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The Nature of Contingency
 The Nature of
Contingency
Quantum Physics as Modal Realism

ALASTAIR WILSON

1
 3
Great Clarendon Street, Oxford, OX2 6DP,
United Kingdom
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© Alastair Wilson 2020
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DOI: 10.1093/oso/9780198846215.001.0001
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To Miranda, with love and gratitude for making ours the
only world I want to inhabit.
 Preface

This book explores how the conceptual foundations of contemporary

physics bear on some traditional metaphysical questions about the nature
and structure of objective reality. The specific target of investigation is the
metaphysics of modality—contingency, necessity, actuality, chance, and
cognate notions—and the specific physical theory that is brought to bear is
Everettian quantum mechanics (EQM), also known as the many worlds
interpretation.
EQM is one of the most popular approaches to quantum mechanics
amongst theoretical physicists. It is effectively presupposed by a large body
of work in quantum cosmology. Unmodified quantum mechanics has
passed every empirical test we have been able to devise, and recent experi-
ments have further restricted the range of viable alternative theories by
closing loopholes in tests of Bell correlations between entangled quantum
systems.¹ In light of progress over the last four decades on the theory of
decoherence, and of progress over the last two decades in understanding
probability in the Everettian setting, EQM—more than ever—appears to be
the most natural way to understand contemporary quantum physics. Its
potentially radical consequences for metaphysics accordingly deserve
examination.
When setting out his metaphysical project of Humean Supervenience,
David Lewis memorably rejected the use of arguments from quantum
mechanics in metaphysics:

I am not ready to take lessons in ontology from quantum physics as it now

is. First I must see how it looks when it is purified of instrumentalist
frivolity, and dares to say something not just about pointer readings but
about the constitution of the world; and when it is purified of doublethink
ing deviant logic; and most of all when it is purified of supernatural
tales about the power of the observant mind to make things jump.
Lewis (1986a: ix)

¹ I have in mind the ‘loophole free’ experiments of Hensen et al. (2015), Giustina et al.
(2015), and Shalm et al. (2015).
x 

EQM is how quantum physics looks once it has been purified in all of the
ways Lewis demanded, without the addition of any superfluous theoretical
structure. It is time to pay attention to its lessons in ontology.
Outside theoretical physics, EQM has hitherto featured mainly as a plot
device for science fiction. What has not been appreciated—at least not
beyond certain technical debates in philosophy of physics—is the potential
of EQM to transform the foundations of metaphysics. In this book I will
be posing some perennially difficult metaphysical questions in the Ever-
ettian context, and offering some provisional answers to them which make
novel use of theoretical resources from quantum physics. The resulting
framework—which I call quantum modal realism—has strong affinities
with the modal realism of David Lewis (Lewis 1986b), but it also has some
unique features which set it apart from all extant theories of modality.
The thought that quantum theory might be relevant to the metaphysics of
modality is not a new one. ‘Quantum logic’ interpretations² involve pro-
found changes to our understanding of logical consequence; a more radical
project in the foundations of metaphysics is hard to imagine. The current
project is more conservative: the goal is a minimally revisionary way of
incorporating quantum theory into our worldview that leaves untouched
our ordinary scientific theorizing about the actual world. In this respect, it is
inspired by pioneering work by Simon Saunders (Saunders 1997, 1998) who
was the first to make explicit the relevance of EQM to questions asked by
metaphysicians about contingency and necessity. Saunders’s own views have
changed significantly over the two decades since those papers were written.
He no longer places such an emphasis on relationality, and is more tolerant
of the language of ‘many worlds’. In my view, these are steps in the right
direction; in this book, I try to take a few more steps.
This idea of this book was conceived while an undergraduate in Oxford in
2002, prompted by tutorials on modality with Bill Newton-Smith and by
classes on the philosophy of quantum mechanics with Jeremy Butterfield.
I then worked on the project under the guidance of Oliver Pooley, David
Wallace, John Hawthorne, Simon Saunders, and Cian Dorr. Numerous
friends and colleagues have provided feedback on these ideas along the
way, too many to name; I am very grateful to them all. The following deserve
special thanks for reading and commenting on substantial chunks of the
manuscript: Adam Bales, Chloé de Canson, Christina Conroy, Nina Emery,

² The canonical proposal is by Putnam (1968).

  xi

Salvatore Florio, David Glick, Dana Goswick, Toby Handfield, Mario

Hubert, Noelia Iranzo Ribera, Matthias Jenny, Nicholas Jones, Dan Mar-
shall, Robert Michels, Kristie Miller, John Murphy, Martin Pickup, Mark
Pinder, Josh Quirke, Michael Raven, Katie Robertson, Miranda Rose, Alex
Silk, Jussi Suikkanen, Tuomas Tahko, Henry Taylor, Paul Tappenden,
Naomi Thompson and two referees for Oxford University Press.
This book forms a part of the FraMEPhys project, supported by the
European Research Council under the European Union’s Horizon 2020
research and innovation programme (grant agreement no. 757295). I also
acknowledge financial support from the Arts and Humanities Research
Council, from University College, Oxford, from the Australian Research
Council, and from a Visiting Fellowship at the Sydney Centre for the
Foundations of the Sciences.
Some material from chapters 2 and 3, including figure 3.1, has been
reproduced from my previous articles in The British Journal for the Philoso-
phy of Science:

‘Objective Probability in Everettian Quantum Mechanics’ 64(4), December

2013, 709–37
‘Everettian Confirmation and Sleeping Beauty’ 65(3), September 2014,
573–98
‘The Quantum Doomsday Argument’ 68(2), June 2017, 597–615
 Introduction: Explaining Contingency

0.1 Emergent Contingency

This book argues that quantum theories are best understood as theories
about the space of possibilities rather than as theories solely about actuality.
When quantum physics is taken seriously in the way first proposed by Hugh
Everett III (Everett 1957a), it can offer us direct insight into the metaphysics
of possibility, necessity, actuality, chance, and a host of related modal
notions. As electromagnetism revealed the nature of light, as acoustics
revealed the nature of sound, as statistical mechanics revealed the nature
of heat, so quantum physics reveals the nature of contingency. Objective
modality is quantum-mechanical.
According to Everettian quantum mechanics (EQM), there exists an
enormous plurality of worlds. The entire universe that we see around us,
with all its atoms and cities and galaxies, is just one among many universes.
Indeed, any way that the laws of quantum physics permit a universe to be is
a way in which some universe is. The collection of all of these universes is
known as the Everettian multiverse. Each universe contained within the
multiverse I will call an Everett world. You, and all the people you will
ever meet, together inhabit just one single Everett world out of the multi-
tude. Although each Everett world is already inconceivably vast, the Everett
multiverse is inconceivably vaster.
What the Everettian multiverse is like is not a contingent matter. In a
sense to be made precise in section 1.2, there is no possibility that the
multiverse could have been any way other than the way it in fact is. Still,
there is contingency in the Everettian picture. Indeed, that there should be
contingency in EQM is a basic condition on its giving an accurate picture of
reality. It is just obviously true that things could have been otherwise. I could
(and no doubt should) have finished this book years ago; alternatively, it
could have been never written at all. You could have been struck by lightning
this morning; alternatively, you could have found a winning lottery ticket on
the pavement. The Tasmanian tiger could have survived in a small pocket of

The Nature of Contingency: Quantum Physics as Modal Realism. Alastair Wilson, Oxford University Press (2020).
© Alastair Wilson 2020.
DOI: 10.1093/oso/9780198846215.001.0001
2 

Tarkine forest and have been rediscovered only last month; alternatively, it
could have never evolved in the first place. Dinosaurs could have developed
human-level intelligence millions of years ago and then laid waste to the
Cretaceous environment through rapid industrialization; alternatively, they
could have ushered in a scaly era of peace and learning.
Of course, it is possible to deny any of these specific claims about
contingent matters. But it is not plausible to deny contingency altogether.
Moreover, contingency is an objective feature of the world: it is not simply a
function of our representations of the world. What is possible is not just a
matter of what we do or do not know, believe, or imagine. But how can
genuine contingency be reconciled with the deterministic Everettian multi-
verse? The answer, implicit in EQM since the very beginning but rarely
adequately emphasized, is that contingency relates only to location within
the multiverse. What the multiverse is like is non-contingent, but where we
are in the multiverse is contingent. Contingency is a wholly self-locating
phenomenon, or (to co-opt a term from the theory of semantic content)
essentially indexical.
One of the most striking features of EQM is that it makes physical
contingency into an emergent phenomenon. At the fundamental level, the
laws of physics are deterministic and physical reality is non-contingent.
Only at non-fundamental (derivative) levels do we find indeterministic
physical laws and genuine contingency in nature. This is a deeply unfamiliar
picture; can we make sense of it? I think that we can. The history of science
contains numerous cases in which some phenomenon, once assumed to be
basic and irreducible, has been discovered to be—somehow or other—
emergent. Earth, air, fire, water, life, mentality, solidity, colour: all of these
have turned out not to be basic ingredients of the world but instead to
be manifestations of previously unsuspected kinds of organization at more
fundamental levels. To take an example a little closer to the present case,
recent work in quantum gravity has begun to take very seriously emergence
hypotheses concerning space and time. Still, even in the company of these
radical hypotheses, the idea that contingency itself is emergent stands out as
especially radical.
The theoretical role of chance is to provide an objective measure over a
space of physically possible histories. Since physical contingency is emergent
in EQM, so too is chance. This Everettian vision of chance as emergent is
becoming familiar through the work of Wallace (2012), Saunders (2005,
2010b) and others; but it naturally leads on to an unfamiliar treatment of
modality as a whole. In chapter 1, I argue that we have overwhelming reason
   3

to extend the Everettian analysis of physical contingency to an analysis of

contingency more generally. I introduce and defend the principle Alignment,
which tells us that to be a metaphysically possible world is to be an Everett
world. Alignment forms the core of my new naturalistic theory of modality:
quantum modal realism.
The remainder of chapter 1 introduces the main features of quantum
modal realism, and catalogues the various theoretical benefits within meta-
physics to which quantum modal realists may lay claim. Quantum modal
realism provides for a comprehensive account of qualitative—or de dicto—
modality, giving us everything we need in order to say how things in general
could have been, would have been, will probably be, cause other things to be,
seem to be, are acted upon, and so forth. By employing the key Lewisian
innovation of counterpart theory, quantum modal realists may extend their
treatment from qualitative modality to non-qualitative—or de re—modality,
which concerns how particular things like you or me could or would be.
Quantum modal realism underwrites an orthodox S5 modal logic. The
reductive account of laws and chances that it provides allows for some
strikingly simple realist theories of the semantics for counterfactual dis-
course, and thus for robust counterfactual-based theories of causation. It
also provides resources for analysing semantic content, both coarse-grained
and fine-grained, and for characterizing the nature of properties. Quantum
modal realists thus inherit most of the riches of what David Lewis called the
‘philosophers’ paradise’ of his own modal realism (Lewis 1986b). Moreover,
the Everettian multiverse comes equipped with a global objective chance
measure which fills crucial gaps in the Lewisian story; this chance measure
permits explanations of the knowability and rational relevance of modal
facts which Lewisian modal realism cannot support.
Chapter 2 delves into the Everettian approach to quantum mechanics that
is at the core of quantum modal realism, sketching and motivating the
physical and metaphysical components of the quantum modal realist
account of modality. After a brief summary of how EQM resolves the
notorious quantum measurement problem, I show how some core prin-
ciples of quantum modal realism that connect the physics of EQM with the
metaphysics of modality play a key role in resolving long-standing problems
with probability in the Everettian setting. These principles are fleshed out in
chapter 3 into a full quantum modal realist theory of objective chance,
including an Everettian Principal Principle connecting chance and credence.
While chance is emergent in the Everettian picture, it is nonetheless a
demonstrably excellent candidate to play the theoretical role of objective
4 

