What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

This second volume continues Richard Routley’s explorations of an improved Meinongian account of non-referring and intensional discourse. It focuses on the essays 2 through 7 of the original monograph, Exploring Meinong’s Jungle and Beyond, following on from the material of the first volume and explores its implications of the Noneist position. It begins with a further development of noneism in the direction of an ontologically neutral chronological logic and associated metaphysical issues concerning existence and change. What follows includes: a detailed (...) response to Quine’s On What There Is; a defense against further objections to noneism; a detailed account of Meinong’s own position; arguments in favour of noneism from common-sense; and a noneist analysis of fictional discourse. We present these essays separately and provide additional scholarly commentaries from a range of philosophers including Fred Kroon, Maria Elisabeth Reicher-Marek and a previously unpublished commentary on noneism by J.J.C. Smart. (shrink)

Primitivist theories of truth have been defended by some of the luminaries of analytic philosophy, including the early Moore and Russell, Frege, Davidson, and Sosa. In this paper, I take up a contemporary primitivist theory that has been systematically developed throughout a sizeable body of work but has yet to receive sustained critical attention—Jamin Asay's primitivist deflationism. Asay's major ambitions are to defend a novel primitivist account of the concept truth and to harmonise that account with a deflationary theory of (...) the property truth. I will elaborate a thoroughgoing critique of primitivist deflationism, arguing that we have reason to doubt all of the five theses that constitute the view. Along the way, I will also highlight a number of possible escape routes for the primitivist deflationist, explaining how they can make the view more resilient even as they compel us to rework some of its central commitments. (shrink)

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)

This essay defends the neo-Quinean approach to ontology against the criticisms of two neo-Carnapians, Huw Price and Amie Thomasson.

This paper seeks to uncover and rationally reconstruct four theoretical prescriptions that H. L. A. Hart urged philosophers to observe and follow when investigating and theorizing about the nature of law. The four prescriptions may appear meager and insignificant when each is seen in isolation, but together as an inter-connected set they have substantial implications. In effect, they constitute a central part of Hart’s campaign to put philosophical investigations about the nature of law onto a path to a genuine research (...) program. The paper takes note of certain prevalent and robust trends in contemporary legal philosophy that detract its practitioners from the four prescriptions, and that have them revert to the some older modes of thinking from which Hart sought a decisive break. A number of contemporary legal philosophers’ views and commitments are taken up and assessed, and in particular those of John Gardner and Leslie Green. (shrink)

This paper seeks to uncover and rationally reconstruct four theoretical prescriptions that H. L. A. Hart urged philosophers to observe and follow when investigating and theorizing about the nature of law. The four prescriptions may appear meager and insignificant when each is seen in isolation, but together as an inter-connected set they have substantial implications. In effect, they constitute a central part of Hart's campaign to put philosophical investigations about the nature of law onto a path to a genuine research (...) program. The paper takes note of certain prevalent and robust trends in contemporary legal philosophy that detract its practitioners from the four prescriptions, and that have them revert to the some older modes of thinking from which Hart sought a decisive break. A number of contemporary legal philosophers' views and commitments are taken up and assessed, and in particular those of John Gardner and Leslie Green. ‘Yet the answer is a prosaic one: don’t ask what time is but how the word ‘time’ is being used’.Friedrich Waismann.I miss the future.Jaron Lanier. (shrink)

I have argued elsewhere for a deflationary conception of metaphysics, which takes well-formed metaphysical questions to be answerable using nothing more mysterious than empirical information and descriptive and normative conceptual work. Here I examine the ways in which our practices of metaphysics should change, if we adopt the deflationary reconception of metaphysics. Adopting this approach does not mean abandoning metaphysics, but it does lead to important differences regarding which debates and positions are worth taking seriously. It also requires us to (...) reevaluate which criteria for choosing metaphysical views are appropriate – particularly where debates about existence are concerned. (shrink)

Philosophers often aim to demonstrate that the things we ordinarily think and say can be reconciled with our considered beliefs about the world. To this end, many philosophers try to paraphrase ordinary language claims by finding equivalent sentences that are less misleading. For instance, though we know that there is no British family that is the average one, we want to say that the average British family has 1.8 children, and we might do that by paraphrasing this claim as: there (...) are nearly twice as many British children as British families. This article aims to introduce and distinguish different paraphrase strategies, sketch their role in metaphysical debates and highlight some crucial questions that proponents of such strategies face. (shrink)

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

Cameron, Eklund, Hofweber, Linnebo, Russell and Sider have written critical essays on my book, The Construction of Logical Space (Oxford: Oxford University Press, 2013). Here I offer some replies.

