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)

Every paper in this collection is worth reading, for one reason or another. Still, due to certain problematic metametaphysical presuppositions most of these discussions miss the deeper mark, on the pessimist as well as the optimist side. My reasons for thinking this come from considering how best to answer three metametaphysical questions. First, why be pessimistic about metaphysics – why be Carnapian in a post-positivist age? There is, I’ll suggest, a post-positivist strategy for reviving Carnapian pessimism, but it is almost (...) entirely neglected here; and the motivations that pessimists offer instead are not compelling. Second, why think that the best way to approach metametaphysical questions is by attention to features of language, and in particular to quantifier semantics, in ordinary or ontological language(s)? Here again we are offered little motivation for this supposition, which, notwithstanding its acceptance by nearly all contributors, faces clear difficulties. Third, granting that quantification is somehow bound up with first-order questions about what exists, what is the nature of this connection, and what are the associated implications for metametaphysics? Here I find the accounts of the connection on offer implausible, especially as compared to an alternative that makes better sense of metaphysical practice and disagreement. The moral following consideration of these questions is that real progress in metametaphysics is likely to occur less by attention to semantic issues pertaining to representation, translation and quantification and more to non-semantic issues pertaining to epistemology and metaphysical determinacy. (shrink)

This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous theory (...) of the notion. In the final sections, I show how this package dovetails with ' interpretationist' theories of meaning to give sober content to thought that some things — perhaps sets, or gerrymandered mereological sums — can be 'postulated into existence'. (shrink)

Imaginative and creative capacities seem to be at the heart of both games of make-believe and figurative uses of language. But how exactly might cases of metaphor or idiom involve make-believe? In this paper, I argue against the pretense-based accounts of Walton (1990, 1993), Hills (1997), and Egan (this journal, 2008) that pretense plays no role in the interpretation of metaphor or idiom; instead, more general capacities for manipulating concepts (which are also called on within the use of pretense) do (...) the real explanatory work. This result has consequences for both our understanding of metaphor and idiom as well as for the use of figurative language by fictionalists in ontology. (shrink)

In an earlier paper in this journal I argued that deflationism is preferable to fictionalism as an alternative to both traditional realism and eliminativism. Gabriele Contessa questions this conclusion, denying that fictionalist arguments beg the question against easy ontological arguments, presenting a new argument against easy ontology, and suggesting a response to the challenge I raise for fictionalists. Below I respond to these points in turn. In so doing, I hope to clarify the broader theoretic orientation of easy ontology—in particular, (...) its rejection of a Quinean criterion of ontological commitment and its commitment to a form of functional pluralism about language. (shrink)

This paper defends the view that ontological questions (properly understood) are easy—too easy, in fact, to be subjects of substantive and distinctively philosophical debates. They are easy, roughly, in the sense that they may be resolved straightforwardly—generally by a combination of conceptual and empirical enquiries. After briefly outlining the view and some of its virtues, I turn to examine two central lines of objection. The first is that this ‘easy’ approach is itself committed to substantive ontological views, including an implausibly (...) permissive ontology. The second is that it, like neo-Fregean views, relies on transformation rules that are questionable on both logical and ontological grounds. Ultimately, I will argue, the easy view is not easily assailed by either of these routes, and so remains (thus far) a tenable and attractive approach. (shrink)

A fictionalist attitude towards an area of discourse encourages us to assent to certain sentences of that discourse without believing that they are true. Prima facie, this amounts to a suggestion that we should also assent to sentences of the form 'S but I don't believe that S'. Traditional versions of fictionalism have an answer to this challenge, but I argue that the answer is unavailable for a currently popular type of fictionalism. This is bad news for fictionalism in general (...) because the currently popular variety is the one that deals best with the Quine-Putnam indispensability argument. (shrink)

Religious fictionalism is the theory that it is morally and intellectually legitimate to affirm religious sentences and to engage in public and private religious practices, without believing the content of religious claims. This article discusses the main features of fictionalism, contrasts hermeneutic, and revolutionary kinds of fictionalism and explores possible historical and recent examples of religious fictionalism. Such examples are found in recent theories of faith, pragmatic approaches to religion, and mystical traditions in religious theology.

