the Moorean truism is just
the
 world.[15]



But it is unclear, however, exactly how these various responses
address the argument as formulated via 1-3. Is the idea that,
*contra* 1, the paraphrase reveals that what is obvious and/or
apparent might not be exactly what we thought? This is puzzling since
the paraphrased claim appears in 1 as the content of intuition and/or
perception, and it is dubious that one can freely paraphrase inside
such contexts. Perhaps it in some sense "comes to the same
thing" if there is a hand, or if the world is handish hereish,
but it still might seem to one specifically as if the former were the
case. Or is the idea that, *contra* 2, the paraphrase reveals
that what is obvious and/or apparent is not *prima facie*
rational to believe? This is puzzling as well, and raises concerns
that the existence of paraphrases would engender a general skepticism
about any intuitions and perceptions. Or is the idea that the argument
goes through to 3, but that the existence of the paraphrase provides
an at least partially undermining defeater to the reason to believe in
a plurality of concrete objects? Again this raises worries about
engendering a general skepticism, for making defeaters too easy to
come by.



The existence monist and nihilist can of course just "bite the
bullet" by accepting 3 but claiming overriding arguments
otherwise. But this is a dialectically difficult situation for her:
whatever support the premises of her arguments otherwise might have
will almost certainly pale in comparison to the support that 3
provides for existence pluralism. Not for nothing are existence monism
and nihilism widely dismissed as crazy
 views.[16]


#### 2.2.2 An exclusion argument



Given the highly plausible case for existence pluralism, it seems as
if the existence monist and nihilist need strong arguments for their
view. For instance, if it could be proven that positing a plurality of
concrete objects (or a plurality of anything, or even a single
concrete object) led irrevocably to contradiction, this should turn
the tide. But nothing like this has ever been proven.



Perhaps the best argument for existence monism is that it provides the
simplest sufficient
 ontology.[17]
 The idea is that we can give a complete account of the phenomena in
which the world is the only concrete object mentioned, so that there
is no need to posit any further concreta. The argument may be
formulated as follows:


4. The world is the only concrete object needed to explain how the
world evolves.



Somewhat more precisely, 4 claims that the complete causal story of
the world can be told in terms of the physical aspect of the world (a
path in physical configuration space), together with whatever laws of
nature govern temporal evolution. No pieces of the world (such as
tables or particles) need be mentioned in this story. To take a toy
example, consider a Newtonian world containing what the folk would
describe as a rock shattering a window. The complete causal story here
can be told purely in terms of the world's occupational manner
vis-a-vis Newtonian configuration
 space.[18]
 The rock and the window need not be mentioned in this story. The
world bears all the causal information.



The argument then adds that recognizing proper parts of the world is
recognizing what is either explanatorily redundant or
epiphenomenal:


5. If the world is the only concrete object needed to explain how the
world evolves, then if there were proper parts of the world, these
proper parts would be explanatorily redundant or epiphenomenal
entities.



If the world suffices to explain everything, then there is nothing
left for its proper parts to explain. Its proper parts can at best
explain what the world already suffices for. So if the proper parts
explain anything at all they are redundant, while if they explain
nothing at all they are epiphenomenal.



The argument continues with a rejection of both explanatorily
redundant and epiphenomenal entities:


6. There are no explanatorily redundant or epiphenomenal
entities.



Such a rejection is best defended on methodological grounds.
Occam's Razor cuts against both explanatorily redundant and
epiphenomenal entities, as there can be no need for positing
 either.[19]
 From which the argument concludes:


7. The world has no proper
 parts.[20]



The conclusion may seem shocking, but the argument is valid, and the
premises seem plausible.



How might the existence pluralist and the existence nihilist reply to
such an exclusion argument? Starting with the existence pluralist, she
might try to deny 4 by *denying that the world exists*. This
might seem an unlikely reply, though there are those who endorse
principles of restricted composition that entail that the world does
not exist. For instance, van Inwagen 1990 holds that composition only
occurs when the result is a *life*, and the world is
(presumably) not a life--a consequence van Inwagen himself (2002:
127) later notes and
 embraces.[21]
 Lowe (2012: 93-5) is more directly skeptical about "the
cosmos" that monists invoke (though see Tallant 2015 (3103-06)
for a reply to Lowe, based on Schaffer's 2009b proposed
identification of the cosmos with the spacetime manifold).



So much the worse for those sorts of principles of restricted
composition, the existence monist might respond. Indeed, insofar as
restricted principles of composition are supposed to improve on
unrestricted composition either with respect to intuitions or with
respect to science, it seems that any plausible principle of
restricted composition should retain the world. For the existence of
the world enjoys both intuitive and empirical support. Intuitively, we
folk speak of "the cosmos" and our poets write verses like
"All are but parts of one stupendous whole, whose body nature
is, and God the soul;" (Alexander Pope; Essay on Man, Epistle
I.IX). Empirically, the cosmos is the very subject matter of physical
cosmology, and quantum cosmology directly attempts to solve for the
wave function of the
 cosmos.[22]



The existence pluralist might do better to deny 5, by maintaining that
*composition is identity*. If the world *is* its proper
parts, then positing the former just is positing the
 latter.[23]
 But there seem to be two main reasons for denying that composition is
identity. First, the whole and its parts differ *structurally*.
Pluralities like "the parts" have a privileged structure
in terms of their individuals. Thus consider a circle (the whole)
divided into two semicircles (the parts). Here the semicircles are
structured into a pair of distinct semicircular
 shapes.[24]
 But (given mereological extensionality) fusions lack such privileged
structure. The circle is just as much the fusion of its two
semicircles, as it is the fusion of its four quadrants, and its
continuum-many points. Second, the whole and its parts differ
*numerically*. As Lewis (1991: 87) writes: "What's
true of the many is not exactly what's true of the one. After
all they are many while it is
 one."[25]
 So, assuming that the extended many-one conception of identity
retains some analogue of Leibniz's law of the indiscernibility
of identicals, the one whole cannot be identical to its many
parts.



The existence pluralist might do best to deny 6. One way to deny 6 is
to invoke *competing methodological considerations*. Perhaps
Occam's Razor cuts against both explanatorily redundant and
epiphenomenal entities, but Occam's Razor is not the only
methodological consideration. There are also considerations of
conservativeness, which seem to favor an ontology that includes you
and I as distinct concrete objects. Though here the existence monist
might reply that Occam's Razor trumps conservativeness when the
two conflict. And there are also considerations of theoretical
elegance, which might still favor the pluralistic account of the
world, if the monistic "world particle" story requires the
use of overly complicated and disunified predicates.



Perhaps a better way for the existence pluralist to deny 6 (and the
best overall way for her to reply to the exclusion argument) is to
argue that Occam's Razor should be modified to take into account
the notion of basicness. For there seems little harm in multiplying
entities that are derivative--what seems problematic is the
multiplication of basic entities. In this vein Armstrong (1997: 12)
speaks of "the ontological free lunch," explaining:



> 
> 
> [W]hatever supervenes, ... is not something ontologically
> additional to the subvenient, or necessitating, entity or entities.
> What supervenes is no addition to being.
> 
> 
> 



So the existence pluralist might suggest that the better
methodological maxim is: do not multiply *basic* entities
without necessity (but help yourself to derivative
 entities).[26]



Turning to the existence nihilist, she might react to the exclusion
argument by claiming to beat the existence monist at her own game. The
existence nihilist denies that any concrete objects exist (this is a
variant way of denying that the world exists, and so a variant way of
denying 4). Just as the complete causal story of the world can be told
in terms of the world's having various configurational
properties, so the story can be told without mentioning any concrete
object at all, and simply speaking of the instantiation of the
relevant properties. This involves what Hawthorne and Cortens 1995
(following Strawson 1959) call a "feature-placing
language." Instead of saying that the world has certain
properties, a feature-placing language just says that there are those
properties, or (to express the same idea in a different way) instead
of saying that the world is \(F\), a feature-placing language just
says that it \(F\)s, where 'it' is understood as a
semantically vacuous placeholder that is present for purely syntactic
reasons. Here the existence nihilist might claim to beat the monist at
her own game, by providing an even simpler sufficient ontology.



