What are the ontological commitments of a sentence? In this paper I offer an answer from the perspective of the truthmaker theorist that contrasts with the familiar Quinean criterion. I detail some of the benefits of thinking of things this way: they include making the composition debate tractable without appealing to a neo-Carnapian metaontology, making sense of neo-Fregeanism, and dispensing with some otherwise recalcitrant necessary connections.

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...) but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

On the truthmaker view of ontological commitment [Heil (From an ontological point of view, 2003); Armstrong (Truth and truthmakers, 2004); Cameron (Philosophical Studies, 2008)], a theory is committed to the entities needed in the world for the theory to be made true. I argue that this view puts truthmaking to the wrong task. None of the leading accounts of truthmaking—via necessitation, supervenience, or grounding—can provide a viable measure of ontological commitment. But the grounding account does provide a needed constraint on (...) what is fundamental. So I conclude that truthmaker commitments are not a rival to quantifier commitments, but a needed complement. The quantifier commitments are what a theory says exists, while the truthmaker commitments are what a theory says is fundamental. (shrink)

This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.

The article is primarily concerned with the notion of a truth-maker. An explication for this notion is offered, which relates it to other notions of making something such-and-such. In particular, it is shown that the notion of a truth-maker is a close relative of a concept employed by van Inwagen in the formulation of his Consequence Argument. This circumstance helps understanding the general mechanisms of the concepts involved. Thus, a schematic explication of a whole battery of related notions is offered. (...) It is based on an explanatory notion, introduced by the sentential connector “because”, whose function is examined in some detail. Finally, on the basis of the explication proposed, an argument is developed to the effect that the objects usually regarded as truth-makers are not apt to play this role. (shrink)

Presentists, who believe that only present objects exist, face a problem concerning truths about the past. Presentists should (but cannot) locate truth-makers for truths about the past. What can presentists say in response? We identify two rival factions ‘upstanding’ and ‘nefarious’ presentists. Upstanding presentists aim to meet the challenge, positing presently existing truth-makers for truths about the past; nefarious presentists aim to shirk their responsibilities, using the language of truth-maker theory but without paying any ontological price. We argue that presentists (...) should be nefarious presentists. (shrink)

There is widespread disagreement as to what the facts are concerning just when a collection of objects composes some further object; but there is widespread agreement that, whatever those facts are, they are necessary. I am unhappy to simply assume this, and in this paper I ask whether there is reason to think that the facts concerning composition hold necessarily. I consider various reasons to think so, but find fault with each of them. I examine the theory of composition as (...) identity, but argue that the version of this doctrine that entails universalism is implausible. I consider the claim that the a priority of such facts leads to their necessity, but give a defence of substantial contingent a priori truths. I ask whether the contingency of such facts would lead to unwelcome possibilities, but argue that the worrying looking possibilities can be blocked if it is desired. Next, I argue against the thought that the Lewis-Sider argument against restricted composition might give us reason to accept the necessity of universalism. Lastly, I respond to two objections from the 2006 BSPC. I conclude in favour of the contingency of the facts concerning when some things compose some thing. (shrink)

The possibility of multi-location—of one entity having more than one exact location—is required by several metaphysical theories such as the immanentist theory of universals and three-dimensionalism about persistence. One of the most pressing challenges for multi-location theorists is that of making sense of exact location—in that extant definitions of exact location entail a principle called ‘functionality’, according to which nothing can have more than one exact location. Recently in a number of promising papers, Antony Eagle has proposed and defended a (...) definition of exact location in terms of weak location that does not entail functionality. This paper provides the first thorough assessment of Eagle’s proposal. In particular, we argue that it cannot account for the location of immanent universals, the multi-location of mereologically changing three-dimensional objects, the multi-location of mereologically complex objects, and that it makes extended simples impossible. (shrink)