Linguistic ontologists and antilinguistic, ‘serious’ ontologists both accept the inference from ‘Fido is a dog’ to ‘Fido has the property of being a dog’ but disagree about its ontological consequences. In arguing that we are committed to properties on the basis of these transformations, linguistic ontologists employ a neo-Fregean meta-ontological principle, on which the function of singular terms is to refer. To reject this, serious ontologists must defend an alternative. This paper defends an alternative on which the function of singular (...) terms is not generally to refer and on which they are generally ontologically noncommittal. This is the best way to reject linguistic, ‘easy’ arguments for the existence of properties. The account recommends neutralism about quantification (drawing on Barcan Marcus and Meinongianism), coherently bringing together two important yet uncombined meta-ontological movements. Moreover, it employs Ramseyan insights about the transformations to provide a nonreductionist, non-error-theoretic redundancy approach to explicit talk about properties. (shrink)

The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.

Upholders of fictionalism about scientific models have not yet successfully explained how scientists can learn about the real world by making comparisons between models and the real phenomena they stand for. In this paper I develop an account of model-world comparisons in terms of what I take to be the best antirealist analyses of comparative claims that emerge from the current debate on fiction.

Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's (...) account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets. (shrink)

For Quine, the ontological commitments of a discourse are what fall under its (objectual) quantifiers. The recent literature, however, is beginning to move away from this picture. There are direct challenges to Quine's criterion, and there are also attempts to provide alternatives. Azzouni suggests that the ontological commitments of a discourse should be determined by an existence predicate instead. The availability of this alternative forces an adjudication between Qune's criterion and the predicate approach to ontological commitment. I argue that to (...) adjudicate between these criteria for ontological commitment, we need first to adjudicate between criteria for what exists. (shrink)

Ontological naturalism is the view that our best construal of what there is, is what science says there is. This paper argues that while such a doctrine is very appealing, unfortunately, determining what there is, is neither as simple, nor as straightforward, as ontological naturalism would have it seem. Determining what there is, it is claimed, involves three steps. First, one must decide which part of scientific discourse should be taken as true. One must then regiment that part of scientific (...) discourse, and finally, one has to apply a criterion for ontological commitment to that regimented discourse. This paper will concentrate on the first and third of these tasks. It is argued that resolving the tasks these steps put before us requires the employment of philosophical maneuvers, that is, maneuvers that neither originate within, nor are ratified by, the practice of science. But these are maneuvers that the ontological naturalist is not entitled to. Thus, ontological naturalism is not a feasible doctrine. (shrink)

Many long-standing problems pertaining to contemporary philosophy of mathematics can be traced back to different approaches in determining the nature of mathematical entities which have been dominated by the debate between realists and nominalists. Through this discussion conceptualism is represented as a middle solution. However, it seems that until the 20th century there was no third position that would not necessitate any reliance on one of the two points of view. Fictionalism, on the other hand, observes mathematical entities in a (...) radically different way. This is reflected in the claim that the concepts being used in mathematics are nothing but a product of human fiction. This paper discusses the relationship between fictionalism and two traditional viewpoints within the discussion which attempts to successfully determine the ontological status of universals. One of the main points, demonstrated with concrete examples, is that fictionalism cannot be classified as a nominalist position. Since fictionalism is observed as an independent viewpoint, it is necessary to examine its range as well as the sustainability of the implications of opinions stated by their advocates. (shrink)

During the past two decades, an interest among philosophers in fictitious and illusory beliefs has sprung up in fields ranging anywhere from mathematics and modality to morality.1 In this paper, we focus primarily on the view that Saul Smilansky has dubbed “free will illusionism”—i.e., the purportedly descriptive claim that most people have illusory beliefs concerning the existence of libertarian free will, coupled with the normative claim that because dispelling these illusory beliefs would produce negative personal and societal consequences, those of (...) us who happen to know the dangerous and gloomy truth about the non-existence of libertarian free will should simply keep quiet in the name of the common good. (shrink)

A number of philosophers have recently become increasingly interested in the potential usefulness of fictitious and illusory beliefs.As a result, a wide variety of fictionalisms and illusionisms have sprung up in areas ranging anywhere from mathematics and modality to morality.1 In this paper, we focus on the view that Saul Smilansky has dubbed “free will illusionism”—for example, the purportedly descriptive claim that the majority of people have illusory beliefs concerning the existence of libertarian free will, coupled with the normative claim (...) that because dispelling these illusions would produce negative personal and societal consequences, those of us who are unfortunate enough to know the dangerous and gloomy truth about the nonexistence of libertarian free will should simply keep quiet in the name of the common good. (shrink)

The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then we will discuss four (...) avenues for replying to Melia. We will argue that the three replies pursued in the literature so far are unpromising. We will then propose one new reply that is much more powerful, and—in the light of this—advise participants in the debate where to focus their energies. (shrink)

Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...) Replies5.1 Yablo’s likely response5.2 Charity6 Conclusion. (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.

