Vagueness and composition, Again

When do some things compose a further thing? Unrestrictivists hold that composition either always occurs or never occurs. Restrictivists deny this, and claim that composition occurs only sometimes. Restrictivism entails that there are cases in which composition occurs, and there are cases in which it does not. But now it seems that we can construct a Sorites series from definite cases of composition to definite non-cases. Somewhere in between, things get messy and we find cases in which it is indeterminate whether composition takes place. So the restrictivist seems committed to holding that composition is potentially vague. This is problematic, as Ted Sider has argued, because the possibility of mereological vagueness entails the seeimginly intolerable possibility of existential vagueness. So restricted composition is intolerable too: composition must either always occur or never occur.

Nikk Effingham has argued that Ted’s argument breaks down once we assume the truth of supersubstantivalism (SS) the thesis that material objects are identical to the regions of spacetimes that they occupy. (This is particularly embrassing for Ted, who defends SS.) But SS isn’t the get-out that restrictivists were hoping for.

Ted’s original argument against restrictivism can be stated as follows:

(1) If restricted composition is true, then it might be vague whether composition takes place in a particular case.
(2) It cannot be vague whether composition takes place
(3) So restricted composition isn’t true

Since (1) is common ground, everything turns on (2). Next, define a numerical sentence as any sentence that says that a given number of concrete objects exist, and note that all such sentences can be expressed solely using logical operators, logical connectives and the predicate “is concrete’. Ted assumes that all of these subsentential expressions are perfectly precise, meaning that all numerical sentences are non-vague. The argument for (2) then runs as follows:

(4) If it could be vague whether composition takes place, it could be vague how many concrete objects existed
(5) If it were vague how many concrete objects existed, it would be vague whether some numerical sentence is true
(6) But it cannot be vague whether some numerical sentence is true

In a nutshell, vagueness in composition generates vagueness in existence, which entails, per impossible, that it might be vague whether some numerical sentence is true.

Nikk argues that the vagueness argument is unsound given SS. Why? Well, SS promotes the following question: which regions are concrete and which are not? In answering this question, we face a trilemma.

The first horn is to hold that no region is concrete. But this is absurd given SS. If no region is concrete, SS entails that no region is a material object, meaning that there aren’t any material objects. And Ted thinks that there are concrete objects, so we can put this option to one side.

The second horn is to hold that all regions are concrete. This isn’t any help to Ted, however. For if all regions were concrete, there would be infinitely many concrete objects (because there are infinitely many regions). But then if it were vague whether composition occurred, it wouldn’t be vague as to how many concrete things there were: there would still be an infinite number of concrete objects. So, if every region is concrete, (4) is false. The vagueness of composition wouldn’t entail that it might be vague whether a numerical sentence is true, and Ted’s argument breaks down.

It looks like the only option for Ted is to grasp the third horn of the trilemma and hold that some regions are concrete and some are not. But it now seems as though we can ape Ted’s argument to establish that it cannot be vague whether a region is concrete. For we can construct a series of cases, from the definitely concrete regions to the definitely abstract regions. But in no continuous series can there be a sharp cut-off point in whether a region is concrete or not. So it cannot be vague whether the region is concrete or not: every region is either definitely concrete or definitely abstract. But as we’ve seen, the latter option is absurd and the former option interferes with Ted’s argument from vagueness.

What options does Ted have? Well, it seems clear that Ted will grasp the second horn of the trilemma. So let’s look more closely at it.

Nikk argued that grasping the second horn of the trilemma was problematic since it forces Ted to reject a key premise of his argument, (4). For even if it were vague whether composition occurred, it wouldn’t be vague as to how many concrete things there were. There would still be an infinite number of concrete objects, because there would still be an infinite number of regions.

The first thing to note is that SS is something of a red herring. The only role that SS plays is to give us (7):

(7) There are an infinite amount of concrete objects

SS entails (7) given that there are an infinite amount of regions. (I’m not sure where that assumption comes from, but I’ll allow it.) But (7) doesn’t require SS — and the truth of (7) is what Nikk relies upon in his argument against Sider.