I propose a way of thinking aboout content, and a related way of thinking about ontological commitment. (This is part of a series of four closely related papers. The other three are ‘On Specifying Truth-Conditions’, ‘An Actualist’s Guide to Quantifying In’ and ‘An Account of Possibility’.).

I propose a way of thinking about content, and a related way of thinking about ontological commitment.

This essay addresses the question of the effect of Russell's paradox on Frege's distinctive brand of arithmetical realism. It is argued that the effect is not just to undermine Frege's specific account of numbers as extensions (courses of value) but more importantly to undermine his general means of explaining the object-directedness of arithmetical discourse. It is argued that contemporary neo-Fregean attempts to revive that explanation do not successfully avoid the central problem brought to light by the paradox. Along the way, (...) it is argued that the need to fend off an eliminative construal of arithmetic can help explain the so-called Caesar problem in the Grundlagen, and that the "syntactic priority thesis" is insufficient to establish the claim that numbers are objects. (shrink)

Our ordinary moral practices not only suppose that some people ought to perform some actions, and that some outcomes are morally better or worse than others, but also that there are rights, duties, goodness, and other apparently abstract moral entities. What should we make of these entities, and the talk of these entities? It is not straighforward to account for these entities in other terms. On the other hand, this paper will argue that talk of such entities is not easily (...) eliminated from good moral theorising. Nor are the prospects for paraphrasing apparent talk about these entities into less committal terms very promising. We should either find a place in our ontology for these creatures of ethics, or explain how they can be employed as a convenient fiction. (shrink)

One familiar form of argument for rejecting entities of a certain kind is that, by rejecting them, we avoid certain difficult problems associated with them. Such problem-avoidance arguments backfire if the problems cited survive the elimination of the rejected entities. In particular, we examine one way problems can survive: a question for the realist about which of a set of inconsistent statements is false may give way to an equally difficult question for the eliminativist about which of a set of (...) inconsistent statements fail to be 'factual'. Much of the first half of the paper is devoted to explaining a notion of factuality that does not imply truth but still consists in 'getting the world right'. The second half of the paper is a case study. Some 'compositional nihilists' have argued that, by rejecting composite objects (and so by denying the composition ever takes place), we avoid the notorious puzzles of coincidence, for example, the statue/lump and the ship of Theseus puzzles. Using the apparatus developed in the first half of the paper, we explore the question of whether these puzzles survive the elimination of composite objects. (shrink)

There is a puzzle about the use of paraphrase in philosophy, presented most famously in Alston's [1958] ‘Ontological Commitments’, but found throughout the literature. The puzzle arises from the fact that a symmetry required for a paraphrase to be successful seems to necessitate a symmetry sufficient for a paraphrase to fail, since any two expressions that stand in the means the same as relation must also stand in the has the same commitments as relation. I show that, while this problem (...) does undermine some conceptions of paraphrase, on a proper understanding of paraphrase the puzzle gets no purchase. Since paraphrase is an important component of Quinean approaches to meta-ontology, this paper constitutes a partial defence of Quinean meta-ontology. Since paraphrase is an important component of traditional methods of philosophical inquiry, this paper constitutes a partial defence of traditional modes of philosophizing as well. (shrink)

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...) In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (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)

Pairs of sentences like the following pose a problem for ontology: (1) Jupiter has four moons. (2) The number of moons of Jupiter is four. (2) is intuitively a trivial paraphrase of (1). And yet while (1) seems ontologically innocent, (2) appears to imply the existence of numbers. Thomas Hofweber proposes that we can resolve the puzzle by recognizing that sentence (2) is syntactically derived from, and has the same meaning as, sentence (1). Despite appearances, the expressions ‘the number of (...) moons of Jupiter’ and ‘four’ do not function semantically as singular terms in (2). Hofweber’s primary evidence for this proposal concerns differences in the focus-related communicative functions of (1) and (2). In this paper I raise several serious problems for Hofweber’s proposal, and for his attempt to support it by appeal to focus-related phenomena. I conclude by offering independent evidence for an alternative, purely pragmatic resolution of the ontological puzzle. (shrink)

This essay defends the neo-Quinean approach to ontology against the criticisms of two neo-Carnapians, Huw Price and Amie Thomasson.

