## 1. Types of Modal Fictionalism



Modal fictionalists often focus on the claim that possible worlds are
merely fictional entities, and apparent commitment to possible worlds
is to be explained in the same sort of way that apparent commitment to
ideal gases or frictionless surfaces is to be explained. Rosen 1990
and others have formulated modal fictionalism as a theory that takes
talk of possible worlds to be on a par with talk about
paradigmatically fictional objects, e.g., Sherlock Holmes
("There is a (non-actual) possible world at which there are blue
swans" is to be understood on the model of "There is a
brilliant detective at 221b Baker Street", in Rosen's
example). This goes with an at least partial account of how we are to
treat paradigmatically fictional claims: that they are, literally and
strictly speaking, false. The literal truth, according to modal
fictionalists, is that there are no merely possible worlds (or merely
possible situations, or outcomes), and there are no merely possible
objects. Strictly and literally speaking, there is no sculpture that I
spent this morning making, though there could have been. When the
flipped coin comes down heads, there is strictly speaking no outcome
of that very throw in which it comes down tails.



What is literally true, however, is that *according to the modal
fiction*, or *according to the fiction of possible worlds*
there is a (merely possible) sculpture I could have spent this morning
making, and there is an (unactualised) outcome of the toss in which
the coin came down tails. What is said in talk about merely possible
worlds and merely possible objects is generally literally false, but
the slightly more longwinded talk about what is true according to the
fiction of possible worlds is literally true. One might think (as
Hinckfuss 1993 does) that talk about possible worlds is (or should be)
governed by implicit presuppositions known to be false so that what is
*said* in the language of possible worlds does not commit one
to the existence of possible worlds, but only to some more economical
proposition: something of the kind "if there were possible
worlds of such-and-such a sort, then ...", or "given
the presupposition that there are possible worlds, ...". Or
you might have some other account of the functioning of talk about
possible worlds: Nolt 1986 suggests we should take typical
"possibilistic discourse" to be a game of make-believe
(Nolt 1986, p. 440), and while Nolt does not tell us specifically what
theory of make-believe he has in mind, there are many theories of
make-believe (most famously Walton 1990) that might be employed by a
modal fictionalist to explain the behaviour of our typical utterances
about possible worlds.  Stephen Yablo (Yablo 1996) is one person
who employs Walton's theory in his fictionalism (or, as he
prefers in Yablo 2001, *figuralism*) about possible worlds.



The main benefit which a fictional approach to possible worlds offers
is, of course, the advantage of using the language of possible worlds,
without the stiff ontological cost of literal commitment to such
worlds. It is an especially tempting account of merely possible
objects (like blue swans, or dragons, or the Holy New Zealand Empire):
even those who accept some abstractionist account of possible worlds
(see van Inwagen 1986) might well be reluctant to accept the literal
existence of their contents. After all, it is often thought that the
distinguishing mark of *merely* possible objects is that they
do not actually exist.



Central to fictionalist treatments of possible worlds are
biconditionals connecting truths about necessity and possibility, on
the one hand, and the contents of the modal fiction, on the other.
Central biconditionals will be all the instances of the following
schemas (where *P* expresses a proposition):



> 
> Possibly *P* iff according to the fiction of possible worlds,
> *P* is true at some possible world.
> 
> 
> Necessarily *P* iff according to the fiction of possible
> worlds, *P* is true at all possible worlds.
> 
> 
> 



Either schema will be adequate to yield the other, given the standard
inter-definition of possibility and necessity, provided enough logical
machinery is available for reasoning within the scope of the
"according to the fiction" operator. As a matter of fact,
the above is a simplification, since, according to Rosen (1990, p.
335), what is true according to the fiction of possible worlds may be
only a proposition connected with *P*: the paraphrase of
*P* into the language of possible worlds. In general, for
Rosen, this will be the analysis of *P* in Lewis's theory
of possible worlds. Rosen states the form of the fictionalist
biconditionals at its most general as:



> 
> *P* iff according to PW, *P*\*.
> 



where "PW" is the fiction of possible worlds, *P*
is any proposition, and *P*\* is its possible-worlds
"paraphrase" (Rosen 1990, p. 335). In simple cases the
above biconditionals will do as they are: for example,



> 
> Possibly, pigs fly iff according to the fiction of possible worlds (or
> according to PW), at some possible world, pigs fly.
> 



In less straightforward cases, however, the proposition expressed by
*P*\* may have to differ from that expressed by
 *P*.[1]
 Fictionalists may also employ other biconditionals when constructing
their fiction -- one example is a biconditional to ensure that
every proposition that is (really) true is according to the fiction
true in the actual
 world.[2]
 A modal fiction may require more contents than those yielded by such
biconditionals: what other contents the fiction of possible worlds
might contain is an important question, and one unsurprisingly which
different modal fictionalists will answer differently.


### 1.1 The Contents of The Fiction of Possible Worlds



Many fictionalists are far from explicit about exactly what the
content of the fiction of possible worlds is to be. (Often they are
also silent on the pressing issue of how one would justify one fiction
rather than another: but more on this in section 4). Two explicit
proposals were made in 1989 and 1990 about which fiction to use.
Gideon Rosen's 1990 proposed using a slightly modified version
of David Lewis's 1986 theory of possible worlds as the modal
fiction. The theory had been proposed by Lewis as the literal truth,
but by treating it as a mere fiction Rosen provided a ready-made story
about possible worlds, their extent and nature. The other proposal was
that of D.M. Armstrong's 1989. Armstrong proposed a
"two-step" fiction, according to which there was a
"great fiction", which asserted the existence of a lot of
"little fictions", each of which completely described a
possible world. Armstrong resisted identifying these complete
descriptions of ways things could be with the possible worlds, as an
abstractionist might, since Armstrong believed that worlds are
supposed to be objects like our cosmos, rather than descriptions,
properties, or other such abstract objects. Armstrong employed the two
stage fiction, on the other hand, because he held that it is true at
each world that it is the only world, and if the fiction were of a
Lewisian pluriverse each world would (according to the fiction) be
such that it was one of many worlds. In this respect, though Armstrong
spells out the concern in quite a different manner, it can be seen as
an anticipation of the Brock/Rosen objection (see section 3, below).
In both the theories of Armstrong and Rosen the "worlds"
in the story are thought to be 'concrete' cosmoi, like our
 own.[3]




A third systematic attempt to specify something like a modal fiction
is worth noting here. Theodore Sider defends an "ersatz
pluriverse" view in Sider 2002, according to which possible
worlds talk should be understood as talk about what is true according
to what is true according to a *pluriverse sentence* that Sider
specifies. Sider constructs this sentence, that simultaneously
describes all the possible worlds and their relationships, using a
range of constraints including the constraint that de dicto necessity
claims that are in fact true are true of all the worlds of the
described pluriverse. Sider distinguishes his view from Rosen-style
modal fictionalism, particularly because Sider thinks that the
"according to" he needs should not be understood as the
sort of "according to the fiction" operator he takes
Rosen's to be. So while Sider's view probably should not
be classed as a variety of modal fictionalism, it is a close cousin.
Berit Brogaard argues that Sider's view is inferior to her
preferred form of modal fictionalism in Brogaard 2006. 