The second point is that whilst the argument Nikk considers is the one that’s given in Four Dimensionalism Ted has refined that argument in his “Against Vague Existence”. Ted’s later argument doesn’t attempt to establish the impossibility of vague composition. Rather, it’s an attempt to establish the impossibility of vague existence. This isn’t surprising: compositional vagueness entails existential vagueness, meaning that the crux of the issue is precisely whether vague existence is possible. And when we look more closely at the later argument, we see that it works whether or not (7) is true.

Ted argues against vague existence as follows:

(8) If vague existence were possible, it could be vague whether an object exists in a world containing only finitely many objects
(9) If it were vague whether an object exists in a world containing only finitely many objects, it might be vague how many objects exist in that world
(10) It cannot be vague how many objects exist in a world containing only finitely many objects
(11) It cannot be vague whether an object exists

Now, Ted’s mature argument against vague existence will work even if there are an infinite number of concrete objects. Of course, the argument requires that it be possible for there to be a finite number of concrete objects. But that seems a reasonable assumption to make — and I’m fairly confident that Ted would happily endorse it. In turn, the fate of SS is irrelevant for the success of Ted’s argument against vague existence. Even if there are an infinite number of concrete objects, we’d only have a problem if it turned out that there were no worlds containing only finitely many objects. But the truth of SS is strictly neutral on that issue, and nothing Nikk says suggests otherwise.

The restrictivist really only has three options in face of Ted’s argument:

(A) Hold that it is impossible for there to be worlds containing only finitely many objects
(B) Hold that vague existence is only possible in worlds containing infinitely many objects
(C) Hold that it can be vague whether a finite numerical sentence is true.

SS doesn’t have a bearing on any of these options. And so it cannot save restrictivism from the vagueness argument. (FWIW, I think that the restrictivist should pursue the third option, and hold that that it can be indeterminate whether a numerical sentence is true. That’s what I argue in my forthcoming OSM paper.)

Metaphysics and the Representational Fallacy Again

Okay, so I never got round to posting anything about Dyke’s book (see the previous post). As ever, various other commitments got in the way. But I have written my review, and I thought I’d blog about some of the issues I raise in the review.

The problem with contemporary metaphysics, Dyke thinks, is that its practitioners are prone to commit the “representational fallacy”. One commits this fallacy when one moves from premises about the structure of our representations of reality to conclusions about the structure of the non-representational world itself. We are prone to commit this fallacy due to a tendency to place too much emphasis on language when doing ontology.

Our tendency to commit the representational fallacy is, Dyke suggests, a consequence of the assumption that there is a direct link between language and ontology, an assumption which Dyke (p. 7) formulates as follows:

There is a privileged true description of reality, the sentences of which (a) stand in a one-one correspondence with facts in the world, and (b) are structurally isomorphic to the facts with which they correspond.

This is Dyke’s Strong Linguistic Thesis (SLT). As Dyke presents them, proponents of SLT “are committed to there being a privileged true description of reality; that description contains only a subset of all the truths that there are, and that subset of truths is ontologically perspicuous” (p. 71).

Dyke approach to ontology is based upon the rejection of SLT. Her proposal, in essence, is based upon a rejection of the Quinean dictum that “to be is to be the value of a bound variable” (chapter 3). For Dyke, the question with which ontologists should be concerned is not that of whether the Fs are among the values of bound variables but that of whether the Fs are among the truth-makers for true sentences involving quantification over Fs. Truthmaking is here not to be understood as an intensional relation — it is not to be analyzed in terms of modal notions such as counterfactual dependence or supervenience. Rather, truthmaking is here to be understood as a hyperintensional relationship, so that the existence of the Fs may make it true that the Gs exist (and not the other way round), even if it is necessary that the Fs exist iff the Gs exist. It is the truthmaker question which should have pride of place in metaphysics, and we will lose the tendency to commit the representational fallacy once it is given centre stage. Having developed her view, Dyke’s spends the latter parts of her book examining the ramifications that her approach has for (inter alia) the debates over moral naturalism, vagueness, material constitution, the existence of mathematical objects, causation, and the nature of modality.