We take as our starting point a thesis to the effect that, at least for true judgments of many varieties, there are parts of reality which make such judgments are true. We argue that two distinct components are involved in this truthmaker relation. On the one hand is the relation of necessitation, which holds between an object x and a judgment p when the existence of x entails the truth of p. On the other hand is the dual notion of (...) projection, which holds between a judgment p and an object x when the truth of p entails the existence of x. A truthmaker for a judgment p is then a necessitator for p which satisfies the further constraint that it is part of p’s projection. We offer a formal theory of the truthmaker relation thus defined, exploiting ontological tools of basic mereology and the theory of dependence. We then apply the theory to a range of problems connected with generic expressions, ellipsis, vagueness, and indexical and perceptual judgments. (shrink)

This bulletin contains a summary of the main topics of discussion in truthmaker theory, namely: the definition of truthmakers, problems with Truthmaker Necessitarianism and Truthmaker Maximalism, the ontological burden of truthmakers and the recalcitrant topic of truthmakers for negative truths.

Three plausible views—Presentism, Truthmaking, and Independence—form an inconsistent triad. By Presentism, all being is present being. By Truthmaking, all truth supervenes on, and is explained in terms of, being. By Independence, some past truths do not supervene on, or are not explained in terms of, present being. We survey and assess some responses to this.

1. IntroductionA popular view in metaphysics is that which propositions are true depends upon how the world is . In more evocative language, truth requires ground. This thought then gets used to do some serious work. As Sider has it, ‘[t]he point of … the principle that truth supervenes on being is to rule out dubious ontologies’. Here, I argue that ‘dubious’ ontologies are theoretically virtuous.

Narrowly speaking, the correspondence theory of truth is the view that truth is correspondence to a fact -- a view that was advocated by Russell and Moore early in the 20 th century. But the label is usually applied much more broadly to any view explicitly embracing the idea that truth consists in a relation to reality, i.e., that truth is a relational property involving a characteristic relation (to be specified) to some portion of reality (to be specified). During the (...) last 2300 years this basic idea has been expressed in many ways, resulting in a rather extended family of views, theories, and theory sketches. The members of the family employ various concepts for the relevant relation (correspondence, conformity, congruence, agreement, accordance, copying, picturing, signification, representation, reference, satisfaction) and/or various concepts for the relevant portion of reality (facts, states of affairs, situations, events, objects, sequences of objects, sets, properties, tropes). The resulting multiplicity of versions and reformulations of the theory is due to a blend of substantive and terminological differences. (shrink)

Many writers have held that in his later work, David Lewis adopted a theory of predicate meaning such that the meaning of a predicate is the most natural property that is (mostly) consistent with the way the predicate is used. That orthodox interpretation is shared by both supporters and critics of Lewis's theory of meaning, but it has recently been strongly criticised by Wolfgang Schwarz. In this paper, I accept many of Schwarze's criticisms of the orthodox interpretation, and add some (...) more. But I also argue that the orthodox interpretation has a grain of truth in it, and seeing that helps us appreciate the strength of Lewis's late theory of meaning. (shrink)

A fundamental entity is an entity that is ‘ontologically independent’; it does not depend on anything else for its existence or essence. It seems to follow that a fundamental entity is ‘modally free’ in some sense. This assumption, that fundamentality entails modal freedom (or ‘FEMF’ as I shall label the thesis), is used in the service of other arguments in metaphysics. But as I will argue, the road from fundamentality to modal freedom is not so straightforward. The defender of FEMF (...) should provide positive reasons for believing it, especially in light of recent views that are incompatible with it. I examine both direct and indirect routes to FEMF. (shrink)

This paper argues that a consideration of the problem of providing truthmakers for negative truths undermines truthmaker theory. Truthmaker theorists are presented with an uncomfortable dilemma. Either they must take up the challenge of providing truthmakers for negative truths, or else they must explain why negative truths are exceptions to the principle that every truth must have a truthmaker. The first horn is unattractive since the prospects of providing truthmakers for negative truths do not look good neither absences, nor totality (...) states of affairs, nor Graham Priest and J.C. Beall’s ‘polarities’ (Beall, 2000; Priest, 2000) are up to the job. The second horn, meanwhile, is problematic because restricting the truthmaker principle to atomic truths, or weakening it to the thesis that truth supervenes on being, undercuts truthmaker theory’s original motivation. The paper ends by arguing that truthmaker theory is, in any case, an under-motivated doctrine because the groundedness of truth can be explained without appeal to the truthmaker principle. This leaves us free to give the ommonsensical and deflationary explanation of negative truths that common-sense suggests. (shrink)

