## 1. Introduction



The core idea of supervenience is captured by the slogan, "there
cannot be an *A*-difference without a
*B*-difference." It is important to notice the word
'cannot'. Supervenience claims do not merely say that it
*just so happens* that there is no *A*-difference
without a *B*-difference; they say that there *cannot*
be one. *A*-properties supervene on *B*-properties if
and only if a difference in *A*-properties *requires* a
difference in *B*-properties--or, equivalently, if and
only if exact similarity with respect to *B*-properties
*guarantees* exact similarity with respect to
*A*-properties. Supervenience claims thus have modal force. The
kind of modal force can vary; different supervenience claims might
attribute different kinds of necessity to the connection between
*B*-properties and *A*-properties (see
 Section 3.1.)
 Even when the modality is fixed, however, there are a number of
distinct claims that might be expressed by the slogan. A good deal of
philosophical work has gone into distinguishing these forms of
supervenience, and into examining their pairwise logical
relations.



We will begin with a few brief historical remarks
 (Section 2),
 and then turn to some general questions about supervenience, such as
whether it is explanatory and whether it is guarantees entailment
 (Section 3).
 We will then explore the various versions of supervenience in some
detail
 (Section 4).
 The technical work is interesting in its own right, but it is
obviously made more interesting by the fact that the different
varieties of supervenience may be useful for different philosophical
purposes. Thus, although most of this entry will be concerned with
supervenience itself rather than its applications, we will end with a
discussion of some of the substantive philosophical issues to which
supervenience is relevant
 (Section 5).



Readers primarily interested only in an overview of the relations
between the main varieties of supervenience should skip to
 Section 4.
 The technical definitions are also collated in an
 Appendix.



## 2. History


### 2.1 'Supervenience' as a Philosophical Term of Art



'Supervenience' and its cognates are technical terms. This
is not news; 'supervene' is rarely used outside the
philosophy room these days. But it occasionally is, and when it is, it
typically has a different meaning. It is typically used to mean
"coming or occurring as something additional, extraneous, or
unexpected" (*Webster's New International
Dictionary*, 3rd edition). This is the sense at issue
in the following passages from the Oxford English Dictionary:
"upon a sudden supervened the death of the king
(1674-48)" and "The king was bruised by the pommel
of his saddle; fever supervened, and the injury proved fatal
(1867)" (cited in Kim 1990, 2-3). It is also the sense at
issue in W.V.O. Quine's autobiographical remark about his
adolescence: "necking, as it was called, supervened in the
fullness of time as necking will" (1985, 43). However, this use
of 'supervenience' is irrelevant to the philosophical use
of the term. The philosophical use of 'supervenience' is
strictly proprietary, and so in no way beholden to its vernacular
use(s). In this way, 'supervene' is different from terms
like 'cause,' 'freedom,' or
'justice'. 'Supervene' receives its sense by
stipulation, and the notion so defined is to be judged by its
philosophical fruits (McLaughlin 1995).


### 2.2 Origin of the Term



What, then, is the origin of the *philosophical* use of the
term? It is not clear. Some have speculated that it originates with
the British Emergentists of the early part of the twentieth century.
This is because the British Emergentist Lloyd Morgan (1923) used the
term 'supervene' to characterize a relation that emergent
properties bear to their base properties, and his use became fairly
widespread in the literature on emergence. However, Morgan used
'supervene' in essentially its vernacular sense, rather
than in its current philosophical sense. He held that emergent
properties are distinct from, and additional to, their base
properties, and arise unpredictably from them. It was this use, not
the current philosophical use, that became fairly widespread in the
literature on emergence (see Van Cleve 1990; and McLaughlin 1992 and
1997b).



It is also frequently claimed that the term 'supervene'
was first used in its contemporary philosophical sense by R.M. Hare,
who used it to characterize a relationship between moral properties
and natural properties (1952, 145). Unlike Morgan, Hare used the term
in essentially the current philosophical sense, but he claims that he
was not the first to do so. He claims that the term was so used in
Oxford in the 1940s, though he does not recall by whom, or in what
context (Hare 1984).



It is important to be clear, however, that whether or not Hare was the
first to use the term 'supervene' in the philosophical
sense, he was by no means the first to assert a supervenience thesis.
For example, while G. E. Moore did not use the term
'supervene', he asserted: "one of the most important
facts about qualitative difference...[is that] two things cannot
differ in quality without differing in intrinsic nature" (1922,
263). And there are many other historical examples of such explicit
statements of supervenience theses. Moreover, though we are not going
to argue the point here, it seems no exaggeration to say that
virtually every major figure in the history of western philosophy has
been at least implicitly committed to some supervenience thesis or
other (or to the denial of one).



But regardless of how long the notion of supervenience has been
around, or who first used the term 'supervenience' in its
philosophical sense, it is indisputable that Donald Davidson played a
key role in bringing the idea to center stage. He introduced the term
'supervenience' into contemporary philosophy of mind in
the following passage:



> 
> [M]ental characteristics are in some sense dependent, or supervenient,
> on physical characteristics. Such supervenience might be taken to mean
> that there cannot be two events alike in all physical respects but
> differing in some mental respect, or that an object cannot alter in
> some mental respect without altering in some physical respect (1970,
> 214).
> 



After Davidson's appeal to supervenience, Terence Horgan (1982,
1984), Jaegwon Kim (1984, 1987, 1988, 1990, 1993), David Lewis (1983),
and others began to examine the notion of supervenience itself, and to
explore its usefulness for a wide variety of philosophical purposes.
The literature then mushroomed.


## 3. Supervenience and Other Relations



Philosophers have distinguished many different varieties of
supervenience. In
 Section 4,
 we will lay out those varieties, and note their pairwise logical
relations. For now, though, we will stick to the core idea of
supervenience--namely, that there cannot be an
*A*-difference without a *B*-difference. A number of
general points of philosophical interest can be made just by working
with that simple and easy idea.


### 3.1 The Modal Force of the Supervenience Relation



In order to sort out how supervenience connects up to other
relations--like entailment, reduction, grounding, ontological
dependence, and explanation--we need to discuss the fact that
supervenience can hold with varying degrees of modal force. That is,
the 'cannot' in "there cannot be an
*A*-difference without a *B*-difference" comes in
different strengths. For example, it can mean "cannot as a
matter of logic," or it can mean "cannot consistently with
the laws of nature".



This raises some controversial issues. For the purposes of this essay,
we make the following three assumptions. First, we assume that
metaphysical necessity is just as strong as logical necessity. There
are, to be sure, metaphysically necessary truths that are not logical
truths, such as the truth that water = H20.
But metaphysical necessity is just as strong as logical necessity in
that the space of metaphysical possibility is exactly the same as the
space of logically possibility: the logically possible worlds = the
metaphysically possible worlds (see, e.g., McLaughlin 1995; Chalmers
1996; and Jackson 1998). This is not entirely uncontroversial, but
little we have to say turns on it. Second, and more importantly in
what follows, we assume that at least certain properties that figure
in laws of nature do not play their nomic roles essentially, so that
it is logically or metaphysically possible for those properties not to
figure in the laws in question. This is also controversial, but we
will not defend it here. (See Shoemaker 1980, Swoyer 1982, and Ellis
2001 for the opposing view.) Finally, we will assume that whatever is
metaphysically necessary is nomologically necessary, but not
conversely. (One can hold that there are nomologically necessary
truths that are not metaphysically necessary, even if one holds that
all nomic properties play their nomic roles essentially; see Fine
2002.)



Some supervenience relations are metaphysically (or logically)
necessary. The property *being a haircut or a halibut*
supervenes with metaphysical necessity on the two base properties
*being a haircut* and *being a halibut*: two things
cannot differ with respect to *being a haircut or a halibut*
without differing either with respect to *being a haircut* or
else with respect to *being a halibut*. Also, the surface areas
of perfect spheres supervene with metaphysical necessity on their
volumes (and *vice versa*) (Lombard 1986). Some supervenience
relations are metaphysically contingent. Consider the Wiedemann-Franz
Law, which entails that the electrical conductivity of a metal
co-varies with its thermal conductivity. This law thus entails that
electrical conductivity and thermal conductivity mutually supervene on
each other. But on the assumption that the law is metaphysically
contingent, the supervenience relation is too. It is only
nomologically necessary that there cannot be a difference in one sort
of conductivity without a difference in the other sort.



So, supervenience relations can hold with either metaphysical or
nomological necessity, and perhaps even with some other kind of
necessity. The fact that supervenience comes in different modal
strengths is important. Sometimes there is widespread agreement that a
certain supervenience relation holds, but dispute over what its modal
force is. One important example is the supervenience of the mental on
the physical. Just about everyone, even a Cartesian dualist, believes
some version of this supervenience claim. But there is vigorous
disagreement about whether the supervenience relation holds with
metaphysical or merely nomological necessity. Ask yourself--could
there be an individual that has no conscious experience at all,
despite being physically indiscernible from an individual that is
conscious (Kirk 1994; Chalmers 1996)? That is, could there be what
philosophers call a 'zombie'? Because it is widely agreed
that the mental nomologically supervenes on the physical, it is widely
agreed that zombies are nomologically impossible--that their
existence would violate psychophysical laws. But some philosophers
(e.g., Chalmers 1996) think that zombies are metaphysically possible.
This remains a matter of lively dispute, and resolving it requires
addressing some hard questions about the relationship between
conceivability and metaphysical possibility. Suffice it to note that
the dispute is precisely over the modal force of the
'cannot' in "there cannot be a mental difference
without a physical difference." (For discussions of the
relationship between conceivability and metaphysical possibility see,
e.g., the essays in Gendler and Hawthorne 2002. For a discussion of
physicalism, see
 Section 5.4
 of this entry and the separate entry on
 physicalism.)


### 3.2 Supervenience and Entailment



Is supervenience a form of entailment? The two relations are logically
similar in certain ways. The entailment relation is reflexive,
transitive, and non-symmetric, and so is supervenience. Supervenience
is reflexive: for any set of properties *A*, there cannot be an
*A*-difference without an *A*-difference (see, e.g., Kim
1984). It is also transitive: if *A*-properties supervene on
*B*-properties, and *B*-properties supervene on
*C*-properties, then *A*-properties supervene on
*C*-properties. However, supervenience is neither symmetric nor
asymmetric; it is *non*-symmetric. Sometimes it holds
symmetrically. Every reflexive case of supervenience is trivially a
symmetric case; consider also the case of the volume and surface area
of perfect spheres mentioned in
 Section 3.1.
 And sometimes it holds asymmetrically. For example, while the mental
may supervene on the physical, the physical does not supervene on the
mental. There can be physical differences without mental differences.
One uncontroversial way to see this is to note that radically
physically different things--a washing machine and a paper bag,
say--can be mentally just alike in virtue of lacking mental
properties altogether. Thus supervenience, like entailment, is
reflexive, transitive, and non-symmetric.