According to ontological nihilism nothing exists. A recent argument purports to show that this view is indefensible, since its most plausible formulations are tacitly committed to quantificational claims that are inconsistent with the nihilist's view that there aren't any existents. I show that this objection begs the question against the nihilist. The objector's argument relies on an equivalence principle implying that claims which nihilists regard as non-quantificational should nonetheless be interpreted as equivalent to quantified claims, given that both kinds of (...) assertion are assertible in the same contexts. This style of reasoning is supported by considerations of charity, which suggest that similarities in inter-personal patterns of language use provide evidence of similarity in the semantic content of speakers' utterances. However, related considerations also suggest that intra-personal patterns of language use constitute significant semantic evidence of the same kind. When we appreciate this and further recognize that nihilists are disposed to assert the negation of any positive, quantified claim, we see that it is too much to expect principles of semantic interpretation based on considerations of charity to decisively refute nihilism. This result has interesting metametaphysical implications concerning the role and scope of analogous arguments based on principles of interpretive charity. (shrink)

It has been widely accepted in the past and it remains accepted in many quarters even now, that an ontologically economical position is to be rejected if the corresponding Platonic or otherwise ontologically prodigal discourse cannot be translated, paraphrased or otherwise ‘reduced’ to discourse exhibiting a more economical ontology. Such an attitude is often accompanied by the claim that the prodigal ontology explains some important truthsandthe demand that the nominalist or fictionalist or economicalist provide an alternative explanation for those truths (...) — perhaps in terms of ontologically economical ersatz substitutes for the prodigal entities. (shrink)

There is a long tradition of drawing metaphysical conclusions from investigations into language. This paper concerns one contemporary variation on this theme: the alleged ontological significance of cognitivist truth-theoretic accounts of semantic competence. According to such accounts, human speakers’ linguistic behavior is in part empirically explained by their cognizing a truth-theory. Such a theory consists of a finite number of axioms assigning semantic values to lexical items, a finite number of axioms assigning semantic values to complex expressions on the basis (...) of their structure and the semantic values of their constituents, and a finite number of production schemata. The theory enables the derivation of truth-conditions for each sentence of the language: something of roughly the form ‘S is true iff P’.1 The claim that speakers stand in a cognitive relation to such theories is advanced, not as a conceptual analysis of semantic competence or understanding, but rather as an empirical hypothesis about human speakers in particular, one part of a broader empirical account of our linguistic competence and cognition generally. It therefore must mesh with the rest of our theorizing in these areas and whatever relevant data from neighboring inquiries there may be. The precise nature of the cognitive relation a speaker is supposed to bear to a truththeory is a matter of some dispute. I speak of ‘‘cognizing’’ (following. (shrink)

Analytic Philosophy, EarlyView. The method of paraphrasing away apparent ontological commitments is a familiar tool for trimming one's ontology. Even so, I argue that aiming to avoid commitment via paraphrase is unjustified. The reason is the standard motivations for paraphrase rest on implicit yet faulty principles regarding ontological categories and categorization- or so I argue. These results also provide indirect support for a permissivist approach to ontology.

It is persons who are ontologically committed. But a person is not ontologically committed by virtue of his character, his height, his social standing or whatever, but by virtue of the sentences he assents to. Hence we should look to sentences for a criterion of ontological commitment. This is precisely what is done by advocates of what I will call the Referential theory. In this paper I argue that the Referential theory faces serious objections related to the role paraphrase must (...) play in it. I then present a modified Referential theory and go on to discuss certain implications of the modified theory. More precisely, the paper divides up as follows. In §1 I present the Referential theory. In §2 I argue that it is in trouble over paraphrase. In §3 I consider a general objection to the arguments of §2. In §4 I present the modified theory. In §5 I consider the implications of the modified theory for polemic over what there is and for the existence of properties or universals. (shrink)

Quinean Ontological Naturalism addresses the question “What is there?” Advocates of the view maintain that we can answer this question by applying Quine’s criterion of ontological commitment to our best scientific theories. In this paper, I discuss two major objections that are commonly offered to this view, what I call the “Paraphrase Objection” and “First Philosophy Objection”. I argue that these objections arise from a common uncharitable characterization of the Quinean Ontological Naturalist’s project that fails to distinguish two distinct roles (...) for Quine’s Criterion, a descriptive role and a normative role. The objections target the descriptive role, but only the normative role is important to Quinean Ontological Naturalism. (shrink)