According to the doctrine of divine simplicity, God is an absolutely simple being lacking any distinct metaphysical parts, properties, or constituents. Although this doctrine was once an essential part of traditional philosophical theology, it is now widely rejected as incoherent. In this paper, I develop an interpretation of the doctrine designed to resolve contemporary concerns about its coherence, as well as to show precisely what is required to make sense of divine simplicity.

There is a traditional theistic doctrine, known as the doctrine of divine simplicity, according to which God is an absolutely simple being, completely devoid of any metaphysical complexity. On the standard understanding of this doctrine—as epitomized in the work of philosophers such as Augustine, Anselm, and Aquinas—there are no distinctions to be drawn between God and his nature, goodness, power, or wisdom. On the contrary, God is identical with each of these things, along with anything else that can be predicated (...) of him intrinsically. (shrink)

Truthmaker theory has been used to argue for substantial conclusions about the categorial structure of the world, in particular that states of affairs are needed to play the role of truthmakers. In this paper, I argue that closely considering the role of aboutness in truthmaking, that is considering what truthbearers are about, yields the result that there is no good truthmaker-based reason to think that truthmakers must be states of affairs understood as existing entities, whether complex or simple. First, I (...) introduce an aboutness-based account of truthmaking as a metaphysically modest alternative to the orthodox necessitarian account of truthmaking. Second, I discuss the distinction between states and events that has been made on the basis of linguistic evidence regarding aspectual markers and nominalisation. I argue that the modest approach to truthmaking allows us to accept that there is a real distinction between states and events without requiring that the distinction is ontologically substantial. Specifically, what we are talking about with state-truthbearers really differs from what we are talking about with event-truthbearers, but this difference need not be understood as a difference in kinds of entities. Because of its overall modesty, this is a theoretically virtuous result. (shrink)

I argue that deflationary theories of truth reveal an important lesson for the broader theory of truth: although the notion of truthmaking has played an essential role in many traditional theories of truth, it can be separated from and survive the rejection of substantive theories of truth. I argue that many of the traditional substantive theories of truth are unified in defining truth in terms of the ontological grounds that are needed to account for truth. Deflationists reject the idea that (...) a theory of truth needs such metaphysical implications, but in so doing they need not rule out the possibility of developing an independently motivated theory of truthmaking. I argue that deflationists can and should embrace truthmaker theory, once it is shorn from its connection to the traditional project of defining truth. (shrink)

In this paper I undermine the Entailment Principle according to which if an entity is a truthmaker for a certain proposition and this proposition entails another, then the entity in question is a truthmaker for the latter proposition. I argue that the two most promising versions of the principle entail the popular but false Conjunction Thesis, namely that a truthmaker for a conjunction is a truthmaker for its conjuncts. One promising version of the principle understands entailment as strict implication but (...) restricts the field of application of the principle to purely contingent truths (i.e. those that contain no necessary proposition at any level of analysis). But a conjunction of purely contingent truths strictly implies its conjuncts. So this version of the principle is committed to the Conjunction Thesis. The same is true of the version of the principle where entailment is understood in the sense of systems T, R, and E of relevant logic, since in these systems conjunctions entail their conjuncts. I argue that the Conjunction Thesis is false because a truthmaker is that in virtue of what a certain proposition is true and it is false that, for example, what the proposition that Peter is a man is true in virtue of is the conjunctive fact that Peter is man and Saturn is a planet (or the facts that Peter is a man and that Saturn is a planet taken together). I also argue against other versions of the principle. (shrink)