For any set of principles governing the fiction of possible worlds,
the question obviously arises as to why that set should be chosen.
Alternatively, there are many stories we could tell about other worlds
(whether they are cosmoi or fictional abstract objects), and the
question arises as to why one rather than any other be chosen to be
*the* modal fiction. (One could of course be more pluralist
than this, and allow that different fictions are suitable for
different purposes. The relativised question may still be asked,
however: why *this* fiction, rather than any other, for
*this* particular purpose?). This task of selecting and
justifying one or more particular stories about worlds will be one of
the challenges discussed in section 4. However, the next distinction
to be discussed makes a big difference to what sort of answer to this
question will be acceptable.


### 1.2 Strong vs. Timid



This next distinction concerns the role the modal fiction is to play
in the theory. Is the fiction of possible worlds intended to provide
an explanation of the applicability modal vocabulary, or not? The view
that the truth of modal claims depends on, or is to be explained by,
the contents of the fiction of possible worlds is often called
"strong modal fictionalism", following Rosen's
description of such a view (Rosen 1990, p. 354, Nolan 1997a). The view
that modal truth does not depend on the contents of the modal fiction
(and usually, that what the contents of the modal fiction are depends
on the modal truth), on the other hand, is known as "timid modal
fictionalism", again following Rosen (Rosen 1990, p. 354).



Both the view put forward by Armstrong 1989 and the primary view
discussed (but not endorsed) by Rosen 1990 seem to have been
fictionalisms of the 'strong' kind (see Nolan 1997a, p.
263). 'Timid' fictionalism about possible worlds is also
mentioned by Rosen 1990, and has been endorsed in passing by Field
(1989, p. 41, 86). Sider 2002 is also on the 'timid' side,
not seeking an analysis at least of basic de dicto necessity. A modal
fictionalist theory which sees the fiction of possible worlds as
providing the resources for an analysis of modal statements would of
course do important theoretical work: since the analysis of claims
involving modal operators is among the most controversial and
difficult issues in metaphysics. The downside is that strong modal
fictionalism seems to face serious objections: see section 4. 



Apart from any objections that might be leveled at strong modal
fictionalism, the advocate of this variety of modal fictionalism faces
the challenge of stating the contents of the modal fiction without
relying on modal notions in a way that would make the explanation of
those modal notions circular. Since the fiction explains the truth of
modal claims, explaining the content of the modal fiction by reference
to modal claims would be circular (e.g., by stipulating that all of
the propositions which are necessary hold in all worlds, or that
objects have in all worlds in which they exist the properties which
they in fact have essentially). Stating, in non-modal terms, general
principles about possible worlds that would enable one to determine,
when presented with a proposition, whether it holds at all worlds, at
some but not others, or none, is a difficult and controversial matter.
Plausibly, a strong modal fictionalist will owe us such a non-modal
specification of the contents of the modal fiction, if our
understanding of the contents of the modal fiction is to allow us a
useful method of assessing the truth of modal claims. Furthermore the
strong modal fictionalist seems committed to *there being* a
fact of the matter about the content of the modal fiction which is not
itself to be explained or analysed in terms of further modal facts of
the matter. 



One particularly pressing instance of this difficulty (noted e.g., by
Rosen 1990, p. 344) is the problem of how to understand the
"according to the fiction of possible worlds..."
operator. Natural initial glosses, as Rosen points out, include: 



> 
> If PW were true, then *P* would be true; If we suppose PW,
> *P* follows; It would be impossible for PW to be true without
> *P* being true as well. (Rosen 1990, p. 344)
> 



The problem is that these seem modal. Rosen offers several possible
responses the fictionalist could make to this problem. He could admit
that his theory does indeed contain a modal primitive, but claim
nevertheless that it is some sort of advance in analysis, reducing all
modal primitives to one. (Though as Rosen says, "According to
the fiction of possible worlds" seems like a very odd
primitive.) Or he could instead attempt to spell out the prefix in a
non-modal way. This has not to date been attempted by many avowed
modal fictionalists, but is one of the many tasks facing a modal
fictionalist who sees the invocation of the fiction as the method for
analysing or explaining modality.



If the modal fictionalist were only timid, on the other hand, then the
fictionalist biconditional could be used to generate a great deal of
the content of the modal fiction: whether or not the fiction claims
that a given proposition is true in all possible worlds (or all
accessible worlds) depends on whether that proposition is indeed
necessarily true; whether or not a proposition is true at some world
(or some accessible world) depends on whether it is possibly true; and
so on. Furthermore, an analysis of truth in fiction in terms of some
modal notion (whether a counterfactual conditional, strict
implication, or whatever) would not make the account circular, since
analysing modal discourse would be no part of the purpose of the
fictional machinery. One recent worked-out modal fictionalist approach
which explicitly analyses the relevant "according to the modal
fiction" operator in terms of modal operators is Divers 1999b.
Among other benefits, Divers argues that this sort of definition
enables one to prove a "modal safety result": that when we
have two modal claims *A* and *B*, and we have the
possible-worlds-analogues of the two modal claims (call them
*A*\* and *B*\* respectively), "Necessarily, if
*B*\* is a consequence of *A*\* then *B* is a
consequence of *A*" (Divers 1999b, p. 330). Such a safety
result would be welcome, for it would provide the guarantee we needed
that "detouring" in our reasoning through claims like
*A*\* and *B*\* would not lead us astray when trying to
determine whether *B* followed from *A*. 



A drawback of timid modal fictionalism is that it leaves the important
issue of a theory of modality to one side. Without some other positive
story, even if it were primitivism about modality, it might seem that
it would be difficult to motivate timid fictionalism over agnosticism
about the status of possible worlds. In this context, the agnostic
option would be to accept that the story of possible worlds is at
least a useful fiction, but for all we know it may be that some theory
that explains possibility in terms of possible worlds is true as well.
Many of the leading candidates for the analysis of modal claims are
those that explain the truth of modal claims in terms of the literal
existence and nature of possible worlds, so without a positive
alternative story, it might seem premature to reject this style of
explanation of modality. However, the project of endorsing
fictionalism about possible worlds and possible objects without
endorsing the further claim that this fiction provides the material to
explain or analyse our modal notions, while in some ways less
philosophically interesting than its strong cousin, is proportionally
less open to serious objections. 


### 1.3 Normative vs. Descriptive



Modal fictionalism can be interpreted as a descriptive theory of what
our talk in fact amounts to, or as a normative proposal for how we
should use talk of possible worlds. (In the terminology of Burgess and
Rosen 1997, this is the distinction between a
"hermeneutic" construal of modal fictionalism and a
"revolutionary" construal of modal fictionalism). If the
theory is that in fact we take possible worlds to be no more than
convenient fictions, and, in the case of strong modal fictionalism,
that facts about the content and nature of the fiction of possible
worlds explain and/or provide the basis of the analysis of our modal
locutions, then the theory is descriptive. This sociological claim
that most philosophers who talk about possible worlds take this talk
to be analogous to talk of e.g., ideal gases is a dubious one: my own
impression is that modal fictionalism is a minority view amongst those
philosophers who work extensively on the philosophy of possible worlds
and its applications, though perhaps fictionalism might be the
majority view when all who have opinions on possible worlds are taken
into account.