chance: it is that element of physical reality to which rational epistemic

agents embedded in Everett worlds conform their expectations.
What goes for the Everettian multiverse and for its constituent worlds
goes also for the physical laws which govern them. Although the laws of the
multiverse—the fundamental laws of quantum mechanics—are determinis-
tic and non-contingent, quantum modal realists can also make clear sense of
derivative laws governing events within individual worlds. Such laws may be
indeterministic and/or contingent. Chapter 4 takes up the task of sorting out
the different ways in which the ideology of lawhood may be applied within
EQM, and in the process offers a new and attractive theory of laws of nature
that reconciles the prominent Humean and anti-Humean viewpoints in a
previously unanticipated way.
While the quantum modal realist’s fundamental reality remains fully
determinate, the emergent multiverse of EQM is indeterminate in two
characteristic ways. Everett worlds are indeterminate both in number and
in nature. In chapter 5, I model this indeterminacy using the precisificational
approach widespread in recent metaphysical discussions. I argue that while
indeterminacy in both the nature and the number of Everett worlds is
ultimately semantic or epistemic in origin, the indeterminacy in the nature
of these worlds may at the same time be regarded as (a naturalized and
emergent form of) metaphysical indeterminacy.
A book like this must necessarily make a number of controversial
assumptions. The most significant of these assumptions concerns physics
rather than philosophy: in what follows, I shall be assuming without sub-
stantial argument that EQM is a coherent and defensible framework for
understanding quantum phenomena. Although some details of the formu-
lation of EQM will be taken up in chapters 2 and 3, in general I shall be
relying on the work of others in explicating and defending the Everettian
approach. While I think the project of this book, if successful, is capable of
providing some limited independent evidential support for EQM, I shall not
attempt to make the case for that claim here.
It is interesting to ask whether any other approaches to quantum theory
can support a theory of modality of the general kind that I propose. Some
elements of my approach can certainly be emulated within Bohmian mech-
anics or within dynamical collapse theories. However, any explanation of
quantum phenomena that posits a fundamental indeterministic or stochas-
tic collapse mechanism will be unable to capture what I see as the central
advantage of quantum modal realism—its genuinely reductive character.
No-collapse approaches such as Bohmian mechanics may also not turn out
    5

to be reductive, if they retain non-quantum contingency in matters such as

the initial distribution of particles. (A modal realist version of the Bohmian
approach seems potentially viable,¹ but it would start to closely resemble
EQM.) In any case, the Everettian approach provides the most obvious route
to a reductive quantum-mechanical account of modality, and this is the
route I will be exploring in this book.
In section 0.2, I turn to the target of my reductive project: objective
modality. Philosophical readers who are already sufficiently puzzled by the
nature of modality to see it as standing in need of explanation may skip to
section 0.3. Those wondering what modality is, or why it should be espe-
cially hard to accommodate in a scientific worldview, should read on.

0.2 Theories of Modality

Ordinary discourse, as well as scientific discourse, is littered with apparent

modal truths: explicit claims of possibility or necessity, counterfactuals, and
ascriptions of abilities or dispositions to name but a few. As Sellars (1948,
1957) emphasized, much of our linguistic practice bears disguised modal
commitments. In light of this, it is an embarrassment to metaphysics that it
has been unable as yet to produce any plausible candidate account of the
nature and source of modality. No extant theory is credible.
Early twentieth-century accounts of modality emphasized the role of
convention in explaining modal discourse. In their simplest form, such
accounts identified the possible with that which is not ruled out by conven-
tion. Simple conventionalism eats its own tail; it cannot give a sensible
account of which conventions are themselves possible and which impossible.
Several authors, recognizing the limits of conventionalism, looked for
accounts of modality with an objective element. The natural place to start
was with objective features of language. Carnap bequeathed us the notion of
a state-description (Carnap 1946), which—while adequate for various pur-
poses in formal semantics—provides little insight into the nature of modal-
ity. Linguistic accounts of modality invariably need to presuppose modal
notions in the form of a primitive notion of consistency of sentences or
propositions. Modality itself goes unexplained.

¹ In conversation, Sheldon Goldstein has expressed some sympathy for a Bohmian modal
realist approach.
6 

Quine’s notorious hostility to modality is often overstated; his primary

objection was to de re modal properties possessed by individual objects,
which he saw as indefensibly privileging one way of picking out an object
over other ways of picking out exactly the same object. Indeed the ‘meta-
physical turn’ that Quine triggered (intentionally or not) within analytic
philosophy led to a renewed interest in the nature of modality. Kripke’s
formal results in model-theoretic semantics for modal logic assuaged any
fears about incoherence or inconsistency of the main logical systems, and his
informal Naming and Necessity (Kripke 1980) soothed Quinean scruples
about de re modality by providing a compelling intuitive gloss on reasoning
about possible individuals via possible worlds.
Possible worlds provide a compelling and fertile set of tools for formal-
izing our thinking about modality, but they only sharpen the problem of
accounting for the metaphysical basis of modal thought and talk. If worlds
are to be more than a bare formal device for model-theoretic metalogical
investigations into modal logic then we must give them some positive
metaphysical interpretation (see Williamson 2013: 139–40 for discussion).
Lewis put the point memorably:

For [metalogical results], we need no possible worlds. We need sets of

entities which, for heuristic guidance, ‘may be regarded as’ possible worlds,
but which in truth may be anything you please. We are doing mathematics,
not metaphysics. Where we need possible worlds, rather, is in applying the
results of these metalogical investigations . . . To apply the results you have
to incur a commitment to some substantive analysis of modality.
Lewis (1986b: 17 19)

If we are to understand modality in terms of possible worlds, we cannot

avoid the core metaphysical questions: what are possible worlds, and what
sorts of possible worlds are there? Subsequent work has helped to identify
two crucial constraints on adequate answers to these questions: the answers
must help us to make sense of how we know which worlds are possible (the
epistemic challenge) and they must help us to make sense of how possible
worlds are relevant to our practical interests (the practical challenge). How
can we know about, and why should we care about, what can be the case as
opposed to what is the case? In the remainder of this section I argue that all
extant theories of the nature of possible worlds fail to address one or both of
these challenges. This book as a whole makes the case that quantum modal
realism has the resources to meet both challenges.
    7

Treating possible worlds as linguistic entities amounts to adopting the

Carnapian state-description approach as a metaphysical hypothesis rather
than simply as a formal model. Linguistic theories of possible worlds do
passably well with respect to the epistemic challenge: competence with a
language at least in principle gives us the ability to detect which strings of
that language are consistent. However, linguistic theories seem to render the
practical problem insoluble. What difference between consistent and incon-
sistent sets of sentences explains why the former but not the latter are
relevant to our practical interests? The obvious answer—that the members
of consistent sets of sentences could all be jointly true, while the members of
inconsistent sets of sentences could not all be jointly true—is unavailable to
those who seek to analyse modality itself in linguistic terms.
As part of a general move away from linguistic theorizing towards
metaphysical theorizing, Alvin Plantinga (1974) proposed replacing state-
descriptions with states of affairs: worlds are a complex kind of property
rather than anything linguistic. This change, however, achieves little with
respect to the circularity problem: it simply turns a primitive notion of
consistency of predicates into a primitive notion of compossibility of prop-
erties. We have no grip on the notion of compossibility of two properties
unless it amounts to it being possible that something should have both
properties; indeed, it seems exactly backwards to analyse possibility in terms
of compossibility. When measured against the epistemic and practical chal-
lenges, the property-based theory is of no use at all. To be told that a world is
possible just in case it does not instantiate incompossible properties is no help
unless we antecedently know how to tell whether two properties are incom-
possible; and without an account of incompossibility in independent terms, it
is unclear why two properties being incompossible should lead us to disregard
in our practical reasoning any scenario which combines those properties.
One way of avoiding the pitfall of accounting for possibility in terms of
some notion that implicitly presupposes possibility is to refuse to account
for possibility in independent terms at all. In this spirit, Peter van Inwagen
proposed an account of possible worlds as sui generis abstract entities, as
points in an abstract space about which nothing could be said except that
they represent certain states of affairs and fail to represent other states of
affairs. This account, dubbed ‘magical’ and criticized as mysterious by Lewis
(1986b), was defended by van Inwagen (1986) on grounds of good company;
he argued that any methodological difficulty with a magical account of
possible worlds was also shared by the realism about set theory endorsed
by Lewis. We need not dwell on the comparison with set theory, since our
8 

purpose is to assess how well a theory of modality measures up against the

epistemic and practical challenges.
The magical proposal fares at least as badly as any account previously
considered. Since it is part of the account that possible worlds have no
features in virtue of which they represent something as possible, they
cannot—as a matter of principle—have any features that would explain
how we can know about them or that could explain how knowledge of
them would be relevant to our practical interests.
The circularity at the heart of the linguistic, property-based and magical
accounts is deeply unsatisfactory. To explain how possible worlds can play
their allotted theoretical roles, defenders of these theories need to appeal to
the very modal judgements that possible worlds are meant to underwrite.
Perhaps we could reluctantly conclude that this is a kind of explanatory
circle we have to learn to live with. Every metaphysical system must contain
some unanalysed primitives, we might argue; and why should these primi-
tives not be modal ones? But even if we endorse this line of thought, we
might still be dissatisfied with the arcane metaphysics often smuggled in
under the title ‘possible worlds’ or ‘states of affairs’. For Plantinga, states of
affairs are sui generis abstract objects; and his theory invokes a multitude of
abstract uninstantiated individual essences. Van Inwagen likewise adopts a
view wherein possible worlds have no intrinsic qualitative features to dis-
tinguish them but are merely abstract placeholders in a system of abstract
relations. Each would have us believe in a host of sui generis abstract objects,
the essence of each of which is to represent some complete possible world
and which plays that role despite lacking any internal qualitative structure.
One does not need to be an austere Quinean to worry about this prolifer-
ation of heavy-duty metaphysics.
A striking alternative to the positing of exotic candidates for possible
worlds is the modal realism of David Lewis (1986b). While the Lewisian view
is radically liberal with respect to the quantity of concrete entities it
endorses, it is radically conservative with respect to their qualities. Lewis’s
proposal for the nature of possible worlds is disarmingly simple: they are
things just like the actual world that we inhabit, just more of the same old
goings-on. Nothing could be more familiar than the material world in which
we live and move and have our being.² But despite the qualitative parsimony

² This familiarity is undermined somewhat by Lewis’s acknowledgement of worlds including

very peculiar entities: ghosts, ‘epiphenomenal rubbish’, and the like. But quantum modal realists
ought not, indeed cannot, recognize worlds like those.
    9

it involves, almost nobody apart from Lewis has ever endorsed Lewisian
modal realism. While the reasons offered for rejecting it have been many
and various, to my mind the most potent objections to modal realism are the
same challenges that I have already argued are fatal to the linguistic,
property-based and magical accounts. That is, Lewisian modal realism is
unable to account for our envisaged epistemic access to the plurality of
worlds, and it is unable to account for their envisaged relevance to our
practical interests. Since my own quantum modal realism has more in
common with Lewisian modal realism than with any of the views so far
discussed, it will be worth spelling out these challenges in more detail to see
how they apply specifically to the Lewisian proposal.
The epistemic challenge is one that Lewis considered explicitly.³ He cites
Skyrms (1980: 326), who puts the point in causal terms: how can we have
knowledge of other Lewisian worlds when we are causally isolated from
them? Still, Lewis never satisfactorily addressed the challenge. Indeed, the
structure of his response to the epistemic objection has no hope of succeed-
ing unsupplemented: it presupposes exactly what the challenge requires it to
explain. Here is the response: ‘If modal knowledge is what I say it is, and if
we have the modal knowledge that we think we do, then we have abundant
knowledge of the existence of concrete individuals not causally related to us
in any way’ (Lewis 1986b: 111). And:

[H]ow do we come by the modal opinions that we in fact hold? . . . In the

mathematical case, the answer is that we come by our opinions largely by
reasoning from general principles that we already accept . . . I suppose the
answer in the modal case is similar. I think our everyday modal opinions
are, in large measure, consequences of a principle of recombination . . .
Lewis (1986b: 113)

The epistemological picture that Lewis is sketching is as follows (I para-

phrase): if modal realism is correct, then our modal beliefs just are beliefs
about the plurality of worlds. So, if modal realism is correct, then we do in
fact have numerous true beliefs about the plurality of worlds, and it cannot
be the case that it is impossible to acquire true beliefs about the plurality of
worlds. Moreover, if these beliefs are in fact true, they are necessarily true
since they concern non-contingent matters. If the method used to form

³ The challenge may originate with Richards (1975).