I argue that there is no metaphysically substantive property of truth. Although many take this thesis to be central to deflationism about truth, it is sometimes left unclear what a metaphysically substantive property of truth is supposed to be. I offer a precise account by relying on the distinction between the property and concept of truth. Metaphysical substantivism is the view that the property of truth is a sparse property, regardless of how one understands the nature of sparse properties. I (...) then offer two new arguments against metaphysical substantivism that employ ideas involving recombination and truthmaking. First, I argue that there are no theoretically compelling reasons to posit the existence of a metaphysically substantive property of truth. Secondly, I argue that if we do posit the existence of such a property, then we end up with a view that is either contradictory or unmotivated. What we’re left with is a metaphysically deflationary account of the property of truth that fully respects the metaphysical ambitions of truthmaker theory, and that is consistent with both the view that truth is a deflated, explanatorily impotent concept and the view that truth is an explanatorily powerful concept. (shrink)

A polemical account of Australian philosophy up to 2003, emphasising its unique aspects (such as commitment to realism) and the connections between philosophers' views and their lives. Topics include early idealism, the dominance of John Anderson in Sydney, the Orr case, Catholic scholasticism, Melbourne Wittgensteinianism, philosophy of science, the Sydney disturbances of the 1970s, Francofeminism, environmental philosophy, the philosophy of law and Mabo, ethics and Peter Singer. Realist theories especially praised are David Armstrong's on universals, David Stove's on logical probability (...) and the ethical realism of Rai Gaita and Catholic philosophers. In addition to strict philosophy, the book treats non-religious moral traditions to train virtue, such as Freemasonry, civics education and the Greek and Roman classics. (shrink)

Together, these entail that for every true proposition p, there exists some thing which could not exist and p be false.

Presentists, who believe that only present objects exist, should accept a thisness ontology, since it can do considerable work in defence of presentism. In this paper, I propose a version of presentism that involves thisnesses of past and present entities and I argue this view solves important problems facing standard versions of presentism.

I propose an account truthmaking that provides truthmakers for negative truths. The account replaces Truthmaker Necessitarianism with a "Duplication Principle", according to which a suitable entity T is a truthmaker for a proposition P just in case the existence of an appropriate counterpart of T entails the truth of P, where the counterpart relation is cashed out in terms of qualitative duplication. My account captures an intuitive notion of truthmakers as "things the way they are", validates two appealing principles about (...) entailment and containment proposed by David Armstrong, and invalidates the controversial Disjunction Thesis. (shrink)

In this article I address the Problem of Universals by answering questions about what facts a solution to the Problem of Universals should explain and how the explanation should go. I argue that a solution to the Problem of Universals explains the facts the Problem of Universals is about by giving the truthmakers (as opposed to the conceptual content and the ontological commitments) of the sentences stating those facts. I argue that the sentences stating the relevant facts are those like (...) 'a has the property F', that is, sentences stating that a particular has a certain property. Finally I show how answering these questions in this way transforms the Problem of Universals, traditionally conceived as the One over Many, that is, the problem of explaining how different particulars can have the same properties, into the Many over One, that is, the problem of explaining how the same particular can have different properties. The Problem of Universals is the problem of the Many over One. (shrink)

Atomism denies that complexes exist. Common-sense metaphysics may posit masses, composite individuals and sets, but atomism says there are only simples. In a singularist logic, it is difficult to make a plausible case for atomism. But we should accept plural logic, and then atomism can paraphrase away apparent reference to complexes. The paraphrases require unfamiliar plural universals, but these are of independent interest; for example, we can identify numbers and sets with plural universals. The atomist paraphrases would fail if plurals (...) presuppose complexes: but an Appendix shows that reference to complexes is not required in the semantics of plurals. (shrink)

Nominalizations are expressions that are particularly challenging philosophically in that they help form singular terms that seem to refer to abstract or derived objects often considered controversial. The three standard views about the semantics of nominalizations are [1] that they map mere meanings onto objects, [2] that they refer to implicit arguments, and [3] that they introduce new objects, in virtue of their compositional semantics. In the second case, nominalizations do not add anything new but pick up objects that would (...) be present anyway in the semantic structure of a corresponding sentence without a nominalization. In the first and third case, nominalizations in a sense ‘create’ new objects’, enriching the ontology on the basis of the meaning of expressions. I will argue that there is a fourth kind of nominalization which requires a quite different treatment. These are nominalizations that introduce ‘new’ objects, but only partially characterize them. Such nominalizations generally refer to events or tropes. I will explore an account according on which such nominalizations refer to truth makers. (shrink)

