Gardeners, poets, lovers, and philosophers are all interested in the redness of roses; but only philosophers wonder how it is that two different roses can share the same property. Are red things red because they resemble each other? Or do they resemble each other because they are red? Since the 1970s philosophers have tended to favour the latter view, and held that a satisfactory account of properties must involve the postulation of either universals or tropes. But Gonzalo Rodriguez-Pereyra revives the (...) dormant alternative theory of resemblance nominalism, showing first that it can withstand the attacks of such eminent opponents as Goodman and Armstrong, and then that there are reasons to prefer it to its rival theories. The clarity and rigour of his arguments will challenge metaphysicians to rethink their views on properties. (shrink)

Gonzalo Rodriguez-Pereyra offers a fresh philosophical account of properties. How is it that two different things (such as two red roses) can share the same property (redness)? According to resemblance nominalism, things have their properties in virtue of resembling other things. This unfashionable view is championed with clarity and rigor.

Ian Hacking’s wide-ranging and penetrating analysis of science contains two well-developed lines of thought. The first emphasizes the contingent history of our inquiries into nature, focusing on the various ways in which our concepts and styles of reasoning evolve through time, how their current application is constrained by the conditions under which they arose, and how they might have evolved differently. The second is the mistrust of the idea that the world contains mind-independent natural kinds, preferring nominalism to ‘inherent (...) structurism’. These two pillars of thought seem at first to be mutually reinforcing: the lack of natural structure can help make sense of scientific variability and revision, while variability and revision provide reason to suspect that natural structure is little more than idealization. In what follows, I argue that these two pillars not only fail to support each other, but in fact conflict. One of them must fall, and it is clear which. (shrink)

Nominalism, which has its origins in the Middle Ages and continues into the Twenty-First Century, is the doctrine that there are no universals. This book is unique in bringing together essays on the history of nominalism and essays that present a systematic discussion of nominalism. It introduces the reader to the distinction between particulars and universals, to the difficulties posed by this distinction, and to the main motivations for the rejection of universals. It also describes the main (...) varieties of nominalism about properties and provides tools to understand how they developed in the history of Western Philosophy. All essays are new and are written by experts on the topic, and they advance the discussion about nominalism to a new level. (shrink)

1. 1. PROGRAM It will be our aim to reconstruct, with precision, certain views which have been traditionally associated with nominalism and to investigate problems arising from these views in the construction of interpreted formal systems. Several such systems are developed in accordance with the demand that the sentences of a system which is acceptable to a nominalist must not imply the existence of any entities other than individuals. Emphasis will be placed on the constructionist method of philosophical analysis. (...) To follow this method is to introduce the central notions of the subject-matter to be investigated into a system governed by exact rules. For example, the constructionist method of investigating the properties of geometric figures may consist in formulating a system of postulates and definitions which, together with the apparatus of formal logic, generates all necessary truths concerning geometric figures. Similarly, a constructionist analysis of the notion of an individual may take the form of an axiomatic theory whose provable assertions are just those which seem essential to the role played by the concept of an individual in system atic contexts. Such axiomatic theories gain in interest if they are supple mented by precise semantical rules specifying the denotation of all terms and the truth conditions of all sentences of the theory. (shrink)

‘Grounding and the indispensability argument’ presents a number of ways in which nominalists can use the notion of grounding to rebut the indispensability argument for the existence of mathematical objects. I will begin by considering the strategy that puts grounding to the service of easy-road nominalists. I will give some support to this strategy by addressing a worry some may have about it. I will then consider a problem for the fast-lane strategy and a problem for easy-road nominalists willing to (...) accept Liggins’ grounding strategy. Both are related to the problem of formulating nominalistic explanations at the right level of generality. I will then consider a problem that Liggins only hints at. This problem has to do with mathematics’ function of providing the sort of covering generalizations we need in scientific explanations. (shrink)