10 

them could not easily have led to the formation of different beliefs, then our
true beliefs might even qualify as knowledge.
The problem with this overall epistemological picture is that it fails to
identify any evidence we have that counts in favour of the principle of
recombination. Accordingly it fails to explain how and why the entire
epistemic practice of forming beliefs about possible worlds through judge-
ments based on recombination got started. Consider an intelligent species
with no modal knowledge: they know some facts about their actual world,
but they do not have any modal beliefs at all, and they do not suspect that
any concrete worlds exist other than their own. Such a species would have
no reason to believe that a principle of recombination holds. The key
question which Lewis cannot answer is: how could we have got here, with
our extensive true modal beliefs, from there, where we had none? It is one
thing to mount a defensive operation of some territory that you control, but
quite another to conquer the territory in the first place. To conquer epi-
stemic territory, you need evidence—and Lewis offers us none.
It is instructive to compare my argument here with Ross Cameron’s
recent claim (Cameron 2007a) that we cannot be justified in believing
Lewisian modal realism. Like me, Cameron criticizes Lewis for mounting a
purely defensive operation, but the basis for his criticism is that Lewis is not
entitled to presuppose the metaphysics of modal realism when providing an
epistemological story about our knowledge of individual modal truth.
According to Cameron, ‘[w]hat Lewis needs to do to respond to the epis-
temological objection is to provide reason independent of the truth of
Lewisian realism to think that one can have knowledge about non-actual
possible worlds’ (Cameron 2007a: 149). I think this requirement is much too
strong: nobody would think it a reasonable requirement of an atomist that
they be able to provide reason independent of the truth of the atomic theory
of matter to think that we can have knowledge of atoms and their properties.
All of our knowledge of atoms, at least initially, came from inferences from
the behaviour of the macroscopic world (Brownian motion, for example);
and these inferences only in fact provide knowledge of atoms and their
properties if the atomic theory of matter is in fact correct.
Unlike Cameron’s objection, my version of the epistemological objection
to modal realism does not problematically overgeneralize. It is incumbent on
an atomist to explain how (if atomism is correct) we came to have know-
ledge of the kinds of phenomena that are (by their own lights) dependent on
the existence of atoms and their properties. How (if atomism is correct) did
we first acquire knowledge that there is Brownian motion going on when
    11

pollen grains are suspended in water? An answer, of course, is that we

ourselves are made of atoms which causally interact with atoms within the
water via a causal chain involving a microscope. The Lewisian realist,
however, cannot offer any comparable story here. Other Lewisian possible
worlds bear no constitutive, causal, or other explanatory relations to the
observable goings-on within our own world. If Lewisian modal realism is
correct, then how we ascended to our current state of modal knowledge is an
intractable mystery, even if our current modal beliefs were (inexplicably)
formed de facto reliably. This is my favoured version of the epistemic
challenge to Lewisian modal realism.
The practical challenge to Lewisian modal realism has been most force-
fully raised by Jubien (1988). Lewis’s response to the practical challenge
closely mirrors his response to the epistemic challenge, and it fails for a
closely related reason; hence, we can be briefer here. Lewis correctly notes
that our modal knowledge is of great practical relevance to us (never mind
exactly why or how); he points out that if modal realism is correct, then our
modal knowledge is knowledge about a plurality of worlds; he infers that if
modal realism is correct, then knowledge about a plurality of worlds is of
great practical relevance to us; finally, he pivots on this inference, concluding
that any general principle about the practical irrelevance of entities which
are causally isolated from us must be false. Again, the problem with this line
of thought is that it constitutes a defensive operation where what is needed is
a positive account.
Consider a species that does not perceive any relevance to their own
practical interests of bizarre hypotheses about a plurality of spatiotemporally
isolated concrete worlds. These creatures care about the nature of the world
they inhabit, but they could not care less about other causally isolated
worlds. Where are such creatures going wrong?—and what could we pos-
sibly say to induce them to take an interest in the other Lewisian worlds? As
long as Lewis has no good answer to these questions, he has no satisfactory
response to the practical challenge.
Despite the compelling epistemic and practical challenges to Lewisian
modal realism, there remains something very attractive about it. It is an
elegant—indeed, a beautiful—theory. While quantitatively unparsimonious,
it is qualitatively parsimonious: there are many worlds, but each of them is
familiar from our actual world. And while hard to believe, it is very easy to
grasp. It is therefore unsurprising that various parasitic theories have been
advanced which borrow from the explanatory resources of Lewisian modal
realism while distancing themselves from Lewisian modal realism’s more
12 

problematic commitments. The most well known of these theories is modal

fictionalism (Rosen 1990) which cashes out modal discourse via the pretence
that a Lewisian plurality of worlds exists. A relative of modal fictionalism is
modal agnosticism (Divers 2004), which makes use of the Lewisian modal
realist story to understand modal discourse while remaining neutral on
whether the Lewisian plurality is real or fictional.
While fictionalism and agnosticism may have advantages with respect to
the epistemic challenges—if we are collective authors of the fiction, then
perhaps we have collective authorial privilege over its content?—these
parasitic theories do not help with respect to the practical challenge. If the
Lewisian story is false, then why have we developed an ingrained practice of
reasoning under the pretence that it is correct? Or, if the Lewisian story is
something on which we should be rationally agnostic, then why have we
adopted a deep-rooted practice of reasoning conditional on the supposition
that it is correct? In both cases, the heuristic of the amodal species introduced
above helps to underscore the point. There seems to be no way to rationally
induce a species interested only in the goings-on within their actual world to
take an interest in a fiction according to which there are many other causally
isolated worlds, and no motivation for members of such a species to dwell on
what follows from the supposition that such a plurality exists.
The general consensus amongst metaphysicians is that Lewisian modal
realism is a bizarre and extravagant fairy tale, and ultimately not a hypothesis
worth taking seriously. The story of the Lewisian plurality is one which we
could never be in an epistemic position to substantiate and one which could
never be relevant to any of our practical interests. And with this rejection of
Lewisian modal realism the debate has largely stalled. None of the theories on
the table are capable—even in principle—of explaining why we modalize.⁴
I do not take the above arguments, quickly sketched as they are, to be
decisive; nor shall I dwell any longer on the claim that all extant theories of
modality are untenable. My main thesis in this book is a more positive one:
that EQM allows us to formulate a powerful and tenable reductive theory.
What follows is an investigation into how the quantum modal realist
position should best be formulated, with the hope that the explanatory
benefits will speak for themselves.
So much for the current state of the metaphysics of modality. I turn in the
next section to an important but under-appreciated question in the area: the

⁴ Divers (2010) argues that this challenge is urgent and underappreciated.

    ? 13

question of whether the primary target of our modal theorizing should be

necessity or contingency.

0.3 Necessity or Contingency First?

The majority of systematic treatments of modal metaphysics take necessity

as their primary explanatory target. The general thought, not often articu-
lated, seems to be that contingency is the ‘default’ modal status for a
proposition and that the job of a theory of modality is to provide an account
of necessity as a deviation from this default status. Gideon Rosen captures
this outlook nicely as follows:

[M]etaphysical possibility is, as it were, the default status for propositions.

When the question arises, ‘Is P metaphysically possible?’ the first question
we ask is ‘Why shouldn’t it be possible?’ . . . P is metaphysically possible
unless there is some reason why it should not be unless there is, as we say,
some sort of obstacle to its possibility. Moreover, the only such obstacle we
recognize is latent absurdity or contradiction. Rosen (2006: 23)

We may take as an example Kit Fine’s (1994) essentialist account of modal-

ity, according to which (roughly) a proposition is necessary just in case it is
true in virtue of the essences of some things. The operative presumption
seems to be that, once such a theory of modality has given us a story about
the nature of necessity, a story about contingency comes for free. If the
essences of things are silent on whether a proposition or its negation holds,
then Finean essentialism counts the proposition as contingent.
Lewisian modal realism is distinctive in that it inverts the above concep-
tion of the target of a theory of modality. There is a clear sense in which the
basic ontological claims of modal realism—those claims needed to describe
the whole plurality of worlds—are necessary. (See section 1.2 for further
elaboration of this point, and a discussion of the connection to modal logic.)
Since Lewisian modal realism is intended to be reductive, these ontological
claims need to be conceptually non-modal, in the sense of Divers & Melia
(2002): modal realists must not presuppose any modal notions in formulat-
ing their theory, if it is to be genuinely reductive. Accordingly, modal realists
must not account for modality in terms of any claims whose modal status
itself calls for explanation. In this sense, then, modal realists must take
necessity as the default status for a truth, and contingency as the modally
14 

loaded status for which they provide a substantive analysis. Since the version
of quantum modal realism that I will spell out in this chapter and the next is
a close relative of Lewisian modal realism, quantum modal realism too is
best understood as making necessity prior to contingency.
We have, then, a distinction between what I will call necessity-first and
contingency-first approaches to analysing modality. These reflect different
attitudes to what is puzzling about modality, and hence different adequacy
conditions on a theory of modality. The distinction between necessity-first
and contingency-first approaches pertains to the metaphysical order of pri-
ority between the two phenomena, not to the epistemological order
of priority. It may be, for example, that our knowledge or understanding of
contingent propositions (I’m hungry; that plant is edible; tigers are dangerous;
it is raining) is a necessary precondition of our having knowledge or under-
standing of necessary propositions. This does not refute the necessity-first
approach, which is a view about the order of metaphysical priority between
necessity and contingency, just as the epistemological priority of facts about
colours over facts about wavelengths of light does not refute the view that
colours can be reduced to wavelengths.
Co-opting the language of grounding that is widely used in contemporary
metaphysics⁵ we may formulate the contrast as follows:

Necessity-first: Necessary facts are such that nothing grounds their necessity.
Contingency-first: Contingent facts are such that nothing grounds their
contingency.

Lewisian modal realism is clearly a necessity-first theory by this classifica-

tion: the necessary facts about the plurality of worlds ground the contin-
gency of those facts that are contingent, but nothing grounds their own
necessity. For Lewis, it is because the principle of recombination holds that
there is a world containing a counterpart of me writing a longer book, and
hence the (necessary) principle of recombination grounds that it is contin-
gent how long this book is. But for facts about the plurality to be necessary
just is for them to obtain (see section 1.2 for further discussion), and hence
the necessity of these facts is not grounded in anything.

