Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

Region R Question: How many objects — entities, things — are contained in R? Ignore the empty space. Our question might better be put, 'How many material objects does R contain?' Let's stipulate that A, B and C are metaphysical atoms: absolutely simple entities with no parts whatsoever besides themselves. So you don't have to worry about counting a particle's top half and bottom half as different objects. Perhaps they are 'point-particles', with no length, width or breadth. Perhaps they are (...) extended in space without possessing spatial parts (if that is possible). Never mind. We stipulate that A, B and C are perfectly simple. We also stipulate that they are connected as follows. A and B are stuck together in such a way that when a force is applied to one of them, they move together 'as a unit'. Moreover, the two of them together exhibit behavior that neither would exhibit on its own — Perhaps they emit a certain sound, or glow in the dark — whereas C is.. (shrink)

_Possible Worlds_ presents the first up-to-date and comprehensive examination of one of the most important topics in metaphysics. John Divers considers the prevalent philosophical positions, including realism, antirealism and the work of important writers on possible worlds such as David Lewis, evaluating them in detail.

Most scientific models are not physical objects, and this raises important questions. What sort of entity are models, what is truth in a model, and how do we learn about models? In this paper I argue that models share important aspects in common with literary fiction, and that therefore theories of fiction can be brought to bear on these questions. In particular, I argue that the pretence theory as developed by Walton (1990, Mimesis as make-believe: on the foundations of the (...) representational arts. Harvard University Press, Cambridge/MA) has the resources to answer these questions. I introduce this account, outline the answers that it offers, and develop a general picture of scientific modelling based on it. (shrink)

In this paper I attempt two things. First, I argue that one can coherently imagine different communities using languages structurally similar to English, but in which the meanings of the quantifiers vary, so that the answers to ontological questions, such as ‘Under what circumstances do some things compose something?’, are different. Second, I argue that nevertheless, one can make sense of the idea that of the various possible assignments of meanings to the quantifiers, one is especially fundamental, so that there (...) is still room for genuine debate as regards the answers to ontological questions construed in the fundamental way. My attempt to explain what is distinctive about the fundamental senses of the quantifiers involves a generalisation of the idea that claims of existence are never analytic.<br>. (shrink)

While many are impressed with the utility of possible worlds in linguistics and philosophy, few can accept the modal realism of David Lewis, who regards possible worlds as sui generis entities of a kind with the concrete world we inhabit.1 Not all uses of possible worlds require exotic ontology. Consider, for instance, the use of Kripke models to establish formal results in modal logic. These models contain sets often regarded for heuristic reasons as sets of “possible worlds”. But the “worlds” (...) in these sets can be anything at all; they can be numbers, or people, or sh. The set of worlds, together with the accessibility relation and the rest of the model, is used as a purely formal structure.2 One can even go beyond establishing results about formal systems and apply Kripke models to English, as Charles Chihara has recently argued.3 Chihara shows, for instance, how to use Kripke models (plus primitive modal notions) to give an account of validity for English modal sentences. In other cases worlds are not really needed at all. It is often vivid to give a counterexample thus: “There is a possible world in which P. Since your theory implies that in all worlds, not-P, your theory is wrong.” But the counterexample could just as easily be given using modal operators: “Possibly, P. Since your theory implies that it is necessary that not-P, your theory is wrong.”. (shrink)

Fictionalist approaches to ontology have been an accepted part of philosophical methodology for some time now. On a fictionalist view, engaging in discourse that involves apparent reference to a realm of problematic entities is best viewed as engaging in a pretense. Although in reality, the problematic entities do not exist, according to the pretense we engage in when using the discourse, they do exist. In the vocabulary of Burgess and Rosen (1997, p. 6), a nominalist construal of a given discourse (...) is revolutionary just in case it involves a “reconstruction or revision” of the original discourse. Revolutionary approaches are therefore prescriptive. In contrast, a nominalist construal of a given discourse is hermeneutic just in case it is a nominalist construal of a discourse that is put forth as a hypothesis about how the discourse is in fact used; that is, hermeneutic approaches are descriptive. I will adopt Burgess and Rosen’s terminology to describe the two different spirits in which a fictionalist hypothesis in ontology might be advanced. Revolutionary fictionalism would involve admitting that while the problematic discourse does in fact involve literal reference to nonexistent entities, we ought to use the discourse in such a way that the reference is simply within the pretense. The hermeneutic fictionalist, in contrast, reads fictionalism into our actual use of the problematic discourse. According to her, normal use of the problematic discourse involves a pretense. According to the pretense, and only according to the pretense, there exist the objects to which the discourse would commit its users, were no pretense involved. My purpose in this paper is to argue that hermeneutic fictionalism is not a viable strategy in ontology. My argument proceeds in two steps. First, I discuss in detail several problematic consequences of any interesting application of hermeneutic fictionalism. Of course, if there is good evidence that hermeneutic fictionalism is correct in some cases, then some of these drastic consequences would have to be accepted.. (shrink)