In reply, the existence monist could say that property instantiations
metaphysically presuppose concrete objects as the instantiators of
such
 properties.[27]
 That is, the existence monist should reply that existence nihilism is
impossible, for positing properties without bearers. If so then at
least one concrete object is required, by the argument that properties
need bearers; and at most one concrete object is required, by the
argument from exclusion discussed above.



To summarize the dialectic as presented so far, the existence monist
must defend both the exclusion argument and the "properties need
objects" argument. The existence nihilist must defend both the
exclusion argument and the possibility of properties without objects.
And both the existence monist and nihilist must establish that the
premises of the exclusion argument--or any alternative argument
they would provide--have sufficient plausibility to override the
considerations from intuition and from perception, which seem to tilt
so strongly towards existence pluralism (SS2.1).



Of course existence monism is not the only form of monism (SS1).
If considerations from intuition and from perception ultimately tell
against existence monism, there is still room to combine existence
pluralism with priority monism. This would yield a view on which many
things exist (as is intuitively obvious and perceptually apparent),
but only as dependent fragments of the one fundamental whole. This may
be the view that many historical monists have held, and is a view that
deserves very serious consideration.


#### 2.2.3 Ontological vagueness



But before turning to priority monism, it is worth mentioning in more
detail the argument from ontological vagueness that motivates Horgan
and Potrc 2000 and 2008. Their core idea, seen in their 2008
(SS7.3), is that the ontologist has three main options. She may
posit a world full of commonsense objects ("slob-jects"),
but at the price of admitting ontological vagueness. Or she may posit
a world of many small precise objects ("snob-jects"),
which may or many not stand in composition relations. Or she may posit
just one precise object, namely the world itself ("the snob-ject
is the blob-ject").



Horgan and Potrc argue that ontological vagueness is impossible
since it entails a contradiction, and take this to rule out an
ontology of common-sense objects. (See Lowe 2012 for a defense of the
coherence of this sort of ontological vagueness, and see Schaffer 2012
for an argument that semantic conceptions of vagueness such as
supervaluationism resolve the problem.)



Horgan and Potrc then take the rejection of ontological vagueness
to force an ontology of precise objects (no "slob-jects"
only "snob-jects"), and take the remaining issue solely to
concern which inventory of precise objects the ontologist should
countenance. They consider three main inventories: a nihilist
inventory of many small precise objects (e.g. particles) with no
composites, a universalist inventory of many small precise objects
plus all composites formed therefrom, and an existence monist
inventory of just one big precise object. And they conclude (2008:
183) that the existence monist inventory is to be preferred on grounds
of parsimony:



> 
> [T]hese three candidates can be ordered with respect to comparative
> ontological parsimony. The simplest is [existence monism]; it
> maximizes ontological parsimony by countenancing just one real
> concrete object, the blobject. Less parsimonious is [nihilism], since
> it countenances all those point-objects... Still less
> parsimonious is [universalism], since it countenances not only all the
> same point-objects, but also a completely unrestricted mereological
> hierarchy of snobjective region-objects as well.
> 



I think that there are at least three problems with this argument. The
first is that the parsimony comparison between the nihilist and
existence monist inventory is problematic, since the ontologies in
question are disjoint. This is not a case where one ontology is a
proper subset of another (rather both are disjoint proper subsets of
the universalist inventory). Rather each inventory is itself minimally
complete. From the perspective of each inventory, there are no
elements that are superfluous.



The second problem--hinted at in SS2.2.2--is that any
added parsimony gains for the existence monist must be weighted
against potential explanatory losses. In particular, the existence
monist is going to struggle to account for linguistic phenomena such
as reference, without positing any objects to serve as referents
(Schaffer 2012). And she will struggle to formulate her own theory,
insofar as her own theory speaks of things such as
"sentences" and "posits" whose very existence
it denies (Lowe 2012).



The third problem is that--given that parsimony considerations
only attach to fundamental posits (SS2.2.2)--there is room to
combine a universalist total ontology with a monistic conception of
what is fundamental, and so reclaim all of the relevant parsimony of
existence monism with none of the wild rejections of obvious
commonsense objects or useful linguistic referents. This is a form of
the priority monist alternative.


## 3. Priority Monism


### 3.1 Overview


#### 3.1.1 Formulation



Priority monism targets concrete objects and counts by basic tokens.
It holds that exactly one basic concrete object exists--there may
be many other concrete objects, but these only exist derivatively. The
priority monist will hold that the one basic concrete object is
*the world* (the maximal concrete whole). To distinguish
herself from the existence monist, she will allow that the world has
proper parts, but hold that the whole is basic and the proper parts
are derivative. In short, she will hold the classical monistic
doctrine that the whole is prior to each of its (proper) parts. This
doctrine *presupposes* that the many proper parts exist, for
the whole to be prior to. Historically, priority monism may have been
defended by Plato, Plotinus, Proclus, Spinoza, Hegel, Lotze, Royce,
Bosanquet, and Bradley, *inter
 alia*.[28]
 But today, priority monism has few
 advocates.[29]
 Indeed, until the last decade, priority monism was seldom even
recognized as a possible position. 'Monism' was typically
understood as existence monism (exactly one concrete object exists),
and summarily
 dismissed.[30]



In order to properly characterize priority monism, one should
introduce a predicate '\(B\)' that denotes the property
of being a basic concrete object. Then one can introduce the
formula:



> 
> 
> *Priority monism*: \(\exists x(Bx \amp \forall y(By \rightarrow x=y))\)
> 
> 
> 



The corresponding logical formulae for priority pluralism and nihilism
then run:



> 
> 
> *Priority pluralism*:
> \(\exists x\exists y(Bx \amp By \amp x\ne y)\)
> 
> 
> 
> *Priority nihilism*:
>  \({\sim}\exists xBx\)[31]
> 
> 
> 



The formulae associated with priority monism are thus the same
formulae as for existence monism/pluralism/nihilism, save for the
replacement of '\(C\)' with '\(B\).'
Note that it is not built into the formulation of *Priority
monism* that the one basic concretum has any particular nature.
*Priority monism*, *Priority pluralism*, and
*Priority nihilism* are so far characterized as strictly
numerical doctrines, concerning the number of basic concreta (one,
many, or none).



It is standard for priority monists and nihilists to also have views
about the "size" of the basic concreta. Like the existence
monist, the priority monist standardly associates her one basic
concretum with the whole cosmos. Using '\(u\)' as a
dedicated constant for the cosmos, one thus reaches:



> 
> 
> *Priority monism (cosmic)*:
> \(\exists !xBx \amp Bu\)
> 
> 
> 



This says that there is exactly one basic concretum, namely the
 cosmos.[32]
 Likewise the priority pluralist standardly associates her many basic
concreta with proper parts of the cosmos:



> 
> 
>  *Priority pluralism (partial)*:
> \(\exists x\exists y(Bx \amp By \amp x\ne y) \amp{\sim}Bu\)
> 
> 
> 



This adds that the cosmos is not among the basic concreta.