⁵ Readers may give the grounding terminology a thin reading, as just marking direction of
explanation in metaphysics. For further discussion of the role of grounding in my project, see
section 0.4 of the introduction.
    ? 15

These formulations of the necessity-first and contingency-first approaches

make them neither exclusive nor exhaustive: it is conceivable that some
unwieldy theory might treat both necessity and contingency as distinct
primitives, or even that an ingenious way to reject both principles might be
found. Perhaps Sider’s neo-conventionalism about modality (Sider 2000,
2011) would be a view of this kind, since it regards both necessity and
contingency as grounded in our modal conventions. Be that as it may, the
quantum modal realism that I develop in this book involves accepting
Necessity-first and rejecting Contingency-first.
The distinction between contingency-first and necessity-first approaches
to modality has not attracted much attention in the metametaphysics
literature; this is surprising, because it has some immediate and striking
methodological consequences. When metaphysicians disagree about
whether some scenario is metaphysically possible, it is typically thought
that the burden of proof is on those who would regard it as impossible to
explain what makes it impossible. This fits with the contingency-first out-
look; if the default status for a proposition is contingency, then the propos-
ition that the disputed scenario obtains is presumptively possible. In a
slogan, things are possible unless proven otherwise.
The contingency-first approach puts the onus on views according to
which some claims are necessary to give a non-trivial account of their
necessity. In this vein we find Ross Cameron (2007b) defending the contin-
gency of principles about composition by encumbering his opponent with
the burden of proof; from the contingency-first perspective, it is quite
reasonable to ask for some distinctive feature of claims about composition
which overrides the default status of contingency. I think it is not generally
recognized just how powerful this burden-shifting manoeuvre can be; the
contingency-first perspective makes it very hard to sustain any synthetic
necessities whatsoever. Logical inconsistency of a proposition, or of its
negation, is a clear defeater for the proposition’s presumptive status of
contingency; it is controversial what else, if anything, is able to defeat this
status. By inverting the contingency-first picture, Lewisian modal realism
and quantum modal realism give rise to a radical shift in the dialectical
position. Now the default modal status for any factual claim is non-
contingency; if we want to establish that some proposition is contingent, it
is incumbent on us to show that it falls into the special class of contingent
propositions. Unless some claim is essentially indexical—unless it is a matter
of self-location within the Everettian multiverse—then it has its truth value
non-contingently.
16 

Adherence to the necessity-first picture provides a route for modal

realists, of Lewisian and Everettian stripes alike, to dodge Simon Blackburn’s
dilemma for theories of the ‘source of necessity’ (Blackburn 1986). Accord-
ing to Blackburn, a theory must either account for the source of necessity in
terms of contingent truths, in which case ‘the original necessity has not been
explained or identified, so much as undermined’ (ibid.: 53), or else they must
account for the source of necessity in terms of necessary truths, in which
case ‘there will be the same bad residual “must” ’ (ibid.: 53). The dilemma is
that necessity itself cannot be explained: ‘[e]ither the explanandum shares
the modal status of the original, and leaves us dissatisfied, or it does not, and
leaves us equally dissatisfied’ (ibid.: 53).
Responses to the dilemma have varied (Hale 2002, Lange 2008, Cameron
2010) but no response has been widely accepted, and the dilemma stands as
a major challenge to reductive theories of modality. The necessity-first
picture dissolves the dilemma in a novel way, since it reconceives the task
of a theory of the source of modality as the task of providing an explanatory
account of contingency. When the conception of the required explanatory
task is inverted in this way, so must Blackburn’s dilemma be inverted; and,
as a challenge to theories of the source of contingency, the inverted dilemma
is uncompelling. In a sense, necessity itself does go unexplained on the
quantum modal realist picture. From the necessity-first perspective, though,
this is exactly as it should be. Rather than offering some independent
positive account of the status of necessity, necessity-first approaches are in
the business of dissolving the need for any such positive account.
What modal realists do, against a theoretical background of purely
necessary claims, is to locate an essentially indexical subject matter as the
source of contingency. The role of necessities in the modal realist approach
is collectively to make room for contingency, not to entail any particular
contingent truths. There is no residual mystery concerning how indexical
questions remain open once the non-indexical facts have all been fixed. The
contingency of all contingent truths can in this way be explained wholly in
terms of necessary truths.

0.4 Naturalistic Metaphysics

This book aims to draw metaphysical conclusions from considerations of

quantum physics. There are familiar obstacles to this general approach.
A single physical theory can bear a variety of legitimate interpretations
   17

that differ metaphysically from one another, so even if we had a complete

and correct physics it would not by itself answer any of the central questions
of metaphysics for us. It will not do to respond to this challenge by
advocating full deference to the metaphysical opinions of actual scientists.
An understanding of how a theory is applied certainly helps with avoiding
confused or unworkable interpretations of that theory. But there are limits:
we should distinguish between metaphysical assumptions that scientists
make for good scientific reasons, and assumptions that they make as a
result of some irrelevant historical or psychological contingency. Observing
this contrast requires a more nuanced approach to letting physics guide
metaphysics.
How is it possible for physics to bear on metaphysics without supplanting
it completely? The methodological position I want to endorse has three main
components:

1) Interpretational Metasemantics: the meanings of a linguistic commu-

nity’s terms are just the meanings that are assigned to them by the best
theory of that community’s linguistic behaviour.
2) Confirmational Holism: theories cannot be adequately assessed in
isolation, and the ultimate unit of theoretical comparison is the
complete system-of-the-world.
3) Physics/Metaphysics Evidential Asymmetry: central principles of phys-
ics are better confirmed than central principles of metaphysics, so
modifying metaphysics is—ceteris paribus—less of a theoretical cost
than modifying physics.

Interpretational metasemantics as I employ it here is a Lewisian doctrine,

with roots in Quine and Davidson.⁶ Confirmational holism is primarily
associated with Quine within analytic philosophy (though it has echoes of
Neurath’s boat, and of earlier pragmatists).⁷ The roots of the physics/meta-
physics evidential asymmetry are in the scientistic spirit of logical positivism
and logical empiricism, transplanted into contemporary metaphysics
through the influence of Quine, Smart and Dennett.⁸ In recognition of the
common factor in the origin of these theses, I will refer to the conjunction of

⁶ See, especially, Lewis (1974, 1983b), Davidson (1973), Quine (1960a). ‘Best theory’ may
evidently be cashed out in various ways; I will aim to remain neutral on the precise form that
interpretational metasemantics should take.
⁷ See, especially, Quine (1951, 1957), Neurath (1944), Duhem (1906).
⁸ See, especially, Quine (1969b), Smart (1963), and Dennett (1969).
18 

1–3 as the Quinean methodology for metaphysics. What work is done by the
various elements of the Quinean methodology?
Firstly, interpretational metasemantics reassures us that there is no gap
between a theory about the meaning of our metaphysical terms making the
best overall sense of our usage of those terms and that theory being correct.
If linguistic usage partly determines meaning through a best-interpretation
competition, we avoid the risks that our metaphysical terms systematically
fail to refer to elements of reality or that we are systematically mistaken
about the properties of their referents. Interpretational metasemantics thus
blunts the force of sceptical arguments in metaphysics, construed as argu-
ments from global underdetermination of theory by data.
Secondly, confirmational holism is a key ingredient in the resolution of
metaphysical questions in the face of the more interesting local form of
underdetermination argument. Such arguments highlight structural simi-
larities between different metaphysical accounts of some specific notion,
threatening to make the choice between these accounts into an arbitrary one.
However, bringing in aspects of the wider theoretical context allows us to
break these local cases of underdetermination: an example of this procedure,
as it applies to the mereological structure of Everett worlds, features in
chapters 2 and 3.
Thirdly, the Quinean’s asymmetric attitude to physics and metaphysics
reflects the vast disparity in the evidence we have in the two domains.
Fundamental physics has astounding and systematic empirical evidential
support. Fundamental metaphysics has no such empirical evidential basis;
and indeed, sometimes it is hard to see what evidence we could possibly
bring to bear on its questions. Bennett (2009) argues that in the face of this
evidential drought we should typically suspend judgement on matters meta-
physical. Sometimes, though, indirect evidence is good enough; and if a
metaphysical principle is indispensable to a total theory that makes best
sense of known physics, that source of evidence for the principle may be the
best we can have. Being so well-confirmed empirically, our physical theories
should be meddled with as little as possible in formulating total theory.
Instead of being modified or rejected on metaphysical grounds, physical
theories should be supplemented with whatever metaphysics suits them best.
In other words, we should compare complete physics-plus-metaphysics
package deals, and adopt whichever metaphysical principles are part of the
best package.
Applications of the Quinean methodology are now familiar from the
work of Lewis, Jackson, Menzies, Sider and others; they sometimes go
   19

under the banner of the ‘Canberra plan’.⁹ Mental states, objective moral
value, causal relations, dispositions, and other metaphysicalia have been
located in naturalistic worldviews by Canberra planners. Even if our patterns
of use of metaphysical terms do not match up perfectly with anything
fundamental within the worldview of physics, such terms may still be
taken to successfully refer if enough of their use can be preserved by
identifying them with some non-fundamental aspect of reality. Latitude
with respect to this use can be relatively wide: there need be no great cost
to demoting individual platitudes about metaphysical terms to false beliefs,
whereas there is a substantial empirical cost to discarding central principles
of contemporary physics.
The version of naturalistic metaphysics I am advocating may be under-
stood as an inter-theoretic reduction of problematic metaphysics to unprob-
lematic physics, with interpretational meta-semantics providing a global
assurance that the best available reduction is ipso facto correct. But do not
be alarmed by the word ‘reduction’; the reductionism involved is of a very
flexible sort. What I have in mind is (generalized) Nagelian reduction, the
programme of explaining the success of a reduced theory by constructing an
analogue of the reduced theory using the resources of the reducing theory.¹⁰
Ernest Nagel (1961) gives a characterization of theoretical unification which
relies neither on the mereological assumptions of Oppenheim and Putnam
(1958) nor on the bridge laws present in Nagel’s earlier proposals and later
influentially criticized by Fodor (1974). The key difference is that a Nagelian
reduction is reduction of theories, and not reduction of theoretical entities:
they consist in formal explanations of why the reduced theory obtains in
terms of the reducing theory. The explanation can take many different forms
depending on the forms of the theories in question. What is important in
Nagelian reduction is an explanatory connection between the theories; in
particular there is no requirement that the entities of the reduced theory be
composed mereologically out of the entities of the reducing theory.
The analogy with Nagelian reduction helps us zero in on the cleanest
way of formulating metaphysical claims. By analogy with the theoretical

⁹ On the Canberra Plan, see Nolan (1996), Jackson (1998), and Braddon Mitchell & Nola
(2009).
¹⁰ These reductions will typically require ‘additional assumptions’ which correspond to
conditions under which the reduced theory applies. Nagel’s central example is the deduction
of the Boyle/Charles law of gases from kinetic theory; the ‘additional assumptions’ in this case
are modelling conditions for gases: treating the particles as elastic spheres, assuming a large
number of particles, and so on.
20 

identifications that emerge from particular Nagelian reductions (heat is

molecular motion; lightning is electrical discharge; water is H₂O; etc.),
naturalistic metaphysics can be cast as the project of finding explanatory
accounts of the individual terms appearing in distinctively metaphysical
questions. One familiar form such identifications may take is ‘to be an X is
to be a Y’, but the more general form is propositional: ‘for it to be the case
that X is for it to be the case that Y’. Such metaphysical analyses entail
necessary and sufficient conditions for the application of the term being
analysed.¹¹
The main advantage of stating metaphysical doctrines in terms of meta-
physical analyses is that it maps onto a characteristic form of explanation in
the natural sciences: reductive explanation. In textbook cases of reduction,
such as the reduction of thermodynamics to statistical mechanics, one com-
ponent of the explanation relies on identities between the referents of certain
theoretical terms. For example, in standard accounts of the relationship
between thermodynamics and statistical mechanics, the thermodynamic
quantity of temperature is identified with the statistical-mechanical quantity
of mean molecular kinetic energy.¹² This identification is explanatory because
it forestalls certain ‘why’-questions which one might initially want to ask; for
example, once we recognize that temperature just is mean molecular kinetic
energy, there is no need to explain why two gases which match in mean
molecular kinetic energy also match in temperature.¹³
This kind of neutralizing of explanatory demands through theoretical
identification is distinctive of the analysis-based formulation of metaphys-
ical doctrines. There is no mystery about why rapid oxidation always
accompanies fire, or about why electrical discharge occurs wherever light-
ning does, or about why water is invariably co-located with hydrogen
dioxide, or (more prosaically) about why bachelors are without exception
unmarried. In each case, some metaphysical analysis is serving to reduce the
space of distinct possibilities for the world; if we know that to be an A is to be