This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)

In this book, Bradley Armour-Garb and James A. Woodbridge distinguish various species of fictionalism, locating and defending their own version of philosophical fictionalism. Addressing semantic and philosophical puzzles that arise from ordinary language, they consider such issues as the problem of non-being, plural identity claims, mental-attitude ascriptions, meaning attributions, and truth-talk. They consider 'deflationism about truth', explaining why deflationists should be fictionalists, and show how their philosophical fictionalist account of truth-talk underwrites a dissolution of the Liar Paradox and its kin. (...) They further explore the semantic notions of reference and predicate-satisfaction, showing how philosophical fictionalism can also resolve puzzles that these notions appear to present. Their critical examination of fictionalist approaches in philosophy, together with the development and application of their own brand of philosophical fictionalism, will be of great interest to scholars and upper-level students of philosophy of language, metaphysics, philosophical logic, philosophy of mind, epistemology, and linguistics. (shrink)

This chapter contains sections titled: 1 A Question about Composition 2 Some Answers 3 How Shall We Decide? 4 Common Sense and Unrestricted Composition 5 Common Sense and Compositional Nihilism 6 Compositional Nihilism and the Self 7 The Appeal to Science 8 Problem or Pseudoproblem? What To Do?

Van Fraassen defines constructive empiricism as the view that science aims to produce empirically adequate theories. But this account has been misunderstood. Constructive empiricism in not, as it seems, a description of the intentional features of scientific practice, nor is it a normative prescription for their revision. It is rather a fiction about the practice of science that van Fraassen displays in the interests of a broader empiricism. The paper concludes with a series of arguments designed to show that constructive (...) empiricism so understood is self-undermining. (shrink)

It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' principle of compossibility (...) can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted. (shrink)

Despite protestations to the contrary, philosophers have always been renowned for espousing theories that do violence to common-sense opinion. In the last twenty years or so there has been a growing number of philosophers keen to follow in this tradition. According to these philosophers, if a story of pure fic-tion tells us that an individual exists, then there really is such an individual. According to these realists about fictional characters, ‘Scarlett O’Hara,’ ‘Char-lie Brown,’ ‘Batman,’ ‘Superman,’ ‘Tweedledum’ and ‘Tweedledee’ are not (...) denotationless terms, but names that really refer. What is truly surprising about this situation is that almost no one has inveighed against this unfortunate real-ist tendency. My aim here will be to challenge this new orthodoxy, and to defend an anti-realist position against the arguments proffered by the realist. (shrink)

The principle of modal ubiquity - that every truth is necessary or contingent - and the validity of possibility introduction, are principles that any modal theory suffers for failing to accommodate. Advanced modal claims are modal claims about entities other than spatiotemporally unified individuals (perhaps, then, spatiotemporally disunified individuals, sets, numbers, properties, propositions and events). I show that genuine modal realism, as it has thus far been explicitly developed, and in so far as it deals with advanced modal claims, cannot (...) accommodate the principles in question. On behalf of the genuine modal realist I motivate and propose a redundancy interpretation of advanced possibility claims and extend that interpretation to the cognate cases of necessity, impossibility and contingency. I then show that the problematic principles as they apply to advanced modal claims can be derived from these interpretations. I show further how the proposed interpretation enables the genuine modal realist to deal with a number of objections that centre on the alleged inadequacy of the genuine modal realist's expressive resources. I conclude that genuine modal realism emerges the stronger for having been shown capable of dealing with advanced modal claims on the basis of no conceptual and ontological resources beyond those it requires to deal with ordinary modal claims. (shrink)

Fictionalism about possible worlds is the view that talk about worlds in the analysis of modality is to be construed as ontologically innocent discourse about the content of a fiction. Versions of the view have been defended by D M Armstrong (in "A Combinatorial Theory of Possibility") and by myself (in "Modal Fictionalism', "Mind" 99, July 1990). The present note argues that fictionalist accounts of modality (both Armstrong's version and my own) fail to serve the fictionalists ontological purposes because they (...) imply that as a matter of necessity there exist many worlds. (shrink)