To get from *Priority monism (cosmic)* to the further claim
that the proper parts of the cosmos are dependent on the whole, one
need only add that the cosmos has proper parts, and that nonbasic
concreta depend on basic concreta. These proper parts will be nonbasic
concreta by *Priority monism (cosmic)*, and hence must depend
on the one and only basic concretum. (Analogous reasoning allows one
to move from *Priority pluralism (partial)* to the further
claim that the cosmos depends on its proper parts.)


#### 3.1.2 Priority



The doctrines of priority monism, pluralism, and nihilism--indeed
the very idea that "basic concrete token" is a legitimate
unit of counting--presuppose a notion of basicness. This notion
of basicness may be understood with reference to the classical
*hierarchical view of reality*. The basic forms the sparse
structure of being, while the derivative forms the abundant
superstructure. The basic is fundamental. It is the ground of all
else. It is (as it were) all God would need to create, while the
derivative is a mere byproduct. The derivative is dependent on,
grounded in, and existent in virtue of the basic.



Such a notion of basicness--and the hierarchical picture
associated with it--is intuitively natural and theoretically
useful, in this context and others. It has classical roots in
Aristotle's notion of *priority in nature*, and has
branched into the contemporary program of *sparse ontology*, in
a way that has proven fruitful in understanding a wide range of
issues. For instance, the physicalist holds that physical entities are
basic, and that mental and moral entities are derivative. For the
abstract objects of pure set theory, it is natural to think that the
empty set is basic, and that the other pure sets are founded on it.
With respect to holes, one might hold that the material host is basic
and that its holes are formed by it. And with respect to objects and
properties, one classical idea is that objects are basic and
properties inhere in them as dependent abstractions (modes). Some are
skeptical of these locutions. But for better or worse, such talk has
rapidly become
 ubiquitous.[33]



There are many ways to make sense of these notion, but one natural
approach is to take basicness as *the foundation of ontological
priority*. That is, suppose that one begins with the notion of
*ontological priority*, understood as an irreflexive and
transitive relation between entities. Then ontological priority will
induce a partial ordering over the domain of entities. Suppose one now
adds the assumption that ontological priority requires
*foundations*. These foundations will be those entities that
are not posterior to any other entities. These are the basic,
ungrounded
 entities.[34]
 Suppose one now adds a third assumption that there is a well-founded
ontological dependency structure *within the domain of concrete
objects*. Then one gets basic concrete objects. Being such an
object is the property denoted by '\(B\)'.



Formally speaking, this natural approach begins with an irreflexive
and transitive ontological priority relation \(P\). A foundational
entity may then be defined as an entity that has nothing prior to
it:



> 
> 
> *Foundational entity*: \(Fx =\_{df} {\sim}\exists yPyx\)
> 
> 
> 



Ontological foundationalism may then be formulated as the following
thesis:



> 
> 
> *Ontological foundationalism*:
> \(\forall x(Fx \vee \exists y(Fy \amp Pyx))\)
> 
> 
> 



In words, ontological foundationalism holds that every entity is
either basic or posterior to something basic. In content, what
ontological foundationalism excludes is the prospect of something
being neither itself foundational nor founded on something else that
is
 foundational.[35]



Within the domain of concrete objects, a basic object is then a
concrete object that has no concrete object prior to it:



> 
> 
> *Basic concreta*: \(Bx =\_{df} Cx \amp{\sim}\exists y(Cy \amp Pyx)\)
> 
> 
> 



Here '\(C\)' continues to denote the property of being
a concrete object (as per the formulation of existence monism:
SS2), and '\(P\)' the priority relation. This
defines the predicate '\(B\)' used in the formulations
of priority monism, pluralism, and nihilism above. Object
foundationalism may then be defined as the following thesis:



> 
> 
> *Concreta foundationalism*:
> \(\forall x(Cx \rightarrow(Bx \vee \exists y(By \amp Pyx)))\)
> 
> 
> 



In words, concreta foundationalism holds that every concrete object is
either basic-among-the-concreta or posterior to something
basic-among-the-concreta.



Given these assumptions, the debate between the priority monist and
the priority pluralist may be described as a debate over what is at
the foundation of the priority relation on concrete objects. The
priority monist holds that whole is prior to (proper) part, and that
the maximal whole is ultimately prior. The priority pluralist holds
that (proper) part is prior to whole, and typically holds that the
minimal parts are ultimately prior. This is not a debate over what
exists. Both sides may accept the same roster of existent beings
(including the world, you and I, planets and particles, etc.) This is
a debate over what is basic.


#### 3.1.3 Tiling



Under a certain natural picture about basic objects, *Priority
monism* and *Priority pluralism* are exhaustive and
exclusive doctrines. The picture is that the basic objects *tile
the cosmos*, in the sense that they cover every portion of reality
without overlap. More precisely, the tiling constraint (c.f. Schaffer
2010a: SS1.3) may be thought of as the conjunction of two
conditions:



> 
> 
> *No gaps*: Sum:\(x(Bx)=u\),
>   
> 
> (Sum:\(x(Bx)\) is the mereological sum of all
> things that are such that \(Bx\).)
> 
> 
> 
> *No overlaps*:  
> 
> \(\forall x\forall y((Bx \amp By \amp x\ne y) \rightarrow{\sim}\exists z(\text{PART}zx \amp \text{PART}zy))\)
> 
> 
> 



*No gaps* expresses the requirement that the sum of all the
basic entities is the cosmos as a whole. No portion of the cosmos is
left uncovered. *No overlaps* expresses the requirement that
the basic entities be mereologically disjoint, having no common
parts.



The picture given by *No gaps* and *No overlaps* is one
on which the basic concreta partition the cosmos. The question of
which concreta are basic becomes the question of *how to carve
nature at the joints*. Or to invoke Lewis's (1986) memorable
picture of the cosmos as a vast mosaic, the question becomes *what
are the tiles from which the cosmic mosaic is
 inlaid*?[36]



*No gaps* rules out *Priority nihilism*. For if nothing
is basic, then the sum of the basic concreta cannot be the cosmos.
This makes *Priority monism* and *Priority pluralism*
exhaustive doctrines.



*No gaps* also renders *Priority monism* equivalent to
*Priority monism (cosmic)*. For if only one concretum is basic,
and it must sum to the cosmos, then it must be the cosmos. Likewise
*No overlaps* renders *Priority pluralism* equivalent to
*Priority pluralism (partial*). For if many concreta are basic,
then the cosmos cannot be among the basic concreta or it will overlap
the others.



Given *No gaps* plus *No overlaps*, further equivalences
follow. On the monistic side, the two conjuncts of *Priority monism
(cosmic)*--\(\exists !xBx\) and \(Bu\)--turn out to be
mutually entailing. And likewise on the pluralistic side, the two
conjuncts of *Priority pluralism (partial)*--\(\exists
x\exists y(Bx \amp By \amp x\ne y)\) and \({\sim}Bu\)--turn out
to be mutually entailing. That is to say that, given the tiling
constraint, the numerical thesis that the number of basic concreta is
one turns out equivalent to the holistic thesis that the basic
concretum is mereologically maximal.



Since *Priority monism* turns out equivalent to *Priority
monism (cosmic)* which turns out equivalent to \(Bu\),
and *Priority pluralism* turns out equivalent to *Priority
pluralism (partial)* and so equivalent to \({\sim}Bu\),
*Priority monism* and *Priority pluralism* turn out to
be contradictories. They are exhaustive and exclusive conceptions of
the basic concreta. Given the tiling constraint, *Priority
monism* and *Priority pluralism* turn out to be exhaustive
and exclusive conceptions of how to carve nature at the joints.