¹¹ When we make any metaphysical claim of this sort, we can seek refuge in semantic ascent.
Instead of asserting, for example, that to be Peruvian is to be from Peru, we can assert that for ‘P
is Peruvian’ to be true is for ‘P is from Peru’ to be true. However, any safety that we buy in this
way is illusory. Semantic ascent allows us to remain agnostic only about the form of the correct
semantic theory for the claims in question; it involves no less strong a first order metaphysical
commitment.
¹² This identification in fact only holds good for the specific case of ideal gases. See e.g.
M. Wilson (1985).
¹³ Theoretical identifications also play key roles in other more complex explanations: for
example, the identification of temperature with mean random molecular kinetic energy helps to
explain why ideal gases in thermal contact will come to the same temperature.
   21

a B, then anything we know to be an A we can also know to be a B. It is of no

great importance whether we count this neutralization of why-questions by
theoretical identification as exposing illegitimate demands for explanation,
or as providing a positive form of explanation in its own right.
There has been plenty of debate in recent metametaphysics over what
sorts of metaphysical relations ‘back’ reductive explanation, with a variety of
notions of constitution and grounding explored in the literature.¹⁴ My aim
here is to remain neutral on this question; readers ought to be able to
understand my project of reducing modality in terms of their preferred
ideology. It will make no difference to the arguments of this book whether
we are seeking an account of what constitutes modal facts, or of what
grounds them, or of what makes them true. In places, I will use the
terminology of grounding for ease of exposition but my hope is that nothing
of importance hangs on this choice. Wherever a claim about grounding is
used, readers should feel free to interpret it as making only a thin claim
about the direction of explanation.
All this metametaphysics is no substitute for metaphysics; it is time for
the main business of the book. In chapter 1, I apply the general methodology
described in this section to construct a new naturalistic theory of the
metaphysics of modality which draws on the resources of EQM.

¹⁴ See, for example, Fine (2012b), J. Wilson (2014), Skow (2016), Bennett (2017), and Dorr
(2016).
 1
Analysing Modality

1.1 The Thesis of Quantum Modal Realism

This book is an extended defence of a metaphysical theory called quantum

modal realism. This section sets out the main principles that constitute that
theory. Here they are, in brief:

• Diverging EQM: Everettian quantum mechanics is correct; Everett

worlds do not mereologically overlap.
• Alignment: To be a metaphysically possible world is to be an Everett
world.
• Indexicality-of-Actuality: Each Everett world is actual according to its
own inhabitants, and only according to its own inhabitants.
• Propositions-as-Sets-of-Worlds: Contingent qualitative propositions are
sets of Everett worlds—a proposition P is true at an Everett world w if
and only if w is a member of P.
• Everettian Chance: The objective chance of an outcome is the quantum
weight (squared amplitude) of the set of Everett worlds in which that
outcome occurs.

Why accept Diverging EQM? In chapter 2 I give some background on

Everettian quantum mechanics, and there I argue for the diverging version of
the theory according to which Everett worlds do not mereologically overlap
and each macroscopic object and event exists in one Everett world only.
While the correctness of EQM more generally is obviously a very substantial
assumption, I shall not defend it in detail: this book presupposes EQM and
explores the metaphysical implications it may have. For fuller defences of
EQM from a philosophy-of-physics perspective, I instead direct the reader
to Wallace (2012) and Saunders (2010a).
Why accept Alignment? I shall argue in chapter 3 that getting right the
relationship between the physics of EQM and the metaphysics of modality
is crucial to an adequate Everettian treatment of objective probability.
A single theoretical identification is needed to close the circle and connect

The Nature of Contingency: Quantum Physics as Modal Realism. Alastair Wilson, Oxford University Press (2020).
© Alastair Wilson 2020.
DOI: 10.1093/oso/9780198846215.001.0001
       23

up weight and chance in the right way—the identification of alternative

metaphysical possibilities with Everett worlds. Once this identification is
made, the way lies open to a rich and powerful new theory of the nature of
modality, one which provides significant further reasons for Everettians to
adopt Alignment.
What is an Everett world? It is a global quantum-mechanical sequence of
events, and the key theoretical device of modern EQM. An immediate
consequence of EQM is that we know Everett worlds by direct acquaintance:
the concrete physical universe around us is an Everett world. EQM—
characteristically, strikingly—posits more universes of the same kind as
ours. The Everett worlds, taken together, comprise the Everettian multiverse.
No two Everett worlds are qualitatively indiscernible: indeterministic quan-
tum events turn out differently in different worlds, and there is a world for
every quantum-mechanically possible sequence of events.
As I understand Everett worlds, they are causally isolated. Causal rela-
tions obtain only between events within individual worlds, and there are no
causal relations between events in different worlds; travel between Everett
worlds, sadly, remains in principle impossible. A real physical quantity,
amplitude, provides a chance measure defined over the whole space of
Everett worlds.¹
A more detailed description of the physics and metaphysics of Everett
worlds is given in sections 2.2–2.4. An intuitive picture of these worlds will
suffice for the arguments of this chapter. I recommend that for the time
being readers think of Everett worlds as parallel universes that fit together
into one giant jigsaw, filling up possibility space with all of the different
histories that physics permits, with each world a complete four-dimensional
spacetime that is governed—from the perspective of its inhabitants—by
indeterministic laws. One of these four-dimensional spacetimes is our
own, and the others are things of the same general kind.
Before we can properly assess Alignment, we need also to say more about
what is meant by ‘metaphysically possible’. I take it that recent metaphysics
has characterized a fairly distinctive theoretical role for metaphysical modal-
ity: at its core it is intended to be an objective modality tied to a distinctive
class of counterfactuals (Lewis 1986b, Williamson 2007) and to the neces-
sary a posteriori (Kripke 1980), and with connections to other notions like

¹ Formally, amplitude is a complex number and the quantity identified with probability via
the Born rule is the modulus squared amplitude. For simplicity, I will use the terms ‘amplitude’
or ‘weight’ interchangeably to refer to the measure over histories given by the Born rule.
24  

conceivability and essence which are perhaps more negotiable. What best
ties these features together, I suggest, is that they are features that we would
expect of whichever objective modality turns out to be metaphysically most
perspicuous. This descriptive way of fixing the reference of ‘metaphysical
modality’ has some substantive realist presuppositions—deflationists about
modality such as Sider (2011) and Cameron (forthcoming) will likely deny
that there is any such thing as the most metaphysically perspicuous objective
modality. Still, such a modality is my analytical target in this book; I shall
argue that the core roles of metaphysical modality can be accounted for
using the theoretical resources of Everettian quantum mechanics.
Taking metaphysical modality as my analytical target will require some
deviations here and there from mainstream opinions about metaphysical
modality, but that is inevitable in an analysis which is intended as theoret-
ically revisionary. What matters is that enough of the core features of
metaphysical modality are captured. For those who remain unconvinced
that the modality I shall characterize in quantum terms deserves the term
‘metaphysical possibility’, I offer a different way of looking at the matter.
We may regard quantum modal realism as eliminating the category of
metaphysical modality and instead employing a combination of physical
modality and logical modality to recapture some of the explanatory work
previously assigned to metaphysical modality. The differences between these
two approaches are largely terminological and I will not dwell on them any
further: ‘metaphysical possibility’ is after all a term of art, and I am primarily
interested in the substantive connections between quantum physics and
chances, counterfactuals, causation and the like.
Alignment entails the following two principles:

Individualism: If X is an Everett world, then X is a metaphysically possible

world.
Generality: If X is a metaphysically possible world, then X is an Everett world.

Individualism is one of a number of options we have when choosing how to

think about the connection between metaphysical modality and EQM.² The

² Individualism is very much a minority view, whether in the context of EQM or in the
context of multiverse theories more generally; as I shall argue in chapter 3, much work on the
metaphysics of EQM and of other multiverse theories uncritically presupposes Collectivism.
Nonetheless, at least one established philosophical tradition seems to invoke the combination of
Individualism with the denial of Generality. This is the branching time (or, in its relativistic
form, branching spacetime) programme, whose genesis owed much to Saul Kripke and to
       25

most natural alternative would be to take Everettian multiverses, rather than

Everett worlds, to play the theoretical role of alternative metaphysically
possible worlds in the Everettian paradigm:

Collectivism: If X is an Everettian multiverse, then X is a metaphysically

possible world.

Individualism and Collectivism say very different things about the structure
of modal reality. According to Collectivism, Everettian multiverses are
metaphysically possible worlds which have the peculiar property of having
many parts, each of which is isomorphic to a possible world of the sort
envisaged by the classical one-world conception of the relation between
physical theory and metaphysical modality. According to Individualism,
Everettian multiverses are complexes of metaphysically possible worlds;
they are not themselves identical to or located within any single metaphys-
ically possible world.
Why accept Individualism? I will argue in chapter 3 that it does crucial
work when it comes to giving a positive theory of Everettian probability.
However, there is a presumption (mostly implicit) in favour of Collectivism
over Individualism amongst those who have thought and written about
EQM. I suggest that this state of affairs can be traced back to the following
a priori assumption:

Physical Actualism: Each model of a complete physical theory represents

exactly one possible world.³

Physical Actualism—combined with the relatively uncontroversial conse-

quence of decoherence theory that models of EQM have the structure of a
multiverse—straightforwardly entails Collectivism. But Physical Actualism

Arthur Prior (the idea was mooted in Kripke’s letter to Prior of 3 September 1958) but which is
now strongly associated with Nuel Belnap and his followers (see e.g. Belnap et al. 2001) and
which has been applied to EQM by Belnap & Muller (2010). Fans of branching (space )time
typically want to allow deterministic worlds as a special case as a very simple branching
structure which happens to have no nodes but they allow that indeterministic worlds are
represented by individual paths through a branching network, rather than by the entire
network.

³ In the presence of redundancy in our physical description, multiple models of a theory may
correspond to one single possible world. This is beside the point for present purposes what
matters is whether one single model of the physical theory may correspond to multiple possible
worlds.
26  

is much less natural in the context of ‘many-history’ physical theories, such

as EQM, than it is in the context of ‘single-history’ theories, such as classical
mechanics. And, as I shall argue in chapter 3, it prevents us from accom-
modating non-trivial objective probability in the Everettian picture. I take
this to be sufficient reason to reject Physical Actualism in full generality,
clearing the way for us to accept Individualism and the resulting elegant
treatment of quantum chance.
Why accept Generality? I will argue for this principle by appeal to the
theoretical unity and simplicity of the systematic metaphysics that it makes
possible. Without Generality, Everettians must distinguish two fundamental
and fundamentally different kinds of possibility; Generality provides theor-
etical uniformity. Generality also enables a wholly reductive theory of
objective modality, and a straightforward account of modal epistemology
which renders it continuous with ordinary scientific inquiry. These results
serve to underwrite applications of objective modality in the metaphysics of
laws, properties and causation, and in the semantics of counterfactuals. In
sum, a theory of modality incorporating Alignment—by entailing both
Individualism and Generality—has decisive theoretical advantages over a
theory of modality incorporating Individualism without Generality.
Adopting Alignment amounts to equating physical possibility (necessity)
with metaphysical possibility (necessity)—or at least taking them to be
coextensive. This equation has recently grown in popularity, with various
versions of necessitarianism about laws being defended by (inter alia)
Shoemaker (1980, 1998), Swoyer (1982), Fales (1993), Ellis (2001), Bird
(2001, 2004, 2007), and Edgington (2004). The version of necessitarianism
on which I will focus is what Schaffer (2005) calls modal necessitarianism:
the view that the laws of the actual world are the laws of all possible worlds.
For arguments in support of modal necessitarianism which are largely
independent of EQM, see A. Wilson (2013b). However, I think the overall
explanatory power of quantum modal realism provides the most compelling
motivation so far adduced for modal necessitarianism, or indeed for any
form of necessitarianism. Quantum modal realism also provides unique
ways to sweeten the pill of accepting modal necessitarianism, as I argue in
section 4.6.
Why accept Indexicality-of-Actuality? The principle could be defended
on grounds of ideological simplicity since it allows us to dispense with a
notion of absolute actuality, or on grounds of avoiding sceptical worries
since it neutralizes the concern that we ourselves might not be actual. But
my main argument for the principle is that it simply falls out of the
       27