In any case, fictionalism about possible worlds might be important
even if the descriptive version is incorrect. A normative claim to the
effect that talk of possible worlds *ought* to be interpreted
as merely fictional discourse, or the corresponding strong
fictionalist claim that modal statements *ought* to be
reinterpreted so as to be explained or analysed as statements about
the content of the fiction of possible worlds, might be found
attractive even if it were conceded that most people who employed the
discourse were not talking fictively, or that the actual commitments
of the folk and most philosophers who employ everyday modal idiom are
to be cashed out in some other way (e.g., as implicit commitment to
some false theory, perhaps one which took modal statements to have
truth conditions in terms of an objective modal reality). 



The two questions, of whether the fictionalist theory is supposed to
describe our current practice, and whether it is supposed to describe
a practice we should adopt instead of realism, are independent. Two
people could agree that normal usage of possible-worlds talk is not
intended literally, but disagree about whether we should accept the
literal existence of possible worlds (that is, they could be
descriptive fictionalists while disagreeing about the normative
question), and likewise two people could be normative fictionalists,
and claim that we should take ordinary possible worlds talk as being
only fictionally true or appropriate, while disagreeing about whether
in fact current usage reflects this fictionalism or instead reveals
non-fictionalist commitments among the users of the vocabulary. (This
independence may be overlooked if we employ Burgess and Rosen's
vocabulary, which suggests that fictionalists face a binary choice of
a "hermeneutic" fictionalist approach or a
"revisionary" approach.) 



Unfortunately, modal fictionalists have often not been explicit about
whether their theory is to be an analysis of the possible-worlds talk
and perhaps modal discourse which is actually employed, or a normative
suggestion about how we might move to a superior theory. It is to be
hoped that those seeking to provide a fully worked out modal
fictionalist position would make more explicit the status of their
proposal. 


### 1.4 Fictionalism about Modality and Modal Fictionalism



So far, it has been taken for granted that the modal fictionalist
treats ordinary modal claims as sometimes literally true, and it is
only claims about possible worlds and their contents which the modal
fictionalist will wish to claim are literally false, but true
according to a story. A more radical modal fictionalism is possible:
one in which modal claims themselves (such as the claim that there
could have been blue swans, or that necessarily, everything is
self-identical) are not literally true, but only true according to a
fiction. (In Nolan 1997a I called a version of modal fictionalism
which took both claims about possible worlds and modal claims to be
true only according to fictions *broad* modal
fictionalism.)



Such extended fictionalism about modality could, I think, come in two
main varieties. One would maintain that modal operators (and
associated pieces of language like essential predication,
counterfactual conditionals, and perhaps other things like assignments
of probabilities) lacked literal application: that all statements
prefixed with a modal operator were either uniformly literally
truthvalueless or uniformly literally false. This faces several
immediate formal difficulties, given the usual characterisation of the
modal
 operators.[4]




A less blanket rejection of modality might only insist on the
falsehood of some modal claims: think of the analogy of a moral
nihilist who rejects only "positive" moral claims, such as
that taking property without permission is wrong, or that it is good
to help the ill, but accepts that it is not wrong to take property
without permission (since nothing is wrong) and that it is not good to
help the ill (since nothing is good). This fictionalist about modality
might reject the literal truth of all claims about necessity, for
example (and, in virtue of the interdefinition, accept the literal
truth of all possibility claims). Or she might assert as little as is
needed to preserve the basic modal inferences from actuality: for
example, every true *P* is possibly true, and actually true,
but this is the limit of literal modal truth. This would be more
analogous to the fictionalist about possible worlds who nevertheless
thinks that there is one possible world -- the actual, and one
collection of possible objects -- the actual objects. 



Fictionalism of this sort extending to modal discourse as well should
be a position worthy of investigation by those attracted to
fictionalist strategies and mistrustful of modality. Since it seems to
lack contemporary advocates, however, it shall not be dwelled upon
 here.[5]



### 1.5 Further Extensions



Modal fictionalism has traditionally been conceived as fictionalism
about possible worlds, and implicitly also about their contents. One
natural way to extend modal fictionalism so understood is to admit
impossible worlds as well. Use of a fiction of impossible worlds is
unlikely to seem too extravagant for many modal fictionalists, but it
might also provide a mechanism for non-fictionalists about possible
worlds to talk of impossible worlds without the extra theoretical
costs they fear. So there is a partially fictionalist option of being
a realist of some stripe about possible worlds but a fictionalist
about impossible worlds (and perhaps other situations, e.g.,
incomplete or underdetermined ones). This partial fictionalism will
face some of the same sorts of questions, and employ the same sorts of
strategies, as modal fictionalism about *possible* worlds.



Another mixed strategy is rarely explicitly endorsed, though it may be
implicit in many theorists' talk. By far the majority of
realists about possible worlds take them to be abstract objects of
some sort: sets of sentences or propositions, uninstantiated
world-properties, unactualised maximal facts, or perhaps even as
sui generis simples. However, their approach to merely possible
objects is often less explicitly spelled out. As well as possible
worlds, merely possible objects such as blue swans, my counterparts,
Newtonian masses, XYZ, and many others are discussed and quantified
over. Some abstractionists will wish to identify such merely possible
objects with actual abstract objects -- perhaps uninstantiated
properties that are less than world-properties, descriptions of parts
of worlds, set-theoretic representatives, or whatever. But many more
will not. This is for at least three reasons. The first is the
intuition, never entirely quelled, that a merely possible blue swan
should be *blue* and a *swan*. Abstract objects are
rarely, if ever, either. The second is that it is often thought that
the whole point about merely possible objects is that they do not
exist, but might have. Admitting their literal existence by
identifying them with actual existing abstract objects will go against
the grain for many. Finally, many theories of possible worlds lack
obvious candidates to play the roles of merely possible objects. This
is most obvious for those theories that take possible worlds to be
simples, but it is also not straightforward to divide a set of
propositions into "object shaped" components, or to
distinguish one merely possible object from its duplicates if one
identifies worlds with world-properties, and furthermore seeks to
divide these up to yield merely possible less-than-world-sized
objects. Fictionalism about merely possible objects is an
underappreciated theory, and should perhaps recommend itself to more
abstractionists about possible worlds than it in fact does.


## 2. Fictionalism in Context


### 2.1 Modal Fictionalism and Fiction



A theory that holds that possible worlds are to be treated as having
the status of fictional objects immediately gives rise to questions
about the status of fictions and fictional objects more generally. The
issue of how to understand the "according to the
fiction..." operator has already been mentioned. Other
issues in the treatment of fiction are the question of whether
"theoretical" fictions are to be seen in the same light as
literary fictions, and the question of what ontological status
fictions possess.