### 3.2 Arguments



What arguments might be given for whether the one whole or some of its
many proper parts is basic? What follows is a survey of some of the
more important arguments that have appeared in the literature, on
behalf of both the priority monist and the priority pluralist (the
priority nihilist will not make any further appearances). This survey
is not intended to be exhaustive. Indeed, there has recently been some
recurrence of interest in the debate over priority monism, and new
arguments are emerging on both
 sides.[37]


#### 3.2.1 Common sense



It is perhaps best to begin from the idea that common sense might
favor priority pluralism, as these considerations are historically
important (perhaps due in part to the historical conflation of
priority monism with existence monism), and linger as something like a
reflex response to priority monism in the contemporary literature. So
*the argument from commonsense*, which is an argument for
priority pluralism, may be posed as follows:


8. Commonsense holds that part is prior to whole.
9. If commonsense holds that part is prior to whole, then there is
reason for thinking that part is prior to whole.
10. There is reason for thinking that part is prior to whole.



The argument is obviously valid, so the only remaining questions
concern the truth of the premises 8 and 9.



As to 8, consider the grains of sand in the heap. Here it seems that
the grains are prior--the heap exists in virtue of the grains. Or
consider the tiles in the mosaic. Here it seems that the tiles are
prior--the mosaic is just an arrangement of tiles. Or consider
the individuals in a community. Here it seems that the individuals are
prior--the community is just a grouping of individuals. In all
these cases, it seems that part is prior to whole. Thus Leibniz (1714:
455) maintains that, in general, "a composite is nothing else
than a collection or *aggregatum* of simple substances."
Relatedly, it is common in the contemporary discussions of
metaphysical grounding and related notions, to see wholes treated as
dependent on their parts. For example, Bennett (2017: 8-9)
offers an initial survey of building relations, and takes her leading
example to be that of the composition of wholes from their parts.



Yet on the other hand consider some gerrymandered division of a
circle. Here it seems that the circle is prior--the gerrymander
is just an arbitrary partition on the circle. Or consider the organs
of the body. Here it seems that the body is prior--the organs are
just functional portions of the body. Or consider the myriad details
of the percept. Here it seems that the percept is prior--the
details are just particulars of the gestalt. In these latter cases, it
seems that whole is prior to
 part.[38]



Generalizing, it seems that commonsense actually has a relatively
nuanced stance on priority relations between whole and part.
Commonsense endorses the priority of the parts in cases of mere
aggregation and arrangement, and the priority of the whole in cases of
arbitrary decompositions, functionally integrated systems, and mental
 unities.[39]
 Overall commonsense seems to distinguish between *mere heaps*
and *genuine unities*. On this point Aristotle
(*Meta*.1041b11-2) speaks of "that which is
compounded out of something so that the whole is one--not like a
heap, but like a syllable..."



So it remains, in evaluating 8, to ask whether commonsense conceives
of the world as a mere heap or a genuine unity. Here the priority
monist might invoke the following passage from Blanshard (1973:
180):



> 
> 
> We are convinced that [Russell's atomistic conclusion] will not
> stand. Our conviction is essentially that of the plain man. Intuitions
> may be of small weight in philosophy, but...the 'invincible
> surmise' of most thoughtful minds [is] that the world is not in
> the final account a rag-bag of loose ends...
> 
> 
> 



Indeed, as James (1909 [1987]: 650) notes in the course of defending
pluralism--which he took to be a radical doctrine--virtually
all (pre-twentieth century) philosophers have conceived of the world
as a genuine unity:



> 
> 
> Whether materialistically or spiritually minded, philosophers have
> always aimed at cleaning up the litter with which the world apparently
> is filled. They have substituted economical and orderly conceptions
> for the first sensible tangle; and whether these were morally elevated
> or only intellectually neat, they were at any rate always
> aesthetically pure and definite, and aimed at ascribing to the world
> something clean and intellectual in the way of inner 
> structure.[40]
> 
> 
> 



So the priority monist should conclude that, if anything, the argument
from commonsense should be reversed. Commonsense does see the cosmos
as more of a genuine unity than a mere heap (more like a syllable than
a heap of sand). One more passage from James (1907 [1991]: 59) may be
useful in mapping the general intellectual landscape, beyond the
provinces of the twentieth century Anglo-American tradition:



> 
> 
> A certain abstract monism, a certain emotional response to the
> character of oneness, as if it were a feature of the world not
> coordinate with its manyness, but vastly more excellent and eminent,
> is so prevalent in educated circles that we might almost call it part
> of philosophic common
>  sense.[41]
> 
> 
> 
> 



In any case, as to 9, it is not obvious that commonsense is entitled
to much of an opinion on the topic. One might well think that the use
of intuitions is particularly perilous on this topic (in contrast to
the more mundane topic of existence pluralism) since the notion of
ontological priority is a somewhat sophisticated theoretical notion. I
would suggest that even if commonsense leans slightly towards priority
monism (as the overall history of metaphysics might be thought to bear
out), this should not matter much. To the extent it provides any
reason to favor priority monism, it seems to be a rather weak
reason.


#### 3.2.2 Quantum emergence



A second argument to consider is *the argument from quantum
emergence* (Schaffer 2010a: SS2.2; see also Ismael and
Schaffer forthcoming). This argument, which is an argument for
priority monism by way of quantum mechanics, may be posed as
follows:


11. The whole possesses emergent properties (due to quantum
entanglement).
12. If the whole possesses emergent properties, then whole is prior to
part.
13. Whole is prior to part.



The argument is obviously valid, so the only remaining questions
concern the truth of the premises 11 and 12.



As to 11, the intended notion of an emergent property is one for which
*mereological supervenience
 fails*.[42]
 Let \(x\) have proper parts. Then \(F\) is an emergent
property of \(x\) iff (i) \(x\) instantiates \(F\), (ii)
\(F\) is an intrinsic property, and (iii) \(x\)'s
instantiating \(F\) does not supervene on the intrinsic properties
of, and spatiotemporal relations among, \(x\)'s proper
parts. Such a property would be an intrinsic property of the whole
that is not determined by the intrinsic properties of and
spatiotemporal relations among its parts.



While any appeal to quantum mechanics sparks interpretive
controversies, it seems that emergent properties are found in the
entangled systems of quantum mechanics. An entangled system is one
whose state vector is not factorizable into tensor products of the
state vectors of its components:



> 
> 
> \(\Psi\_{\text{system}} \ne \Psi\_{\text{component1}} \otimes 
>  \Psi\_{\text{component2}} \otimes \Psi\_{\text{component3}} \otimes \ldots\) 
> 
> 
> 



What this inequality means is that the quantum state of an entangled
system contains information over and above that of the quantum states
of the components. The intrinsic properties of entangled whole systems
do not supervene on the intrinsic properties of and spatiotemporal
relations among their component parts. Here Esfeld (1999: 26)
notes:



> 
> 
> In the case of entanglement, it is only the description of the whole
> in terms of a pure state, such as the singlet state, which completely
> determines the local properties of the parts and their
> relations... Therefore, quantum physics exhibits a substantial
> holism.
> 
> 
> 



In a similar vein, Maudlin (1998: 56) concludes:



> 
> 
> The physical state of a complex whole cannot always be reduced to
> those of its parts, or to those of its parts together with their
> spatiotemporal relations, even when the parts inhabit distinct regions
> of space... The result of the most intensive scientific
> investigations in history is a theory that contains an ineliminable
> holism.
> 
> 
> 



Entangled systems are wholes that contain new information, found in
the correlation coefficients of their wave functions.