I take up the task of examining how someone who takes seriously the ambitious programme of conceptual analysis advocated by the Canberra School can minimise the eliminative consequences which I argue the Ramsey-Carnap-Lewis recipe of conceptual analysis is likely to have for many folk discourses. The objective is to find a stable means to preserve the constative appearance of folk discourse and to find it generally successful in its attempts to describe an external world, albeit in non-scientific terms that do (...) not reflect the nature of things. The view I settle on, quasi-fictionalism, is modelled on a modified descriptivist version of Kendall Walton’s account of prop-oriented games of make-believe. (shrink)

When we use a directly referential expression to denote an object, do we incur an ontological commitment to that object, as Russell and Barcan Marcus held? Not according to Quine, whose regimented language has only variables as denoting expressions, but no constants to model direct reference. I make a case for a more liberal conception of ontological commitment—more wide-ranging than Quine’s—which allows for commitment to individuals, with an improved logical language of regimentation. The reason for Quine’s prohibition on commitment to (...) individuals, I argue, is that his choice of regimented language is heavily informed by his holist epistemology, in which objects are introduced via a description of their explanatory role. But non-holists can coherently attempt to commit to individuals using directly referential expressions, modelled in a formal language as constants. While holding on to the insight that a logical language is a helpful medium for ontology, I propose instead a more permissive language of regimentation, one expanded to permit the use of constants to record attempts to commit to individuals, which allows us to make sense of non-holist theories with alternative name-based or name-and-variable-based criteria of ontological commitment as well as Quinean theories. (shrink)

Fictionalism has recently returned as a standard response to ontologically problematic domains. This article assesses moral fictionalism. It argues (i) that a correct understanding of the dialectical situation in contemporary metaethics shows that fictionalism is only an interesting new alternative if it can provide a new account of normative content: what is it that I am thinking or saying when I think or say that I ought to do something; and (ii) that fictionalism, qua fictionalism, does not provide us with (...) any new resources for providing such an account. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

Ordinary use of empty names encompasses a variety of different phenomena, including issues in semantics, mental content, fiction, pretense, and linguistic practice. In this paper I offer a novel account of empty names, the cognitive theory, and show how it offers a satisfactory account of the phenomena. The virtues of this theory are based on its strength and parsimony. It allows for a fully homogeneous semantic treatment of names coped with ontological frugality and empirical and psychological adequacy.

Hans Hahn, mathematician, philosopher and co-founder of the Vienna Circle, attempted to reconcile the validity and applicability of both logic and mathematics with a strict empiricism. This article begins with a review of this attempt, focusing on his view of the relation of language to logic and his answer to the question of why we need logic. I then turn to some recent work by Stephen Yablo in an attempt to show that Yablo's fictionalism, and in particular his use of (...) metaphor, can shed light on Hahn's philosophy of logic. (shrink)

In this paper, I defend an indexical analysis of the abstract-concrete distinction within the framework of modal realism. This analysis holds the abstract-concrete distinction to be conceptually inseparable from the distinction between the actual and the merely possible, which is assumed to be indexical in nature. The resulting view contributes to the case for modal realism by demonstrating how its distinctive resources provide a reductive analysis of the abstract-concrete distinction. This indexical analysis also provides a solution to a sceptical problem (...) regarding our concreteness, which parallels the sceptical problem that motivates indexicalism about actuality. (shrink)

Confirmational holism is central to a traditional formulation of the indispensability argument for mathematical realism (IA). I argue that recent strategies for defending scientific realism are incompatible with confirmational holism. Thus a traditional formulation of IA is incompatible with recent strategies for defending scientific realism. As a consequence a traditional formulation of IA will only have limited appeal.