combination of Alignment with Diverging EQM: I include it as a separate

principle only for clarity. It is already a key part of the conceptual basis of
EQM that all Everett worlds are on a par, none physically or ontologically
privileged in any way; Everett (1957b: 3) was explicit about this aspect of the
theory. And if the Everett worlds are the metaphysically possible worlds,
then it immediately follows that all metaphysically possible worlds are on a
par, none physically or ontologically privileged in any way. Indexical actual-
ity is the only notion of actuality that properly respects this constraint. The
consequences of quantum modal realism for the concept of actuality are
explored further in section 1.9.
Why accept Everettian Chance? Here I simply refer the reader to chapter 3,
which contains an extensive discussion of the theoretical role of objective
chance and the extent to which the quantum weights can play that role.
To foreshadow, the argument is that the quantum weights are the clear
best candidates to play the chance role within the context of EQM—so,
following the metaphysical methodology set out in the introduction, weights
are chances.
David Lewis (Lewis 1986b) offered a dizzying array of philosophical
explanations based on the resources of his own reductive analysis of meta-
physical modality. In addition to their central application to the analysis of
modal thought and talk (Lewis 1986b section 1.2), modal realist resources
are applied to the semantics of counterfactuals and hence to the semantics of
causal and dispositional claims (ibid. section 1.3), to the analysis of semantic
and mental content in general (ibid. section 1.4), and to the metaphysics of
properties and laws (ibid. section 1.5). Despite the differences between
quantum modal realism and Lewisian modal realism, we can capture the
key achievements of the Lewisian approach in the quantum modal realist
picture. In the remainder of this chapter, I give an argument for quantum
modal realism from overall theoretical virtue that echoes the structure of
Lewis’s argument for Lewisian modal realism.
While not all of the Lewisian analyses of modal notions carry over directly
to the Everettian context, quantum modal realists can in each case adapt the
core idea. The resulting quantum modal realist analyses retain the most
compelling feature of the Lewisian analyses: their genuinely reductive char-
acter. As I read him, most central to Lewis’s case for modal realism was his
dissatisfaction with primitive modality. Motivated by a principle of depend-
ence of truth on being, Lewis wanted all truths to be accounted for in terms
of how things are. Modal realism is an implementation of this broader
project, by explaining modal truths in terms of non-modal truths about
28  

the configuration of objects across modal space. The theory explains how
things possibly are and necessarily are in terms of how things are simpliciter:
we do not need to expand our primitive ideology in order to understand
modality. Quantum modal realism likewise enables an explanatory account
of modal truth in terms of non-modal being.
Although Lewis rather puzzlingly claimed to regard the lack of arbitrari-
ness in the modal realist worldview as a problem (Lewis 1986b: 128), he
made regular appeal to avoidance of arbitrariness elsewhere in his theoriz-
ing; and in any case there is a long tradition, tracing back at least to
Parmenides, of viewing avoidance of arbitrariness as an important virtue
in fundamental metaphysics. Lewisian modal realism scores spectacularly
well on this count: it seems to render reality as a whole entirely non-
arbitrary. The principle of recombination applies uniformly with no excep-
tions, no arbitrary ‘gaps in logical space’. Quantum modal realism likewise
minimizes arbitrariness: the Schrödinger equation applies universally, with
an Everett world for every quantum-mechanically possible history. There
are no arbitrary gaps in the multiverse. All arbitrariness in both forms of
modal realism is reduced to perspectival arbitrariness: why did I occupy this
particular perspective rather than any other?
One place in which arbitrariness might seem to remain within quantum
modal realism is in the initial quantum state of the universe. Since quantum
modal realists model contingency as variation across Everett worlds, there
can be no contingency in an initial state that these worlds have in common.
It remains an open theoretical and empirical question, however, what this
initial quantum state is like: different candidate frameworks for a fundamen-
tal theory, such as string theory or loop quantum gravity, are characterized by
very different-looking initial states. If it were to turn out that the true initial
quantum state of our universe has arbitrary-seeming features that lack any
apparent theoretical explanation, that would be prima facie evidence against
quantum modal realism—since it would suggest a source of contingency in
reality that goes beyond quantum contingency. But at present there is no
reason to believe this is how things will turn out. (See chapter 6 for more
discussion of potential contingency in overall cosmology.)

1.2 Quantum Modal Realism at Work: Modality

The basic form of the quantum modal realist analysis of modality is encoded
in the principles Alignment and Indexicality-of-Actuality. Everett worlds are
     :  29

metaphysically possible worlds, and our own Everett world is the actual
world. So, at a first pass: for an event to be metaphysically possible is for it
to occur in some Everett world, for it to be metaphysically necessary is for
it to occur in all Everett worlds, and for it to be actual is for it to occur in
our own world. This account of modality will be refined and reformulated
over the course of this section, but we can already make out some of
its general features. In particular, the space of Everett worlds is character-
ized in quantum-theoretic terms independently of the notion of metaphys-
ical modality, and consequently quantum modal realism is a reductive
theory: it accounts for metaphysical modality without presupposing any
modal notions.
There are fewer worlds encompassed in quantum modal realism than
there are in the more familiar Lewisian modal realism. No worlds that
conflict with quantum physics exist. Still, we have Everett worlds for all
the most obviously possible courses of events. To enumerate exactly which
Everett worlds there are and what they are like, we would need a fully
completed science; but even with existing scientific knowledge we can
have plenty of substantive knowledge about the space of Everett worlds.
The roles of intertheoretic relations and of special science knowledge are
key. For example, consider the possibility of kangaroos without tails. We
know what sorts of macroscopic configurations of materials a kangaroo
corresponds to, we know what sorts of microscopic configurations of
atoms and molecules are capable of realizing those macro-configurations,
we know that quantum theory permits microscopic configurations of that
sort, and we know that physical and chemical processes that would generate
such configurations are assigned non-zero quantum-mechanical chances. In
contrast, we know of no physical processes that could give rise to ghosts of
people from the distant past (as opposed to hallucinations of ghosts, or to
ghost-shaped clouds of dust), so we have no reason to think that there are
any ghosts in any Everett world.
The quantum modal realist, like the Lewisian modal realist, may use
restrictions on the space of metaphysical possibilities to characterize inter-
esting restricted modalities that can serve various theoretical purposes. From
the base space of Everett worlds—the entire plurality—we can extract any
sub-plurality and quantify only over those worlds to generate a new
restricted modality. For example, restricting to worlds with initial segments
that match the actual past generates a notion of historical modality: it is
historically possible that humanity should continue to flourish for a million
years, but not historically possible that World War II should not occur. In
30  

possible-worlds semantics for modal logic,⁴ varying the accessibility relation

implements such restrictions and allows clean characterization of any num-
ber of distinct modalities. Some of the more interesting restricted modalities
will make an appearance in chapter 4.
As noted in section 1.1, quantum modal realism collapses two types of
modality that are usually regarded as distinct: physical modality and meta-
physical modality. Consequently, quantum modal realists have no need of
the Lewisian account of physical modality as a restricted modality with the
accessibility relation fixed by the laws of nature. However, it is no defi-
ciency of quantum modal realism that it does not treat physical modality as
a restricted modality. All realists about objective modality must accept
some space of worlds as the most inclusive, and decline to give a treatment
of this basic modality as a restriction on any further modality. Moreover,
realist theories can still consistently incorporate more inclusive forms of
possibility, as long as these more inclusive modalities can be given some
non-realist interpretation. Lewisian modal realism is not itself inimical to a
broader notion of logical possibility where the only necessary truths are
logical truths, although the Lewisian modal realist does owe us some
analysis of this logical possibility in terms of metaphysical possibility.
Similarly, quantum modal realists can offer constructions of various
logical and conceptual modalities. These matters are considered further
in section 1.4.
As Lewis remarked, ‘modality is not all diamonds and boxes’. The claims
of de dicto possibility, necessity, and actuality that we have so far considered
are only a small fragment of our modal thought and talk. In section 1.3 of
Lewis (1986b), Lewis mentions a number of modal idioms which are hard to
capture using familiar quantified modal logic, but which are straightforward
to capture by quantifying in creative ways over the individuals in some range
of Lewis-worlds. Quantum modal realists can likewise quantify over a
limited range of individuals in a limited range of Everett worlds, to make
sense of claims such as ‘there are three possible ways for this plan to succeed’
and ‘a mammal could resemble a bird more closely than a mammal could
resemble an amoeba’. The results of this quantification in the Everettian
theory will of course not align exactly with the results in the Lewisian theory,
since the space of worlds quantified over differs in extent; but the structural
features of the analysis are the same, making it equally flexible.

⁴ For introductions to possible worlds semantics, see Divers (2002) and Melia (2003).
     :  31

A key notion which Lewis analyses directly by way of his modal realism is
supervenience. Recent metaphysics has found much use for this notion, and
numerous different flavours of supervenience have been discussed;
McLaughlin and Bennett (2018) give a comprehensive summary. The ques-
tion of whether the mental facts supervene on the physical facts has long
been a popular way to draw the battle-lines between dualists and material-
ists; Humeans and non-Humeans in the metaphysics of laws of nature have
argued over nomological supervenience theses such as Lewis’s Humean
Supervenience; and metaphysically inclined philosophers of language dis-
pute whether semantic facts supervene on natural facts.
The account of supervenience that I will offer is, in effect, identical to
Lewis’s. Again, it is given directly in terms of the reductive base rather than
via a detour through a formal language containing modal operators. Lewis
(1986b) argued that analyses of supervenience that make use of modal
logic’s familiar diamonds and boxes can express what he calls ‘narrow’
supervenience but not ‘broad’ supervenience:

1) Narrow psychophysical supervenience: could two people differ mentally

without also themselves differing physically?