There is reason to think that the world forms a single entangled
system, due to the fact that everything interacted in the Big Bang.
Everything is a shard of the primordial atom. As Gribbin (1984: 229)
explains:



> 
> 
> Particles that were together in an interaction remain in some sense
> parts of a single system, which responds together to further
> interactions. Virtually everything we see and touch and feel is made
> up of collections of particles that have been involved in interactions
> with other particles right back through time, to the Big Bang...
> Indeed, the particles that make up my body once jostled in close
> proximity and interacted with the particles that now make up your
> body. We are as much parts of a single system as the two photons
> flying out of the heart of the Aspect experiment.
> 
> 
> 



Indeed Zeh (2003: 33) notes that, given quantum decoherence, all
seemingly localized particlesque behavior "can be dynamically
described in terms of a unitarily evolving (hence strongly entangled)
universal wave function." Thus there is reason to think that the
cosmic whole possesses emergent properties, as 8 maintains.



Though of course the claim that the world forms a single entangled
system will be controversial (as will any claim that involves an
interpretation of quantum mechanics), in at least two respects. First,
certain kinds of anti-realist and relationalist interpretations of
quantum mechanics (e.g., Rovelli 1996) posit an irreducible relation
between the quantum system and an external observer, which preclude
assigning a quantum state to the whole world (for lack of an observer
external to it). Secondly, some interpretations (e.g.,
Ghirardi-Rimini-Weber) posit a separate dynamics of wave-function
collapse that breaks entanglements. But virtually any realist
interpretation of quantum mechanics that also posits an initial
singularity (the Big Bang) and unitary Schrodinger evolution will
posit an entangled universe, since an initial singularity generates
entanglement and Schrodinger evolution preserves it.



I think that the best line for the priority pluralist to take is to
deny 11, by holding that (i) entanglement represents a new fundamental
relation between individual particles (as opposed to a new emergent
property of whole systems), and (ii) mereological supervenience should
be revised to concern the supervenience of the intrinsic properties of
wholes on the intrinsic properties of their parts plus any
*fundamental* (as opposed to merely spatiotemporal) relations
among their parts. Entangled quantum systems so understood will now
count as mereologically supervenient so
 understood.[43]



The priority pluralist's "fundamental relation" move
actually takes two main forms, each of which comes with distinct
concerns. One form posits a single irreducibly \(n\)-place
relation for \(n\)-particles. Thus Darby (2012: 14) argues that
fundamental entanglement relations (unlike spatiotemporal relations
and other fundamental external relations) cannot be treated as binary
relations, but must be regarded as irreducibly \(n\)-place
relation for \(n\)-particles:



> 
> 
> It is not true, then, that all else supervenes on anything less than
> the intrinsic properties of the whole system. The n-place relations
> instantiated by the members of an n-party system are going to have to
> go into the supervenience basis.
> 
> 
> 



This is problematic in two respects, the first of which is that it
marks an unprecedented departure from more localist pictures. Thus
Darby (2012: 14) continues: "[I]t is no longer possible to think
of the world as being built up with these relations one component at a
time." The second respect in which this fundamental
\(n\)-place relation is problematic is that it makes the
fundamental properties and relations at an entangled
\(n\)-particle world at least partially distinct from the
fundamental properties and relations at an entangled
\(n+1\)-particle world (or at any entangled world with any number
of particles other than \(n)\). This seems like a loss of
unity.



A second form of the priority pluralist's "fundamental
relation" move posits only binary entanglement relations, but
allows these to hold between individual particles and whole composite
systems. Thus Calosi (2014) shows that one can treat e.g., a fully
entangled three particle system by positing a binary entanglement
relation between the first particle and the composite system made up
of the second and third particles. This is problematic insofar as it
posits fundamental entanglement relations relating entities that (by
the lights of the pluralist) are nonfundamental. How can the
fundamental level "see" the composite system made up of
particles 1 and 2, in order to put that composite system in
fundamental relation to particle 3, if the only individuals found at
the fundamental level are noncomposite?



As to 12, the idea is that a whole that does possess emergent
properties is thus "more than the sum of its parts." Thus
consider the entangled quantum universe. As Toraldo di Francia (1998:
28) aptly summarizes:



> 
> 
> Since any particle has certainly interacted with other particles in
> the past, the world turns out to be *nonseparable* into
> individual and independent objects. The world is in some way a single
> object.
> 
> 
> 



Likewise Nadeau and Kafatos (1999: 4) say:



> 
> 
> If nonlocality is a property of the entire universe, then we must also
> conclude that an undivided wholeness exists on the most basic and
> primary level in all aspects of physical reality,
> 
> 
> 



and then go on (1999: 5) to speak of "a seamlessly
interconnected whole called the cosmos." This fits with the
priority monist picture on which the whole cosmos is basic and its
proper parts are derivative.


#### 3.2.3 Atomless gunk



A third argument to consider is *the argument from gunk*
(Schaffer 2010a: SS2.4), where "gunk" is something
every part of which has proper parts, and so is lacking any ultimate
parts. This argument, which is an argument for priority monism by way
of principles of modality, may be posed as follows:


14. Either the ultimate parts must be basic at all worlds, or the
ultimate whole must be basic at all worlds.
15. There are gunky worlds without ultimate parts (and hence no
ultimate parts to be basic at those worlds).
16. The ultimate whole must be basic at all worlds.



The argument is obviously valid, so the only remaining questions
concern the truth of the premises 14 and 15.



As to 14, the idea is that the direction of priority must be a
necessary truth, at least with respect to all metaphysically possible
worlds. It would be odd if there were worlds that were otherwise
indiscernible, save for differing over what was prior to what. The
direction of priority seems to have the same status as other
fundamental metaphysical claims (e.g., the debate over
 universals).[44]
 To know the direction of priority seems to be part of what Rosen
(2006: 35) has in mind when he speaks of knowing:



> 
> 
> ...what might be called the *form* of the world:
> principles governing how objects in general are put together. If the
> world is a text then these principles constitute its syntax. They
> specify the categories of basic constituents and the rules for their
> combination. They determine how non-basic entities are generated from
> or 'grounded' in the basic
>  array.[45]
> 
> 
> 



That said, one might expect the priority pluralist to challenge 14,
for one of the following two reasons. First, the priority pluralist
might (on considering gunk, and maintaining her thesis that the parts
are prior to the whole) declare that nothing is basic in gunky worlds.
Things get ever more basic without limit. But this would run counter
to ontological foundationalism, and the widespread idea that being
needs an ultimate ground (SS3.1). This is no longer priority
pluralism but priority nihilism, as least for gunky worlds.



Second, the priority pluralist might (on wanting to maintain basic
entities in a gunky scenario, but not wanting to take the whole as
basic) take some intermediate level of mereological structure to be
basic. But this is hardly thematic for the pluralist, as now she would
be treating these intermediate structures monistically, as prior to
their parts. In any case it seems arbitrary, especially in cases where
there is no natural joint in the gunk. For instance, in the case of a
homogeneously pink cube of gunk, all the levels of mereological
structure (save for the top) are intermediate, and all are
homogeneously pink. Is there supposed to be a fact of the matter as to
which intermediate level is really basic?