There is much in Dyke’s approach to metaphysics with which I am sympathetic. The question of what it is in virtue of which true sentences are true should, I think, be a proper focus of metaphysical inquiry. But despite my general sympathies with her approach, I think that Dyke’s handling of the issues problematic in a number of respects.

For one thing, I think that Dyke is wrong to suggest that her truthmaker-first approach to ontology requires us to reject SLT: Dyke can accept that there is a privileged description of reality, some set which contains a subset of all the truths that there are and which is ontologically perspicuous. For instance, even if one accepts that tensed sentences are non-paraphrasable but made true by tenseless facts, it is perfectly consistent to also hold that the privileged true description of reality contains only tenseless sentences. Each tenseless fact, each truthmaker for the tensed truths, will correspond to a particular tenseless sentence and there will therefore be a set $ of these sentences. The sentences that are members of $ might not mean the same as tensed sentences, but they will be tenseless representations of the tenseless facts in virtue of which tensed sentences are true. And so there is no conflict with SLT — the members of $ are a subset of the truths which stand in a one-to-one correspondence with the tenseless facts which make the tensed sentences true, and in this way the members of $ provide an ontologically perspicuous representation of tenseless reality. To put the point otherwise, Dyke needn’t be a thorough-going anti-Quinean about ontological commitment. If we have a language L whose quantifiers ranged over all and only the fundamental entities — the basic entities which make everything else true — then there is no reason why Dyke should deny that to be is to be in the range of L’s variables.

A second problem relates to way in which Dyke proposes to understand the relationship between truthmaking and ontological commitment. For if we agree with Dyke that the ontological question is the question of what makes things true, a natural question arises regarding ontological commitment. If the existence of lumps of clay makes it true that there are statues, as Dyke (chapter 7) suggests, we want to know whether this is an account on which we are ontologically committed to both states and lumps of clay, or whether this is an account on which we are only ontologically committed to lumps of clay. So does Dyke think that the ontological commitments of a theory are its truthmaking commitments, or does she think that the ontological commitments of a theory are to both its truthmaking entities and its truthmade entities? As far as I understand the following passage, Dyke endorse the latter construal in the case of statues:

It is possible to be a realist about statues, that is, to think that statues exist as a part of extralinguistic reality, and that their existence is independent of our ability to describe them, but they do not exist “over an above,” or as entities in addition to, the lumps of clay out of which they are constituted (p.147)

But at other times Dyke seems to suggest that the ontological commitments of a theory are only its truthmaking commitments. For instance, in applying her view to the case of mathematical objects, Dyke characterizes her view as one which “claims that mathematical statements can be true and yet not be committed to the existence of mathematical entities” (p.163) because the question of whether mathematical objects exist “is not to be answered by examining mathematical sentences” but by examining their truthmakers (p.165). But if the question of whether mathematical objects exists is to be answered by looking for the truthmakers for mathematical statements, then the question of whether statues exist is to be answered by looking for the truthmakers for statue statements. In the latter case, Dyke concedes that statues exist even though statue claims are made true by lumps of clay, whereby it becomes unclear whether Dyke is defending a form of realism, or a form of anti-realism.

Metaphysics and the Representational Fallacy

I’ve been asked to review Heather Dyke’s recent book Metaphysics and the Representational Fallacy (Routledge, 2007).

Dyke’s book is a critique of the methodology of contemporary metaphysics. The basic line is that contemporary metaphysicians are prone to draw conclusions about the structure of the non-representational world from premises about the structure of our representations (whether mental or linguistic) of the world. But this inference, according to Dyke, is fallacious – to pursue metaphysics this way is to commit “the representational fallacy”. Dyke’s project is then to develop a new strategy for doing metaphysics which avoids the representational fallacy.

Over the next couple of months, I’ll be posting my thoughts on each chapter. More soon…

Kaplan and Necessitation

I just came across a weird comment that Kaplan makes in his seminal paper ‘Demonstratives’ that I thought I’d highlight.