There is room in principle to distinguish claims about
paradigmatically fictional characters (like Sherlock Holmes or
hobbits) from the treatment one wishes to apply to claims which serve
useful theoretical purposes but which are not to be taken literally,
or at least not at face value: to distinguish "fabulous"
and "fictional" entities, to use Bentham's not
entirely perspicuous terminology (Bentham 1959). One might wish to do
this, for example, if one thought that paradigmatic story-telling
consisted of utterances that were not truth-apt (not anyway through
the same mechanism as ordinary utterances), while claims about, say,
ideal gases were better construed as standard sorts of assertions that
were literally false. In practice, however, recent modal fictionalism
discussions have proceeded as if the theory holds that possible worlds
are fictional in the fullest sense of the word.



The ontological status of fictions is an important issue to settle if
we are to determine whether modal fictionalism is any advance
metaphysically on rival realist theories of possible worlds. On pain
of circularity, the ontology of fiction, as conceived by the
fictionalist, had best not include possible worlds (as the ontology of
fiction offered in Lewis 1978 does), but there are other sources of
concern. Rosen points out that fictionalists must believe in fictions,
stories, theories, or somesuch, and that if these are construed as
abstract objects, they will not be philosophically uncontroversial
(Rosen 1990, p. 338). Rosen argues that belief in abstract objects
like stories and theories is less revisionary than belief in Lewisian
possible worlds, at least. However, it is hardly clear that an
ontology of abstract representational entities is any more or less
objectionable than the ontology of abstractionist theories of possible
worlds. (Lycan 1993, p. 16, Nolan 1997a, pp. 271-273).
Alternatively, fictionalists could commit themselves to more concrete,
"nominalistically respectable" fictions only: the relevant
fictions or theories of possible worlds might be conceived of only as
ink-marks on pieces of paper, or information states inside brains, or
perhaps as some amalgam of these and other actual, concrete ontology.
This approach is not problem-free either (see section 4): it is far
from clear that it will serve as a basis for paradigm fictions, let
alone be enough to explain possible worlds.


## 3. Technical Problems



There are a variety of technical objections to modal fictionalism, and
if these objections succeeded they would derail specific proposals
like that of Rosen 1990 and perhaps cause difficulties for modal
fictionalism in general. The most discussed of these objections is the
Brock/Rosen objection, an objection to the theory of Rosen 1990,
published independently in Brock 1993 and Rosen 1993. (In the case of
Rosen 1993, a variety was also leveled at the fictionalism of
Armstrong 1989).


### 3.1 The Brock/Rosen Objection



The reader is advised to consult Brock 1993 and Rosen 1993 for an
exact statement of their objections, but in essence the problem arises
when we consider the modal status of certain claims about possible
worlds themselves. One of the principal fictionalist biconditionals,
as we have seen, is the biconditional connecting necessary truths and
what the fiction asserts about all possible worlds:



> 
> Necessarily *P* iff, according to the modal fiction, at all
> worlds, *P*\*,
> 



where *P*\* is the possible-worlds paraphrase of *P*.
According to the fiction employed by Rosen 1990 (i.e. the theory which
David Lewis offers as fact), there are many co-existing concrete
possible worlds -- each one its own cosmos. Furthermore, this
claim is true at any of these possible worlds. So, according to the
modal fiction, at all worlds it is true that there are many other
possible worlds. However, it follows from the biconditional that
since, according to the modal fiction, at all worlds, there are many
possible worlds, it follows that necessarily, there are many possible
worlds. Since necessarily *P* implies *P*, it follows
that there are (literally!) many possible worlds. But the whole point
of modal fictionalism was to deny (or at least avoid asserting) that
there were many possible worlds. So modal fictionalism, at least of
the variety described, is self-refuting.



So the objection goes. (The version presented above is Brock's
from Brock 1993 -- for some of the detail of Rosen's
argument, see below or Rosen 1993.) Two direct responses have been
offered to this problem in the literature. The first, by Peter Menzies
and Philip Pettit (Menzies and Pettit 1994), conceded that the
objection "is decisive against the letter of the Rosen
proposal" (p. 29), and sought to provide modified fictionalist
biconditionals to produce a modal fictionalist theory which would not
be susceptible to the Brock/Rosen objection. Nolan and
O'Leary-Hawthorne 1996 produced a version of the Brock/Rosen
objection which they believed circumvented the Menzies and Pettit
solution offered in section 3 of Menzies and Pettit's paper.
Section 5 of Menzies and Pettit gave another translation scheme meant
to avoid the Brock/Rosen objection; it is argued in the following
supplementary document that this scheme too is unsatisfactory.



> 
>  [A Persisting Problem For Fictionalism About Possible Worlds]
>  



I shall not dwell on the details of the Menzies/Pettit position, since
the other response to the Brock/Rosen objection has been more
influential: the response of Noonan 1994. Noonan claims that the
Brock/Rosen objection is not even successful against the letter of the
original proposal in Rosen 1990 (Noonan 1994, p. 133). He argues that
careful attention to the procedures actually given by Lewis (Lewis
1968) for paraphrasing modal claims into claims in the language of
possible worlds will show that "according to the fiction of
possible worlds, at any world, there are many worlds" will not
be able to be derived, and so the move to "necessarily, there
are many worlds" cannot be carried through. Thus if
fictionalists stick closely to the possible-worlds
"translations" given in Lewis 1968, they will be able to
avoid the threatened collapse.



The way the Brock/Rosen objection is raised by Rosen begins with an
apparently harmless statement of contingency: (numbering of claims are
Rosen's, and while Brock and Rosen's presentations are
reasonably informal, the formal translations are given by Noonan, and
his numberings for those are provided)



> 
> (2) Necessarily, it is contingent whether kangaroos exist
> 



or to put it in formal modal logic (*Kx* = *x* is a
kangaroo):



> 
> # (*[?]*xKx* & *![?]*xKx*)
> 



From this, Rosen claims, the "standard analysis"
delivers:



> 
> (3) At all worlds, there are worlds where kangaroos exist and worlds
> where they don't.
> 



Ignoring for our purposes the complications which need to be
introduced if we are to add accessibility relations between worlds,
the Lewis 1968 equivalent of (2) is



> 
> (3L) [?]*w*(*Ww*-
> [?]*w*'(*Ww*' &
> [?]*x*(*Ixw*' & *Kx*)) &
> [?]*w*''(*Ww*'' &
> ![?]*x*(*Ixw*'' & *Kx*))))
> 



Noonan points out that this formula does not imply



> 
> (4L) [?]*w*(*Ww*-
> [?]*w*'(*Ww*' &
> *Iw*'*w* &
> [?]*w*''(*Ww*'' &
> *Iw*''*w* &
> !*w*'=*w*'')))
> 



which is the formula required in Lewis 1968 to be able to move back to
"necessarily, there are two worlds", and which is the
formula Brock and Rosen would need to derive if they were to show that
Rosen's (2) (or Brock's equivalent) led the modal
fictionalist to have to say that there are literally several worlds.
The reason why (3L) does not imply (4L) is that it is not enough for
there to be two worlds at a given world (*V*, let us call it)
that there be existential quantification over two worlds within the
scope of an existential quantifier committing us to *V*: the
two worlds must also be "in" *V*, in the sense that
the two place predicate "*I*" must hold between
*V* and each of the worlds. This is what happens in (4L), but
it does not happen in (3L), where there are two existential
quantifiers over worlds in the scope of the outside universal
quantifier, but where the worlds existentially quantified over are not
asserted to be "in" any of the worlds *w*.



