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)

Truthmaker theorists hold that there is a metaphysically explanatory relation that holds between true claims and what exists. While some critics try to provide counterexamples to truthmaker theory, that response quickly leads to a dialectical standoff. The aim of this paper is to move beyond that standoff by attempting to undermine some standard arguments for truthmaker theory. Using realism about truth and a more pragmatic account of explanation, I show how some of those arguments can be undermined.

According to the presentist, it is always the case that the only existing objects are those that exist at the present time, and the only properties and relations that are instantiated are those that are instantiated at the present time. The truth-supervenes-on-being thesis (TSB) is that there can be no difference in what is true without a corresponding difference in what exists and in what properties and relations are instantiated. The truth-supervenes-on-being objection says that presentism cannot accommodate TSB. Lucretianism is (...) the thesis that the world instantiates irreducibly past-tensed properties. Though not popular, it is not entirely uncommon for presentists to endorse Lucretianism as a means to respond to the truth-supervenes-on-being objection. Defenses of Lucretianism itself are still less common. Appropriately up-to-date defenses are lacking altogether. I take up such a defense, arguing that the attacks on Lucretianism fail, and that there is, therefore, no compelling truth-supervenes-on-being objection to presentism. (shrink)

This paper is an investigation in the use of truthmaker theory for exploring the relation of logic to world, and as a tool for metaphysics. A variant of truthmaker theory, which we call the simple theory, is defined and defended against objections. It is characterized formally, and its central features are derived. As part of this project, we give a formal metaphysics based on nondeterministic necessitation relations among possible entities. In what is called the fundamental theorem of truthmaking, it is (...) shown that, as long as a logic is sound and complete, its inferential structure will be isomorphic to the necessitation structure of our metaphysics. We thus arrive at a purely structural logic–world relationship which can be used for metaphysical investigations. Other products of our investigation are a sound and complete semantics for first-order logic with identity and a solution to a result of Restall which has threatened to make truthmaker theory trivial. (shrink)

The starting point of this paper is the idea that linguistic representation is the result of a global process: a process of interaction of a community of cognitive-linguistic agents, with one another and with the environment. I maintain that the study of truth, meaning and related notions should be addressed without losing perspective of this process, and I oppose the ‘static’ or ‘analytic’ approach, which is fundamentally based on our own knowledge of the conventional meaning of words and sentences, and (...) the ability of using them that we have as competent speakers. I argue that the analytic perspective is responsible for five recurring difficulties in truthmaker theory: (1) the lack of attention to the difference of explanatory role between the distinct notions proposed as primary truthbearer; (2) the adscription of purely extra-linguistic truthmakers to ‘synthetic truths’, ignoring the contribution of the linguistic factor; (3) the adscription of purely linguistic truthmakers to ‘logical’ and ‘analytic truths’, ignoring the contribution of the worldly factor; (4) the difficulties in the search for minimal truthmakers; (5) the problems in the treatment of ‘negative facts’ and of other ‘logically complex facts’. I do not provide an account of how to solve these difficulties, but I do show how the ‘process model’ helps to clear up confusion regarding them. (shrink)

Metaphysics has had a long history of debate over its viability, and substantivity. This thesis explores issues connected to the realism question within the domain of metaphysics, ultimately aiming to defend a realist, substantive metaphysics by responding to so-called deflationary approaches, which have become prominent, and well supported within the recent metametaphysical and metaontological literature. To this end, I begin by examining the changing nature of the realism question. I argue that characterising realism and anti-realism through theories of truth unduly (...) places epistemology prior to ontology, and is unwarranted in assuming a non-neutrality between theories of truth and positions within the realism debate. I therefore propose a characterisation of realism and anti-realism understood through truthmaking. This produces a suitable working characterisation of realism that will be used within the remainder of this project. In the second section, I trace the historical influences upon current deflationary approaches to metaphysics, most prominently those of Carnap, and Putnam. I argue that Quine’s supposed attack on Carnap’s anti-metaphysical thought fails, and show how current deflationary thought, most prominently exhibited by Hirsch, came to focus on linguistically derived concerns over the substantivity of metaphysics. In the third section, I outline a number of issues for the deflationist, and defend the coherency and legitimacy of the unrestricted existential quantifier. Focusing on the linguistic aspect of deflationism, I argue that the conception of language that the deflationist relies upon lacks suitable empirical and theoretical support within linguistics and other related domains. Furthermore, I suggest that linguistic analysis in fact supports the claim that the quantifier carries no inherent restrictions. This restores our ability to suitably posit the unrestricted existential quantifier, as a quantifier wherein the domain is only restricted by metaphysically substantive restrictions. Through this, I argue that metaphysics is a substantive domain of discourse. Lastly, I sketch a positive account of how, under an empirically and theoretically justified conception of language, metaphysics can be coherently held to be a realist, substantive enterprise, contra claims that hold that the nature of language inherently prevents metaphysics being considered to be a substantive domain of discourse. (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)