Nonetheless, that *B*-properties entail *A*-properties
is neither necessary nor sufficient for *A*-properties to
supervene on *B*-properties. (The notion of property entailment
in play is this: property *P* entails property *Q* just
in case it is metaphysically necessary that anything that possesses
*P* also possesses *Q*.) To see that such entailments do
not suffice for supervenience, consider the properties *being a
brother* and *being a sibling*. Possessing the former
entails possessing the latter; every brother is a sibling. But
*being a sibling* does not supervene on *being a
brother*. Two people can differ with respect to being a sibling
despite being exactly alike with respect to being a brother. To see
this, suppose that Sarah has a sister and Jack is an only child. Thus
Sarah is a sibling and Jack is not, though neither is a brother. So
the *B*-properties can entail the *A*-properties, even
though *A* does not supervene on *B*.



To see that supervenience does not suffice for entailment, recall that
supervenience can hold with only nomological necessity. In such cases,
there is no entailment; thermal conductivity properties do not
*entail* electrical conductivity properties, for example.



But what about supervenience with *metaphysical* or
*logical* necessity? Even that does not in general guarantee
that there are *B*-properties that entail the
*A*-properties. At best, the logical supervenience of
*A* on *B* means that how something is *B*-wise
entails how it is *A*-wise. But it does not follow that every
*A*-property is entailed by a *B*-property, or even that
some *A*-property is entailed by a *B*-property.
Consider two examples. First, on the assumption that there are
negative properties, every property *F* will supervene with
logical necessity on its complement not-*F*. After all, two
things cannot differ with respect to whether they are *F*
without differing with respect to whether they are not-*F*, and
conversely. But obviously being *F* does not entail being
not-*F* (McLaughlin 1995, 1997a). Second, consider a case in
which the property set *B* contains only the property
*P* and the property *Q*, and property set *A* is
the unit set of the conjunctive property *P*&*Q*.
That is, *A* = {*P*&*Q*}, and *B* =
{*P*, *Q*}. *A* supervenes with metaphysical
necessity on *B*. But there is no property in *B* that
entails the *A*-property.



Now, there might be *special* sets of properties for which the
supervenience of *A* on *B* guarantees that there are
*B*-properties that entail the
*A*-properties--namely, property sets that are closed
under the Boolean operations of complementation, infinitary
conjunction, infinitary disjunction (see Kim 1984), and operations
involving quantification. Closing {*F*} and {~*F*} under
these operations will result in the same set, namely {*F*,
~*F*, *F* & ~*F*, *F* v
~*F*...}. In both cases just above, then, the
*closure* of *B* under these operations in fact contains
a property that entails the *A*-property.



Discussions of supervenience often appeal to property sets that are
closed under such operations. But this is not a trivial assumption,
for two reasons. First, it is controversial whether complementation,
conjunction, and disjunction are legitimate property-forming
operations. Whether they are largely depends upon what properties are
taken to be. If properties are just the semantic values of predicates,
then there are negative, conjunctive, and disjunctive properties,
because negative, conjunctive, and disjunctive predicates can have
semantic values. But if properties are universals there may not be any
such properties (Armstrong 1978, 1989). And if properties are ways a
thing might be, then property sets cannot be closed under Boolean
operations. That would entail that for any property *F*,
*being *F* and ~*F** is also a property. However,
that is not a way anything might be. (However, see Priest 2010 for an
opposing view.) Second, even if it is assumed that the
property-forming operations are legitimate, the fact is that we are
quite often interested in property sets that are not closed under
them. Consider negation. Even assuming that there are negative
properties, the fact is that we do not standardly count cats as having
geological properties because they are neither ignaceous, sedimentary,
nor metamorphic. And it seems strange to say that Descartes was
committed to mental substances having physical properties simply
because he thought they are not spatially extended. Since not every
property set is closed under every property-forming operation,
supervenience is not in general sufficient for entailment. (For
further discussion of supervenience and various property-forming
operations, see Van Cleve 1990; Oddie and Tichy 1990; Bacon 1990,
1995; Glanzberg 2001; Bader 2012.)



One particularly interesting case of entailment failure arises when
the property sets are not closed under quantification. This opens room
for cases in which the supervening set *A* contains properties
formed by quantification, like *being such that every F is a
G*, and the subvening set *B* does not. If *B* does
not include such properties, there are no properties in *B*
that entail them. As Bertrand Russell noted many years ago, "you
cannot ever arrive at a general fact by [deductive] inference from
particular facts, however numerous" (Russell 1918, 235; quoted
in Bricker 2005). But general properties, nevertheless, logically
supervene on particular ones: no two possible worlds can differ in
what general facts hold without differing in what particular facts
hold (see Skyrms 1981, Lewis 1992, and Bricker 2005). Thus, general
facts logically supervene on particular facts, even though the latter
do not entail the former.



The upshot is that the logical supervenience of property set
*A* on property set *B* will only guarantee that each
*A*-property is entailed by some *B*-property if
*A* and *B* are closed under both infinitary Boolean
operations and property-forming operations involving
quantification.


### 3.3 Supervenience and Reduction



Everyone agrees that reduction requires supervenience. This is
particularly obvious for those who think that reduction requires
property identity, because supervenience is reflexive. But on any
reasonable view of reduction, if some set of *A*-properties
reduces to a set of *B*-properties, there cannot be an
*A*-difference without a *B*-difference. This is true
both of ontological reductions and what might be called
"conceptual reductions"--i.e., conceptual
analyses.



The more interesting issue is whether supervenience suffices for
reduction (see Kim 1984, 1990). This depends upon what reduction is
taken to require. If it is taken to require property identity or
entailment, then, as we have just seen
 (Section 3.2),
 even supervenience with logical necessity is not sufficient for
reduction. Further, if reduction requires that certain epistemic
conditions be met, then, once again, supervenience with logical
necessity is not sufficient for reduction. That *A* supervenes
on *B* as a matter of logical necessity need not be knowable
*a priori*.


### 3.4. Supervenience and Ontological Innocence



The issues about entailment and reduction are related to a question
about whether supervenience with metaphysical necessity is
*ontologically innocent*--whether the
*A*-properties are anything "over and above" the
*B*-properties. 



Some think that supervenience--at least when accompanied by
grounding; see
 sect. 3.5
 below--is indeed ontologically innocent in this sense. After
all, if the A-properties supervene with metaphysical necessity on the
B-properties, then they come along automatically given the
B-properties. To borrow Kripke's metaphor (1972, 153-154),
once God fixes the B-properties, she is all done; she does not need to
do anything further to get the A-properties going. Indeed, she cannot
block them. Given the distribution of B-properties, there is no
further question about which A-properties are instantiated. So, it is
claimed, the latter are nothing over and above the former. However,
other people vigorously resist this idea. How can the A-properties not
count as a further ontological commitment, if they are numerically
distinct from the B-properties? (Both Jonathan Schaffer (2015) and
Karen Bennett (2017, chapter 8.2) have recently argued that the best
way to make sense of this is as follows. Grounded entities are
nonfundamental, and nonfundamental entities do not count against the
simplicity of a theory, although they do count towards the total
number of things there are.) 



This dispute is central to various issues in metaphysics and the
philosophy of mind. For example, nonreductive physicalists often say
that mental properties are distinct from but nonetheless
"nothing over and above" physical ones. Their reductivist
opponents, however, clearly think that this is illegitimate. This can
be seen in the charge that nonreductive physicalists face the
exclusion problem--that they are unable to account for the causal
efficacy of the mental without claiming that all of its effects are
"double-caused." (See the entry on
 mental causation.)



Another example concerns composition. Some people--those who
believe in "unrestricted mereological
composition"--think that any two or more things whatsoever
compose a larger thing. They typically claim that while the (single)
fusion is not *identical* to its (many) parts (the exception is
Baxter 1988), it does supervene on them, and is thus "nothing
over and above" those parts. So, for example, there is a
mereological fusion of your left elbow, Tony Blair, and the
Mississippi River, and it is distinct from, but nothing over and
above, those three parts. Lewis, speaking of a fusion of a trout and a
turkey, says that "it is neither fish nor fowl, but it is
nothing else: it is part fish and part fowl" (1991, 80) and that
"mereology is innocent" (87). However, opponents of
unrestricted mereological composition are unsurprisingly unconvinced:
"what does 'nothing over and above' mean? This
slippery phrase has had a lot of employment in philosophy, but what it
means is never explained by its employers" (van Inwagen 1994,
210). Indeed, the thought that composition is not in the least
ontologically innocent has led some to claim that there aren't
any composite objects (or that living organisms are the only composite
objects; see van Inwagen 1990, Merricks 2001, Dorr and Rosen 2002, and
the entry on
 mereology).



So, on the one hand, there is what might be called the
"supervenience intuition". Many nonreductive physicalists
think that the metaphysically necessary supervenience of the mental on
the physical means that mental properties are nothing over and above
physical ones, and most (all?) believers in unrestricted mereological
composition think that the metaphysically necessary supervenience of
fusions on their parts means that fusions are nothing over and above
those parts. On the other hand, there is what might be called the
"distinctness intuition"--if mental properties and
mereological fusions are *distinct* from physical properties
and mereological atoms, respectively, then surely they count as
something over and above them. 



This can be made to look as though it is just a terminological issue
about how to best use phrases like "nothing over and
above" and "ontological innocence". But there are
very real issues here. The central difference between the two sides is
that one emphasizes the fact that the two kinds of properties or
entities are numerically distinct, and the other emphasizes the fact
that there is nonetheless a close *nonidentity* relation
between them. And what matters in any given case is i) just which
particular nonidentity relation holds, and ii) whether the fact that
that relation holds is enough to defuse whatever problem is on the
table. 



In the mereological fusion case, the issue is really just whether
fusions exist at all. Those who believe in unrestricted mereological
composition think that the existence of the atoms entails the
existence of the fusions, and their opponents do not. The debate here
is only about whether the fusions are (or would be if they existed)
anything "over and above" their parts insofar as that
would perhaps make them a significant ontological commitment, leading
some (not Schaffer or Bennett; see above) to be suspicious of the
principle of unrestricted mereological composition.



In the nonreductive physicalism case, the issue is about whether all
nonidentity relations are on a par as far as the exclusion argument is
concerned. Nonreductive physicalists think that mental properties
supervene with metaphysical necessity upon physical properties
(whether they are also entailed by physical properties depends upon
what property-forming operations the set of physical properties is
taken to be closed under; see
 Section 3.2).
 The interesting question is not whether this enables them to truly
say that mental properties are "nothing over and above"
physical ones, but rather whether it enables them to solve the
exclusion problem. (For views that more or less say that it does, see
Yablo 1987, Shoemaker 2001, Bennett 2003, Melnyk 2003). Note that this
issue also arises in the case of mereological fusions; Merricks (2001)
uses a version of the exclusion problem to argue against the existence
of nonliving composites.



One more example, which is similar to the fusion case. We have just
seen that general truths supervene with metaphysical necessity on
particular truths, but are not entailed by them
 (Section 3.2).
 This led Russell to say that "you must admit general facts as
distinct from and over and above particular facts" (1918, 236).
It would be a mistake to focus too much on Russell's claim that
general facts are "over and above" particular facts; he
clearly just means that they are numerically distinct from particular
facts. The interesting issue is rather whether Russell is right that
we must admit general facts into our ontology at all. (See Bricker
2005 for an argument to the contrary.)