Rosen 1995 has accepted Noonan's resolution of the problem
apparently posed by the Brock/Rosen objection. Rosen has thus changed
his preferred proposal, so that instead of a general endorsement of
the position outlined by Lewis 1986, Rosen's recommendation for
modal fictionalists now relies more heavily on Lewis 1968. Instead of
the simpler biconditionals discussed near the beginning of this entry
and in Rosen 1990, the revised proposal is to take equivalences
asserted by Lewis 1968 between modal claims and claims couched in
terms of quantification over possible worlds, and treat those
equivalences instead as specifying connections between modal
statements and claims about what is true according to the fiction. If
a modal claim is literally true, its associated world-claim is true
according to the fiction, and vice versa.



So the state of play seems to be this: while the Brock/Rosen style
objection remains something for a modal fictionalist to be wary of
when constructing the fiction of possible worlds, it is possible to
avoid the objection by being suitably careful about what fictionalist
biconditionals to employ: and if Noonan is right, strict adherence to
the fictionalist modification of the equivalences offered by Lewis
1968 provides one suitable way of being careful. It is not
uncontroversial, of course, that Noonan's strategy is the one a
modal fictionalist should employ: Divers 1999a and 1999b, Kim 2002 and
Divers and Hagen 2006 argue that it is not.



How best to respond to the Brock-Rosen objection continues to be a
matter for debate: both Liggins 2008 and Woodward 2008 offer
alternatives for the modal fictionalist.


### 3.2 Hale's Dilemma



Bob Hale (in Hale 1995b) posed a dilemma for modal fictionalism (more
specifically, Rosen's version of modal fictionalism, though
other varieties face a similar dilemma). A modal fictionalist who
maintains the version outlined in Rosen 1990 believes that the fiction
of possible worlds (PW) is not literally true. A question arises about
the modal status of the fiction: is it necessarily false, or
contingently false? In either case, Hale argues, the modal
fictionalist is in trouble.



Should modal fictionalists claim that the story of possible worlds is
necessarily false, then Hale argues that they cannot gloss their
"according to the fiction of possible worlds ...."
prefix as "were the fiction of possible worlds true, then
... would be true". This is because, according to Hale,
conditional claims with antecedents which are necessarily false are
automatically true, so if the fiction of possible worlds is taken to
be necessarily false, then all conditionals of the form "were
the fiction of possible worlds true then ..." are true, and
not merely the ones that the modal fictionalist wishes to endorse. If
the modal fiction is to be useful, not everything should be true
according to it: examples of claims that had better not be true
according to it include the claim that 2+2=7, or the claim that there
are no possible worlds.



On the other hand, if the fiction of possible worlds (PW) is only
contingently false, Hale claims this also lands the Rosen's
fictionalism in trouble, since if its falsehood is only contingent,
then the fiction might have been literally true (or it is possible
that the fiction be true). But according to Hale the "official
fictionalist paraphrase" of what this possibility would amount
to "cannot adequately capture the content of the claim that
possibly PW is true". (p 65) Hale claims this is so because the
claim "According to PW, there is a possible world at which PW is
true" is equivalent for Rosen's fictionalist to "If
PW were true, there would be a world at which PW is true": and
this conditional is one which would be true whether or not PW was
true.



A modal fictionalist might try to resist either horn of the dilemma.
On the first horn, modal fictionalists might employ another gloss on
what it is to be true according to PW, or they might endorse one of
the various theories of conditionals on which conditionals with
necessarily false antecedents are not automatically true. On the
second horn, even fictionalists who accepted that they were committed
to analysing their claim that PW could have been true as "If PW
were true, there would be a world at which PW is true" could
dispute Hale's claim that this is inadequate (see for example
Divers 1999b, pp. 325-326).



A third option, explored by Rosen 1995, is not to take PW to be false,
but rather altogether lacking a truth-value -- e.g., in virtue of
employing terms with no literal application, such as "...
is a world-mate of...". Hale's dilemma is directed
primarily against fictionalists who take the literal content of their
fiction to be false, and those fictionalists prepared to ascribe some
other status to their fictional claims avoid the dilemma as initially
stated (though this route may encounter difficulties of its own,
especially if it retains some sort of conditional analysis of the
"according to PW" prefix).



Rosen 1995 and Divers 1999b are among the responses to Hale, and Hale
has in turn responded to Rosen 1995 in Hale 1995a, where Hale argues
that several of the responses suggested by Rosen in turn face serious
problems. Skiba 2019 points out some complications that arise from
addressing this challenge in a way that does not compromise a
Divers-style "safety result" of the sort discussed above,
though Skiba argues that modal fictionalists can handle these
complications.


## 4. Other Concerns



In addition to the technical challenges facing modal fictionalism
outlined in the previous section, modal fictionalism has been
challenged on a number of less technical grounds. Not all of these
challenges are equally cogent against every variety of modal
fictionalism, and some explicitly have as their targets only some
versions of the doctrine.


### 4.1 Artificiality



Fictions are human products: they have authors, and those authors have
a good deal of control over what is true according to them (though
exactly how much control is controversial). Alternatively, if it is
thought that fictions are timeless Platonic abstract entities (sets of
propositions, perhaps), we should say that which fictions we consider
and express is a matter of human activity: and the
'authors' of those eternal Platonic fictions actually
expressed have a good deal of control over which of a variety of such
fictions they express. However, "theoretical fictions"
introduced as an alternative to realist theories, and which are
supposed to play a serious role in inquiry, do not seem to be able to
be as arbitrary. Not any old story told about possible worlds will
serve as the modal fiction, at least if it is to provide the heuristic
and other advantages of talk about possible worlds. The suspicion is
that in some respects talk of possible worlds cannot be like paradigm
fiction, since the 'choice' of which story about possible
worlds should count as the modal fiction is not as up to us as what to
say about Sherlock Holmes was up to Conan
 Doyle.[6]




Modal fictionalists can certainly respond to the more general worry
that fictionalism makes it too arbitrary which particular story about
possible worlds ought to be employed. After all, the purposes of the
fiction constrain what sorts of fiction are suitable, just as not any
old story about a gas will serve to provide an "ideal gas"
which has a behaviour approximated by real gases. Some story must be
told about what sorts of constraints are appropriate, and why: and
this can be difficult in its own right (see the "which fiction
should be employed" section, below). Even if there are
substantial constraints on what story will be adequate, and these
constraints are not due merely to facts about us or our choices, there
may still be some scope for the story to be artificial to a small
degree, for some points of detail may be left underdetermined by the
constraints. This may also be considered a problem, but it is unlikely
to be fatal.



There is a more specific worry that remains even if a suitable account
of what constraints there are on the modal fiction can be given. This
is that it is too contingent a matter whether there is a modal fiction
at all. After all, if there had never been any sentient creatures, no
stories would ever have been told, and even if the modal fiction is
construed as a Platonic entity (a collection of propositions,
perhaps), it may never have been a fiction if it was never expressed
by story-tellers. (Of course if nothing hangs on whether or not it is
a fiction, then this will not worry the Platonist modal fictionalist).
This worry, again, is particularly pressing if modal truth is to
depend on the contents of the fiction, since it does not seem that
whether or not blue swans are possible, for example, depends on
whether or not anyone ever told stories. There are responses to this
worry, and responses to these responses: see Nolan 1997a, Kim 2005 or
Dombrovszki 2017.