It’s familar that Kaplan’s ‘logic of demonstratives’ – his system LD – gives rise to failures of the rule of necessitation, which we can understand as saying that one may infer that “Necessarily, p” is L-valid if one has established that “p” is L-valid. This rule is at the heart of standard modal logics, holding even in very weak systems like K. But Kaplan thinks it fails for LD: we may not infer that “Necessarily p” is LD-valid if one has established that “p” is LD-valid. The standard examples are things like “I exist” and “I am here now”. Both of these sentences are LD-valid. But Kaplan tells us that their necessitations – “Necessarily, I exist” and “Necessarily, I am here now” are false, so we have breakdowns of necessitation.

The weird bit is that Kaplan then says that the counterexamples to necessitation are not limited to cases involving “pure indexicals” like ‘I’, ‘here’ and ‘now’; we can construct counterexamples in the “indexical-free” fragment of the language. The example he gives is “something exists”. This is LD-valid, but its necessitation – “necessarily, something exists” – is false. Or so Kaplan claims, anyway. What’s funny about this case is that “something exists” remains valid when we allow Kaplanian character to vary across models. (“something exists” is not only valid in the logic of demonstratives, it’s valid in classical logic.) Admittedly, this is one of the odd consequences of standard classical logic, but it’s interesting because Kaplan’s rejection of necessitation seems to be more full-blooded than it might initially seem.

The reason I mention this is because one of the things I’ve been playing around with is the idea that the following rule – call it “restricted necessitation” – holds in Kaplan’s system:

From ‘”S” is CL-valid’, infer that “box-S” is LD-valid

Where CL-valid is defined in terms of what’s true in all classical models. If we take Kaplan at his word, then he doesn’t even want this inference rule (since “something exists” is CL-valid, but not, Kaplan thinks, LD-valid).

There is of course stuff about empty domains to be take into account here. As Robbie pointed out to me, there is an obvious rationale for Kaplan to ban the empty domain in the context of LD since every context has an agent (speaker, writer, what-have-you), and every model has a designated context, and every element of the context has to be a member of the domain. So perhaps the way to get the right results is to allow empty domains in the case of logical consequence, but ban them when we come to a priori (LD) consequence.

Possible World Semantics: What is it good for?

Recently, I’ve been thinking about some issues regarding actualist accounts of possible worlds semantics. Kripkean semantics, at least construed as an applied semantics, poses a number of problems for the actualist realist, since it seems to entail the existence of merely possible individuals. Plantinga offered a solution to this problem: think of the members of “the set of all possible individuals” are individual essences, rather than individuals. We then say things like: “Possibly There is an F” is true at w iff there is some w-accessible world v such that at v, there is an essence that is coexemplified with Fness” and “Necessarily, something is G” is true at w iff every w-accessible world v is such that at v, some essence is coexemplified with Gness”. If we set things up right, we can then invalidate various nasty principles, like the Barcan Formula and its converse.

Question: what on earth has this got to do with English sentences like “there could have been talking donkeys”?

Now, part of the folklore conception of model-theoretic semantics is that the model-theory ranges over a class of interpretations of a language, amongst which we hope to find the “intended” interpretation: the one that “gets the interpretation right”. The role of the model-theory, on this conception, is to provide a constitutive account of both logical consequence (truth-preservation under every interpretation) and truth simpliciter (true on the intended interpretation). If you were thinking of Plantinga’s semantics in this way, I guess I can see what’s odd about it – on the intended interpretation of our language, I’d be quantifying my essence rather myself if I said “I exist”). But I’m also coming to think that the folklore conception is questionable.

One philosopher who explicitly rejects it is Hartry Field. In his recent work on the semantic paradoxes, Field offers a “paracomplete” solution to the paradoxes which secures the full-intersubsitutivity of “True (<A>)” and “A” (in extensional contexts) at the expense of rejecting certain instances of excluded middle. Field’s model-theoretic semantic theory is based upon Kripke’s fixed-point construction and Field explicitly denies that the value of this construction can be found in its provision of a constitutive account of either logical consequence or truth. It’s value, Field contends, is to be found in its provision of an extensionally correct characterization of logical consequence. In other words, the construction provides an answers the question “what follows from what?” and can thereby be used by classical logicians to figure out what inferences can be made in Field’s non-classical account.