All told, there may not be a straightforward answer to the question of
whether supervenience with metaphysical necessity is ontologically
innocent. Whether it is depends upon whether it is a tight enough
relation to do the work required to solve whatever concern is in play,
and that will obviously depend upon what that concern *is*. So
whether metaphysically necessary supervenience is "ontologically
innocent" may well depend upon the case. In one case,
metaphysically necessary supervenience might do the job, in another
case entailment might be required, and in another perhaps nothing
short of numerical identity will do.


### 3.5 Supervenience, Grounding, and Ontological Dependence



There is now a large literature on grounding and ontological
dependence, including an entry for each in this encyclopedia. Roughly,
one fact grounds another when the latter obtains in virtue of the
former: the former in some sense makes the latter obtain. It is a
productive, generative relation. (Bennett 2017 claims that there are
several such relations, which she calls building relations. Talk of
production and generation naturally invites a question about the
relation between grounding or building and causation; see Schaffer
2016, Bennett 2017 chapter 4, Bernstein 2017, and A. Wilson 2018 for
discussion of the relation between grounding and causation.) Roughly,
an entity ontologically depends on another when the former would not
exist without the latter. Much, much more can be and has been said
about these relations, but this is enough for our purposes. 



Grounding and ontological dependence are distinct from each other. The
simplest way to see this is by means of the kinds of case that
revealed to David Lewis that causation is distinct from causal
dependence (1973): preemption and overdetermination. Just as cases of
causal overdetermination and preemption involve causation without
causal dependence, so too do cases of 'grounding
overdetermination' and 'grounding preemption'
involve grounding without ontological dependence. For example, the
fact that I exist grounds the fact that something exists, but the
obtaining of the latter fact does not depend upon the obtaining of the
former; the fact that something exists is massively overgrounded.



Because grounding and ontological dependence are distinct, the claim
that supervenience is not the same as grounding is distinct from the
claim that supervenience is not the same as ontological dependence.
Nonetheless, many of the same considerations are relevant.



One such consideration is that these relations may not have the same
relata. Supervenience is typically said to be a relation between
properties or families of properties, but at least some of
grounding's advocates say that it is a relation between facts
only (e.g. Rosen 2010, Audi 2012), and ontological dependence seems to
obtain between members of a variety of ontological categories.
However, it is not clear how seriously to take this kind of concern,
since notions of fact supervenience and property grounding can easily
be defined. 



A second way to see that supervenience is not identical to either
grounding or ontological dependence is to note that the latter two
relations are widely (though not universally) thought to be
irreflexive and asymmetrical. Nothing can ground or ontologically
depend upon itself, and nothing can ground or ontologically depend on
something that also grounds or depends on it. But as we have seen,
supervenience is reflexive and not asymmetrical (see
 Section 3.2).
 (For challenges to the claim that dependence and/or grounding are
irreflexive and asymmetric, see Jenkins 2011, Bliss 2014, Wilson 2014,
and Barnes 2018; for a reply to these challenges, see Bennett 2017,
sect. 3.2). 



A third way to see that supervenience is not the same as either
grounding or ontological dependence is that the following conditionals
are false:


* if *A* supervenes on *B*, *B* grounds
*A*
* if *A* supervenes on *B*, *A* ontologically
depends on *B*



As McLaughlin put it in 1995, a mere supervenience claim does not
entail any "in virtue of" claim. Here are a couple of ways
to see this. As noted above, for any property *F*, being
*F* supervenes on being ~*F*: two things cannot differ
with respect to being *F* without differing with respect to
being ~*F*. But, of course, being ~*F* does not ground
being *F*, and being *F* does not ontologically depend
on being ~*F*!



Another way to see that the conditionals are false is to notice that
properties everything has necessarily and ones that nothing can
possibly have supervene, with the same sort of necessity, on
*any* property whatsoever. (The fact that the necessary and the
impossible supervene on anything and everything poses not one but
*two* problem for attempts to use supervenience to define
physicalism. See
 Section 5.4.)
 The property *being self-identical* supervenes on the property
*being an antique*; the property *being both a kangaroo and
not a kangaroo* supervenes upon the property *being dusty*.
The reason is simple enough. No two things can differ with respect to
either necessary or impossible properties, period; thus no two things
can differ with respect to such properties without also differing with
respect to *B*-properties, for any property set *B*.
Nothing can be both a kangaroo and not a kangaroo, so no two things
can differ with respect to that property, and thus no two things can
differ with respect to that property without also differing with
respect to being dusty, or being purple, or being a steam engine, etc.
But it is not the case that being both a kangaroo and not a kangaroo
is ontologically dependent upon being dusty, or that being dusty
grounds being both a kangaroo and not a kangaroo. Being dusty has
nothing to do with it at all.



For yet another reason for denying that the supervenience of
*A*-properties on *B*-properties entails anything about
grounding or ontological dependence, see the discussion of certain
forms of global supervenience in Section 4.3.5.

 Author's
note: the main ideas in this section have been in place since the
original 2005 edition, though the section was substantively revised in
2018 to be more careful about the differences between grounding,
ontological dependence, and ontological priority. (The 2023 revision
merely involved trivial edits.)

### 3.6 Supervenience, Realization, and Emergence



Like 'supervenience', both 'realization' and
'emergence' are philosophical terms of art. Their
definitions are stipulative and thus can only be judged by their
theoretical usefulness, not by accord with common usage.



Realization is primarily taken to be a relationship between
properties, though derivative notions of property instance realization
and state of affairs realization have been defined. We will focus on
property realization. There is more than one use of the term
'property realization' in literature. Perhaps the leading
use is the one found in the literature on the functionalist theory of
mind. (See, e.g., Block 1980; Melnyk 2003, 2006). On the functional
view of realization, one property *G* realizes another
*F* just in case *G* occupies (or fills or plays) the
causal role associated with *F*, 'the
*F*-role'--that is, just in case instances of
*G* have the kinds of causes and kinds of effects that comprise
the *F*-role. Thus, for instance, a neural property will
realize pain just in case it has the kinds of causes and effects that
comprise the pain-role. (According to analytical functionalism, the
pain-role is the causal role that folk psychology associates with
pain; according to psychofunctionalism, it is the causal role that
scientific psychology associates with pain.) If more than one property
plays the *F*-role, then *F* is multiply realizable.
(See the entry on
  multiple realizability.)
 



Sydney Shoemaker (2007, chapter 2) defines a related notion of
property realization, which he calls the 'subset view of
realization'. He says that "as a first approximation,
property *P* has property *Q* as a realizer just in case
(1) the forward-looking causal features of property *P* are a
subset of the forward-looking causal features of property *Q*,
and (2) the backward-looking causal features of *P* have as a
subset the backward-looking features of *Q*" (2007, 12).
Once again, if *P* has more than one realizer, then *P*
is multiply realizable. (McLaughlin (2007) argues that this subset
notion of realization, will not serve Shoemaker's purposes.)




There are other, less well-entrenched notions of realization in the
literature (e.g., Gillett 2003; Shoemaker 2007, chapter 3), but it
would take us too far afield to spell these out in detail.



What is the relation between supervenience and realization, in either
of the above senses? It looks like realization is sufficient for
supervenience, at least for non-local versions of supervenience. But
supervenience is not sufficient for realization, for reasons that are
familiar from section 3.5: necessary properties supervene on anything,
and properties supervene on their own negations. Further, because
realization is a distinctively causal notion, there are additional
considerations here. The interesting case has to do with epiphenomenal
properties--those that have no causal powers and play no causal
role. Perhaps mathematical properties are epiphenomenal in this way.
Let *F* be such a property, and let it supervene upon
*G*. *F* is not functionally-realized by *G*,
since *G* does not play *F*'s distinctive causal role
(*F* does not have one). So this is another reason to deny that
supervenience is sufficient for functional realization. But *F*
*is* Shoemaker-realized by *G*. That's because
*F*'s causal powers are the null set, and the null set is a
subset of every set. Epiphenomenal properties are thus
Shoemaker-realized by anything at all, including *G*.
(Shoemaker's view of realization, like his view about the causal
individuation of properties (1980), is simply not well-suited to the
epiphenomenal case.) 



What about emergence? The term is used in a variety of ways, in the
sciences as well as philosophy. These uses are so wildly divergent
that it is not clear that there is a common core notion. (See the
essays in Bedau and Humphreys 2008, in Gibbs, Hendry, and Lancaster
2019, Wilson 2021, and the entry on
 emergent properties.)
 But one canonical source of emergence talk is the British Emergentist
tradition, particularly the work of C.D. Broad. Broad thought of
emergent properties as fundamental properties possessed by complex
objects (Broad 1925; McLaughlin 1992, 1997, 2019). A number of
philosophers have suggested that Broad's notion can be characterized
by means of supervenience with mere nomological necessity (e.g. van
Cleve 1990, Chalmers 2006). One question that arises, then, is whether
the appeal to nomological as opposed to metaphysical necessity can
distinguish emergence from tighter relations like realization; Jessica
Wilson (2005; 2021, 143-149) and others have argued that it
cannot.


### 3.7 Supervenience and Explanation



Supervenience claims, by themselves, do nothing more than state that
certain patterns of property (or fact) variation hold. They are silent
about why those patterns hold, and about the precise nature of the
dependency involved (see Kim 1993, 167; 1998, 9-15; Blackburn
1984, 186; Schiffer 1987, 153-154; and McGinn 1993, 57). But few
supervenience theses are plausibly brute, that is, unexplainable. It
is natural to look further, and to try to explain why
*A*-properties supervene on *B*-properties. When such
supervenience is explainable, there is
'superdupervenience' (a term coined by William Lycan; see
also Schiffer 1987; Horgan 1993; and Wilson 1999).



Sometimes it is easy to see what explains a supervenience thesis.
Consider the examples of trivial supervenience relations from
 Section 3.5.
 It is obvious why there cannot be an *A*-difference without a
*B*-difference if *A* is a set of necessary or
impossible properties--namely, because there cannot be an
*A*-difference at all. The supervenience relation is explained
by the necessity or impossibility of the supervening properties. It is
also obvious why *A*-properties supervene on
*A*-properties. Of course, property identity claims are
sometimes not *a priori* knowable; consider, for example, the
fact that the property *being water* is identical with the
property *being H20.* Still the fact
that *being water* is identical with *being
H20* explains why there cannot be a
difference with respect to being water without a difference with
respect to being H20. And supervenience with
only nomological necessity can be explained by appeal to laws of
nature. It is in virtue of the Wiedemann-Franz Law that electrical
conductivity supervenes with nomological necessity on thermal
conductivity.



Because we expect supervenience theses to be explainable, it is hard
for us to rest content with a supervenience thesis if we do not see
what would explain why it is true. If it is claimed, for instance,
that moral properties supervene on non-moral properties, we expect
there to be an explanation of why this is so. Appeals to unexplainable
supervenience theses can thus seem to be mystery mongering.