Sauchelli 2013 is a recent contribution to this debate that points out
another aspect of the problem about artificiality, especially for a
fictionalist who intends an analysis of modal claims in terms of a
fiction of possible worlds. Many people at different times and in
different places have made modal claims: Sauchelli mentions the
example of Caesar considering whether he could cross the Rubicon. Most
people have little or no contact with fictions of possible worlds, or
theories of possible worlds intended to be factual but useable as
fictions. Those people lack *access* to the fictions that are
supposed to underpin the truth of their modal claims. Sauchelli claims
this makes for both an implausible modal epistemology for figures like
Caesar and an implausible account of how people like Caesar can even
*understand* modal claims. 



Woodward 2011 uses "the artificiality objection" to refer
to both the problem discussed in this section and the problem
discussed in section 4.3. That paper contains a response to
*this* artificiality objection on pp. 537-548.


### 4.2 Incompleteness



Fictions are often incomplete: they are silent about some issues. The
Sherlock Holmes stories make no representation one way or the other
about the exact population of India, or whether the number of hairs on
Dr Watson's head is odd or even. Arguably, the modal fiction
will be incomplete too: there will be some propositions such that
neither they nor their negations will be true according to the
fiction. This prospect raises several worries.



First, there is the "incompleteness problem" discussed by
Rosen in Rosen 1990, pp. 341-345. There are some modal issues
(and corresponding issues about the nature of possible worlds) that a
realist may well be silent on: not because they believe there is no
answer, but rather because they believe themselves ignorant of the
answer. A fictionalist who treats the realist's theory as a
fiction, on the other hand, will be silent upon the same issues
-- but this can lead to a more serious problem. If the fiction is
silent on an issue (Rosen's example concerns the size of
worlds), it is not that the issue is unknown -- it is that the
fiction does not represent a fact of the matter one way or the other.
So it might appear for the fictionalist there is not an unknown modal
fact -- either the claim is false because the corresponding
worlds-claim is not true according to the fiction, or something
involving a truth-value gap is going on. Rosen also discusses what
effect this might have on modal claims corresponding to such silences.
A detailed discussion and critique of Rosen on this issue can be found
in the following supplementary document:



> 
>  [Rosen's Incompleteness Worry]
>  



What is uncontentious is that modal fictionalists operating with
fictions which are incomplete in the way, e.g., that the fiction of
Rosen 1990 is, will face difficulties, or at least departures from
orthodoxy which will be found unattractive by some. Woodward 2012
offers an approach that ensures modal claims are indeterminate in
truth value when the fiction of possible worlds is apparently silent
about corresponding questions about possible worlds, through offering
a treatment of the fiction on which it is indeterminate what the
fiction itself represents in these cases. Skiba 2017 criticises both
the approach taken in the note above and the approach Woodward offers,
and suggests one way out for the modal fictionalist is to endorse
apparently contradictory sentences that threaten to follow, but to
treat these *apparent* contradictions as only apparent, since
under analysis the modal sentences that appear to contradict each
other really express compatible propositions about the modal
fiction.



Another "incompleteness" worry in the literature is that
expressed in Nolan 1997a. This is also a worry that the modal fiction
will not represent as much as is desirable, though the concern is not
confined to those areas in which realists might confess ignorance.
(The concern resembles an objection Lewis brings against "sparse
linguistic ersatzism" in Lewis 1986, pp. 142-165.) A modal
fiction, to be adequate, must represent a very great deal about
possible worlds, since there are infinitely many claims about possible
worlds that must be part of the content of the fiction, if there are
to be enough possible-worlds claims to correspond to all the modal
claims we would accept. Only a tiny proportion of the propositions
about possible worlds needed will be able to be stated explicitly by
the modal fictionalist: constraints of time and space and publication
costs will mean that the fictionalist will need to describe the
fictional worlds in only a few volumes, while an exhaustive explicit
description of even a single possible world as complex as our actual
world is beyond our finite resources.



What modal fictions will presumably have, however, are generalisations
about possible worlds: for instance, principles of recombination and
plenitude, principles about what truths are respected by all worlds,
and so on. The modal fictionalist might reasonably hope that these
generalisations *imply* all of the specific claims needed by
the fiction. Implication is, however, a modal notion: not that this is
automatically a problem, but it will be a problem for the
"strong" modal fictionalist, who seeks to reductively
analyse modality in terms of what is true according to the fiction.
The strong modal fictionalist's analysis will be circular if he
has to appeal to something like implication (or related modal notions)
to spell out what claims are represented as true by the fiction, as it
seems he must if the bulk of the claims are to be represented only
implicitly. It seems that a strong modal fictionalist will be stuck
with a radically incomplete fiction, if he relies only on what his
modal fiction explicitly says, or he faces the task of specifying the
implicit content of the modal fiction without recourse to modal
notions like implication.



A strong modal fictionalist could attempt to capture non-explicit
content in ways that did not rely on modal resources: one way this
could be attempted would be to offer a syntactic account (or some
other non-modal account) of some sort of consequence relation, and to
stipulate that the fiction is to be considered closed under the
relation thus specified. However, this is not easy to do in such a way
that all of the necessary semantic consequences are indeed
"consequences" of the explicit generalisations given.
Furthermore, success at this project threatens to undermine the strong
modal fictionalist's project in another way: for if it was
possible to give a specification of a relation of
"consequence" without relying on primitive modal notions,
and that did the work of semantic consequence, then this would offer
an analysis of "broadly logical" consequence (and
presumably related notions, such as logical necessity and possibility)
directly, rather than in terms of what was true according to a modal
fiction, thus making the strong modal fictionalist's analysis of
modality in terms of the fiction redundant. So the strong modal
fictionalist faces a serious challenge in providing a fiction capable
of representing what is needed for his theory to be adequate.


### 4.3 Which Fiction Should Be Employed?



An essential part of an adequate modal fictionalist theory is a
specification of the fiction of possible worlds which is to be
employed. As well as selecting one of the many potential candidate
stories about worlds, it is also essential to provide an explanation
and justification of the choice. This is very rarely done by modal
fictionalists (Armstrong 1989 provides an exception). This is not to
say that it cannot be done, or cannot be done plausibly: but
justifying the choice of fiction is not something that can be
neglected if a modal fictionalist theory is to be convincing.
Christopher Peacocke (Peacocke 1999, p. 154) charges Rosen's
modal fictionalist with "fetishism" unless the
fictionalist can say what is so distinctive about the particular
fiction chosen.