If Plantinga’s model-theory is understood as serving a similar role to the role that Field’s model-theory plays, then worries about how Plantinga’s semantics connects up to our ordinary modal talk appear a bit misguided. For such worries assume that Plantinga is deploying his semantics in order to provide a constitutive account of the content of our ordinary modal talk and though many possible worlds theorists might intend their Kripkean semantic theories to provide just that, there is an alternative, Fieldian, understanding of the job that Kripkean semantics does. On this understanding, the semantics is there to answer questions like “does ∀x◇Fx follow from ◇∀xFx?” and “does ◇∀xGx follow from ◇◇∀xGx?” and the value of the semantics is that it provides extensionally correct answers to these questions. Of course, it is a legitimate to demand that Plantinga’s model-theory must deploy only those ontological and conceptual resources that are acceptable by his own lights. But in this regard, it seems to me that Plantinga’s theory is a complete success.

So I’m now thinking that worries about the relationship between Plantinga’s semantics and ordinary English have to be handled pretty carefully. I can see problems if we make certain assumptions about what the semantics is supposed to give us. But if we have a more minimal account of the core role that the model-theory plays, as Field does, then lots of worries appear misconcieved.

FWIW, I’m also thinking that the literature on modal semantics is often totally unclear about what Kripke semantics is supposed to do for us. It seems to me that the “it’s just heuristic” stuff you often here makes alot of sense if you read it as distancing somebody from the folklore conception of model-theoretic semantics sketch earlier.

Poems and Possibilia

I couldn’t resist this post. Apparently, the following poem used to be up on David Lewis’ office door.

Things That Might Have Been by Jorge Luis Borges

I think about things that might have been and never were.
The treatise on Saxon myths that Bede omitted to write.
The inconceivable work that Dante may have glimpsed
As soon as he corrected the Comedy’s final verse.
History without two afternoons: that of the hemlock, that of the cross.
History without Helen’s face.
Man without the eyes that have granted us the moon.
Over three Gettysburg days, the victory of the South.
The love we never shared.
The vast empire the Vikings declined to found.
The globe without the wheel, or without the rose.
John Donne’s judgment of Shakespeare.
The Unicorn’s other horn.
The fabled Irish bird which alights in two places at once.
The child I never had.

from The History of the Night (1977)

Update

I’m delighted to say that I’ve been offered, and have accepted, a postdoctoral research fellowship at the University of Leeds, affiliated to the Centre for Metaphysics and Mind. The group of researchers at the Centre is terrific and I’m really happy that I’ve got the opportunity to continue to be part of it.

Frege, Geach and Modal Expressivism

Another talk that I went to in Geneva was Amie Thomasson’s, which was about modal expressivism. I was really glad I got to hear it, since I’d missed it when she gave it in Leeds earlier this year because, ironically enough, I was over in Geneva giving a couple of papers. Needless to say, Amie’s talk was really good. I wasn’t totally convinced, since her account was obviously inspired by Brandom’s recent work (which I haven’t got round to reading yet) whereas my expressivist sympathies are more rooted in Crispin Wright’s work on the area (e.g. in Wittgenstein on the Foundations of Mathematics and ‘Inventing Logical Necessity’). Anyways, here is something about modal expressivism I’ve been mulling over for a while which, with a hat-tip to Amie, I thought I’d give an airing.

Suppose that you are being tempted towards being an expressivist about moral talk. Roughly, you are tempted to accept the negative thesis that moral claims do not function to express beliefs or to state facts (in any substantial sense of ‘belief’ or ‘facts’). Accepting this negative thesis saddles you with an explanatory challenge. You need to say what moral claims do do if they don’t express beliefs or state facts. In order to meet this explanatory challenge, you probably accept a positive thesis according to which moral claims function to express attitudes of approval or disapproval towards particular kinds of action. So when you say “murder is wrong”, you’re expressing a certain kind of negative attitude towards murderous actions. (You might think that you are expressing desires or issuing commands, or something else. Put those differences to one side for now.)