Turning to 15, there seem to be good reason for accepting gunky
possibilities. The best tests for whether a scenario is possible are
whether it is conceivable, logically consistent, and posited in
serious scientific theories. Gunk passes every test (Schaffer 2003).
It is conceivable. For instance, it is conceivable that everything is
extended, and that everything that is extended has two extended
halves. This generates a Zeno sequence of halvings without limit.
Further, gunk is logically consistent. Or at least, there are gunky
models of classical mereology (Simons 1987: 41). Finally, gunk is
scientifically serious. In this vein Georgi (1989: 456) has suggested
that effective quantum field theories might form an infinite tower
which "goes down to arbitrary short distances in a kind of
infinite regression... just a series of layers without
end." Perhaps there are competing considerations that weigh
against the possibility of gunk. Here we enter into deep issues
concerning the extent of what is
 possible.[46]



There is also room for the priority pluralist to claim a *tu
quoque*, by arguing for the possibility of "worldless
junk," which is something every whole of which is a proper part,
so that there is no ultimate whole. In this vein Bohn (2009) argues
that junk has an equal claim to gunk for being metaphysically
possible. If there are both gunky as well as junky metaphysical
possibilities--and even "hunky" possibilities that
are both gunky and junky--then one will not be able to appeal to
either ultimate parts or an ultimate whole consistently across
metaphysical possibilities. (As with *tu quoque* replies
generally, the rejoinder from gunk leaves open what went
"wrong" in the original argument of
 14-16.[47])



But the priority monist can point to some crucial differences between
gunk and junk that arguably justify only recognizing the metaphysical
possibility of the former. Indeed it is doubtful that junk passes
*any* of the tests for possibility that gunk passes. As to
conceivability, it is hard to conceive that there is no limit to
summation at which one has taken in *everything*. As to logical
consistency, as least if this is judged with respect to classical
mereology (arguably our best systematization of the logic of
part-whole relations, and certainly the most orthodox), there is a
difference as well: classical mereology has gunky models but not junky
models. The onus is on the defender of junk to produce an overall
logic of part-whole relations which tolerates junky models while being
as plausible as orthodox classical
 mereology.[48]
 And as to scientific seriousness, while there is lots of work on
physical cosmology, it appears that virtually all of it takes for
granted that there is such a thing as *the cosmos*. Indeed it
hardly seems to be an empirical question whether there could be such a
thing as "the world," and the reasons mentioned in
SS2.2 for thinking that there is such a thing equally serve as
arguments against the prospect of there being only worldless junk.


#### 3.2.4 Heterogeneity



A fourth argument to consider is *the argument from
heterogeneity*. This argument, which is an argument for priority
pluralism, may be posed as follows:


17. Fundamental entities must be homogeneous.
18. If the whole world were fundamental, then the whole world would be
homogeneous.
19. The whole world is not homogeneous.
20. The whole world is not fundamental.



The argument is obviously valid, so the only remaining questions
concern the truth of the premises
 17-19.[49]



The truth of 19 is perhaps evident. There is qualitative variation in
the world. Things are not uniform in all directions. The world is in
fact not the kind of perfectly homogeneous sphere that Parmenides
(quoted in Robinson 1968: 115) imagined it to be:



> 
> 
> But since there is a furthest limit, it is complete on every side,
> like the body of a well-rounded sphere, evenly balanced in every
> direction from the middle; for it cannot be any greater or any less in
> one place than in another.
> 
> 
> 

 Rather, as even existence monists like Horgan and
Potrc (2008: 168) will immediately acknowledge, "The cosmos
exhibits enormous spatiotemporal structural complexity and
nonhomogeneity."


So the question is whether priority monism can account for the
qualitative heterogeneity of the cosmos. Further, 18 follows from 17.
So the real question comes down to the status of 17.



Why think that fundamental entities must be homogeneous (as per 17)?
Here are the best two (related) attempts one might make at defending
17. *First attempt*: nothing can differ from itself. For a
fundamental entity to be heterogeneous would be for it to be
internally diverse, which would render it different from
 itself.[50]
*Second attempt*: the priority pluralist has a way of
accounting for heterogeneity that the monist lacks. The pluralist has
many fundamental entities, which may all be homogeneous, but might
still be different *from each other*. Hence if the only way to
account for heterogeneity were to have many fundamental homogeneous
parts differing from each other, then the priority pluralist would
have the only way to account for heterogeneity. Perhaps this line of
thought is behind the following passage from Turner (1911):



> 
> 
> The weak point of all metaphysical Monism is its inability to explain
> how, if there is but one reality, and everything else is only apparent
> there can be any real changes in the world, or real relations among
> things.
> 
> 
> 



Having made an attempt to defend 17, it is time to turn to replies on
behalf of the priority monist. The starting reply is that internal
heterogeneity within the basic must be allowed by everyone. Or at
least, the priority pluralist's way of accounting for
heterogeneity (above) is insufficient to account for all forms of
heterogeneity. For there might be *heterogeneity all the way
down*, in the sense of matter every part of which has
heterogeneous proper
 parts.[51]
 If this is possible, it shows that the pluralistic strategy of
accounting for heterogeneity in terms of differences between
internally homogeneous parts is insufficient. In a partially similar
vein, Taylor (1961: 88) claims that the pluralist can gain no
advantage:



> 
> 
> Either [the pluralist's] units are mere units without internal
> variety, and then it is easy to show that they are the merest
> nothings, or they have internal variety of their own, and therefore
> simply repeat within themselves the problem they are supposed to
> solve.
> 
> 
> 



It must be possible to account for heterogeneity in other ways. It
remains to describe these ways.



What is needed is to find ways to allow for internal heterogeneity,
which would not entail that anything is "different from
itself." Here are three possibilities, the first of which is to
use *distributional
 properties*.[52]
 The world might, for instance, have the property of being
polka-dotted. Here there would be no question of the world being
"different from itself," or having any other problematic
status. The claim that the world is polka-dotted is a coherent claim,
which would entail heterogeneity among its derivative dots and
background.



The second way to allow for heterogeneity without contradiction is to
*relationalize properties*. Here the idea (for monadic
properties at least) is that instantiation is a three-place relation
holding between an object, a property, and a region. So the world
might be heterogeneous by, for instance, instantiating red here and
green
 there.[53]



The third way to allow for heterogeneity without contradiction is to
*regionalize* *instantiation*. Here the idea is that,
instead of regionalizing the properties, one might regionalize the
instantiation relation itself. So the world might be heterogeneous by,
for instance, instantiating-here red and instantiating-there green.
(Since the regionalization is incorporated into the copula rather than
the predicate, this may be expressed *adverbially*, as
"the world is here-ly red and there-ly green," or
"the world is red in a here-ly way, and green in a there-ly
 way."[54])



Perhaps there is a better way to defend 17, and perhaps there are
problems with all three of the monistic strategies that have been
sketched (distributional properties, relationalized properties, and
regionalized instantiations). This takes us deeper into issues about
objects and
 properties.[55]


#### 3.2.5 Intrinsicness



A fifth argument to consider--drawn from Sider (2007b:
SS4)--is *the argument from
 intrinsicness*.[56]
 This argument, which is an argument against priority monism, turns on
the idea that the best analyses of intrinsicness presuppose the
fundamentality of parts, and may be posed as follows:


21. There are real differences between the intrinsic and the extrinsic
properties of subcosmic objects.
22. If there are real differences between the intrinsic and the
extrinsic properties of subcosmic objects, then subcosmic objects must
bear fundamental properties.
23. If subcosmic objects bear fundamental properties, then priority
monism is false.
24. Priority monism is false.



The argument is evidently valid, so the only remaining questions
concern the truth of the premises 21-23.



The priority monist could in principle try to contest 21, but the
notion of an intrinsic property looks to have important theoretical
work to
 do.[57]
 For instance, intrinsicness seems connected to other core notions
like duplication (duplicates agree in all of their intrinsic
properties) and change (change is change in intrinsic properties). If
one wants to say that some subcosmic objects are duplicates and some
not, or say that some subcosmic objects undergo change and some do
not, then it seems that one needs to posit a real difference between
the intrinsic and extrinsic properties of subcosmic objects. It seems
to me that the priority monist should hope to *capture* this
plausible distinction rather than erase it.