According to Hume’s principle, a sentence of the form ⌜The number of Fs = the number of Gs⌝ is true if and only if the Fs are bijectively correlatable to the Gs. Neo-Fregeans maintain that this principle provides an implicit definition of the notion of cardinal number that vindicates a platonist construal of such numerical equations. Based on a clarification of the explanatory status of Hume’s principle, I will provide an argument in favour of a nominalist construal of numerical equations. (...) The neo-Fregean objections to such a construal will be examined and rejected. And the implications of the nominalist construal for the use of numerals and for the understanding of ontological questions for the existence of numbers will be spelled out. (shrink)

Many who take a dismissive attitude towards metaphysics trace their view back to Carnap’s ‘Empiricism, Semantics and Ontology’. But the reason Carnap takes a dismissive attitude to metaphysics is a matter of controversy. I will argue that no reason is given in ‘Empiricism, Semantics and Ontology’, and this is because his reason for rejecting metaphysical debates was given in ‘Pseudo-Problems in Philosophy’. The argument there assumes verificationism, but I will argue that his argument survives the rejection of verificationism. The root (...) of his argument is the claim that metaphysical statements cannot be justified; the point is epistemic, not semantic. I will argue that this remains a powerful challenge to metaphysics that has yet to be adequately answered. (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)

We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.

This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...) (called modal Meinongianism), applies it to specific fields, and discusses its open problems. Part I of the book provides a historical introduction to, and critical discussion of, the dominant philosophical view of existence: the “Kantian-Fregean-Quinean” perspective. Part II is the full-fledged introduction to the Meinongian theories of existence as a real property of individuals: after starting with the so-called naïve Meinongian conception and its problems, it provides a self-contained presentation of the main neo-Meinongian proposals, and a detailed discussion of their strengths and weaknesses. Part III develops a specific neo-Meinongian theory of existence employing a model-theoretic semantic framework. It discusses its application to the ontology and semantics of fictional objects, and its open problems. The methodology of the book follows the most recent trends in analytic ontology. In particular, the meta-ontological point of view is largely privileged. (shrink)

I discuss and defend two arguments against semantic theories which wish to avoid commitment to propositions. The first holds that on the most plausible semantics of a class of natural language sentences, the truth of sentences in that class requires the existence of propositions; and some sentences in that class are true. The second holds that, on the best understanding of the form of a semantic theory, the truth of a semantic theory itself entails the existence of propositions. Much of (...) the discussion engages Davidsonian alternatives to a propositionalist semantic theory. (shrink)

…entities? 2. How to be a nominalist 2.1. “Speak with the vulgar …” 2.2. “…think with the learned” 3. Arguments for nominalism 3.1. Intelligibility, physicalism, and economy 3.2. Causal..

The basic question of ontology is “What exists?”. The basic question of metaontology is: are there objective answers to the basic question of ontology? Here ontological realists say yes, and ontological anti-realists say no. (Compare: The basic question of ethics is “What is right?”. The basic question of metaethics is: are there objective answers to the basic question of ethics? Here moral realists say yes, and moral anti-realists say no.) For example, the ontologist may ask: Do numbers exist? The Platonist (...) says yes, and the nominalist says no. The metaontologist may ask: is there an objective fact of the matter about whether numbers exist? The ontological realist says yes, and the ontological anti-realist says no. Likewise, the ontologist may ask: Given two distinct entities, when does a mereological sum of those entities exist? The universalist says always, while the nihilist says never. The metaontologist may ask: is there an objective fact of the matter about whether the mereological sum of two distinct entities exists? The ontological realist says yes, and the ontological anti-realist says no. Ontological realism is often traced to Quine (1948), who held that we can determine what exists by seeing which entities are endorsed by our best scientific theory of the world. In recent years, the practice of ontology has often presupposed an ever-stronger ontological realism, and strong versions of ontological realism have received explicit statements by Fine (this volume), Sider (2001; this volume), van Inwagen (1998; this volume), and others. (shrink)

Metaphysics is concerned with the foundations of reality. It asks questions about the nature of the world, such as: Aside from concrete objects, are there also abstract objects like numbers and properties? Does every event have a cause? What is the nature of possibility and necessity? When do several things make up a single bigger thing? Do the past and future exist? And so on. -/- Metametaphysics is concerned with the foundations of metaphysics. It asks: Do the questions of metaphysics (...) really have answers? If so, are these answers substantive or just a matter of how we use words? And what is the best procedure for arriving at them—common sense and conceptual analysis? Or assessing competing hypotheses with quasi-scientific criteria? -/- This volume gathers together sixteen new essays that are concerned with the semantics, epistemology, and methodology of metaphysics. My aim is to introduce these essays within a more general (and mildly opinionated) survey of contemporary challenges to metaphysics . (shrink)