As with so many other challenges, timid modal fictionalism can
immediately provide the outlines of an answer to this question.
(Though it is to be remembered that timid modal fictionalism is able
to avoid so many theoretical difficulties only because the fiction is
not asked to do much theoretical work). If the truths of possibility
and necessity (and conditionality, and other modal truths) obtain
without dependence on the content of the modal fiction, it is surely
reasonable to suppose that whichever fiction it is correct to employ,
it must respect those independently obtaining modal truths. Strong
modal fictionalists must also ensure that the contents of the fiction
are associated with the modal claims they wish to make in the
appropriate way, of course, but this will be of less help to them in
establishing the content of the modal fiction. For if the content of
the modal fiction is to explain the truth of the modal claims, it must
be able to be fixed independently, on pain of circularity. This is
especially so if the strong modal fictionalist holds, as one well
might, that it is our understanding of the modal fiction that provides
(perhaps implicitly) our epistemic access to which modal claims are
true and which false. Giving a non-circular specification of the
content of the modal fiction is one of the very difficult challenges
facing the strong modal fictionalist.



While strong modal fictionalists cannot appeal to an independently
constituted body of modal truths, one thing they can do is insist that
the modal fiction respect our ordinary modal *judgments*: that
is, that by and large if we *accept* a modal claim as true, the
associated claim involving possible worlds will be true according to
the modal fiction. (Rosen 1990, p. 337, speaks of the desideratum that
modal fictionalism "*ratify* a substantial body of prior
modal opinion".) This is presumably not to forbid any departures
from our pre-theoretic modal judgements, should they be required, but
it would provide a way even for the strong fictionalist to rule out
gratuitous departures from our modal opinions.



The next obvious source of content for the modal fiction is the
literal truth about our actual world (Rosen 1990, p. 335). The
addition of all literally true non-modal propositions (in a suitable
sense of "non-modal") to the fiction as part of its
description of the actual world is useful, since it provides a rich
source of content that can be extended by, for instance, a principle
of recombination, to yield claims about non-actual worlds. It would
also seem to be required, for if the fiction fails to be committed to
the actual world verifying a certain non-modal truth *q*, the
inference from *q* to Actually-*q* and back will be
jeopardised. Some particular non-modal truths may prove especially
useful: Armstrong 1989, pp. 138-139 mentions analytic truths,
truths in virtue of the meanings of terms, in this connection. One can
either add the actual-world non-modal content by including an
"encyclopedia" in the fiction, as Rosen does, or one could
allow it in by, for example, stipulating as extra bridge-laws
biconditionals of the form:



> 
> *P* iff According to PW, at the actual world, *P*
> 



for all non-modal propositions *P*.



As well as conformity with our pre-theoretic modal judgements and
inclusion of an encyclopedia of actual non-modal truths, Rosen 1990
mentions another source of information to apply in specifying the
modal fiction. We have practices of forming modal beliefs involving
imagining situations in accord with principles of recombination,
non-arbitrariness, and so on (p. 339-40). Rosen points out that while
a realist has the challenge of explaining why this practice of
imagining should be a guide to modal truth, the fictionalist need not
face this challenge if those practices are part of the process of
constructing the fiction of possible worlds. If the constraints, or
limits, on our imaginative practices when considering hypothetical
situations are vital in our practice of making many of our modal
judgements, it would make sense to similarly constrain the modal
fiction.



There are no doubt many other sorts of constraints which a modal
fictionalist may appeal to in order to narrow down the class of
fictions about possible worlds which are acceptable for her purposes.
Even after all of these constraints are in place, however, there may
still be the theoretical possibility that more than one fiction about
possible worlds (complete or incomplete) satisfies them equally well.
A fictionalist facing a choice between equally deserving fictions
would need to address the issue of what attitude to take to other
modal fictionalists who choose differently. (Should they be judged
incorrect? Correct, because judgements about the content of the modal
fiction are relative to which (acceptable) fiction is adopted? Or
should they be judged to be talking about something else?). Or perhaps
the fictionalist could find some way to avoid making the choice of one
single fiction. Woodward 2011 explores one way to avoid making this
choice: he suggests modifying the fictionalist biconditional to relate
modal claims to a *range* of acceptable fictions, allowing for
some truth-value gaps when the acceptable fictions diverge from each
other.



If the fictions disagreed sufficiently, there may even be fictions
which meet the constraints but which differ on matters which are
linked through the fictionalist's biconditionals with literal
modal claims. (This is only possible if the modal truths themselves
are not being appealed to as constraints on acceptable fictions, so is
not a problem which faces the timid modal fictionalist). If the
constraints are not enough to uniquely determine the truth-value of
every modal claim, then not only the determinacy of the content of the
fiction but the determinacy of the truth-value of some modal claims is
at stake. Are those modal claims true or false, or neither? Might they
be fiction-relative, so there are no-fault disagreements about
them?



This is not the place to attempt to settle the matter of whether
constraints are likely to uniquely determine a modal fiction, nor
whether it would be genuinely objectionable if they did not do so.
Rather, the issues are mentioned as ones to be kept in mind when
formulating or defending a modal fictionalist theory.


### 4.4 The Theoretical Primitives of Modal Fictionalism



Metaphysical theories often rely on resources which are taken as
"primitive": roughly, theoretical resources which are not
to be further explained or analysed. Different theories of the same
subject matter will often take different resources to be primitive,
and while it is a difficult question to decide whether one set of
primitives is better or worse than another, evaluation of the relative
simplicity, naturalness, or other merits of theoretical primitives is
part of the evaluation of rival theories. This sort of comparison can
can be especially relevant in areas where disputes between rival
theories are not to be settled easily by experiment or observation.
Such disputes make up one of the battlegrounds between fictionalists
and their rivals, with anti-fictionalists claiming that the unanalysed
theoretical resources which fictionalists rely on render fictionalist
theories unattractive, or at least relatively unattractive compared to
some rival or other.



The central piece of theoretical machinery the modal fictionalist
employs is the "According to PW ..." operator. When
it is glossed in tempting ways, as "if PW were true, then
..." or "it follows from PW that ...", it
seems to be a modal notion: and if this is not to be further
explained, the modal fictionalist cannot use the fiction of possible
worlds and its contents as the basis of an analysis of modality in
terms of something else. (This sort of analysis is sometimes known as
a *reductive* analysis.) This will only be of concern to some
modal fictionalists, of course -- timid fictionalists will not
have been looking for a reductive analysis of modality based on their
fiction in the first place -- and some timid fictionalists such
as Divers 1999b explicitly endorse modal explanations of the
fictionalist operator (Divers 1999b, p. 335). Such fictionalists may
be happy to take advantage of possible analyses of "according to
the fiction" operators in modal terms, and in so doing provide
an answer to the question of how to understand such expressions: but
on the other hand, their position may not be attractive to someone
primarily concerned to analyse modal operators. (Even timid
fictionalism is compatible with a reductionist account of modality, of
course, since the timid fictionalist may seek to explain modality in
some other terms. It is just that it is not hospitable to reductionist
accounts of modality in terms of possible worlds).



A fictionalist who wishes to provide an analysis of modality, on the
other hand, had better not take their "according to PW
..." operator to be analysed in terms of standard modal
devices, or alternatively in terms of possible worlds (see Rosen 1990,
pp. 344-345). The canonical version of the theory that Rosen
presents takes the "According to PW ..." operator to
be a primitive one: that is, one which is not to be further analysed,
in modal or non-modal terms (Rosen 1995, p. 70). Rosen points out that
one might think that his favoured prefix is a modal locution, and if
so even his position cannot be said to entirely reduce the modal in
favour of the non-modal (Rosen 1990, pp. 344-345). Nevertheless, as he
points out, it may still be thought to be some theoretical advance to
be able to explain all of the other modal notions using only this one.
It is hard to know how the issue of whether or not "according to
PW..." should count as a modal operator is to be decided:
in any case, it will not be further pursued here.