A central problem for any truthmaker theory is the problem of negative truths. In this paper, I develop a novel, piecemeal strategy for solving this problem. The strategy puts central focus on a truth-relevant notion of aboutness within a metaphysically modest version of truthmaker theory and uses key conceptual tools gained by taking a deeper look at the best attempts to solve the problem of intentionality. I begin this task by critically discussing past proposed solutions to P-NEG in light of (...) Russell’s debate with Demos. This reveals a central difficulty with addressing the problem, specifically that one cannot be committed to incompatibility facts in one’s account of negation and of the truth of negative truths. I then present an aboutness-based version of truthmaker theory. Utilising what I call the strict and full account of aboutness, I extract aboutness-based theories of truth and falsity. I use this machinery to present a promising new strategy for solving P-NEG which does not have the problems of alternative approaches. Finally, I present and respond to some potential objections. (shrink)

Presentism faces a serious challenge from truthmaker theory. Standard solutions to the truthmaker objection against presentism proceed in one of two ways. Easy road presentists invoke new entities to satisfy the requirements of truthmaker theory. Hard road presentists, by contrast, flatly refuse to give in to truthmaker demands. Recently, a third way has been proposed. This response seeks to address the truthmaking problem by tensing our truthmaker principles. These views, though intuitive, are under-developed. In this paper, I get serious about (...) a fundamentally tensed approach to truthmaking by sketching out the underlying ontological picture needed to make sense of tensed truthmaker theory. (shrink)

Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to be (...) general, applying to all predications, whether the subject of predication is a person, a planet, or a property.2 Despite the controversy surrounding the metaphysics of predication, many theistic philosophers—including the majority of contemporary analytic theists—regard Platonism as extremely attractive. At the same time, however, such philosophers are also commonly attracted to a form of traditional theism that has at its core the thesis that God is an absolutely independent.. (shrink)

Many philosophers believe that truth is grounded: True propositions depend for their truth on the world. Some philosophers believe that truth’s grounding has implications for our ontology of time. If truth is grounded, then truth supervenes on being. But if truth supervenes on being, then presentism is false since, on presentism, e.g., that there were dinosaurs fails to supervene on the whole of being plus the instantiation pattern of properties and relations. Call this the grounding argument against presentism. Many presentists (...) claim that the grounding argument fails because, despite appearances, supervenience is compatible with presentism. In this paper, I claim that the grounding argument fails because, despite appearances, truth’s grounding gives the presentist no compelling reason to adopt the sort of supervenience principle at work in the grounding argument. I begin by giving two precisifications of the grounding principle: truthmaking and supervenience. In Sect. 2, I give the grounding argument against presentism. In Sect. 3, I argue that we should distinguish between eternalist and presentist notions of grounding; once this distinction is in hand, the grounding argument is undercut. In Sect. 4, I show how the presentist’s notion of grounding leads to presentist-friendly truthmaking and supervenience principles. In Sect. 5, I address some potential objections. (shrink)

This paper sets out a new framework for discussing a long-standing problem in the philosophy of mathematics, namely the connection between the physical world and a mathematical domain when the mathematics is applied in science. I argue that considering counterfactual situations raises some interesting challenges for some approaches to applications, and consider an approach that avoids these challenges.

The metaphysics of relations is still in its infancy. We use the idea of truthmaking to gain purchase on this metaphysics. Assuming a modest supervenience conception of truthmaking, where true relational predications require multiply dependent truthmakers, these are indispensable relations. Though some such relations are required, none are needed for internal relatedness, nor for several other kinds of relational predication. Discerning the metaphysically basic kinds of relations is fraught with uncertainties, but must be tackled if progress is to be made.