### 3.8 Tallying Up



Supervenience gives us less than some philosophers have thought. Even
logically or metaphysically necessary supervenience is compatible with
there being no *B*-properties that entail any
*A*-properties. Supervenience is not itself explanatory, and
does not guarantee that the *A*-properties either reduce to,
ontologically depend upon, or are grounded by the
*B*-properties. It might provide a way to capture the thought
that *A*-properties or facts are not a further ontological
commitment over and above the *B*-properties or facts, but this
is controversial. At heart, all a supervenience claim says is that
*A*-properties *covary with* *B*-properties.
Nevertheless, as we shall see in
 Section 5,
 supervenience has a variety of philosophical uses.


## 4. Varieties of Supervenience



The slogan "There cannot be an *A*-difference without a
*B*-difference" is applied both to *particular
individuals* and to entire *possible worlds*. In the former
case, the slogan expresses the idea that two individuals cannot differ
in *A*-respects without also differing in *B*-respects.
This sort of claim is an individual supervenience claim. In the latter
case, the slogan expresses the idea that two possible worlds cannot
differ with respect to their world-wide pattern of distribution of
*A*-properties without also differing with respect to their
world-wide pattern of distribution of *B*-properties. That sort
of claim is a global supervenience claim. Both individual and global
supervenience claims come in a variety of modal strengths. In this
section, we will distinguish various forms of both individual and
global supervenience, and examine some logical relationships among
them.


### 4.1 Weak and Strong Individual Supervenience



Kim (1984, 1987) distinguished two different kinds of individual
supervenience, weak and strong. They are defined by means of
quantification over possible worlds, as follows:



> 
> *A*-properties *weakly supervene* on
> *B*-properties if and only if for any possible world *w*
> and any individuals *x* and *y* in *w*, if
> *x* and *y* are *B*-indiscernible in *w*,
> then they are *A*-indiscernible in *w*.
> 
> 
> *A*-properties *strongly supervene* on
> *B*-properties if and only if for any possible worlds
> *w*1 and
> *w*2 and any individuals *x*
> in *w*1 and *y* in
> *w*2, if *x* in
> *w*1 is *B*-indiscernible from
> *y* in *w*2, then *x*
> in *w*1 is *A*-indiscernible
> from *y* in *w*2. (Kim
> 1987.)
> 
> 
> 



*x* and *y* are *A*-indiscernible if and only if
they are exactly alike with respect to every *A*-property;
similarly for *B*-indiscernibility. (Here times are omitted,
but of course objects may be *A*-indiscernible at one time, but
not at another.) The possible worlds quantified over might include all
metaphysically possible worlds, or only nomologically possible worlds
(etc.), depending upon what degree of modal force is intended.



As the names indicate, strong individual supervenience is stronger
than weak individual supervenience. (We shall hereafter follow
established usage and drop the word 'individual' unless
clarity requires it.) Weak supervenience says that there is no
possible world that contains individuals that are
*B*-indiscernible but *A*-discernible. Strong
supervenience entails that there are no possible individuals that are
*B*-indiscernible but *A*-discernible, *whether they
are in the same world or different worlds.* When the range of
worlds is the same, strong supervenience theses entail weak
supervenience theses, but the latter do not in general entail the
former. It is important to note, however, that when *A* is
restricted to intrinsic properties, strong and weak supervenience are
arguably equivalent; see Section 4.3.4. 



Occasionally philosophers appeal to weak supervenience rather than
strong supervenience. Hare, for example, said that his claim that
value properties supervene on other properties was intended to be an
appeal only to weak supervenience (1984, 4). And Davidson similarly
claimed that his appeal to supervenience was intended to be an appeal
only to weak supervenience (1985, 1993, esp. 4n4). (He said this in
response to Kim (1984), who argued that Davidson cannot appeal to
strong supervenience on pain of commitment to strict psychophysical
laws, which are incompatible with Davidson's well-known thesis
of the anomalism of the mental, according to which there are no strict
psychophysical laws. See the entry on anomalous monism.)



But appealing to weak supervenience while denying strong generates a
certain explanatory burden. You will recall that we always want an
explanation of why a supervenience relation holds (see
 Section 3.7).
 Thus someone who asserts a weak supervenience thesis but denies the
corresponding strong supervenience thesis must provide an explanation
of why the weak supervenience thesis is true that does not entail that
the relevant strong supervenience thesis is true as well. And that can
look mysterious: if there can be things in *different* worlds
that are *A*-discernible but not *B*-discernible, why
can't there be two such things within a single world? If
everything within each world that is *B*-indiscernible is
*A*-indiscernible, how can different worlds enforce
*different* *B*-*A* property pairings? (See
Blackburn on the need to explain the "ban on mixed
worlds," 1973, 1985, and especially 1984, 184.)



Sometimes there is an explanation of why weak supervenience holds
despite the fact that strong supervenience does not. If, within a
world, two individuals assert exactly the same propositions, then they
are exactly alike vis-a-vis having asserted a true proposition:
the one asserted at least one true proposition if and only if the
other did. The reason is that a proposition will have a unique
truth-value relative to a world. The following weak supervenience
thesis thus holds: for any world *w*, and any individuals
*x* and *y* in *w*, if *x* and *y*
are indiscernible with respect to what propositions they have
asserted, then they are indiscernible with respect to having asserted
a true proposition. Contingent propositions, however, are true in some
worlds and false in others. It is thus possible for two individuals in
different worlds to assert exactly the same propositions, and yet
differ with respect to having asserted a true proposition. The one
might assert many true propositions, while the other fails to assert
any true proposition. It follows that the following strong
supervenience thesis is false: for any worlds
*w*1 and
*w*2, any individuals *x* in
*w*1 and *y* in
*w*2, if *x* in
*w*1 is indiscernible from *y*
in *w*2, with respect to what
propositions they have asserted, then *x* in
*w*1 is indiscernible from *y*
in *w*2 with respect to having
asserted a true proposition.



In contrast, it is by no means clear why mental properties would
weakly supervene on physical properties without strongly supervening
on them; and the analogous question arises for moral properties and
nonmoral properties. Davidson and Hare owe us an explanation of why
mental and moral properties weakly supervene, respectively, on
physical and nonmoral ones--and it must be an explanation that
does not entail that strong supervenience holds as well. Simon
Blackburn's well-known argument against moral realism basically
constitutes an attempt to answer this question for Hare. Though
Blackburn speaks of 'supervenience' and
'necessitation' rather than weak and strong supervenience,
his argument against moral realism rests on *exactly* the
demand for explanation that we have been exploring. He claims, 1) that
moral properties weakly supervene on nonmoral properties, but do not
strongly supervene on them, 2) that this requires explanation, and 3)
that projectivists can do this better than moral realists (1973,
1985.) We are content to note that some such answer is required from
anyone who holds a weak supervenience thesis without the corresponding
strong supervenience thesis.



One final matter concerning the notions of weak and strong
supervenience remains to be discussed. This is that they are sometimes
formulated differently, by means of modal operators rather than
quantification over possible worlds:



> 
> 
> *A* *weakly supervenes*m** on
> *B* if and only if necessarily, if anything *x* has some
> property *F* in *A*, then there is at least one property
> *G* in *B* such that *x* has *G*, and
> everything that has *G* has *F*, i.e., iff 
> 
> 
> 
> > 
> > #[?]*x*[?]*F*[?]*A*[*Fx*
> > - [?]*G*[?]*B*(*Gx* &
> > [?]*y*(*Gy* - *Fy*))]
> > 
> 
> 
> 
> *A* *strongly supervenesm* on
> *B* if and only if necessarily, if anything *x* has some
> property *F* in *A*, then there is at least one property
> *G* in *B* such *x* has *G*, and
> necessarily everything that has *G* has *F*, i.e., iff
> 
> 
> 
> 
> > 
> > #[?]*x*[?]*F*[?]*A*[*Fx*
> > - [?]*G*[?]*B*(*Gx* &
> > #[?]*y*(*Gy* - *Fy*))]
> > 
> 
> 
> 
> (Kim 1984)
> 
> 
> 



Notice that strong superveniencem is
formulated just like weak superveniencem,
except that it contains one more necessity operator.



Kim initially maintained that the modal operator versions are
equivalent to the above possible world definitions of weak and strong
supervenience respectively (see esp. 1987, 79-82). But they are
not; they are stronger. On certain assumptions (e.g. that modal
operators are to be understood as quantifiers over worlds), the modal
operator versions of strong and weak supervenience respectively entail
the possible world versions; but not *vice versa* (McLaughlin
1995).



The reasoning here is basically the same as that given in
 Section 3.2
 above for why supervenience does not guarantee entailment. Both
weakm and strongm supervenience
say i) that it is necessary that everything that has an
*A*-property has some *B*-property or other, and ii)
that that *B*-property entails the *A*-property. But
neither i) nor ii) follows from the possible world versions of either
weak or strong supervenience--unless *B* is assumed to be
closed under the Boolean operations of complementation, infinitary
conjunction, infinitary disjunction, and property-forming operations
involving quantification (McLaughlin 1995). Without that assumption,
the possible worlds versions allow things with *A*-properties
to lack *B*-properties altogether, and *a fortiori* to
lack any *B*-property that entails their *A*-properties.
Of course, possible worlds supervenience requires that each pair of
*B*-less intraworld (weak) or interworld (strong) individuals
must have the *same* *A*-properties, but the possible
world versions allow *B*-less individuals to have
*A*-properties. The modal operator versions do not.



It should therefore come as no surprise that the cases that served as
counterexamples to the claim that supervenience is a form of
entailment also serve as counterexamples to the equivalence of the
possible worlds and modal operator formulations of supervenience.
Being *F* strongly supervenes on being not-*F*, but
fails to even weakly supervenem on it.
{*P* & *Q*} strongly supervenes on {*P*,
*Q*}, but fails to even weakly
supervenem on it. The possible world
versions of weak and strong supervenience are weaker than the
corresponding modal operator versions. The latter go beyond the basic
idea that there cannot be an *A*-difference without a
*B*-difference. Again, though, the modal operator versions
*are* equivalent to the possible worlds versions if the base
set *B* is closed under Boolean operations, and operations
involving quantification.


### 4.2 Regional Supervenience



Terence Horgan (1982) has proposed a version of supervenience in terms
of individual regions of space-times, rather than in terms of objects.
A weak and a strong version of Horgan's "regional
supervenience" can be formulated as follows:



> 
> *A*-properties *weakly regionally supervene* on
> *B*-properties if and only if for any possible world *w*
> and any space-time regions *r*1 and
> *r*2 in *w*, if
> *r*1 and
> *r*2 are *B*-duplicates in
> *w*, then they are *A*-duplicates in *w*.
> 
> 
> *A*-properties *strongly regionally supervene* on
> *B*-properties if and only if for any possible worlds
> *w*1 and
> *w*2 and any space-time regions
> *r*1 in
> *w*1 and space-time region
> *r*2 in
> *w*2, if
> *r*1 in
> *w*1 is a *B*-duplicate of
> *r*2 in
> *w*2, then
> *r*1 in
> *w*1 is an *A*-duplicate of
> *r*2 in
> *w*2.
> 
> 
> 



Regional supervenience is a form of individual supervenience that
takes the individuals to be regions of space-time. Nonetheless, it is
worth separate mention because Horgan (1982) has argued that it has
some of the attractive features of global supervenience.