This chapter is a discussion of Class and Resemblance Nominalism. According to the traditional versions of these theories, properties are classes of particulars. Thus, the property of being red is the class of red particulars, and the property of being square is the class of square particulars. Several objections have been advanced against these theories, and one of the most powerful of such objections is the so-called Coextension Difficulty, according to which Class and Resemblance Nominalism have to wrongly (...) identify distinct but coextensive properties. After discussing the nature of Class and Resemblance Nominalism, some problems of these theories and how they can be deal with, the superiority of Class and Resemblance Nominalism over other theories of properties and the superiority of Resemblance Nominalism over Class Nominalism, I concentrate on the Coextension Difficulty. With respect to this I argue that Class and Resemblance Nominalism can be developed in such a way that they admit properties without identifying them with classes, and this allows them to avoid the Coextension Difficulty, since such versions of these theories are not forced to wrongly identify distinct but coextensive properties. Thus the Coextension Difficulty is not a lethal problem for Class and Resemblance Nominalism. (shrink)

In "nominalism and realism" armstrong carefully demolishes various nominalist responses to plato's "one over many" problem but simply dismissed the quinean response as "ostrich nominalism". The paper argues that plato's problem is pseudo. So to ignore it is not to behave like an ostrich. Rather to adopt realism because of this problem that isn't there is to be a "mirage realist." there are some good reasons that lead armstrong to realism but he is largely a mirage realist. Quine (...) does not ignore any real problem for nominalism and so is not an ostrich nominalist. (shrink)

Dispositional Essentialism, as commonly conceived, consists in the claims that at least some of the fundamental properties essentially confer certain causal-nomological roles on their bearers, and that these properties give rise to the natural modalities. As such, the view is generally taken to be committed to a realist conception of properties as either universals or tropes, and to be thus incompatible with nominalism as understood in the strict sense. Pace this common assumption of the ontological import of Dispositional Essentialism, (...) the aim of this paper is to explore a nominalist version of the view, Austere Nominalist Dispositional Essentialism. The core features of the proposed account are that it eschews all kinds of properties, takes certain predicative truths as fundamental, and employs the so-called generic notion of essence. As I will argue, the account is significantly closer to the core idea behind Dispositional Essentialism than the only nominalist account in the vicinity of Dispositional Essentialism that has been offered so far—Ann Whittle’s Causal Nominalism—and is immune to crucial problems that affect this view. (shrink)

I argue that constructive nominalism is preferable to scientific realism. Rather than reflecting without distortion the way the mind-independent world is, theories refract. They provide an understanding of the world as modulated by a particular theory. Truth is defined within a theoretical framework rather than outside of it. This does not undermine objectivity, for an assertion contains a reference to the framework in terms of which its truth is claimed.

Nominalism about attributes has serious difficulties in accounting for truths involving abstract nouns. Prominent among such truths are statements of comparative similarity among attributes. This paper argues that one cannot account for the truth of such statements without invoking attributes.

Theoria, EarlyView. -/- In his recent book Thin Objects, Øystein Linnebo (2018) argues for the existence of a hierarchy of abstract objects, sufficient to model ZFC, via a novel and highly interesting argument that relies on a process called dynamic abstraction. This paper presents a way for a nominalist, someone opposed to the existence of abstract objects, to avoid Linnebo's conclusion by rejecting his claim that certain abstraction principles are sufficient for reference (RBA). Section 1 of the paper explains Linnebo's (...) argument for RBA. It offers a reading of Linnebo's work upon which he has two arguments for RBA: one deductive and one abductive, and argues that whilst the deductive argument is unsound the abductive one is prima facie plausible. The nominalist must therefore find a way to respond to the abductive argument. Section 2 outlines just such a response, by offering an alternative explanation of the cases Linnebo wishes to argue from. Most interestingly, it shows that abstraction in Linnebo's most difficult case (the “reference to ordinary bodies” case) can be achieved using mereological means, rather than relying on RBA. (shrink)