The priority monist could in principle also try to contest 23, but 23
stems from a plausible connection between *being a fundamental
object* and *bearing fundamental properties* (Sider 2008:
SS1). It would be a cost to sever this connection. (Though it may
be that all parties will need to sever this connection in the end: for
instance, if priority relations themselves are fundamental, then there
will be nonfundamental objects in fundamental relations.)



So it seems to me that most of the action should be on 22, which
essentially encodes a certain conception of intrinsicness defended (in
different forms) by Lewis 1986, Sider 1996, and Rosen 2010, which
seems to build in some sort of preconceptions of fundamentality for
the parts and dependence on the parts. Thus Lewis (1986: 61) says:



> 
> 
> [T]wo things are *duplicates* iff (1) they have exactly the
> same perfectly natural properties, and (2) their parts can be put into
> correspondence in such a way that corresponding parts have exactly the
> same perfectly natural properties, and stand in the same perfectly
> natural relations.
> 
> 
> 



Lewis (1986: 62) then adds: "Then we can go on to say that an
*intrinsic* property is one that can never differ between
duplicates." This requires subcosmic objects to bear perfectly
natural (/fundamental) properties. Otherwise it will be (vacuously)
true, for any two subcosmic objects, that Lewis's two conditions
for duplication are satisfied: these objects and their parts will have
no perfectly natural properties whatsoever and *a fortiori*
cannot differ in this
 respect.[58]



In a somewhat similar vein, Rosen (2010: 112) proposes:



> 
> 
> \(F\) is an intrinsic property iff, as a matter of necessity, for all
> \(x\): If \(x\) is \(F\) in virtue of \(j(y)\)--where \(j(y)\) is
> a fact containing \(y\) as a constituent--then \(y\) is part of
> \(x\); and if \(x\) is not-\(F\) in virtue of \(j(y)\), then \(y\) is
> part of \(x\).
> 
> 
> 



Given that the priority monist accepts that "in virtue of"
claims about facts run in concord with priority relations between
objects, from the cosmos down (e.g., I am sitting in virtue of the
cosmos being as it is), this would have the bad result that no
property that an object can have while being subcosmic can be an
intrinsic property. For if a given subcosmic object \(a\) has
property \(F\), the priority monist will say that \(a\) is
\(F\) in virtue of the fact that the cosmos is such and so, where
the cosmos is not part of \(a\).



The priority pluralist who defends anything like Lewis's or
Rosen's conception of intrinsicness can thereby make the case
for 22. She might also--following Sider--make the more
modest case that these are the best definitions going. The priority
monist who would reject 18 thus, as Sider (2007b: 6) says, "owes
us a story."



The priority monist should ideally reply by giving a successful
definition of intrinsicness that is compatible with her
 view.[59]
 But this may be too much to ask for: no one seems to have a fully
successful definition of intrinsicness . Perhaps the notion--or
some allied notion such as duplication--must in the end be taken
as
 primitive.[60]


 In that case the priority monist is off the hook, since she too can
simply appeal to primitive intrinsicness to mark the real difference
between the intrinsic and extrinsic properties of subcosmic objects.


Pending a successful definition, the priority monist may still play
defense in two main (and connected) ways. First, she may argue that
both Lewis's and Rosen's conceptions of intrinsicness are
independently known to be problematic (c.f. Weatherson and Marshall
2012: SS3), so that it is not such a big deal if priority monism
is incompatible with either conception. Secondly, she may turn the
tables, and--following Trogdon (2009)--maintain that any
conflict between priority monism and a proposed definition of
intrinsicness reflects badly on the proposed definition of
intrinsicness. As Trogdon (2009: 137) explains, "For me,
pluralism and monism are each epistemic possibilities, so it is a
virtue of an account of intrinsicality to be neutral between
them."



That said, it is perhaps fair to acknowledge some advantage to the
priority pluralist at this stage of the discussion on intrinsicness,
insofar as her view fits with certain at least partially plausible
attempts to define intrinsicness, and insofar as it is not yet know
whether the priority monist can make the same claim.


#### 3.2.6 Combinatorial constraints and internal relations



A sixth argument to consider--drawn in part from Schaffer
2010b--is *the argument from free recombination*. This
argument, which may potentially be run in favor of either priority
pluralism or priority monism, begins with the idea that priority
pluralism is connected to the modal claim of free recombination. If
there really were multiple basic independent units of being--as
the priority pluralist claims--then these units should be, in
Hume's (1748: 54) words, "entirely loose and
separate." They should be freely recombinable in any which way.
Any way the one can be and any way the other can be ought to be
compossible. A disconnected pluralistic heap thus should be amenable
to free recombination, and thus failure of free recombination is the
modal signature of an interconnected monistic cosmos. The argument
from free recombination thus begins with:


25. Priority pluralism holds if and only if there are multiple
concreta that are open to free recombination.



Given 25, the priority pluralist may try to argue from the right
bijunct to priority pluralism, and the priority monist may try to
argue from the denial of the right bijunct to the denial of priority
pluralism (which still leaves open priority nihilism, but at least
eliminates the more popular competitor). So the argument
continues:


26. There are (/are not) multiple concreta that are open to free
recombination.
27. Priority pluralism holds (/does not hold).



Obviously the priority pluralist who runs this argument will run 26
and 27 as stated, while the monist (or nihilist) will run their
parenthetical variants.



The argument--in whichever direction it is run--is evidently
valid, so it remains to consider the premises. There are two main
reasons why one might challenge 25. First, one might challenge the
left-to-right direction of 25 (from priority pluralism to free
recombination) by holding that free recombination is independently
blocked. For instance, those who posit brute necessary connections in
nature posit such brute necessary connections between the priority
pluralist's basic units of being. Obviously here one enters into
deeper issues concerning modality, and the extent to which brute
necessary connections are or are not
 tolerable.[61]



A second reason why one might challenge 25 is a challenge to the
right-to-left direction (from free recombination to priority
pluralism). While priority pluralism arguably entails free
recombination, it is not obvious that priority monism should entail
any lack of free recombination. Just because multiple concreta have a
common ground in the cosmos does not mean that these concreta
*cannot* be freely recombined. Perhaps modal constraint entails
ontological connection; but it is not obvious why ontological
connection should entail modal constraint. If so then the priority
monist might have a special flexibility with respect to whether or not
there is free recombination.



But it is likely that most of the action will fall on 26. Whether or
not one permits free recombination between multiple concreta will turn
on one's background views on other matters. For instance, if one
combines "causal essentialist" views of properties on
which properties confer their powers essentially, with "natural
kind" views of things on which things fall under their natural
kinds essentially, one will find that all things have essential
"fit" requirements into their causal
 contexts.[62]



Perhaps what is most interesting about the connection between modal
constraints and the debate over priority monism is that it shows that
"Humeanism" about fundamentality and
"Humeanism" about modality may come as a package
 deal.[63]
 There seem to be at least three main packages of views to consider.
First, there is the package of pluralism plus modal freedom between
these multiple units of being. Secondly, there is the package of
pluralism plus brute necessary connections in nature. Thirdly, there
is the package of priority monism without modal freedom between
multiple concreta. This monistic option may allow one to combine a
rejection of brute necessary connections in nature with an absence of
free
 recombination.[64]



The argument from combinatorial constraints may be connected to the
classic monistic argument from the internal relatedness of all things
(Schaffer 2010b). A strong notion of internal relatedness is one on
which two entities are internally related if and only if neither can
exist without the other (necessarily, either both exist or neither
exist). The idea of combinatorial constraints may be seen as a useful
weakening of this strong notion of internal relatedness. So
understood, to claim that all things are internally related just is to
claim that there are combinational constraints between all things, and
the inference from the internal relatedness of all things to priority
monism just is the inference from combinatorial constraints to a
holistic common ground, which accounts for the constraints. 