### 4.3 Global Supervenience



Often, claims of the form 'there cannot be an
*A*-difference without a *B*-difference' are not
made about individuals, nor about nonmaximal space-time regions, but
rather about entire possible worlds. This is global supervenience,
typically formulated as follows:



> 
> *A*-properties *globally supervene* on
> *B*-properties if and only if for any worlds
> *w*1 and
> *w*2, if
> *w*1 and
> *w*2 have exactly the same world-wide
> pattern of distribution of *B*-properties, then they have
> exactly the same world-wide pattern of distribution of
> *A*-properties.
> 



The notion of a global supervenience thesis has been employed for a
number of philosophical purposes. Notably, it has been used to
characterize physicalism (see
 Section 5.4),
 and to capture David Lewis' Humean supervenience thesis:
"all there is to the world is a vast mosaic of local matters of
particular factE all else supervenes on that" (1986a,
ix-x).



Global supervenience is often claimed to serve purposes that neither
strong nor weak individual supervenience will serve. First, it is
sometimes claimed that global supervenience naturally handles
relational properties like *being an original Van Gogh* or
*being a dollar bill*. As we shall see, however, strong or weak
supervenience can handle relational properties too. Second, global
supervenience naturally handles the supervenience of factors other
than properties or relations. On a Humean view of laws of nature, for
instance, laws of nature are general facts that supervene on
particular facts. But that can be captured by individual property
supervenience, even if only in a baroque way. A third potential
difference between global and individual supervenience is that the
former, but not the latter, is compatible with the supervening and
subvening properties being possessed by different individuals (see
Haugeland 1982). Thus, for example, global supervenience is useful if
there can be distinct but spatio-temporally coincident
objects--it leaves room to say that the properties of a clay
statue supervene upon the properties of the distinct lump of clay that
constitutes it (see
 Section 5.5).



What the difference between individual and global supervenience really
comes to will be discussed throughout the rest of this section.


#### 4.3.1 Strong Individual Supervenience and Global Supervenience



It is clear that strong individual supervenience entails global
supervenience (see Kim 1984). The question that has attracted
attention is the converse--whether global supervenience entails
strong individual supervenience. In this section, we describe the
initial stages of this debate, which took place when the going notion
of global supervenience was that outlined just above. In Section
4.3.2, we explain how that notion has been replaced by a family of
more precise notions, and explore how it affects the question of
whether global supervenience entails strong individual supervenience.
(Most of the reminder of this section paraphrases McLaughlin 1995,
55-56.)



The debate began when Kim purported to show that "global
supervenience is nothing but strong supervenience" (1984, 168).
In response, Brad Petrie (1987) argued that global supervenience does
not entail strong supervenience. His strategy was to try to provide a
counterexample to a strong supervenience thesis that is not a
counterexample to the corresponding global supervenience thesis. Here
is his case. Let set *A* = {*S*} and that *B* =
{*P*}. Consider two worlds
*w*1 and
*w*2 that are as follows: world
*w*1 contains exactly two objects,
*x* and *y*. And world
*w*2 contains exactly two objects,
*x*\* and *y*\*. The following purports to be a complete
depiction of the contents of those worlds:




|  |  |  |
| --- | --- | --- |
| *W*1 |  | *W*2 |
|  |  |  |
| *Px* |  | *Px*\* |
| *Sx* |  | ~*Sx*\* |
| *Py* |  | ~*Py*\* |
| ~*Sy* |  | ~*Sy*\* |



The existence of *w*1 and
*w*2 is incompatible with the thesis
that *A* strongly individually supervenes on *B* because
*x* in w1 is *B*-indiscernible
but *A*-discernible from *x*\* in
*w*2. But the existence of these
worlds is not itself a counterexample to the *global*
supervenience of *A* on *B*. Since
w1 and *w*2
do not have the same global pattern of distribution of
*B*-properties, it seems not to matter that the worlds do not
have the same global pattern of distribution of *A*-properties.
Thus Petrie claimed that "since global supervenience is, and
strong supervenience is not, consistent with this example, the two
concepts of supervenience are not equivalent" (1987, 121).



In response, Kim conceded that global supervenience fails to entail
strong supervenience (1987, 318), and went on to claim that
Petrie's example also shows that global supervenience fails to
entail weak. Notice that *w*1 alone
violates the weak supervenience of *A* on *B*, but also
fails to be a counterexample to the global supervenience of *A*
on *B*. Kim thus concluded that global supervenience fails to
entail weak or strong individual supervenience.



Paull and Sider pointed out that these argument strategies are no good
(1992). The problem is that one cannot simply point to two worlds that
do not themselves falsify a global supervenience thesis, and then
claim that the case is compatible with that thesis. Those two worlds
might entail the existence of other worlds that are *not*
compatible with the global supervenience thesis. A global
supervenience thesis is a claim about *all* worlds, not just
two. The upshot is that although a global supervenience thesis fails
to entail either a weak or strong supervenience thesis in virtue of
logical form, it might nevertheless be the case that plausible
metaphysical principles entail that whenever the former holds, so does
the latter.



Paull and Sider appeal to a plausible principle to show that the
existence of Petrie's *w*1 and
*w*2 entail the existence of a pair
of worlds that constitutes a counterexample to the global
supervenience of *A*-properties on *B*-properties (1992,
838). The basic idea is that for any object in any possible world,
there is another world containing an "isolated duplicate"
of it. Intuitively, the duplicate exists all alone in its world; more
precisely, an object y is isolated in a world "if and only if
that world contains only (i) *y*, (ii) *y*'s
parts, and (iii) objects whose existence is entail by any of the
objects mentioned in (i) and (ii)" (1992, 838-9).
Crucially, isolated duplicates share the intrinsic properties of the
things with which they are duplicates. (Two caveats. First, this is
not intended to be a *definition* of 'intrinsic'.
For some attempts to do so, see e.g., Lewis 1983a, Langton and Lewis
1998, and a variety of articles in *Philosophy and Phenomenological
Research* 63). Second, notice that the principle does not say that
each thing can itself exist in isolation; it simply says that each
thing has a duplicate that does. It consequently does not entail that
nothing has any essential extrinsic properties.)



Paull and Sider's isolation principle does the job. Consider
again the worlds *w*1 and
*w*2 that Petrie described. Petrie
purported to describe the worlds in full. Thus, *P* and
*S* are presumably supposed to be intrinsic properties. It
follows from the isolation principle that there is a world
*w*3 that contains an isolated
duplicate of *x*--call it
"*z*"--and a world
*w*4 that contains an isolated
duplicate of *x*\*--call it "*z*\*." As
Paull and Sider note, these worlds will be as follows:




|  |  |  |
| --- | --- | --- |
| *W*3 |  | *W*4 |
|  |  |  |
| *Pz* |  | *Pz*\* |
| *Sz* |  | ~*Sz*\* |



Unlike *w*1 and
*w*2,
*w*3 and
*w*4 constitute a counterexample to
the global supervenience of *A*-properties on
*B*-properties. They have the same pattern of distribution of
*B*-properties, but different patterns of distribution of
*A*-properties. So, Paull and Sider claim that Petrie failed to
show that global supervenience does not entail strong
supervenience.



But Paull and Sider went on to provide a new argument for that claim.
They appealed to a set *B* containing just two properties,
*P* and *Q*, and a set *A* containing only one
property, *M*. An object has *M* just in case it has
*P*, and some other object is *Q*. That is to say,
*Mx* =*df* *Px* &
[?]*yQy*. This definition guarantees that *A*
globally supervenes on *B*. They then described the following
two worlds:




|  |  |  |
| --- | --- | --- |
| *W* |  | *W*\* |
|  |  |  |
| *Ma* |  | ~*Mc* |
| *Pa* |  | *Pc* |
| ~*Mb* |  |  |
| *Qb* |  |  |



This pair of worlds shows that *A* does not strongly supervene
on *B*. And the principle of isolation cannot be applied to
generate a counterexample to global supervenience. An isolated
duplicate of a would be both *A*- and *B*-indiscernible
from c (an isolated duplicate of a would *not have M*).
Consequently, Paull and Sider concluded that global and strong
supervenience are not equivalent. (1992, 841).



Klagge (1995) objected to this line of argument. He pointed out that
Paull and Sider include an extrinsic property *M* in the
supervenient set *A*, but only intrinsic properties *P*
and *Q* in the subvenient or base set *B*. And, he
claimed, if we allow that there are the sorts of property-forming
operations required to construct extrinsic property *M*, then
Paull and Sider have not exhaustively characterized worlds *w*
and *w*\*. For, given those property-forming operations, it is
plausible that there will, for instance, be a property *P*#
that can be defined as follows: *P*#
=*df* *Px* &
[?]*y*(*y*[?]*x*). (Basically, a thing is
*P*# just in case something else is *P*.) *a* in
*w* and *c* in *w*\* differ on this property;
*a* has *P*# while *c* does not. That is right.
But Klagge took that to show that *w* and *w*\* do not
provide a counterexample to the strong supervenience of *A* on
*B* after all. That, however, does not follow. It would follow
only if *a* and *c* thereby counted as
*B*-discernible, and they do not. Paull and Sider stipulate
that *B* contains only *P* and *Q*. Thus,
*a* and *c* are *B*-indiscernible, despite the
fact that *a* has *P*# and *c* does not.



But Klagge was clearly right that Paull and Sider's example
involves a supervenient set *A* that contains an extrinsic
property and a subvenient set *B* that contains only intrinsic
properties, and he was right that this is important. It invites the
question whether global supervenience might entail strong
supervenience when *A* and *B* are sets of intrinsic
properties. And it invites the question whether global supervenience
might entail strong supervenience when *A* and *B* both
include extrinsic properties of certain sorts. Indeed, in response to
Paull and Sider, Kim suggests that "equivalence seems to fail,
through the failure of implication from global to strong
supervenience, only when extrinsic properties are present in the
supervenient set but disallowed from the subvenient base" (1993,
170; see also McLaughlin 1997a, 215). We will return to these
questions in the next several sections. Answering them requires
getting clearer about global supervenience; to this we now turn.