Explanation has played myriad roles in truthmaker theory. The notion of explanation is sometimes thought to give content to the very idea of truthmaking, and is sometimes used as a weapon to undermine the entire point of truthmaker theory. I argue that the notion of explanation is dialectically useless in truthmaker theory: while it’s true that truthmaking offers a form of explanation, this claim is theoretically unilluminating, and leaves truthmaker theorists vulnerable to various kinds of attack. I advocate an alternative (...) approach to truthmaker theory that downplays the role of explanation, and show how it releases the enterprise from a variety of problematic commitments that have troubled truthmaker theorists. The “ontology-first” approach to truthmaking that I advocate not only restores the initial impulse behind truthmaking, but also has a number of theoretical advantages. Most prominently, it dodges the infamous problem of negative existentials, and lessens truthmaker theory’s dependence on contentious intuitive judgments about both explanation and truthmaking. (shrink)

This chapter is a work in applied metaphysics. Recent discussions of monism and metaphysical dependence are deployed to develop a view—the doctrine of divine priority (DDP)—that is a viable alternative to the doctrine of divine simplicity (DDS). DDS and the traditional motivation for it are discussed, then DDP is introduced by way of an analogy involving Jonathan Schaffer’s distinction between two forms of monism. It is argued that DDP is an alternative to DDS by showing that it is consistent with (...) the traditional motivation for the latter view, and argued that DDP is a viable alternative by showing that objections to its peculiar implications rest on assumptions that can reasonably be rejected. In the concluding section, the findings of the main discussion are summarized and DDP’s potential theological import is illustrated with a brief discussion of a possible solution to the Problem of the Trinity it affords. (shrink)

It is a common criticism of presentism – the view according to which only the present exists – that it errs against truthmaker theory. Recent attempts to resolve the truthmaker objection against presentism proceed by restricting truthmaker maximalism (the view that all truths have truthmakers), maintaining that propositions concerning the past are not made true by anything, but are true nonetheless. Support for this view is typically garnered from the case for negative existential propositions, which some philosophers contend are exceptions (...) to truthmaker maximalism. In this article, we argue that a ‘no truthmakers’ approach to the truthmaker objection is critically flawed. (shrink)

Truthmaker theory promises to do some useful philosophical work: equipping us to argue against phenomenalism and Rylean behaviourism, for instance, and helping us decide what exists (Lewis 1999, 207; Armstrong 1997, 113-119). But it has proved hard to formulate a truthmaker theory that is both useful and believable. I want to suggest that a neglected approach to truthmakers – that of Ian McFetridge – can surmount some of the problems that make other theories of truthmaking unattractive. To begin with, I’ll (...) outline some of the most prominent accounts of truthmaking in the current literature. Then the second part of the paper will explain McFetridge’s theory and argue for its superiority over these accounts. (shrink)

Metaphysical semantics is supposed to connect the nonfundamental to the fundamental in a distinctively “linguistic” way, explaining how nonfundamental truths can be grounded in fundamental facts , and so inducing a radically eliminative vision of the nonfundamental as mere talk. I wonder how the story goes when a single nonfundamental truth can be grounded in many different fundamental facts. For instance, the truth that Moore has hands can presumably be grounded in many different distributions of fields, arrangements of particles, vibrations (...) of strings, or whatnot. I am asking how metaphysical semantics can accommodate this sort of multiple realizability. (shrink)

Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...) that this is not so.I outline two contemporary philosophical accounts of mathematics thatpay a great deal of attention to the applicability of mathematics and showthat even these leave a large part of the puzzles in question unexplained. (shrink)

I argue against the standard view that ontological debates can be fully described as disagreements about what we should believe to exist. The central thesis of the paper is that believing in Fs in the ontologically relevant sense requires more than merely believing that Fs exist. Believing in Fs is not even a propositional attitude; it is rather an attitude one bears to the term expressed by 'Fs'. The representational correctness of such a belief requires not only that there be (...) Fs, but also that the term expressed by 'Fs' should not misrepresent them. In certain cases we might believe that there are Fs without believing our conception of Fs applies to them. This may well be the situation we are in with regard to abstract entities of various sorts. (shrink)