2) Broad psychophysical supervenience: could two people differ mentally

without there being a physical difference somewhere, whether in the
people themselves or somewhere in their surroundings?
Lewis (1986b: 14 15)

Both of these notions are easy enough to express if we allow ourselves the
modal realist’s quantification over possible worlds:

Among all the worlds, or among all the things in all the worlds, . . . there is
no difference of the one sort without difference of the other sort. Whether
the things that differ are part of the same world is neither here nor there.
Lewis (1986b: 17)

According to this account of supervenience, narrow psychophysical super-

venience is the thesis that no world contains two things which differ
mentally without differing physically; and broad psychophysical superveni-
ence is the thesis that no two worlds differ in any of the mental properties
instantiated at them without differing in the physical properties instantiated
at them.
32  

Narrow psychophysical supervenience can be modelled using a modal

sentential operator: it is the thesis that it is not the case that, possibly, there
are two things which differ mentally without also differing in their intrinsic
physical character. Lewis argues, however, that the closest we can get to
broad psychophysical supervenience using a sentential operator is the fol-
lowing: it is not the case that, possibly, there are two things which differ
mentally without differing in their intrinsic or extrinsic physical character.
But then:

What we have said is not quite what we meant to say, but rather this: there
could be no mental differences without some physical difference of the sort
that could arise between people in the same world. The italicised part is a
gratuitous addition. Lewis (1986b: 16)

He counts it a significant advantage of his modal realism that it allows both

notions to be stated, and to be distinguished from one another: ‘The moral is
that we’d better have other-worldly things to quantify over—not just a
primitive modal modifier of sentences’ (Lewis 1986b: 17). Quantum modal
realism provides us with the desired other-worldly things to quantify over;
so it is no surprise that the Lewisian analysis of supervenience carries over
unmodified to quantum modal realism. An Everettian broad psychophysical
supervenience thesis says that no two Everett worlds differ in any of the
mental properties instantiated at them without differing in the physical
properties instantiated at them.
One central application of the notion of supervenience is to characterize
global metaphysical outlooks. The most familiar such thesis is David Lewis’s
doctrine of Humean Supervenience:

All there is to the world is a vast mosaic of local matters of particular fact,
just one little thing and then another . . . We have geometry: a system of
external relations of spatiotemporal distances between points . . . And at
those points we have local qualities: perfectly natural intrinsic properties
which need nothing bigger than a point at which to be instantiated. For
short: we have an arrangement of qualities. And that is all. There is no
difference without difference in the arrangement of qualities. All else
supervenes on that. Lewis (1986a: ix)

Humean Supervenience is intended to rule out ingredients of reality—

disembodied minds, causally epiphenomenal ectoplasm, and the like—that
     :  33

float free from the sort of field-theoretic ontology which he took to be

suggested by fundamental physics. Humean Supervenience incorporates a
thesis about the fundamental elements of reality—they are intrinsic proper-
ties instantiated at spacetime points—but the philosophically boldest part of
the thesis is the claim that all phenomena of any kind at any scale asym-
metrically modally depend on phenomena of the kind described by funda-
mental physics. Despite Lewis’s regular association with the worst excesses
of analytic metaphysics, Humean Supervenience was proposed in a spirit of
respect for the ontology of physics and for the foundational role of physics in
constituting and constraining special-science phenomena.
Humean Supervenience is not the only global supervenience thesis in
town. Alternatives include Bigelow’s liberal thesis that ‘truth supervenes on
being’ (Bigelow 1988: 132–3), Armstrong’s Aristotelian-style supervenience
thesis that all facts supervene on facts about which entities instantiate which
universals (Armstrong 2010), Chalmers and Jackson’s A Priori Entailment
Thesis (Chalmers and Jackson 2001), and Chalmers’s more recent variety of
‘scrutability theses’ (Chalmers 2012). We need not delve into the details: all
of these theses quantify over metaphysically possible worlds, and so all of
them carry over straightforwardly to the Everettian context. Alignment tells
us that Everett worlds are the metaphysically possible worlds, and accordingly
Humean Supervenience and its kin just are theses about variation across the
space of Everett worlds. Which of the various supervenience theses should
quantum modal realists endorse? I leave this question open here.
There are plenty of other philosophically interesting notions in the
vicinity of supervenience. Instead of asking—say—what the laws of nature
supervene on, we can ask what determines the laws, or what fixes them, or
what grounds them, or what they depend on, or in virtue of what they are
the laws, or what makes them the laws. Which of these questions you take to
be most interesting will depend on your preferred metametaphysical ideol-
ogy. Making sense of many of the questions requires recognizing ‘worldly’
(rather than merely representational) hyperintensional distinctions—
distinct yet necessarily equivalent facts or properties—which goes beyond
the objective modal distinctions of either Lewisian modal realism or quan-
tum modal realism. However, defenders of strong notions of grounding
or ontological dependence typically regard them as primitive; quantum
modal realists can do likewise if they wish, and are accordingly no worse
off than anyone else with respect to making sense of generalized determin-
ation relations. Further discussion of these matters will be deferred to
section 1.4.
34  

Lewis offered a theory of coarse-grained propositions as sets of worlds.

For the purposes of resolving the probability problem in EQM, chance-
bearing propositions will in chapter 3 be similarly analysed in terms of sets
of Everett worlds. This analysis is fine for ordinary factual propositions of
the kind we use most frequently to communicate in everyday life and
scientific practice. However, we may legitimately worry that the analysis
will be inapplicable to the propositions expressing various parts of EQM,
such as the Schrödinger equation itself. The structure of this difficulty is not,
of course, unique to EQM; it has been discussed in the context of Lewisian
modal realism under the rubric of advanced modalizing. Quantum modal
realism is a form of modal realism—it says that multiple alternative possi-
bilities genuinely exist—so it is unsurprising that it faces an analogous
problem with advanced modalizing.
In the remainder of this section, I will explain the challenge of advanced
modalizing, and discuss some potential responses to it—initially in the context
of Lewisian modal realism. My preferred account of advanced modalizing will
afterwards be adapted to the setting of quantum modal realism. The resulting
conception of the modal status of the fundamental facts vindicates the
necessity-first approach to analysing modality that I endorsed in section 0.3
of the introduction.
Advanced modal claims, as characterized by Divers (1999) in the context
of Lewisian modal realism, are modal claims about entities that are spatio-
temporally unrelated to us. For most metaphysicians, this will include modal
claims about entities sometimes described as ‘necessary existents’, such as
numbers, sets, properties, and so on. But they will also include modal claims
about individuals in other Lewisian worlds. A Lewisian modal realist is
committed to the existence of such individuals; others might be committed
to their non-existence. But whether we believe in such individuals or not, we
can still ask about their modal status; we can ask, in particular, whether their
existence is a contingent matter or a necessary matter. If there is a Lewisian
pluriverse, could there have failed to be one? And if (as most of us believe)
there is no Lewisian pluriverse, could there have been one?
Lewis’s original statement of Lewisian modal realism was given in ‘Coun-
terpart theory and quantified modal logic’ (Lewis 1968). The view was
there presented as a way of providing truth-conditions for expressions in a
formal language containing modal operators (the universe language) using
expressions in a formal language lacking modal operators (the pluriverse
language). This original, explicitly metalinguistic, characterization of modal
realism has perhaps helped to obscure the status of advanced modalizing.
Another random document with
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Among the earliest particulars which Robert gave, was the fact that
he was not alone in his confinement. Various others, all in antique
garb, were in there with him—a corpulent middle-aged gentleman
with tied queue and velvet knee-breeches who spoke English fluently
though with a marked Scandinavian accent; a rather beautiful small
girl with very blonde hair which appeared as glossy dark blue; two
apparently mute Negroes whose features contrasted grotesquely
with the pallor of their reversed-colored skins; three young men; one
young woman; a very small child, almost an infant; and a lean,
elderly Dane of extremely distinctive aspect and a kind of half-malign
intellectuality of countenance.
This last named individual—Axel Holm, who wore the satin small-
clothes, flared-skirted coat, and voluminous full-bottomed periwig of
an age more than two centuries in the past—was notable among the
little band as being the one responsible for the presence of them all.
He it was who, skilled equally in the arts of magic and glass working,
had long ago fashioned this strange dimensional prison in which
himself, his slaves, and those whom he chose to invite or allure
thither were immured unchangingly for as long as the mirror might
endure.

Holm was born early in the seventeenth century, and had followed
with tremendous competence and success the trade of a glass-
blower and molder in Copenhagen. His glass, especially in the form
of large drawing-room mirrors, was always at a premium. But the
same bold mind which had made him the first glazier of Europe also
served to carry his interests and ambitions far beyond the sphere of
mere material craftsmanship. He had studied the world around him,
and chafed at the limitations of human knowledge and capability.
Eventually he sought for dark ways to overcome those limitations,
and gained more success than is good for any mortal.
He had aspired to enjoy something like eternity, the mirror being his
provision to secure this end. Serious study of the fourth dimension
was far from beginning with Einstein in our own era; and Holm, more
than erudite in all the methods of his day, knew that a bodily
entrance into that hidden phase of space would prevent him from
dying in the ordinary physical sense. Research showed him that the
principle of reflection undoubtedly forms the chief gate to all
dimensions beyond our familiar three; and chance placed in his
hands a small and very ancient glass whose cryptic properties he
believed he could turn to advantage. Once "inside" this mirror
according to the method he had envisaged, he felt that "life" in the
sense of form and consciousness would go on virtually forever,
provided the mirror could be preserved indefinitely from breakage or
deterioration.
Holm made a magnificent mirror, such as would be prized and
carefully preserved; and in it deftly fused the strange whorl-
configured relic he had acquired. Having thus prepared his refuge
and his trap, he began to plan this mode of entrance and conditions
of tenancy. He would have with him both servitors and companions;
and as an experimental beginning he sent before him into the glass
two dependable Negro slaves brought from the West Indies. What
his sensations must have been upon beholding this first concrete
demonstration of his theories, only imagination can conceive.
Undoubtedly a man of his knowledge realized that absence from the
outside world if deferred beyond the natural span of life of those
within, must mean instant dissolution at the first attempt to return to
that world. But, barring that misfortune or accidental breakage, those
within would remain forever as they were at the time of entrance.
They would never grow old, and would need neither food nor drink.

To make his prison tolerable he sent ahead of him certain books and
writing materials, a chair and table of stoutest workmanship, and a
few other accessories. He knew that the images which the glass
would reflect or absorb would not be tangible, but would merely
extend around him like a background of dream. His own transition in
1687 was a momentous experience; and must have been attended
by mixed sensations of triumph and terror. Had anything gone
wrong, there were frightful possibilities of being lost in dark and
inconceivable multiple dimensions.
For over fifty years he had been unable to secure any additions to
the little company of himself and slaves, but later on he had
perfected his telepathic method of visualizing small sections of the
outside world close to the glass, and attracting certain individuals in
those areas through the mirror's strange entrance. Thus Robert,
influenced into a desire to press upon the "door," had been lured
within. Such visualizations depended wholly on telepathy, since no
one inside the mirror could see out into the world of men.
It was, in truth, a strange life that Holm and his company had lived
inside the glass. Since the mirror had stood for fully a century with its
face to the dusty stone wall of the shed where I found it, Robert was
the first being to enter this limbo after all that interval. His arrival was
a gala event, for he brought news of the outside world which must
have been of the most startling impressiveness to the more
thoughtful of those within. He, in his turn—young though he was—
felt overwhelmingly the weirdness of meeting and talking with
persons who had been alive in the seventeenth and eighteenth
centuries.

The deadly monotony of life for the prisoners can only be vaguely
conjectured. As mentioned, its extensive spatial variety was limited
to localities which had been reflected in the mirror for long periods;
and many of these had become dim and strange as tropical climates
had made inroads on the surface. Certain localities were bright and
beautiful, and in these the company usually gathered. But no scene
could be fully satisfying; since the visible objects were all unreal and
intangible, and often of perplexingly indefinite outline. When the
tedious periods of darkness came, the general custom was to
indulge in memories, reflections, or conversations. Each one of that
strange, pathetic group had retained his or her personality
unchanged and unchangeable, since becoming immune to the time
effects of outside space.
The number of inanimate objects within the glass, aside from the
clothing of the prisoners, was very small; being largely limited to the
accessories Holm had provided for himself. The rest did without
even furniture, since sleep and fatigue had vanished along with most
other vital attributes. Such inorganic things as were present, seemed
as exempt from decay as the living beings. The lower forms of
animal life were wholly absent.
Robert derived most of his information from Herr Thiele, the
gentleman who spoke English with a Scandinavian accent. This
portly Dane had taken a fancy to him, and talked at considerable
length. The others, too, had received him with courtesy and good-
will; Holm himself, seeming well-disposed, had told him about
various matters including the door of the trap.
The boy, as he told me later, was sensible enough never to attempt
communication with me when Holm was nearby. Twice, while thus
engaged, he had seen Holm appear; and had accordingly ceased at
once. At no time could I see the world behind the mirror's surface.
Robert's visual image, which included his bodily form and the
clothing connected with it, was—like the aural image of his halting
voice and like his own visualization of myself—a case of purely
telepathic transmission; and did not involve true inter-dimensional
sight. However, had Robert been as trained a telepathist as Holm, he
might have transmitted a few strong images apart from his
immediate person.