#### 4.3.2 Different Versions of Global Supervenience



Until now, we have been relying mainly on a notion of global
supervenience that is defined in terms of what amounts to a notion of
*A*/*B*-indiscernibility of worlds:



> 
> *A*-properties *globally supervene* on
> *B*-properties if and only if for any worlds
> *w*1 and
> *w*2, if
> *w*1 and
> *w*2 have exactly the same world-wide
> pattern of distribution of *B*-properties, then they have
> exactly the same world-wide pattern of distribution of
> *A*-properties.
> 



But what is meant by a 'world-wide pattern of
distribution' of *A*- or *B*-properties? The
notion is usually cashed out by appeal to the notion of there being a
certain kind of isomorphism or mapping between worlds. For any
property set *f*, define the notion of an *f*-preserving
isomorphism as follows:



> 
> An isomorphism I between the inhabitants of worlds
> *w*1 and
> *w*2 preserves *f*-properties
> if and only if for any *x* in
> *w*1, *x* has a
> *f*-property *P* in
> *w*1 just in case the image of
> *x* under I (the individual to which I maps *x*) has
> *P* in *w*2.
> 



This purposely avoids appeal to any special relationship that the
mapped individuals may bear to each other (such, e.g., occupying
corresponding locations in their respective worlds). This is to remain
as neutral as possible on such issues, and because any features used
to pick out the mapped things would automatically then globally
supervene on any properties whatever (see McLaughlin 1995, 1997a). See
Steinberg 2014 for an alternative way of characterizing world-wide
patterns of property distribution.



Given this notion, various different forms of global supervenience
emerge. Stalnaker 1996, McLaughlin 1996, 1997a, and Sider 1999 all
distinguish between a weak and a strong notion of global
supervenience, as follows:



> 
> *A*-properties *weakly globally supervene* on
> *B*-properties iff for any worlds
> *w*1 and
> *w*2, if there is a
> *B*-preserving isomorphism between
> *w*1 and
> *w*2, then there is an
> *A*-preserving isomorphism between them.
> 
> 
> *A*-properties *strongly globally supervene* on
> *B*-properties iff for any worlds
> *w*1 and
> *w*2, every *B*-preserving
> isomorphism between *w*1 and
> *w*2 is an *A*-preserving
> isomorphism between them.
> 
> 
> 



Shagrir (2002) and Bennett (2004a) have both formulated an
intermediate version:



> 
> *A*-properties *intermediately globally supervene* on
> *B*-properties if and only if for any worlds
> *w*1 and
> *w*2, if there is a
> *B*-preserving isomorphism between
> *w*1 and
> *w*2, then at least one isomorphism
> between them is both *A*-and-*B*-preserving.
> 



Indeed, any number of versions of global supervenience can be
formulated, simply by specifying exactly how many
*A*-and-*B*-preserving isomorphisms there must be
between worlds between which there is a *B*-preserving
isomorphism. Such versions all count as forms of intermediate global
supervenience, however, and will be ignored in what follows. Notice
too that it is not always clear which version is intended when someone
appeals to the notion of global supervenience. Shagrir (2002) and
Bennett (2004a) suggest that there is some reason to think that people
often intend intermediate; Leuenberger (2009) argues that none of the
precisified versions really captures the original concept. Shagrir
later argued that strong does the most "justice to the notion of
global supervenience" (2013).



It is easy to see that strong global supervenience entails
intermediate global supervenience, which in turn entails weak global
supervenience. If *every* *B*-preserving isomorphism
between two worlds must itself be *A*-preserving, then if there
are any *B*-preserving isomorphisms between two worlds at all,
at least *one* of them must be *A*-preserving. So,
strong global supervenience entails intermediate. And if at least one
of any existing *B*-preserving isomorphisms between two worlds
must itself be *A*-preserving, then it obviously follows that
if there is a *B*-preserving isomorphism between two worlds,
there must also be an *A*-preserving one. Thus, intermediate
global supervenience entails weak global supervenience.



It is also easy to see that strong individual supervenience entails
strong global supervenience. Suppose that *A*-properties fail
to strongly globally supervene on *B*-properties. That means
that there are two worlds *w*1 and
*w*2 between which there is a
*B*-preserving isomorphism that fails to be
*A*-preserving. So, for some *x* in
*w*1, the image of *x* under I
in *w*2--call it y--has all
and only the same *B*-properties as *x* in
*w*1, but differs from *x* in
*w*1 in at least one of its
*A*-properties. But that is just to say that *x* in
*w*1 is *B*-indiscernible yet
*A*-discernible from *y* in
*w*2. It follows that
*B*-properties fail to strongly supervene on
*A*-properties. Thus, strong individual supervenience entails
strong global supervenience, and thereby also entails intermediate and
weak global supervenience as well.



But strong global supervenience fails to entail strong individual
supervenience, at least when *A* and *B* are any
nonempty sets of properties. Showing this only requires tiny
modifications to Paull and Sider's argument that the notion of
global supervenience spelled out just in terms of world-wide patterns
of distribution of properties fails to entail strong individual
supervenience (Section 4.3.1), and so we will not state the argument
here. (See Shagrir 2002, 188.) Once again, the key to the argument is
a case in which the supervening set contains extrinsic properties, and
the subvening set does not.



Let us now see what is the case when the supervening and subvening
property sets are brought into line with each other. Recall the
earlier hypothesis that global and strong individual are equivalent
when Paull-Sider style cases are blocked (see Section 4.3.1). So,
then, does strong global entail strong individual when the supervening
set contains only intrinsic properties? When the subvening set
contains both intrinsic properties and all of the extrinsic properties
that can be generated from them?



The answer to both questions is "yes." And it turns out
that related argumentative strategies can also be reapplied back to
the case of weak and strong individual supervenience. We outline these
strategies in the next two sections. However, some of the proofs
themselves are complicated, and we thus refer to the reader to the
original literature.


#### 4.3.3 Equivalences for an Extrinsic Base



Strong global supervenience entails strong individual supervenience as
long as the base set *B* is taken to be closed under
complementation, infinitary conjunction, infinitary disjunction, and
property-forming operations involving quantification and identity. Kim
anticipates this equivalence (1993, 170), and Robert Stalnaker
provides the proof (1996, 238). It should also be noted that John
Bacon argues that if sets of properties *A* and *B* are
closed under the operations mentioned above and also an operation he
calls "resplicing," then weak and strong individual
supervenience both hold or fail to hold together (1986). For
*B* to be closed under resplicing is for it to be the case that
for any property *P* such that its extension *Pw* in a
world *w* is the extension of some property in *B*,
*P* is a member of *B*.



We have already noted that it is controversial whether such
property-forming operations are legitimate, and, even if they are, we
are often interested in property sets that are not closed under them.
See
 Section 3.2.
 Still, so long as the property-forming operations are legitimate,
then even if *B* itself is not closed under them, there will
always be a larger set *B*+ which is. That is good
enough to entail that for every strong global supervenience thesis
there is a logically equivalent strong individual supervenience
thesis. Indeed, if all of these property-forming operations (including
Bacon's resplicing) are legitimate, then there are property sets
with respect to which weak individual supervenience, strong individual
supervenience, and strong global supervenience are all equivalent.



But since there has been considerable dispute over the legitimacy of
the various alleged property-forming operations, the issues remain
unresolved.


#### 4.3.4 Equivalencies for Intrinsic Properties



If we bring the property sets into line by restricting both the
supervening and subvening sets to intrinsic properties--however
*exactly* the notion of an intrinsic property is to be captured
(see e.g. Langton and Lewis 1998)--we get even clearer results.
Many varieties of supervenience turn out to be equivalent for
intrinsic properties.



Both Shagrir (2002) and Bennett (2004a) argue that strong individual
supervenience is equivalent to strong global supervenience when
*A* and *B* are sets of intrinsic properties. Bennett
also argues that in such a case even *weak* global
supervenience entails strong individual supervenience. The argument
relies upon Paull and Sider's isolation principle, explained in
Section 4.3.1 above; the basic idea is to show that any
counterexamples to strong individual supervenience can be
"isolated" to generate counterexamples to weak global
supervenience--i.e., pairs of worlds between which there is a
*B*-preserving isomorphism but no *A*-preserving
one.



Here, again, we can also obtain related results about
*individual* supervenience. Mark Moyer (2008) argues that weak
and strong individual supervenience are equivalent in the special case
of intrinsic properties. He appeals to a recombination principle
similar to Paull and Sider's principle of isolation, but with a
twist. The intuitive idea is that any two things in any two worlds can
be isolated from their surroundings and then put into a world with
each other. More formally:



> 
> *Recombination Principle*. For any worlds
> *w*1 and
> *w*2, any individual *x* in
> *w*1 and any individual *y* in
> *w*2, there is a world
> *w*3 that contains individuals
> *x*' and *y*' such that *x*' in
> *w*3 is an intrinsic-duplicate of
> *x* in *w*1 and y' in
> *w*3 is an intrinsic-duplicate of
> *y* in *w*2.
> 



If this principle is right, then any cross-world pair of individuals
that witness the violation of a strong supervenience claim have
intrinsic-duplicates within a single world. If the supervening
properties are intrinsic, those duplicates will violate weak
supervenience as well. 



If all of these results are right, then weak individual supervenience,
strong individual supervenience, weak global supervenience,
intermediate global supervenience, and strong global supervenience are
*all* equivalent in the special case when *A* and
*B* are sets of intrinsic properties.


#### 4.3.5 Individual and Global Supervenience Redux



In Section 4.3.3, we saw that weak and strong individual supervenience
are equivalent to strong global supervenience in the special case in
which the base set *B* is closed under certain property forming
operations. And in 4.3.4, we saw that weak and strong individual
supervenience, and weak, intermediate, and strong global supervenience
are all equivalent in the special case in which *A* and
*B* are sets of intrinsic properties. The upshot is that strong
global and strong individual supervenience come apart "only when
extrinsic properties are present in the supervenient set but
disallowed from the subvenient base," as Kim and others
predicted (Section 4.3.1). See Shagrir 2009 for discussion of the case
of relations.



However, weak and intermediate global supervenience are not equivalent
to strong individual supervenience even when extrinsic properties are
let into the base--more precisely, when the base is closed under
the relevant property-forming operations. So, perhaps they have
distinctive philosophical work to do, work that cannot be done by
strong individual supervenience. For example, Sider (1999) appeals to
weak global supervenience to handle cases of spatio-temporal
coincidence, though he retracts this in his (2008). See
 Section 5.5.



But it is controversial whether these forms of supervenience are
strong enough to be philosophically useful. As both Shagrir (2002) and
Bennett (2004a) have pointed out, only strong global supervenience
guarantees that the world-wide distribution of *B*-properties
determines the world-wide distribution of *A*-properties. Both
weak and intermediate global allow what is called 'intraworld
variation'--both allow *B*-indiscernible individuals
in a world to have different *A*-properties. (Contrast weak
individual supervenience, which allows crossworld variation, but does
ban "mixed worlds.") Indeed, weak global supervenience
allows the *A*-preserving and *B*-preserving
isomorphisms to be utterly independent of each other. Suppose some
property *being griffic* merely weakly globally supervenes on
the physical. Then although a world physically just like this one has
to contain the same number of griffic things as this world, it does
not matter which things they are. In this world it might be the Eiffel
Tower and the Queen Mother; in the physical duplicate it might be a
tea towel and the Grand Canyon.



In any case, those who assert a weak or intermediate global
supervenience thesis while denying the corresponding strong global
supervenience thesis need to provide an explanation of why weak or
intermediate global supervenience holds that does not entail that
strong global supervenience holds. (Recall the discussion of weak and
strong individual supervenience in
 4.1).
 That is, they need to explain what enforces the links between
*A*- and *B*-preserving isomorphisms that are required
by weak and intermediate global, without also enforcing the claim that
*every* *B*-preserving isomorphism itself be
*A*-preserving.