Fictionalists maintain that possible worlds, numbers or composite objects exist only according to theories which are useful but false. Hale, Divers and Woodward have provided arguments which threaten to show that fictionalists must be prepared to regard the theories in question as contingently, rather than necessarily, false. If warranted, this conclusion would significantly limit the appeal of the fictionalist strategy rendering it unavailable to anyone antecedently convinced that mathematics and metaphysics concern non-contingent matters. I try to show that their arguments (...) can be resisted by developing and defending a strategy suggested by Rosen, Nolan and Dorr, according to which the fiction-operator is to be analysed in terms of a counterfactual that admits of non-trival truth-values even when the antecedent is impossible. (shrink)

Questions about necessity (or what has to be, or what cannot be otherwise) and possibility (or what can be, or what could be otherwise) are questions about modality. Fictionalism is an approach to theoretical matters in a given area which treats the claims in that area as being in some sense analogous to fictional claims: claims we do not literally accept at face value, but which we nevertheless think serve some useful function. However, despite its name, “Modal Fictionalism” in its (...) usual manifestations is not primarily fictionalism about claims of necessity and possibility, but rather a fictionalist approach to claims about possible worlds. (For instance, modal fictionalism is not normally fictionalist about the claim that “it is possible that there be a species of tail-less kangaroo”, but rather about the claim that “there is a possible world in which there is a species of tail-less kangaroo”.) The practice of taking possible worlds to be merely convenient fictions, or of treating talk about possible worlds as being useful without being literally correct, is quite common in philosophical circles. It is only recently, however, that philosophers have seriously examined the implications of taking possible worlds to be merely fictional objects, like Sherlock Holmes or a frictionless surface. (shrink)

Modal Fictionalism, the theory that possible worlds do not literally exist but that our talk about them should be understood in the same way that we understand talk about fictional entities, is an increasingly popular approach to possible worlds. This paper will distinguish three versions of Modal Fictionalism, and will show that the third, a version endorsed by some of the most prominent Modal Fictionalists, faces at least three serious objections: that it makes modality too artificial, the modal fiction does (...) not have the representative resources it needs, and the approach has trouble accounting for propositions. (shrink)

It is our contention that an ontological commitment to propositions faces a number of problems; so many, in fact, that an attitude of realism towards propositions—understood the usual “platonistic” way, as a kind of mind- and language-independent abstract entity—is ultimately untenable. The particular worries about propositions that marshal parallel problems that Paul Benacerraf has raised for mathematical platonists. At the same time, the utility of “proposition-talk”—indeed, the apparent linguistic commitment evident in our use of 'that'-clauses (in offering explanations and making (...) predictions)—is also in need of explanation. We account for this with a fictionalist analysis of our use of 'that'-clauses. Our account avoids certain problems that arise for the usual error-theoretic versions of fictionalism because we apply the notion of semantic pretense to develop an alternative, pretense-involving, non-error-theoretic, fictionalist account of proposition-talk. (shrink)

There is a class of fictionalist strategies (the reflexive fictionalisms) which appear to suffer from a common problem: the problem that the entities which are supposedly fictional turn out, by the lights of the fictionalist theory itself, to exist. The appropriate solution is to reject so-called strong fictionalism in each case: that is, to reject the variety of fictionalism which takes appeal to the domain of fictional entities to provide an explanation or analysis of the operators or predicates with which (...) the objects are systematically correlated. (shrink)

The Brock-Rosen problem has been one of the most thoroughly discussed objections to the modal fictionalism bruited in Gideon Rosen’s ‘Modal Fictionalism’. But there is a more fundamental problem with modal fictionalism, at least as it is normally explained: the position does not resolve the tension that motivated it. I argue that if we pay attention to a neglected aspect of modal fictionalism, we will see how to resolve this tension—and we will also find a persuasive reply to the Brock-Rosen (...) objection. Finally, I discuss an alternative reading of Rosen, and argue that this position is also able to fend off the Brock-Rosen objection. (shrink)

A pretence theory of a discourse is one which claims that we do not believe or assert the propositions expressed by the sentences we utter when taking part in the discourse: instead, we are speaking from within a pretence. Jason Stanley argues that if a pretence account of a discourse is correct, people with autism should be incapable of successful participation in it; but since people with autism are capable of participiating successfully in the discourses which pretence theorists aim to (...) account for, all these accounts should be rejected. I discuss how pretence theorists can respond, and apply this discussion to two pretence theories, Stephen Yablo's account of arithmetic and Kendall Walton's account of negative existentials. I show how Yablo and Walton can escape Stanley's objection. (shrink)

This is a survey of contemporary work on ‘fictionalism in metaphysics’, a term that is taken to signify both the place of fictionalism as a distinctive anti‐realist metaphysics in which usefulness rather than truth is the norm of acceptance, and the fact that philosophers have given fictionalist treatments of a range of specifically metaphysical notions.