Regardless of its status as a modal locution, Rosen recognizes that it
is a very unsatisfying primitive: the notion of a proposition being
true according to PW is an unlikely one to be considered basic and
unanalysable. Whether or not this is a fatal flaw of Rosen's
proposal is, he acknowledges, "a matter of somewhat delicate
judgement" (Rosen 1990, p. 349). What he does have to say about
it, however, is that arguably many realists about possible worlds have
also not provided a satisfactory analysis of the "according to
the fiction ..." operator, and so face the same
 challenge.[7]




The issue of whether "According to PW..." is a
satisfactory theoretical primitive is presumably partly to be settled
by seeing what rival theories are possible, and what primitives they
need to rely on to account for modality and for fiction. Beyond that,
how to settle disputes about the relative attractiveness of primitives
is a difficult issue in philosophical methodology. Taking such an
apparently complex operator to be unanalysable looks unattractive
(Nolan 1997a, pp. 273-274), but the position is perhaps not
untenable. A better option for the modal fictionalist interested in
analysing modality in terms of the modal fiction might be to attempt a
non-modal explanation of what is true according to fiction. In any
case, this problem, like many problems for modal fictionalism, does
not arise for the timid modal fictionalist. For those fictionalists
for which it is a problem, however, the unattractiveness and
unintuitiveness of taking "According to PW..." or a
similar device to be primitive remain a largely unaddressed
challenge.


### 4.5 Does Modal Fictionalism Deliver Possible Worlds Semantics?



John Divers in Divers 1995 argues that modal fictionalism cannot
deliver the benefits of the standard possible worlds semantics for
modal discourse. There is a discussion of Divers's argument in
the following supplementary document: 



> 
>  [Modal Fictionalism and Possible Worlds Semantics]
>  


### 4.6 Three More Concerns



Modal fictionalism has attracted a range of other objections and
concerns. Some of these can be generalised to other fictionalist
projects; some generalise to other approaches to possible worlds; and
some seem to rely on specific features of modal fictionalist
proposals. Rather than trying to describe each controversy in detail,
I will briefly outline three with some references for those who wish
to track down the relevant
 literature.[8]



**The Threat from Abstractionism:** Fictionalists seem to
need fictions, in the sense of stories or story-like entities. Some
realists about possible worlds treat possible worlds themselves as
representational entities of the same general sort that fictions seem
to be: these theorists are "abstractionists" in the
terminology of van Inwagen 1986, or "ersatzers" in the
terminology of Lewis 1986. Abstractionists may take worlds to be
constructions out of sentences, or perhaps more commonly identify
worlds with maximal propositions or with constructions out of
propositions (e.g. sets of propositions). Once we have representations
that are rich enough to represent every possibility, fictionalists
need to explain why they prefer to be be fictionalists rather than
identifying possible worlds with the appropriate representations.



Abstractionist realism seems more straightforward than fictionalism in
a number of ways, so fictionalists, particularly platonist
fictionalists, risk being victims of their own success and collapsing
into a kind of realism. (Nolan 1997a p 272 mentions this worry.) Rosen
1990, particulary on pp 328-9, mentions some motivations for a
fictionalist to not be an abstractionist. Turp 2011 discusses a
similar challenge: on many accounts of the ontology of fiction,
fictional worlds would themselves be some sort of existing abstract
object, of the sort that a fictionalist who wishes to reject
abstractionism seems committed to rejecting. Finally, Dombrovszki 2017
endorses the existence of the possible worlds postulated by a modal
fiction: in his "hybrid modal fiction" possible worlds are
creatures of fiction but nevertheless exist (much as so-called
"fictional realists" hold that Sherlock Holmes is a
fictional object that exists). If Dombrovszki is right, this is not so
much a threat from abstractionism as an opportunity to be a modal
fictionalist and a realist about possible worlds at the same time.



**Concern About Concern:** Rosen 1990 (pp 349-354)
discusses an "argument for concern" against modal
fictionalism, analogous to an argument from concern famously offered
by Saul Kripke against David Lewis's counterpart theory. (Kripke
1980 p 45) Hubert Humphrey, upon losing an election, cares that he
could have won. On the face of it, he does not care that someone like
him elsewhere in reality does win. Yet according to David
Lewis's analysis of what it is for Humphrey to have possibly
won, his possibly winning amounts to a "counterpart" of
Humphrey winning a (counterpart) election in another possible
world.



Likewise, Humphrey presumably does not care very much whether a
special story about him claims that he wins in an alternative
universe. Rosen, along with many other philosophers, thinks that this
would not directly show there was any problem with a theory that
accounted for the possibility of Humphrey winning in terms of the
goings-on in another concrete universe, or the contents of a
distinctive fiction: Humphrey might care about a fact without
realising what the analysis of that fact involves (Rosen 1990 p 349).
Rosen instead suggests there may be a "pragmatic" cost to
the view: those who come to accept it may have to revise substantially
what they care about, either by caring more about the goings-on of a
story, or less about what could have happened. There is also the
question of why we should care about what happens in any of the
plausible candidate fictions: this perhaps touches on the question of
choosing a fiction discussed in 4.3, above.



Lewis 1986 pp 195-197 argues that a version of the argument from
concern can be at least raised about any realist possible worlds
theory account of possibility: and, he would likely add, any
fictionalist account as well. If Humphrey is unfamiliar with
possible-worlds-jargon, he may not take himself to have any concern
with possible worlds when it hurts that he could have won. Of course,
theorists may wish to offer reasons why some accounts do better in
respecting the facts about what we are concerned with than others. (Or
indeed give general reasons why no argument from concern is a
challenge to theories of possibility.)



**About Aboutness:** Armour-Garb (2015, 1212-1218)
raises a concern for a modal fictionalist seeking an "elliptical
rendering" of modal claims in terms of a claim about what is true
according to a fiction of possible worlds. It is that the modal claims
we begin with are not *about* the same things as the paraphrases in
terms of a fiction of possible worlds. For example, instead of the claim that possibly, there are blue swans, which seems to be about swans and their color, we in effect get a claim about a fiction (we get a claim that means "according to MF, there are blue swans in a possible world"). 


 This is a problem, according to
Armour-Garb, because the point of modal claims involves them being
about the things they normally seem to be about, so the modal
fictionalist's substitute is inadequate. A theorist could, of
course, endorse the fictionalist biconditional without thinking that
modal claims are about a fiction of worlds at all. Rosen 1990 does
talk, in the case of strong modal fictionalism, of an
"analysis" of modal claims in terms of claims about what
is true according to the modal fiction, so modal fictionalists who
want to follow him in this need to be clear about whether they think
this analysis gives the meaning of the modal claims they use. And if
the analysis is intended to give the meaning of modal expressions, they should make clear why
it does not change the subject from what we took ourselves to be
saying all along.