At present, these issues remain open, and the status of weak and
intermediate global supervenience is controversial.


### 4.4 Similarity Based Supervenience



This essay has thus far focused on varieties of
*indiscernibility*-based supervenience. But in some cases we
might be interested in a notion according to which things that are
very much alike in *B*-respects must also be very much alike in
*A*-respects. This is similarity-based supervenience (Kim
1987). (The remainder of this section closely paraphrases McLaughlin
1995).



Weak and strong versions of similarity-based supervenience can be
defined in the expected fashion:



> 
> A *weakly supervenessim* on *B* if and only
> if for any world *w*, and for any *x* and *y* in
> *w*, if *x* and *y* are not largely different
> with respect to *B*-properties, then they are not largely
> different with respect to *A*-properties.
> 
> 
> A *strongly supervenessim* on *B* if and only
> if for any worlds *w*1 and *w*2,
> and for any *x* in *w*1 and *y* in
> *w*2, if *x* in *w*1 is not
> largely different from *y* in *w*2 with
> respect to *B*-properties, then *x* in
> *w*1 is not largely different from *y* in
> *w*2 with respect to *A*-properties.
> 
> 
> 



These are versions of individual supervenience; global versions can
also be formulated. Strong implies weak, but not conversely, except
for the special case of intrinsic properties. (The latter can be shown
by slight modification of Moyer's argument mentioned in Section
4.3.4.)



Similarity-based supervenience is logically independent of
indiscernibility-based supervenience: neither implies the other.
Similarity-based supervenience fails to imply indiscernibility-based
supervenience. It may be that there can be *A*-differences
without *B*-differences, but that there cannot be
*large* *A*-differences without *large*
*B*-differences. And indiscernibility-based supervenience
likewise fails to imply similarity-based supervenience. The reason is
that there may be small *B*-differences that are critical
points for big *A*-differences. When that happens,
similarity-based supervenience will fail, even though
indiscernibility-based supervenience may hold. For example, it might
well be the case that small physical differences can be accompanied by
large mental and moral differences. Similarly, a small physical
difference like a misplaced brush stroke might have a large effect on
the aesthetic value of a painting. Suffice it to note that it remains
an open question whether there are any interesting philosophical uses
of similarity-based supervenience.


### 4.5 Multiple Domain Supervenience



Thus far this essay has focused primarily on single domain
supervenience (the exceptions are the discussions of weak and
intermediate global supervenience). *A* form of supervenience
counts as single domain when and only when the *A*- and
*B*-properties are possessed by the very same
individuals--when the way something is in *A*-respects is
a function of the way *it* is in *B*-respects. Both weak
and strong individual supervenience are clear cases of single domain
supervenience. But in some cases, what we want to say is that there
cannot be an *A*-difference in certain things without a
*B*-difference in certain *other* things--distinct
things to which the former things are related in a certain way. When
and if this is the case, there is multiple domain supervenience.



One place such a notion seems useful is in discussions of coincidence
and material constitution. Those who think that a clay statue is
distinct from the lump of clay that make it up will claim that certain
properties of the statue must supervene on properties of the lump of
clay that constitutes it. For example, there could not be two statues
that are discernible in shape without the statues being constituted by
lumps of clay discernible in shape. For further discussion, see
 Section 5.5.



Kim (1988) has formulated a weak and strong version of multiple domain
supervenience. Let *D*1 and
*D*2 be non-empty domains of
individuals, *R* be a relation between
*D*1 and
*D*2, and *R*|*x* be
the subset of *D*2 to which
*x* is *R*-related. We can define the following
notions:



> 
> (*A*, *D*1) *weakly
> multiple domain supervenes* on (*B*,
> *D*2) relative to *R* just in
> case necessarily for any *x* and *y* in
> *D*1, if *R*|*x* and
> *R*|*y* are *B*-indiscernible, then *x*
> and *y* are *A*-indiscernible.
> 



> 
> (*A*, *D*1) *strongly
> multiple domain supervenes* on (*B*,
> *D*2) relative to relation *R*
> just in case for any *x* and *y* in
> *D*1 and any worlds
> *w*1 and
> *w*2, if *R*|*x* in
> *w*1 is *B*-indiscernible from
> *R*|*y* in *w*2,
> *x* in *w*1 is
> *A*-indiscernible from *y* in
> *w*2. (Kim 1998)
> 



When *R* is identity, these are equivalent, respectively, to
single domain weak and single domain strong individual supervenience.
It is because *R* might be a relation other than identity, for
example material constitution, that the definitions have the potential
for added utility. Here again, slight modification of Moyer's
argument (Section 4.3.4) can be used to show that weak and strong
multiple domain supervenience are equivalent when the supervening set
is intrinsic.



Coincidence-friendly supervenience is another kind of multiple-domain
supervenience (proposed by Dean Zimmerman 1995, 88)). It can be
formulated as follows (see Bennett 2004, 520):



> 
> *Coincidence-Friendly Supervenience* : For all *x* and
> *y*, and all worlds *w*1 and
> *w*2, if *x* in
> *w*1 is *B*-indiscernible from
> *y* in *w*2, then for each
> thing *x*\* in *w*1 to which
> *x* is *R*-related, there is something *y*\* in
> *w*2 that is *R*-related to
> *y* and that is *A*-indiscernible from *x*\*.
> 



That is a strong version, but a weak version can be formulated as
follows:



> 
> *Weak Coincidence-Friendly Supervenience:* For any world
> *w* and any *x* and *y* in *w*, if
> *x* in *w* is *B*-indiscernible from *y*
> in *w*, then for each thing *x*\* to which *x* is
> *R*-related in *w*, there is something y\* that
> *y* is *R*-related in *w* and *x*\* is
> *A*-indiscernible from *y*\*.
> 



Here again, when *R* is identity, these forms of supervenience
are equivalent, respectively, to weak and strong individual
supervenience. And here again, the weak and strong versions are
equivalent when *A* is a set of only intrinsic properties.



Weak and strong coincident-friendly supervenience count as kinds of
multiple-domain supervenience, but they differ from Kim's weak
and strong multiple domain supervenience in at least one important
respect. The final quantifier in the definitions of
coincident-friendly supervenience is existential, rather than
universal as it is in Kim's weak and strong multiple domain
supervenience. As a result, Kim's multiple domain supervenience
says that if *a* and *b* are *B*-indiscernible,
each thing *R*-related to a must be *A*-indiscernible
from *everything* *R*-related to *b*.
Coincidence-friendly supervenience says only that each thing
*R*-related to a must be *A*-indiscernible from
*something* *R*-related to *b*. This matters if
*R* is *B*-indiscernibility, as it plausibly is in the
case of spatio-temporal coincidence--the main philosophical
application of multiple-domain supervenience.



Finally, Ralf Bader (2013) has developed versions of multiple-domain
supervenience to model relations between complex entities and their
parts, including those permitted by non-classical metrologies.


## 5. Applications


### 5.1 An Argumentative Strategy



Recall that everyone agrees that the reduction of *A* to
*B* implies the supervenience of *A* on *B*
 (Section 3.3).
 This gives rise to one central use of supervenience. Arguing against
a supervenience thesis that must be true if some program of reduction
or conceptual analysis is to succeed is a common way of arguing that
the program cannot succeed. McLaughlin (1984, 1995) calls this style
of argumentation 'argument by appeal to a false implied
supervenience thesis'--or, for short, argument by appeal to
a FIST.



Here are a few well-known arguments by appeal to a FIST. Suppose
someone claims that there are neurophysiological properties, perhaps
yet to be discovered, to which intentional properties like believing
that *P* reduce. This claim implies that intentional properties
supervene on neurophysiological properties. The Twin Earth thought
experiments given by Tyler Burge (1979) and Hilary Putnam (1975) are
(putative) counterexamples to that supervenience claim; they are cases
of neurophysiologically indiscernible people whose thoughts have
different contents.



Another argument by appeal to a FIST is Chalmers' appeal to the
(putative) metaphysical possibility of zombies (see
 Section 3.1
 and
 Section 5.4).
 This is intended to show that phenomenal properties do not
metaphysically supervene on, and thus do not reduce to, physical
properties. This line of argument is available even though
physicalists have not yet proposed any such reduction. If it succeeds,
then the project of reducing phenomenal properties to physical
properties is doomed to failure.



Consider a third example, from epistemology. *A* simple causal
theory of perceptual knowledge says that a subject's perceptual
knowledge that *P* can be analyzed in terms of
*P*'s bearing the right kind of causal relation to the
subject's belief that *P*. To test this claim, we need
not await proposals as to what the kind of causal relation in question
is. For this project of conceptual analysis can succeed only if two
believers that *P* cannot differ with respect to perceptually
knowing that *P* without differing with respect to how
*P* is causally connected to their belief that *P*.
Alvin Goldman's fake barn country case (1976) yields a
(putative) counterexample to this supervenience claim.



Of course, it is controversial whether any of these arguments
*succeed*, because it is controversial whether the alleged
counterexamples to the supervenience claims are really possible. But
in all three cases, the style of argument is the same--argument
by appeal to a FIST. (See McLaughlin 1984, 1995.)


### 5.2 Internalism/Externalism



Distinctions between internalism and externalism arise in many areas
in philosophy--philosophy of mind, philosophy of language,
epistemology, and ethics. All of these distinctions can be
characterized by means of supervenience theses. For example, an
internalist about mental content accepts, and an externalist denies,
that what a mental state is about supervenes upon neurophysiological
properties, or "what's in the head." The dispute is
about whether two thinkers can differ in the contents of their mental
states without also differing in some neurophysical respect.
Similarly, an internalist about epistemic justification accepts, and
an externalist denies, that whether a belief is justified supervenes
upon the mental properties of the believer. The dispute is about
whether two believers can differ in whether their beliefs are
justified without also differing in some mental respect. And an
internalist about moral motivation accepts, and an externalist denies,
that moral motivation supervenes upon moral judgment. The dispute is
about whether two (rational) people can differ in how they are
motivated to act without also differing in their judgments about which
of those actions they ought to perform.



Relatedly, supervenience can also be used to capture the traditional
distinction between internal and external relations. As Lewis has
noted (1986b, 62), an internal relation (such as *being taller
than*) supervenes on the intrinsic natures of its relata. An
extrinsic relation (such as *being 3 kilometers from* ) does
not. The main difference between this case and those above is that
here there is no real dispute about whether the supervenience thesis
holds or not; it is widely agreed that there are two kinds of
relations.


### 5.3 Haecceitism



Haecceitism is the view that identity properties, like *being Kofi
Annan* or *being that particular table*, do not supervene
on qualitative properties. On this view, every two numerically
distinct things differ haecceitistically, but no other difference
follows. Questions about whether there could be qualitatively
indiscernible but numerically distinct things becomes important in
modal metaphysics.