The following objection is familar: even if you have a decent story about what simple moral claims do, you’re going to run into trouble when those claims are embedded in various contexts. This is the Frege-Geach problem. In various presentations of the problem, focus is often upon modus ponens arguments, such as

(1) If getting Elizabeth to murder is wrong, getting Ross to murder is wrong.
(2) Getting Elizabeth to murder is wrong
Therefore (3) Getting Ross to murder is wrong

Even you, qua expressivist, have a good story about (2), the challenge is to say what’s going on when (2) figures in conditional contexts, as it does in (1).

FIRST “OBSERVATION”: The focus on conditionals looks misleading. Classically, (1) is equivalent to a negated conjunction. But there is no obvious problem with conjunction for the non-cognitivist (it’ll just be expressing both attitudes). So the problem is about negation. This is unsurprising, I guess, since a negated context is the simplest embedded context.

SECOND “OBSERVATION”: If conjunction is okay for the expressivist, then the expressivist will be in a good position if she can give us an account of negation. For, as is familiar, once you have negation and conjunction, you can define other constructions, such as disjunction, out of them.

These observations, I think, have conseqences for the Frege-Geach problem for modal expressivism. On this account, modal claims don’t function to express modal beliefs or to state modal facts. They do something else. Perhaps, for instance, they function to express ones acceptance of policies. On this idea, claiming “necessarily p” expresses ones acceptance of a policy of never giving up believing that p and claiming “possibly p” expresses ones rejection of policies whereby not-p is sacrosant.

Now, consider the following claim:

(4) not-possibly P

Remember the first observation: the Frege-Geach problem was about negation. But, familarly, the modal operators are duals, meaning that (4) is equivalent to (5):

(5) necessarily not-p

Notice what we’ve done: we’ve gone from a claim where a modal operator is embedded in a negated context, and moved to a claim where the modal operator is “out front”. So, negation is alot easier if you are a modal expressivist – at least in some contexts, you can simply move from an embedded context to a non-embedded context. And once you’ve done that, you can simply give your expressivist story about possibility claims.

THIRD “OBSERVATION”: Even if the previous points stand, the modal expressivist isn’t home and dry. For not all embedded contexts are as simple as the one outlined above. For instance, we can’t do the same trick when we have claims like (6):

(6): It is not the case that (not-p and necessarily p)

What this suggests is that there was something wrong with the initial two “observations”. Even if you have an expressivistically acceptable account of conjunction and negation, you are not home and dry. Why? Because we’ll be able to come up with a context where those connectives are embedded in more complicated ways and it won’t be obvious how to extend our previous account of negation and conjunction to those cases. I’m tempted to say that there is some sort of compositionality worry lurked around here, but I’m not sure. What seems clear is that the difficulties for the expressivist increase as we increase the syntactic complexity of the claims we’re considering. That’s interesting, I think.

Fundamentality and Ontological Commitment

I just got back from the Eidos Metaphysics conference in Geneva. It was really good fun and a great opportunity to catch up with people. One talk I went to was Robert Schwartzkopff’s, which was about the kind of metaphysical picture that is popular at Leeds. I just thought I’d write a little something about some issues that arose.

Following Kit Fine and others, we might be tempted to draw a distinction between what exists and what fundamentally exists (or really exists, or metaphysically exists, or whatever). Despite initial reticence, I’m quite attracted to this view (if you hang around in Leeds long enough, you end up being sympathetic to lots of funny views like this).

Question: what should we, qua fundamentalists, say about ontological commitment?