#### 3.2.7 Nomic integrity and island universes



A seventh argument to consider--drawn from Schaffer 2013--is
*the argument from nomic integrity*. This argument notes that
the world is a single integrated causal system, and uses that
observation to argue for priority monism as follows:


28. Basic objects evolve by the fundamental laws.
29. The cosmos is the one and only thing which evolves by the
fundamental laws.
30. The cosmos is the one and only basic object.



The core idea is that our fundamental laws of nature govern the
temporal evolution of the cosmos as a whole, applying at most
approximately and derivatively to any merely partial subsystem, such
that "the cosmos ticks like a single clockwork" and
"reality acts as one" (Schaffer 2013: 67). As Ellis (2001:
249) says:



> 
> It is possible to say a great deal about the world as a whole. We can
> point to global structuring principles, universal processes of world
> evolution, general symmetries, a common ontological basis of reality,
> a single origin of the universe, and various universally conserved
> quantities ... The world [has] a highly integrated and coherent
> structure.
> 



In other words, the causal/nomic structure of the world makes it look
more like an integrated unity than a mere heap.



The priority pluralist or nihilist could deny 29, but 29 seems to fit
a fairly standard image in philosophy of science. Thus Maudlin (2007:
172) writes:



> 
> [T]he fundamental laws of nature appear to be laws of temporal
> evolution: they specify how the state of the universe will, or might,
> evolve from a given initial state.
> 



29 is just an expression of the idea that nomic evolutions concern
states of the whole universe, and not mere subsystems. One way to
support this idea is to note that nomic evolutions concern the
behavior of *closed systems*, and only the universe as a whole
forms a closed system.



Rather the priority pluralist or nihilist is more likely to deny 28,
and say that it is too demanding a standard for basicness. In this
vein, Miller (2014) responds by allowing that it is a necessary
condition on a plurality being the plurality of basic objects that
they plurally evolve by the fundamental laws, but adding that further
constraints on fundamentality can also come in to filter out bad
pluralities (such as the plurality of each left foot, plus the rest of
the cosmos minus the fusion of all the left feet).



Priority pluralists can also use modalized versions of 28
("Necessarily, basic objects evolve by the fundamental
laws") plus the possibility of island universes to pose a
problem for the priority monist (Schaffer 2013: 83, Baron and Tallant
2016, Siegel 2016). An island universe in the sense relevant to the
argument is not a spatiotemporally disconnected universe with multiple
disconnected regions (as discussed by Lewis 1986: 71-3), but a
causally disconnected universe with multiple causally/nomically
separate closed systems. The counter-argument (compare Baron &
Tallant 2016: 590) is that such island universes are possible, and
so--given a modalized version of 28--scenarios with a
plurality of basic objects are possible, and so priority monism is not
necessarily true. Tack on the premise that if priority monism is true
then it is necessarily true, and it follows that priority monism is
false.



The main options for the priority monist seem to be denying the
modalized version of 28 (Schaffer 2013: 84), and so claiming that
priority monism holds even at island universes; or denying the final
premise that if priority monism is true then it is necessarily true,
and instead claiming that the matter is contingent (Siegel 2016). But
whatever option the priority monist should take, it is hard to see how
an argument premised on the claim that it is necessary that basic
objects evolve by the fundamental laws, could refute priority monism
in the end, given the claim in 29 that the cosmos is the one and only
thing which actually evolves by the fundamental laws. That much at
least gets us the actual truth of priority monism.


#### 3.2.8 Modal cut and paste



There are further arguments to consider against priority monism, which
use modal cut and paste principles to either paste our cosmos into a
bigger world, or cut parts of our cosmos to make a smaller world. Here
is a way to run *the pasting argument*:


31. If priority monism is true, then priority monism is necessarily
true.
32. Fundamentality is an intrinsic property that does not differ among
duplicates.
33. It is possible that a duplicate of our cosmos could be embedded as
a proper part of a larger cosmos.
34. If priority monism is necessarily true then fundamentality is not
an intrinsic property and does differ among duplicates.
35. Priority monism is not true.



The core idea is that it is possible that a duplicate of our cosmos
Cos could be embedded in a still larger world \(w^+\). If priority monism
is necessary then it holds at \(w^+\) so Cos (being a mere proper part of
\(w^+\) is not fundamental at \(w^+\). But if Cos is not fundamental at \(w^+\), and
fundamentality never differs between duplicates then the cosmos is not
actually fundamental at our world, since it has a non-fundamental
duplicate at \(w^+\).



The priority monist could deny 31, but that presumably means
abandoning the argument from gunk (in particular thesis 14). The
priority monist could also deny 33 but that seems desperate. It may be
that the priority monist is best advised to deny 32, and maintain that
fundamentality is an extrinsic property. After all, she identifies
fundamentality with the extrinsic status of mereological maximality.
It is not clear what the positive argument would be for 32, but the
priority monist could float some independent counterexamples such as:
(1) a given phenomenal feel, which is not fundamental at physicalist
worlds but is fundamental at dualist worlds; and (2) the entire
physical world, which is fundamental at physicalist worlds but is not
fundamental at worlds where it is sustained by a more fundamental
deity.



A related argument is *the cutting argument*, from Steinberg
(2015: 2026; see also Benocci 2017 and Calosi forthcoming), which uses
the idea of cutting out parts of our cosmos to make a smaller world.
The argument may be phrased as:


36. Priority is an internal relation.
37. If priority monism is true, then priority monism is necessarily
true.
38. Any object and its parts could be an entire world.
39. Some parts are prior to wholes.



The guiding idea here is to use 36, 38, and 39 to show that monism is
possibly false, by finding a whole whose parts are prior to it, and
then cutting away the rest to leave a world whose parts remain prior
to it.



36 is much harder to deny than 31, 37 is just 32 again, 38 seems
plausible, and 39 is just the commonsense attitude towards mere heaps
(SS3.2.1). Steinberg thinks the priority monist should deny 39,
but take this to be "a heavy burden" and seems inclined to
reject priority monism. Benocci denies 37, and Calosi denies 38.



There may be a *tuquoque* argument in the works against the
priority pluralist, that replaces 37 with the analogue claim for the
pluralist: 


40. If priority pluralism is true, then priority pluralism is
necessarily true.



And then replaces 39 with:


41. Some wholes are prior to parts.



41 is just the commonsense attitude towards integrated unities, that
are not like a heap but like a syllable (SS3.2.1). Like all
*tu quoque* arguments, this does not show what went
wrong in the original. But something must go. 36-38 paired with
36, 38, and 40 seem to drive us to the extreme view that every
possible part-whole complex exhibits the same direction of dependence
(leaving open which direction this is), no matter how heap-like or how
syllable-like it may be. Perhaps what these arguments reveal is that
the nuanced stance of commonsense is not sustainable. This leaves open
which direction needs revision.



Obviously there is a great deal more that could be said, but overall
it is perhaps fair to conclude that priority monism deserves serious
reconsideration, of a kind that it is now beginning to receive. There
seem to be no knockdown arguments against priority monism. Or at
least, none of the arguments against priority monism surveyed here
seem in any way decisive. This may be surprising to those raised on
the idea that monism can only be some obscure or ridiculous idea.
Moreover, there may even be some decent arguments for priority monism.
Or at least, the arguments for priority monism surveyed here seem to
have some potential, given further cultivation. This terrain has lain
fallow for nearly one hundred years.