The semantics of noun phrases (NPs) is of crucial importance for both philosophy and linguistics. Throughout much of the history of the debate about the semantics of noun phrases there has been an implicit assumption about how they are to be understood. Basically, it is the assumption that NPs come only in two kinds. In this paper we would like to make that assumption explicit and discuss it and its status in the semantics of natural language. We will have a (...) look at how the assumption is to be understood more precisely, what its methodological status should be, whether it has been abandoned in recent work in semantics, and whether it should be abandoned in future work. To do all this, it’s best to start with some historical context. (shrink)

Prop oriented make-believe is make-believe utilized for the purpose of understanding what I call “props,” actual objects or states of affairs that make propositions “fictional,” true in the make-believe world. I, David Hills, and others have claimed that prop oriented make-believe lies at the heart of the functioning of many metaphors, and one variety of fictionalism in metaphysics invokes prop oriented make-believe to explain away apparent references to entities some find questionable or problematic (fictional characters, propositions, moral properties, numbers). Elisabeth (...) Camp has argued against my and David Hills’ views of metaphor. Her arguments, many of them echoed by Catharine Wearing, demolish a very implausible account of metaphor, but leave entirely untouched the views that Hills and I actually proposed. Clarifying what we say about metaphor serves also as a defense of fictionalist theories that invoke prop oriented make-believe. (shrink)

In this entry I will offer a survey of the contemporary debate on fic- tionalism, which is a distinctive anti-realist view about certain regions of discourse that are valued for their usefulness rather than their truth.

Ontology is the study of what there is, what kinds of things make up reality. Ontology seems to be a very difficult, rather speculative discipline. However, it is trivial to conclude that there are properties, propositions and numbers, starting from only necessarily true or analytic premises. This gives rise to a puzzle about how hard ontological questions are, and relates to a puzzle about how important they are. And it produces the ontologyobjectivity dilemma: either (certain) ontological questions can be trivially (...) answered using only uncontroversial premises, or the uncertainties of ontology are really a threat to the truth of basically everything we say or believe. The main aim of this dissertation is to resolve these puzzles and to shed some light on the discipline of ontology. I defend a view inspired by Carnap’s internal-external distinction about what there is, but one according to which both internal and external questions are fully factual and meaningful. In particular, I argue that the trivial arguments are valid, but they do not answer any ontological questions. Furthermore, I propose an account of the function of our talk about properties, propositions and natural numbers. According to this account our talk about them has no ontological presuppositions for its literal and objective truth. This avoids the ontology-objectivity dilemma, and solves the puzzles about ontology. To do this I look at quantification and noun phrases in general, and at their relation to ontology. I argue that quantifiers are semantically underspecified in a certain respect, and play two different roles in communication. I discuss the relation between syntactic form and information structure, the function of certain non-referential, non-quantificational noun phrases, the uses of bare number determiners, and how arithmetic truths are learned and taught. The more metaphysical issues discussed include: inexpressible properties, logicism about arithmetic, nominalism, Carnap’s view about ontology, the problem of universals, the relationship between ontology and objectivity, different projects within ontology, non-existent.... (shrink)

This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes (...) it difficult to understand how we can have knowledge of them and how they can have any relevance for our mathematical theories. I begin by characterizing a realist position in the philosophy of mathematics and discussing two of the most influential arguments for that kind of view. Next, after highlighting some of the difficulties that realism faces, I look at a few alternative approaches that attempt to account for our mathematical practice without making the assumption that there exist abstract mathematical entities. More specifically, I examine the fictionalist views developed by Hartry Field, Mark Balaguer, and Stephen Yablo, respectively. A common feature of these views is that they accept that mathematics interpreted at face value is committed to the existence of abstract objects. In order to avoid this commitment, they claim that mathematics, when taken at face value, is false. I argue that the fictionalist idea of mathematics as consisting of falsehoods is counter-intuitive and that we should aim for an account that can accommodate both the intuition that mathematics is true and the intuition that the causal inertness of abstract mathematical objects makes them irrelevant to mathematical practice and mathematical knowledge. The solution that I propose is based on Rudolf Carnap's distinction between an internal and an external perspective on existence. I argue that the most reasonable interpretation of the notions of mathematical truth and existence is that they are internal to mathematics and, hence, that mathematical truth cannot be used to draw the conclusion that mathematical objects exist in an external/ontological sense. (shrink)