One view, which Ross Cameron has suggested, is that the friend of fundamentality should reject the normal Quinean criterion in favour of something else. Why? Well, I guess the idea is that the Quinean criterion will have us being ontologically committed to non-fundamental things (tables, say), because we’re committed to saying that “there are tables” expresses a truth. But fundamentalists, at least as they are often conceived, are tough desert dwellers who don’t want non-fundamental things like tables, and sums, and numbers in their ontologies. Rather, they just want the fundamental things. So, the Quinean criterion gives the wrong results and we better put something else in its place (perhaps something in terms of requirements or perhaps something in terms of truthmaking or perhaps something else). Then hopefully, we’ll be able to say that “there are tables” expresses a truth without being ontologically committed to tables and without the need to mess out with paraphrase or assertoric force or anything like that. On this view, the ontological question is “what fundamentally exists?” and the ontological project is to answer this question and not Quine’s question “what exists?”.

One thing that isn’t immediately clear, however, is that this is what the fundamentalist has to say. Here is how I tend to look at the matter at the moment. Quine asked the right question when he asked “what exists?”. And let’s spot Quine that his criterion for ontological commitment was broadly right. On this view, fundamentalists are ontologically committed both to fundamental things and to non-fundamental things. But this isn’t to say that the distinction between the fundamental and the non-fundamental doesn’t play an important role.

Suppose we have two theories, T1 and T2. T1 and T2 have exactly the same ontological commitments by Quinean standards. But T1 says that many more things are fundamental than T2 does. Both Ross and I will agree that T2 is the better theory. Ross will say that this is because T2 has less ontological commitments than T2 and that this, ceteris parabis, gives us reason to prefer T2 to T1. I can’t say that, because I’m buying the Quinean criterion, but I will say that T2 is simpler in terms of its fundamental ontology and that this, ceteris paribus, gives us reason to prefer T2 over T1. So, for both Ross and I, the distinction between the fundamental and the non-fundamental plays an important role when it comes to theory choice.

At this point, you might think that the difference between Ross’s view and mine is purely terminological. I’m identifying the ontological commitments of a theory with the entities which that theory says exists either fundamentally or derivatively. Ross is identifying the ontological commitments of a theory with the entities which that theory says exists fundamentally. But since we’re both agreeing that on the role that the distinction plays in terms of theory choice, we’re just differing over how to use the word ‘ontological commitment’.

To be honest, I wouldn’t care too much if this was the case. And I don’t think Ross would either. Now I’m going to finally get round to reading Ross’s latest paper on this topic, “Quantification, Naturalness and Ontology”, which is available from his webpage.

Fictionalism & Fetishism

According to the version of modal fictionalism developed by Gideon Rosen, we should regard talk of possible worlds and the like as “an innocent façon de parler, involving no commitment to worlds of any sort”. The fictionalist’s interpretation of modal talk can be stated as follows:

(F) A iff According to Genuine Realism, A*

(Where ‘A’ is any sentence, ‘A*’ is its translation into the language of counterpart theory and ‘Genuine Realism‘ names a fiction based broadly on Lewis’s version of realism.

A common objection to modal fictionalism is that the account is, in some sense or other, hopelessly artificial. This isn’t really a single objection, but a cluster of related worries. In Being Known, Christopher Peacocke raises one version of the worry:

“The charge of fetishism lodged against the modal fictionalist is that there is no saying what is so special about the theory of possible worlds that is mentioned in the schema asserted by the modal fictionalist. Since the fictionalist does not take [Genuine Realism] to be true, why should we be peculiarly interested in what follows from it, rather than some other theory?”

The charge is that the fictionalist has an unreasonable fetish in the sense that she has no good reason to choose Genuine Realism as her fiction, as opposed to choosing a different fiction.

Of course, there are various constraints that the fictionalist can appeal to in order to provide non-arbitrary reasons as to why certain fictions are inadequate. For instance, the fictionalist does not think – assuming that she does not buy into paraconsistent logic – that an inconsistent fiction of possible worlds should be used. Rather, the challenge for the fictionalist is to provide some non-arbitrary reason for holding that Genuine Realism has some sort of authority that the other fictions lack.