Gideon Rosen’s [1990 Modal fictionalism. Mind, 99, 327–354] Modal Fictionalist aims to secure the benefits of realism about possible-worlds, whilst avoiding commitment to the existence of any world other than our own. Rosen [1993 A problem for fictionalism about possible worlds. Analysis, 53, 71–81] and Stuart Brock [1993 Modal fictionalism: A response to Rosen. Mind, 102, 147–150] both argue that fictionalism is self-defeating since the fictionalist is tacitly committed to the existence of a plurality of worlds. In this paper, I (...) develop a new strategy for the fictionalist to pursue in response to the Brock–Rosen objection. I begin by arguing that modal fictionalism is best understood as a paraphrase strategy that concerns the propositions that are expressed, in a given context, by modal sentences. I go on to argue that what is interesting about paraphrastic fictionalism is that it allows the fictionalist to accept that the sentence ‘there is a plurality of worlds’ is true without thereby committing her to the existence of a plurality of worlds. I then argue that the paraphrastic fictionalist can appeal to a form of semantic contextualism in order to communicate her status as an anti-realist. Finally, I generalise my conception of fictionalism and argue that Daniel Nolan and John O’Leary-Hawthorne [1996 Reflexive fictionalisms. Analysis, 56, 26–32] are wrong to suggest that the Brock-Rosen objection reveals a structural flaw with all species of fictionalism. (shrink)

The modal fictionalist faces a problem due to the fact that her chosen story seems to be incomplete—certain things are neither fictionally true nor fictionally false. The significance of this problem is not localized to modal fictionalism, however, since many fictionalists will face it too. By examining how the fictionalist should analyze the notion of truth according to her story, and, in particular, the role that conditionals play for the fictionalist, I develop a novel and elegant solution to the incompleteness (...) problem. (shrink)

It is sometimes said that no living philosopher is a genuine modal realist. This is no doubt an exaggeration. But at least this much is true: while we all partake of possible world talk when philosophizing, most of us regard this talk as incurring no commitment to a plurality of concrete worlds.

In "How to Speak of the Colors", Mark Johnston’s claims that eliminativism would require us to jettison colour discourse. In this paper, I challenge Johnston’s claim. I argue that a particular version of eliminativism, i.e., prescriptive colour fictionalism, allows us to continue employing colour discourse as we have thus far in the absence of colours. In doing so, it employs statistical models in its base discourse to derive high-level statistical constructs that can be linked to the fiction via bridge principles.

In this paper, I will defend modalfictionalism. The paper has two parts. In thefirst part, I will suggest a revised version ofmodal fictionalism which can avoid certaintechnical problems. In the second part, I willpropose a nominalized version of modalfictionalism and a general scheme offictionalism for the nominalist.

Modal fictionalists face a problem that arises due to their possible-world story being incomplete in the sense that certain relevant claims are neither true nor false according to it. It has recently been suggested that this incompleteness problem generalises to other brands of fictionalism, such as fictionalism about composite or mathematical objects. In this paper, I argue that these fictionalist positions are particularly threatened by a generalised incompleteness problem since they cannot emulate the modal fictionalists’ most attractive response. I then (...) defend mathematical and compositional fictionalism by showing that the reasons for which the incompleteness problem has been thought to affect them are mistaken. This leads to the question of whether there are other fictionalist positions to which the problem does in fact generalise. I give a general account of the features of a fictionalist position that generate the incompleteness problem and argue that whenever a fictionalist position does exemplify these features then the problem can be addressed in analogy to the modal fictionalists’ preferred response. (shrink)

I defend pretence hermeneutic fictionalism against the Autism Objection. The objection is this: since people with autism have no difficulty in engaging with mathematics even if they cannot pretend, it is not the case that engagement with mathematics involves pretence. I show that a previous response to the objection is inadequate as a defence of the kind of pretence hermeneutic fictionalism put forward as a semantic thesis about the discourse in question. I claim that a more general response to the (...) Autism Objection is to deny the premise that people with autism cannot pretend. To motivate this response, I appeal to psychological studies suggesting that people with autism can understand pretence and they can pretend under certain conditions. Finally, I provide explanations for why it is the case that people with autism do not have a problem with engaging in mathematics whereas they have so much difficulty with other kinds of figurative language and pretence. (shrink)