According to ontological nihilism there are, fundamentally, no individuals. Both natural languages and standard predicate logic, however, appear to be committed to a picture of the world as containing individual objects. This leads to what I call the \emph{expressibility challenge} for ontological nihilism: what language can the ontological nihilist use to express her account of how matters fundamentally stand? One promising suggestion is for the nihilist to use a form of \emph{predicate functorese}, a language developed by Quine. This proposal faces (...) a difficult objection, according to which any theory in predicate functorese will be a notational variant of the corresponding theory stated in standard predicate logic. Jason Turner (2011) has provided the most detailed and convincing version of this objection. In the present paper, I argue that Turner's case for the notational variance thesis relies on a faulty metasemantic principle and, consequently, that an objection long thought devastating is in fact misguided. (shrink)

Fictionalism and deflationism are two moderate meta-ontological positions that try to occupy a middle ground between the extremes of heavy-duty realism and hard-line eliminativism. Deflationists believe that the existence of certain entities (e.g.: numbers) can be established by means of ‘easy’ arguments—arguments that, supposedly, rely solely on uncontroversial premises and trivial inferences. Fictionalists, however, find easy arguments unconvincing. Amie Thomasson has recently argued that, in their criticism of easy arguments, fictionalists beg the question against deflationism and that the fictionalist alternative (...) interpretation of easy arguments is untenable. In this paper, I argue that both charges are unsubstantiated. Properly understood, the fictionalist’s objection to ‘easy’ arguments takes the form of a dilemma—either the premises of ‘easy’ arguments are not truly uncontroversial or the inferences on which they rely are not truly trivial. Moreover, I argue not only that, contrary to what Thomasson claims, the fictionalist’s interpretation of easy argument is tenable but that the fictionalist might, in fact, have a better explanation of the seemingly trivial nature of the inferences involved in easy arguments than the deflationist’s. (shrink)

I argue that Agustín Rayo’s symmetric ‘just is’ statements cannot be defined in terms of notions like essence, grounding or metaphysical truth-conditions. I go on to argue that one of these latter notions, which allow us to express an asymmetric relationship between facts, is needed to do some of the work that Rayo intends ‘just is’ statements to do, such as stating reductionist claims.

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)

This article offers an approach that combines, on the one hand, the philosophical notion of reflexivity, which is related to the ideas of self-reference and paradox, and, on the other hand, the sociological discussion of epistemic reflexivity as a problem of coherence, which was mainly initiated by certain branches of ethnomethodology and social constructionism. This combinatory approach argues for reflexivity as an epistemic criterion of ontological coherence, which suggests that social ontologies should account for the possibility of self-reflective subjectivity – (...) for otherwise they result in a paradoxical conclusion according to which a social scientist reflects on her or his ontological commitments even though these commitments deny her or him the capacity for self-reflection. This analysis presupposes that all human sciences are categorically premised on social ontologies; and it argues for an analytical distinction between self-reflection, which refers to the agential capacity for reflecting on one’s own commitments, and the epistemic criterion of reflexivity hereby proposed. These two analytically distinct though interdependent socio-theoretical concepts are frequently conflated in the literature; thus, this article also aims at a ‘clearing of the ground’ that can be of categorical use to the human sciences. (shrink)

In his book Philosophy of Logic, Putnam (1971) presents a short argument which reads like—and indeed, can be reconstructed as—a formal proof that a nominalistic physics is impossible. The aim of this paper is to examine Putnam’s proof and show that it is not compelling. The precise way in which the proof fails yields insight into the relation that a nominalistic physics should bear to standard physics and into Putnam’s indispensability argument.