It is often taken for granted that truth is mind-independent, i.e. that, necessarily, if the world is objectively speaking in a certain way, then it is true that it is that way, independently of anyone thinking that it is that way. I argue that proponents of correspondence-truth, in particular immanent realists, should not take the mind-independence of truth for granted. The assumption that the mind-independent features of the world, i.e. ‘facts’, determine the truth of propositions, does not entail that truth (...) is independent of minds. This follows only on the further assumption that there exist propositions about every feature of reality independent of minds, which is something the immanent realist can and should deny. (shrink)

We defend two claims: (1) if one is attracted to a strong non-maximalist view about truthmaking, then it is natural to construe this as the view that there exist fundamental truths; (2) despite considerable aversion to fundamental truths, there is as yet no viable independent argument against them. That is, there is no argument against the existence of fundamental truths that is independent of any more specific arguments against the ontology accepted by the strong non-maximalist. Thus there is no argument (...) that the strong non-maximalist herself will find dialectically motivating. (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)

Epistemicism about vagueness is the view that vagueness, or indeterminacy, is an epistemic matter. Truthmaker-gap epistemicism is the view that indeterminate truths are indeterminate because their truth is not grounded by any worldly fact. Both epistemicism in general and truthmaker-gap epistemicism originated in Roy Sorensen's work on vagueness. My aim in this paper is to give a characterization of truthmaker-gap epistemicism and argue that the view is incompatible with higher-order vagueness: vagueness in whether some case of the form ‘it is (...) determinate that A’ or ‘it is indeterminate whether A’ is true. Since it is highly likely that there is higher-order vagueness, truthmaker-gap epistemicism is in an uncomfortable position. (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)

Recent discussion of the problem of negative existentials for truthmaker theory suggests a modest solution to the problem: fully general negative truths like do not require truthmakers, whereas partially general negative truths like do. This modest solution provides a third alternative to the two standard solutions to the problem of negative existentials: the endorsement of truthmaker gaps, and the appeal to contentious ontological posits. We argue that this modest, middle-ground position is inconsistent with certain plausible general principles for truthmaking. The (...) only stable positions are to treat all negative truths as requiring truthmakers, or admit that no negative truths require truthmakers. Along the way, we explore some previously unaddressed questions for nonmaximalist truthmaker theory. (shrink)

Recent attempts to resolve the truthmaker objection to presentism employ a fundamentally tensed account of the relationship between truth and being. On this view, the truth of a proposition concerning the past supervenes on how things are, in the present, along with how things were, in the past. This tensed approach to truthmaking arises in response to pressure placed on presentists to abandon the standard response to the truthmaker objection, whereby one invokes presently existing entities as the supervenience base for (...) the truth of past-directed propositions. In this paper, I argue that a fundamentally tensed approach to truthmaking is implausible because it requires the existence of cross-temporal supervenience relations, which are anathema to presentism. (shrink)

Lewis's notion of a "natural" property has proved divisive: some have taken to the notion with enthusiasm, while others have been sceptical. However, it is far from obvious what the enthusiasts and the sceptics are disagreeing about. This paper attempts to articulate what is at stake in this debate.

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)

This paper attempts to define indexicality so as to semantically distinguish indexicals from proper names and definite descriptions. The widely-accepted approach that says that indexical reference is distinctive in being dependent on context of use is criticized. A reductive approach is proposed and defended that takes an indexical to be (roughly) an expression that either is or is equivalent to ‘here’ or ‘now’, or is such that a tokening of it refers by relating something to the place and/or time that (...) would have been referred to had ‘here’ and ‘now’ been tokened instead. Alternative reductive approaches are criticized. (shrink)

Truthmaker theorists hold that propositions about higher-level entities (e.g. the proposition that there is a heap of sand) are often made true by lower-level entities (e.g. by facts about the configuration of fundamental particles). This generates a problem: what should we say about these higher-level entities? On the one hand, they must exist (since there are true propositions about them), on the other hand, it seems that they are completely superfluous and should be banished for reasons of ontological parsimony. Some (...) truthmaker theorists—most prominently David Armstrong—have tried to solve this puzzle by arguing that these entities are ‘an ontological free lunch’, i.e. real existents that are still ‘no addition of being’. This answer is prima facie attractive, but I argue in this paper that the standard approaches to truthmaking—modal theories and grounding theories—are unable to vindicate the doctrine of the ontological free lunch, and thus fail to solve the problem of higher-level entities. Fortunately, there is a non-standard account of truthmaking available, the reductive explanation account, which succeeds where the standard approaches fail. (shrink)

Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...) the indispensability argument. (shrink)

Presentists face a challenge from truthmaker theory: if you hold both that the only existing objects are presently existing and that truth supervenes on being, then you will be hard pressed to identify some existent on which a given true but traceless claim about the past supervenes. One reconciliation strategy, advocated by Cameron (2011), is to appeal to distributional properties so to serve as presently existing truthmakers for past truths. I argue that a presentist ought to deny that distributional properties (...) can serve as truthmakers. (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.