Rosen suggests that Genuine Realism might gain its authority in virtue of “being an explicit formulation of our own imaginative habits”. His thought appears to be that if the fictionalist can establish that Genuine Realism is the best way to systematise our imaginative habits, then the fictionalist will have established that Genuine Realism important advantage over its rivals, which the fictionalist can exploit in order to give it its authority. As Rosen notes, this strategy would seem to make fictionalism a conceptualist account of modality, whereby the source of modal distinctions in us, in our capacity to imagine or conceive alternatives to the actual state of things. And though Rosen admits that conceptualist accounts have their problems, he states that his intention is merely to offer a “potentially fruitful” approach for the fictionalist to take in response to the charge of fetishism. However, it seems to me that the real motivation behind this kind of strategy is largely independent from any kind of conceptualist theory of modality. For our prior modal opinions are formed largely on the basis of our imaginative capacities so, rather than framing the point in terms of our imaginative habits, a less loaded suggestion might be that Genuine Realism gains its authority from being the fiction that is the most conservative over our prior modal opinions. In this setting, Rosen’s suggestion is that the fictionalist can argue that Genuine Realism is the authoritative fiction on the grounds that her interpretation of modal talk, based as it is on Genuine Realism, is extensionally accurate. And there is something to this suggestion. For let No Blue Swans be a fiction such that, according to it, there is no world containing a blue swan. An interpretation of modal talk in terms of the content of No Blue Swans would therefore be inaccurate by the fictionalist’s lights. And it seems plausible that the inaccuracy of this interpretation provides a good reason to prefer Genuine Realism to this rival fiction. By extension, the fictionalist has good reason to prefer Genuine Realism to No Talking Donkeys, No Flaming Zombies and other such fictions.

However, even if the strategy provides the fictionalist with good reason to prefer Genuine Realism to No Blue Swans and the like, the fictionalist has not yet given us any reason to prefer Genuine Realism over any other fiction. But suppose that there is a fiction of possible worlds such that an interpretation of modal talk in terms of that fiction is extensionally equivalent to the fictionalist’s interpretation in terms of Genuine Realism. If any such fiction exists, then the fictionalist cannot appeal to prior modal opinion – or to our imaginative habits – in order to give us reason to think that Genuine Realism has authority.

This shows that the fictionalist probably cannot appeal to considerations of extensional accuracy in order to justify her use of Genuine Realism over rival, extensionally equivalent fictions. For instance, there may be no reason to prefer a fiction based on Lewis’s own theory to a fiction based on Kris McDaniel’s version of Lewisian realism. The worst case scenario: there are a range of fictions, including, but not exhausted by, Genuine Realism such that there are no criteria available to the fictionalist which can be used to justify using Genuine Realism over the other fictions in the range. In this setting, the charge of fetishism seems to stick and the fictionalist’s account certainly looks artificial.

Is this game over? I don’t think so. For the crucial question is whether the fictionalist should be worried by this result. Certainly, one might think that some departure from the letter of Rosen’s fictionalism is required, but the spirit of the account can be retained. For the fictionalist might move from her original schema (F) to the following schema (F!):

(F!) A iff According to every fiction in the range, A*

The proposed schema is, in a sense, supervaluationist formulation of modal fictionalism. Rather that singling out a single fiction in the way that Rosen singles out Genuine Realism, the supervaluational fictionalist picks out a range of fictions and formulates her account in terms of what is true according to every fiction in that range. One can even see Rosen’s view as a limiting case where Genuine Realism exhausts the range of fictions. But even if it doesn’t, the charge of fetishism is avoided. The supervaluational fictionalist grants to Peacocke that there is no saying what is special about Genuine Realism in the sense that she grants that there is no saying why this fiction is more special than the other fictions in the range. As we have seen, however, the fictionalist does have principled reasons for thinking that there is something special about each fiction in the range. For example, each fiction in the range will be extensionally accurate and each will be an equally good formulation of our imaginative habits. But the supervaluational fictionalist realizes that it would be arbitrary to give any one theory in the range a special status and so refuses to do so. She avoids fetishizing any one fiction in the range by giving equal weight to each.
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