Can Quine’s criterion for ontological commitment be comparatively applied across different logics? If so, how? Cross-logical evaluations of discourses are central to contemporary philosophy of mathematics and metaphysics. The focus here is on the influential and important arguments of George Boolos and David Lewis that second-order logic and plural quantification don’t incur additional ontological commitments over and above those incurred by first-order quantifiers. These arguments are challenged by the exhibition of a technical tool—the truncation-model construction of notational equivalents—that compares the (...) ontological role and increased expressive strength of non-first-order ideology to first-order ideology. (shrink)

In recent years, a new dispute has risen to prominence: the dispute between realists and anti-realists about causal powers. Albeit sometimes overlooked, the meta-ontological features of this “question of realism for powers” are quite peculiar. For friends and foes of causal powers have characterized their contrasting views in a variety of different ways; as existence claims, as semantic or truth-making claims, as fundamentality claims, as claims about the nature of certain properties. Not only does this multiplicity of interpretations make it (...) unclear what the genuine bone of contention is, if there is one; some of them appear to be mutually exclusive. Some light can be shed on this apparent yet widespread confusion by distinguishing three degrees of ontological involvement in dispositional truths; viz., three ways, of increasing robustness, to read ontological commitments from dispositional truths. Relatedly, by exploring the literature, and focusing on some selected examples of power realism and anti-realism, we can observe that power realists vastly disagree over the intrinsic nature ad make-up of dispositional properties. Such examples furthermore invite the thought that the question of realism for powers is best understood not as the debate around the existence of properties with a distinctive identity, but rather as a debate about metaphysical hierarchy. Finally, some anti-realists positions are indistinguishable from realist ones, using merely intensional resources: power realism is best appreciated by going hyperintensional. (shrink)

An introduction to analytic ontology. Part 1 deals with the question, What is ontology?, focusing on (i) the interplay between ontological and broadly metaphysical concerns, and (ii) the difference between material ontology and formal ontology. Part 2 deals with the question, How is ontology done?, focusing on (i) the delicate interplay between ontology and truth-making (or: between meaning and existence), and (ii) the differences between revolutionary vs. hermeneutic, prescriptive vs. descriptive, and absolute vs. relative approaches to ontology. Part 3 surveys (...) the state of the art in a number of areas, both in material ontology (e.g., the problem of universals, the status of objects and events, the ontology of mathematics, of the physical sciences, of the social sciences) and in formal ontology (identity, ontological dependence, part-whole relations). (shrink)

Comprehensive Linguistic Approach to Frege's Commitment Puzzle There is a puzzle, noticed by Frege, about inferences from sentences like (F1) "Jupiter has four moons" to sentences like (F2) "The number of moons of Jupiter is four". They seem to be truth-conditionally equivalent but, apparently, they say something about completely different things. (F1) seems to be about moons, while (F2) about numbers. This phenomenon raises several puzzles about semantics, syntax, and is one of main tools of easy ontology. Recently, new linguistic (...) and pragmatic solutions were proposed. Linguistic solutions of Thomas Hofweber and Katharina Felka are refreshed versions of the traditional paraphrastic approach that involve consideration of conversational contexts as well as syntactical structure of copular sentences. The pragmatic solution resorts to bracketing or indifference to certain possible alternatives and contexts of a sentence. I discuss their strong and weak points and propose to include in further research John Biro's account of the expression "the number of planets", which solves the problems of the new linguistic approaches. (shrink)

On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist (of course they do!) The question is whether or not they are fundamental.

Let us agree that everything that there is exists, and that to be, to be real, and to exist are one and the same. Does everything that there is exist to the same degree? Or do some things exist more than others? Are there gradations of being? I argue that some entities exist more than others. Moreover, many of the notions in play in contemporary metaphysical discourse, such as fundamentality, perfect naturalness, and grounding ought to be cashed out in terms (...) of degree of existence. (shrink)

In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by (...) mathematics in our scientific explanations is a purely expressive one, merely allowing us to say more about the physical world than we would otherwise be able to. Mathematical objects do not need to exist for mathematics to play this role. This proposal puts a normative constraint on our use of mathematical language: we ought to use mathematically presented theories to express belief only in the consequences they have for non-mathematical things. In Part II, I will argue that what the normative proposal recommends is in fact what people generally do in both pure and applied mathematical contexts. I motivate this claim by showing that it is predicted by our best general means of analysing natural language. I provide a semantic theory of applied arithmetical sentences that reveals they do not purport to refer to numbers, as well as a pragmatic theory for pure mathematical language use which reveals that pure mathematical utterances do not typically communicate content that implies the existence of mathematical objects. In conclusion, I show that the emerging hermeneutic fictionalist position is preferable to any alternative interpretation of mathematical discourse as aimed at describing a domain of independently existing abstract mathematical objects. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...) forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)