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)

After sketching some aspects of truthmaker doctrines and "truthmaker projects", and canvassing some prima facie objections to the latter, I turn to an issue which might seem to involve confusion about the nature of character of truthmakers if such there be, viz for statements of identity and (specially) distinctness. The real issue here is versions of the Identity of Indiscernibles. I discuss ways of discriminating versions, which are almost certainly true but trivial, which almost certainly substantive but false, and explore (...) an interesting intermediate possibility which might if developed yield a plausibly true yet not-entirely-trivial version of the doctrine: it is equivalent to what I call "the Denial of Bare Distinctness". (shrink)

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(No abstract is available for this citation).

Truthmakers are supposed to explain the truth of propositions, but it is unclear what kind of explanation truthmakers can provide. In this paper, I argue that ‘truthmaker explanations’ conflate two different explanatory projects. The first project is essentially concerned with truth, while the second project is concerned with reductive explanation. It is the latter project, I maintain, which is really central to truthmaking theory. On this basis, a general account of truthmaking can be formulated, which, when combined with a specific (...) theory of reduction (the ‘conceptual entailment approach’), yields a new analysis of truthmaking. This analysis is intuitively appealing and avoids the problem of necessary truths, which poses a serious obstacle for standard accounts. (shrink)

This essay is a reflection on the idea of truth-making and its applications. I respond to a critique of my 1986 paper on truth-making and discuss some key principles at play in the Truth-maker Program as it has emerged over the past 25 years, paying special attention to negative and general truths. I maintain my opposition to negative and general facts, but give an improved account of how to do without them. In the end, I accept Truth-maker Maximalism and a (...) weakened form of Truth-maker Necessitarianism, reject the assumption that truth-makers must be entities, and urge that the idea of a truth-maker be broadened and loosened so that it applies to anti-realistic as well as realistic truths. (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)

Truthmaker theorists claim that for every truth, there is something in virtue of which it is true—or, more cautiously, that for every truth in some specified class of truths, there is something in virtue of which it is true. I argue that it is hard to see how the thought that truth is grounded in reality lends any support to truthmaker theory.

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)

Supervenience is a topic-neutral, broadly logical relation between classes of properties or facts. In a slogan, A supervenes on B if and only if there cannot be an A-difference without a B-difference. The first part of this paper considers different ways in which that slogan has been cashed out. The second part discusses applications of concepts of supervenience, focussing on the question whether they may provide an explication of determination theses such as physicalism.

The Principal Principle (PP) says that, for any proposition A, given any admissible evidence and the proposition that the chance of A is x%, one's conditional credence in A should be x%. Humean Supervenience (HS) claims that, among possible worlds like ours, no two differ without differing in the spacetime-point-by-spacetime-point arrangement of local properties. David Lewis (1986b, 1994a) has argued that PP contradicts HS, and the validity of his argument has been endorsed by Bigelow et al. (1993), Thau (1994), Hall (...) (1994), Strevens (1995), Ismael (1996), Hoefer (1997), and Black (1998). Against this consensus, I argue that PP might not contradict HS: Lewis's argument is invalid, and every attempt – within a broad class of attempts – to amend the argument fails. (shrink)

For many years there has been a debate in truthmaking theory between proponents of the substantive and deflationary approaches. Substantivists about truthmaking maintain that we need entities called truthmakers, while deflationists of truthmaking argue that the asymmetric form of the T-schema is sufficient. In contrast to incompatibilists, who argue that one should adopt only one of these approaches, I propose a compatibilist theory of truthmaking in which the two approaches complement each other through the distribution of different functions of truthmaking. (...) I find that this helps to solve the problem of truthmaking of certain contentious truths, such as negative truths. (shrink)

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)

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.

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)

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)

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)

Suppose nothing exists. Then it is true that nothing exists. What makes that true? Nothing! So it seems that if nothing existed, then the principle that every truth is made true by something (the truthmaker principle) would be false. So if it is possible that nothing exists, a claim often called 'metaphysical nihilism', then the truthmaker principle is not necessary. This paper explores various ways to resolve this conflict without restricting metaphysical nihilism in such a way that it would become (...) trivial and uninteresting. (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 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)

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)

Truthmaking non-maximalism usually assumes that some truths do not have truthmakers. I suggest, however, that non-maximalism can be understood more specifically, and that different types of non-maximalism can be distinguished. To do so, I refer to two positions. The first is deflationary truthmaking, some of whose proponents assume that no truths have truthmakers. The second distinguishes between truths that do not have truthmakers but depend on being, and truths that do not have truthmakers and moreover do not depend on being. (...) Given the combinations of these positions, I propose a new classification indicating the positions available to a non-maximalist. I argue that one of these positions is particularly worth adopting because of its advantages over the other options. (shrink)