The issue here is an instance of something more general. Supervenience
plays a useful role in answering questions about the identity and
individuation conditions for things belonging to some kind. As
Davidson pointed out, there is a *prima facie* puzzle (1980,
ch. 5) about how to address such questions. The answer to the question
"When are two events identical?" is
trivial--"Never." And the answer to the question
"When is an event identical with itself?" is likewise
trivial--"Always." But surely there is a substantive
question lurking here. Davidson himself opted to get around this worry
by means of semantic ascent. But an alternative is to move to what
David Lewis calls 'a nonduplication principle' (see J.
Bennett 1988). Instead of asking when two events are identical, we can
ask a fill in the blank question: 'no two events can be just
alike with respect to \_\_\_\_\_\_'? Davidson would fill in the blank
with 'their causes and effects'. Kim would fill in the
blank with 'their subject, time, and constitutive
property' (1976); others fill in the blank in other ways.



What matters here is just that nonduplication principles are
supervenience theses. They are supervenience theses that take the
supervening set *A* to be the identity facts for particular
entities of whatever kind is in question. There cannot be a difference
in whether an event has a property like *being event e* without
a difference in its causes and effects (Davidson) or in its subject,
constitutive property, and time (Kim). Note that any view that accepts
a nonduplication principle for some sort of entity is *ipso
facto* anti-haecceitist. Both Davidson and Kim are
anti-haecceitists about events.


### 5.4 Characterizing Physicalism



Roughly speaking, physicalism is the view that somehow or other,
everything is settled by the physical. This is of course vague along a
number of dimensions. One question, beyond the scope of this essay, is
what exactly 'physical' means (see Stoljar's entry
on physicalism). Another question is about the scope of the
quantifier: should it really range over everything, or should the
thesis be restricted to the mental (thus leaving room for non-physical
entities like platonic numbers, abstract universals, or God)? While
the sociological question of which of these theses is usually intended
is also beyond the scope of this essay, the distinction will appear
again. And a third question is what exactly 'settled by'
means. 



This last question is the relevant one here, because for a roughly 30
year period beginning with Davidson's "Mental Events"
(1970, 214), philosophers used supervenience as a placeholder for the
needed relation. That is, physicalism was regularly characterized as
the view that everything--or perhaps just the
mental--supervenes on the physical. More specifically, it was
frequently characterized as a i) metaphysically necessary ii) strong
global supervenience thesis that is iii) restricted to only a certain
range of worlds. We shall say a bit about each in turn, before
mentioning the more recent turn to instead characterizing physicalism
in terms of grounding.


#### 5.4.1 Why say that the thesis is metaphysically necessary?



Physicalists take the supervenience thesis to hold with metaphysical
necessity, because a merely nomologically necessary supervenience
thesis is compatible with dualism. Dualists can maintain that there
are fundamental psychophysical laws that maintain the supervenience
connection (McLaughlin 1992, Chalmers 1996). Since no physicalist will
agree, capturing physicalism requires a supervenience thesis that
holds with full-blown metaphysical necessity. 


#### 5.4.2 Why use strong global supervenience?



Physicalism is characterized in terms of global supervenience as
opposed to individual supervenience because an individual's mental
states do not locally supervene on her intrinsic brain states for
reasons that do not impugn physicalism as intuitively understood.
Notably, the contents of her propositional attitudes depend upon the
surrounding environment if any kind of externalism is true (See Putnam
1975 and the entry on externalism). 



But why strong global supervenience instead of one of the weaker two
varieties, intermediate or weak (see
 4.3.2)?
 The answer is that neither of those is strong enough. An intermediate
global supervenience thesis would allow a world physically
indiscernible from this one, in which precisely the same mental
properties are instantiated as are instantiated here, but in which
physically indiscernible individuals swap mental lives. A weak global
supervenience characterization of physicalism would go further. It
would allow a world physically indiscernible from this one, in which
precisely the same mental properties are instantiated as are
instantiated here, but in which they are differently distributed among
entities without any restriction. For example, a weak global
supervenience characterization of physicalism is compatible with the
existence of a world physically indiscernible from this one in which
Taylor Swift and Peter Singer exchange mental lives (see
 4.3.5).
 Physicalism should not allow either sort of mental property
swapping.


#### 5.4.3 Why restrict the thesis to a certain range of worlds?



Still, physicalism cannot just be the thesis that the mental facts (or
all the facts) strongly globally supervenience with
logical/metaphysical necessity on the physical facts and laws, because
many physicalists want to allow for the metaphysical possibility of
things like ghosts or Cartesian souls. They think that there actually
aren't any such things, not that there could not be any, nor
even that there could not be any compatibly with the physical facts of
our world. They thus do in fact allow that two worlds could be
physical duplicates but differ mentally, in virtue of only one of them
containing disembodied spirits, say. (Note that because the worlds are
physical duplicates, those spirits either exert no causal influence on
the physical at all, or else only exert redundant,
'overdeterministic' causal influence on the physical.)



Various philosophers have offered various ways of defining physicalism
to allow for this possibility, while continuing to rely upon global
supervenience. The key in all cases is to limit the range of worlds in
which the global supervenience thesis holds. For example, David Lewis
took physicalism to be the claim that



> 
> Among worlds where no natural properties alien to our world are
> instantiated, no two differ without differing physically; any two such
> worlds that are exactly alike physically are duplicates (Lewis 1983b,
> 364).
> 

 Jackson offers the following:


> 
> Any world which is a minimal physical duplicate of our world is a
> duplicate *simpliciter* (Jackson, 1998, 12).
> 



where a minimal physical duplicate is what results from duplicating
all the physical facts and "stopping right there." And David
Chalmers says that physicalism is true in a world w just in case every
positive fact that obtains in w also obtains in any world physically
indiscernible from w (1996, 39-40). Each of these three
definitions allows for worlds in which physicalism fails: worlds that
are physical duplicates of the actual world, and in which there are
ghosts or souls.


#### 5.4.4 Beyond supervenience physicalism



Unfortunately, even these sophisticated supervenience formulations
fail to provide an adequate characterization of physicalism. There are
at least three reasons for this failure, and necessarily existing
entities or necessarily obtaining facts generate not one but two of
them. 



Recall that necessary beings (whether entities, facts, or whatever)
supervene on anything whatsoever, for the simple reason that such
things exist in every world. Because no two worlds can differ in
whether they exist, full stop, no two worlds can differ in whether
they exist without differing in *x*, for whatever *x*
you like (see
 section 3.5).
 



The first problem that necessary beings pose is only a problem for
wide scope physicalism, the version of the view that says that truly
everything, not just the mental facts, supervenes on the physical
facts. The difficulty is that some putative necessarily existing
things, like Platonic numbers or God, do not seem physicalistically
kosher. Yet their actual existence is compatible with a global
supervenience formulation of physicalism.



The second problem is a problem for both wide scope physicalism and a
narrower version only about the mental. As discussed in
 section 3.5),
 the fact that necessarily existing things supervene on anything
whatsoever shows that supervenience is not ontological dependence or
determination. After all, the putative fact that God exists globally
supervenes on the fact that my cat is named Snoop without the former
in any way depending on the latter. This is supervenience on the
cheap, not anything strong enough for physicalism. (For other putative
counterexamples to the sufficiency of the supervenience thesis, see
Witmer 1999 and Hawthorne 2002.)



The third issue is closely related to the second, though it doesn't
turn on necessary existence in particular. It is that many think the
correct statement of physicalism should be in some way explanatory in
a way that the bare supervenience claim is not. One version of this is
to say that physicalism should say that the physical facts explain the
mental ones. The supervenience claim alone says no such thing, as
shown by the case of necessary existents as well as the case of
properties supervening on their negations. A different version of this
is to say that physicalism requires
'superdupervenience'--that physicalism should explain
why the relevant global supervenience theses holds (see Blackburn
1984, Horgan 1993, Melnyk 2003, and Wilson 2005). Concerns like these
should be familiar from sections
 3.5
 and
 3.7).
 



Some think that these concerns can be avoided by moving from
characterizing physicalism in terms of supervenience to characterizing
physicalism in terms of grounding (e.g. Rosen 2010, 111; Dasgupta
2014, 557; Schaffer 2017, section 4). Because grounding is supposed to
be hyperintensional, it is not the case that necessary beings or facts
are grounded by just anything. And grounding is supposed to back
explanations as well.



However, whether the appeal to grounding really advances anything is a
matter of dispute (Wilson 2016). See Stoljar's entry on physicalism
for further discussion. Further, note that we have only raised
challenges for the claim that a strong global supervenience thesis is
*sufficient* for physicalism. It remains open that some such
thesis is *necessary* for physicalism. If it is, then grounding
physicalism needs to entail supervenience physicalism. (For
considerations against, see Skiles 2014; for considerations in favor,
see Bennett 2017, 3.3.) And if it is, physicalism would remain
testable by exposing it to would-be arguments by appeal to FISTS, such
as the zombie argument. 


### 5.5 Coincident Entities and the "Grounding Problem"



It is fairly widely held that more than one object can occupy the same
spatio-temporal location. Such objects are said to be
spatio-temporally coincident. The classic example is a statue,
Goliath, and the lump of clay that constitutes it, Lumpl (see Gibbard
1975). On one version of the story, Lumpl sits around on a shelf for a
few days before the sculptor shapes it into Goliath on a Thursday
morning. It looks like Lumpl existed on the previous Wednesday and
that Goliath did not, and consequently looks like Leibniz's Law
entails that they are distinct objects. On another version of the
story, Lumpl and Goliath are created and destroyed at precisely the
same moment. Here the two do not have different temporal properties,
but they do have different *modal* ones--Lumpl would still
exist if we squashed it into a ball, but Goliath would not. Again,
Leibniz's Law apparently entails that they are distinct. (See
Rea 1997a for many interesting papers on this issue.)



The main objection to the view that Goliath and Lumpl are distinct is
what can be called 'the grounding problem'. How can Lumpl
and Goliath differ in their modal properties, given that they are
alike in every *other* way? What grounds their difference in
persistence conditions? In virtue of what do they have the persistence
conditions they do?



The grounding problem is sometimes characterized in terms of
supervenience failure. Lumpl and Goliath differ in their persistence
conditions without differing in their physical or categorical
properties (see Yablo 1987 for a discussion of categoricity). And it
is true that many forms of supervenience fail: weak and strong
individual supervenience and strong global supervenience all fail. But
there are forms of supervenience that *can* hold. Both weak and
intermediate global supervenience hold, as does (as the name suggests)
coincidence-friendly supervenience, and possibly other versions of
multiple-domain supervenience (c.f. Zimmerman 1995, Rea 1997b, Sider
1999, Baker 2000). All of these forms hold on the plausible assumption
that any two regions physically/categorically just like this one will
contain an object with Goliath's persistence conditions, and an
object with Lumpl's persistence conditions.



But the crucial question is not whether any form of supervenience
holds, but rather whether those that hold constitute a satisfactory
answer to the grounding problem. For a defense of the positive answer,
see Sider 1999; for a defense of the negative answer, see Bennett
2004b. For a new take, see Sider 2008.