Throughout this period of revelation I had, of course, been

desperately trying to devise a method for Robert's release. On the
fourth day—the ninth after the disappearance—I hit on a solution.
Everything considered, my laboriously formulated process was not a
very complicated one; though I could not tell beforehand how it
would work, while the possibility of ruinous consequences in case of
a slip was appalling. This process depended, basically, on the fact
that there was no possible exit from inside the glass. If Holm and his
prisoners were permanently sealed in, then release must come
wholly from outside. Other considerations included the disposal of
the other prisoners, if any survived, and especially of Axel Holm.
What Robert had told me of him was anything but reassuring; and I
certainly did not wish him loose in my apartment, free once more to
work his evil will upon the world. The telepathic messages had not
made fully clear the effect of liberation on those who had entered the
glass so long ago.
There was, too, a final though minor problem in case of success—
that of getting Robert back into the routine of school life without
having to explain the incredible. In case of failure, it was highly
inadvisable to have witnesses present at the release operations—
and lacking these, I simply could not attempt to relate the actual
facts if I should succeed. Even to me the reality seemed a mad one
whenever I let my mind turn from the data so compellingly presented
in that tense series of dreams.
When I had thought these problems through as far as possible, I
procured a large magnifying-glass from the school laboratory and
studied minutely every square millimeter of that whorl-center which
presumably marked the extent of the original ancient mirror used by
Holm. Even with this aid I could not quite trace the exact boundary
between the old area and the surface added by the Danish wizard;
but after a long study decided on a conjectural oval boundary which I
outlined very precisely with a soft blue pencil, I then made a trip to
Stamford, where I procured a heavy glass-cutting tool; for my
primary idea was to remove the ancient and magically potent mirror
from its later setting.

My next step was to figure out the best time of day to make the
crucial experiment. I finally settled on two-thirty A.M.—both because
it was a good season for uninterrupted work, and because it was the
"opposite" of two-thirty P.M., the probable moment at which Robert
had entered the mirror. This form of "oppositeness" may or may not
have been relevant, but I knew at least that the chosen hour was as
good as any—and perhaps better than most.
I finally set to work in the early morning of the eleventh day after the
disappearance, having drawn all the shades of my living-room and
closed and locked the door into the hallway. Following with
breathless care the elliptical line I had traced, I worked around the
whorl-section with my steel-wheeled cutting tool. The ancient glass,
half an inch thick, crackled crisply under the firm, uniform pressure;
and upon completing the circuit I cut around it a second time,
crunching the roller more deeply into the glass.
Then, very carefully indeed, I lifted the heavy mirror down from its
console and leaned it face-inward against the wall; prying off two of
the thin, narrow boards nailed to the back. With equal caution I
smartly tapped the cut-around space with the heavy wooden handle
of the glass-cutter.
At the very first tap the whorl-containing section of glass dropped out
on the Bokhara rug beneath. I did not know what might happen, but
was keyed up for anything, and took a deep involuntary breath. I was
on my knees for convenience at the moment, with my face quite near
the newly made aperture; and as I breathed there poured into my
nostrils a powerful dusty odor—a smell not comparable to any other I
have ever encountered. Then everything within my range of vision
suddenly turned to a dull gray before my failing eye-sight as I felt
myself overpowered by an invisible force which robbed my muscles
of their power to function.
I remember grasping weakly and futilely at the edge of the nearest
window drapery and feeling it rip loose from its fastening. Then I
sank slowly to the floor as the darkness of oblivion passed over me.

When I regained consciousness I was lying on the Bokhara rug with

my legs held unaccountably up in the air. The room was full of that
hideous and inexplicable dusty smell—and as my eyes began to
take in definite images I saw that Robert Grandison stood in front of
me. It was he—fully in the flesh and with his coloring normal—who
was holding my legs aloft to bring the blood back to my head as the
school's first-aid course had taught him to do with persons who had
fainted. For a moment I was struck mute by the stifling odor and by a
bewilderment which quickly merged into a sense of triumph. Then I
found myself able to move and speak collectedly.
I raised a tentative hand and waved feebly at Robert.
"All right, old man," I murmured, "you can let my legs down now.
Many thanks. I'm all right again, I think. It was the smell—I imagine—
that got me. Open that farthest window, please—wide—from the
bottom. That's it—thanks. No—leave the shade down the way it
was."
I struggled to my feet, my disturbed circulation adjusting itself in
waves, and stood upright hanging to the back of a big chair. I was
still "groggy," but a blast of fresh, bitterly cold air from the window
revived me rapidly. I sat down in the big chair and looked at Robert,
now walking toward me.
"First," I said hurriedly, "tell me, Robert—those others—Holm? What
happened to them, when I—opened the exit?"
Robert paused half-way across the room and looked at me very
gravely.
"I saw them fade away—into nothingness—Mr. Canevin," he said
with solemnity; "and with them—everything. There isn't any more
'inside,' sir—thank God, and you, sir!"
And young Robert, at last yielding to the sustained strain which he
had borne through all those terrible eleven days, suddenly broke
down like a little child and began to weep hysterically in great,
stifling, dry sobs.

I picked him up and placed him gently on my davenport, threw a rug

over him, sat down by his side, and put a calming hand on his
forehead.
"Take it easy, old fellow," I said soothingly.
The boy's sudden and very natural hysteria passed as quickly as it
had come on as I talked to him reassuringly about my plans for his
quiet restoration to the school. The interest of the situation and the
need of concealing the incredible truth beneath a rational
explanation took hold of his imagination as I had expected; and at
last he sat up eagerly, telling the details of his release and listening
to the instructions I had thought out. He had, it seems, been in the
"projected area" of my bedroom when I opened the way back, and
had emerged in that actual room—hardly realizing that he was "out."
Upon hearing a fall in the living-room he had hastened thither, finding
me on the rug in my fainting spell.
I need mention only briefly my method of restoring Robert in a
seemingly normal way—how I smuggled him out of the window in an
old hat and sweater of mine, took him down the road in my quietly
started car, coached him carefully in a tale I had devised, and
returned to arouse Browne with the news of his discovery. He had, I
explained, been walking alone on the afternoon of his
disappearance; and had been offered a motor ride by two young
men who, as a joke and over his protests that he could go no farther
than Stamford and back, had begun to carry him past that town.
Jumping from the car during a traffic stop with the intention of hitch-
hiking back before Call-Over, he had been hit by another car just as
the traffic was released—awakening ten days later in the Greenwich
home of the people who had hit him. On learning the date, I added,
he had immediately telephoned the school; and I, being the only one
awake, had answered the call and hurried after him in my car without
stopping to notify anyone.

Browne, who at once telephoned to Robert's parents, accepted my

story without question; and forbore to interrogate the boy because of
the latter's manifest exhaustion. It was arranged that he should
remain at the school for a rest, under the expert care of Mrs.
Browne, a former trained nurse. I naturally saw a good deal of him
during the remainder of the Christmas vacation, and was thus
enabled to fill in certain gaps in his fragmentary dream-story.
Now and then we would almost doubt the actuality of what had
occurred; wondering whether we had not both shared some
monstrous delusion born of the mirror's glittering hypnotism, and
whether the tale of the ride and accident were not after all the real
truth. But whenever we did so we would be brought back to belief by
some monstrous and haunting memory; with me, of Robert's dream-
figure and its thick voice and inverted colors; with him, of the whole
fantastic pageantry of ancient people and dead scenes that he had
witnessed. And then there was the joint recollection of that damnable
dusty odor.... We knew what it meant: the instant dissolution of those
who had entered an alien dimension a century and more ago.
There are, in addition, at least two lines of rather more positive
evidence; one of which comes through my researches in Danish
annals concerning the sorcerer, Axel Holm. Such a person, indeed,
left many traces in folklore and written records; and diligent library
sessions, plus conferences with various learned Danes, have shed
much light on his evil fame. At present I need say only that the
Copenhagen glass-blower—born in 1612—was a notorious
Luciferian whose pursuits and final vanishing formed a matter of
awed debate over two centuries ago. He had burned with a desire to
know all things and to conquer every limitation of mankind—to which
end he had delved deeply into occult and forbidden fields ever since
he was a child.
He was commonly held to have joined a coven of the dreaded
witchcult, and the vast lore of ancient Scandinavian myth—with its
Loki the Sly One and the accursed Fenris-Wolf—was soon an open
book to him. He had strange interests and objectives, few of which
were definitely known, but some of which were recognized as
intolerably evil. It is recorded that his two Negro helpers, originally
slaves from the Danish West Indies, had become mute soon after
their acquisition by him; and that they had disappeared not long
before his own disappearance from the ken of mankind.
Near the close of an already long life the idea of a glass of
immortality appears to have entered his mind. That he had acquired
an enchanted mirror of inconceivable antiquity was a matter of
common whispering; it being alleged that he had purloined it from a
fellow-sorcerer who had entrusted it to him for polishing.
This mirror—according to popular tales a trophy as potent in its way
as the better-known Aegis of Minerva or Hammer of Thor—was a
small oval object called "Loki's Glass," made of some polished
fusible mineral and having magical properties which included the
divination of the immediate future and the power to show the
possessor his enemies. That it had deeper potential properties,
realizable in the hands of an erudite magician, none of the common
people doubted; and even educated persons attached much fearful
importance to Holm's rumored attempts to incorporate it in a larger
glass of immortality. Then had come the wizard's disappearance in
1687, and the final sale and dispersal of his goods amidst a growing
cloud of fantastic legendry. It was, altogether, just such a story as
one would laugh at if possessed of no particular key; yet to me,
remembering those dream messages and having Robert
Grandison's corroboration before me, it formed a positive
confirmation of all the bewildering marvels that had been unfolded.
But as I have said, there is still another line of rather positive
evidence—of a very different character—at my disposal. Two days
after his release, as Robert, greatly improved in strength and
appearance, was placing a log on my living-room fire, I noticed a
certain awkwardness in his motions and was struck by a persistent
idea. Summoning him to my desk I suddenly asked him to pick up an
ink-stand—and was scarcely surprised to note that, despite lifelong
right-handedness, he obeyed unconsciously with his left hand.
Without alarming him, I then asked that he unbutton his coat and let
me listen to his cardiac action. What I found upon placing my ear to
his chest—and what I did not tell him for some time afterward—was
that his heart was beating on his right side.
He had gone into the glass right-handed and with all organs in their
normal positions. Now he was left-handed and with organs reversed,
and would doubtless continue so for the rest of his life. Clearly, the
dimensional transition had been no illusion—for this physical change
was tangible and unmistakable. Had there been a natural exit from
the glass, Robert would probably have undergone a thorough re-
reversal and emerged in perfect normality—as indeed the color-
scheme of his body and clothing did emerge. The forcible nature of
his release, however, undoubtedly set something awry; so that
dimensions no longer had a chance to right themselves as chromatic
wave-frequencies still did.
I had not merely opened Holm's trap; I had destroyed it; and at the
particular stage of destruction marked by Robert's escape some of
the reversing properties had perished. It is significant that in
escaping Robert had felt no pain comparable to that experienced in
entering. Had the destruction been still more sudden, I shiver to think
of the monstrosities of color the boy would always have been forced
to bear. I may add that after discovering Robert's reversal I
examined the rumpled and discarded clothing he had worn in the
glass, and found, as I had expected, a complete reversal of pockets,
buttons, and all other corresponding details.
At this moment Loki's Glass, just as it fell on my Bokhara rug from
the now patched and harmless mirror, weighs down a sheaf of
papers on my writing-table here in St. Thomas, venerable capital of
the Danish West Indies—now the American Virgin Islands. Various
collectors of old Sandwich glass have mistaken it for an odd bit of
that early American product—but I privately realize that my paper-
weight is an antique of far subtler and more paleologean
craftsmanship. Still, I do not disillusion such enthusiasts.
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