In this dissertation I consider the merits of certain nominalist accounts of phenomena related to the character of ordinary objects. What these accounts have in common is the fact that none of them is an error theory about standard cases of predication and none of them deploys God or uniquely theistic resources in its explanatory framework. -/- The aim of the dissertation is to answer the following questions: -/- • What is the best nominalist account on offer? • How might (...) it be improved? • Does it ultimately succeed? -/- I will argue that while so-called trope theory is the best account on offer, it can be significantly improved—or replaced—by a novel version of nominalism that is modeled after trope theory. Ultimately, however, I will argue that even the novel version fails. -/- The dissertation unfolds as follows. In Chapter 1, I introduce Austere Nominalism (AN), which is perhaps the most extreme version of nominalism that falls within the scope of the dissertation. AN is often described as the view that there exist only concrete particulars. According to AN, it is unnecessary to posit any entities other than ordinary objects—turkeys, tables, and the like—in order to account for explananda related to the character of those objects. (Such explananda include the phenomenon of attribute agreement, of attribute possession, of true subject-predicate sentences, etc.) In this chapter I argue that AN fails to provide an adequate account of these explananda. In addition, introducing and criticizing AN serves an important heuristic role for the rest of the dissertation. To understand this role, we must distinguish between the basic explanatory strategy deployed by the austere nominalist and the type of explananda for which she deploys that strategy. The austere nominalist deploys the strategy to account for the character of ordinary objects. As I argue in Chapter 1, this deployment is a failure. As I go on to show in Chapter 2, the widespread rejection AN has led to a variety of rival accounts of the character of ordinary objects. In rejecting AN, however, these accounts also tacitly reject its basic explanatory strategy. Thus goes the baby with the bathwater, since, arguably, there are some attractive features of AN’s basic explanatory strategy. Indeed, those who defend the most prominent version of nominalism—trope theory—seem to overlook the advantages of AN’s basic strategy, and by so doing, make an unnecessary concession to the realist. Or so I argue in Chapter 3. And, as I will argue in Chapter 4, the strongest version of nominalism is a novel account, modeled after trope theory, that deploys AN’s basic strategy at a more fundamental level than that of ordinary objects. This novel account—troper theory—is closer in spirit to AN than is traditional trope theory. (Thus, AN serves as a foil for the discussion of other nominalist views.) Finally, in the Afterword I indicate how troper theory is equally vulnerable to some of the traditional objections that plague trope theory. Thus, if you are not convinced that traditional objections to trope theory are conclusive and you want to be a nominalist, then you should abandon trope theory and adopt troper theory. If you take traditional objections against trope theory to have significant force, then you should reject both theories. (shrink)

The article considers, in a historical setting, the links between varieties of nominalism—the extreme nominalism of the Quine-Goodman variety and the trope nominalism current today—and types of idealism. In so doing arguments of various twentieth century figures, including Husserl, Bradley, Russell, and Sartre, as well as a contemporary attack on relations by Peter Simons are critically examined. The paper seeks to link the rejection of realism about universals with the rejection of a mind-independent “world”—in short, linking (...) class='Hi'>nominalism with idealism. (shrink)

Bertrand Russell argued that any attempt to get rid of universals in favor of resemblances fails. He argued that no resemblance theory could avoid postulating a universal of resemblance without falling prey to a vicious infinite regress. He added that admitting such a universal of resemblance made it pointless to avoid other universals. In this paper I defend resemblance nominalism from both of Russell's points by arguing that (a) resemblance nominalism can avoid the postulation of a universal of (...) resemblance without falling into a vicious infinite regress, and (b) even if resemblance nominalism had to admit a universal of resemblance, this would not make it pointless to avoid postulating other universals. (shrink)

My aim in this paper is to offer a Hegelian critique of Quine’s predicate nominalism. I argue that at the core of Hegel’s idealism is not a supernaturalist spirit monism, but a realism about universals, and that while this may contrast to the nominalist naturalism of Quine, Hegel’s position can still be defended over that nominalism in naturalistic terms. I focus on the contrast between Hegel’s and Quine’s respective views on universals, which Quine takes to be definitive of (...) philosophical naturalism. I argue that there is no good reason to think Quine is right to make this nominalism definitive of naturalism in this way – where in fact Hegel offers a reasonably compelling case that science itself requires some commitment to realism about universals, kinds, etc. Furthermore, even if Hegel is wrong about that, at least his case for realism is still a naturalistic one, as it is based on his views on concrete universality, which is an innovative form of in rebus realism about unive.. (shrink)

It is widely assumed that platonism with respect to a discourse of metaphysical interest, such as fictional or mathematical discourse, affords a better account of the semantic appearances than nominalism, other things being equal. Of course, other things may not be equal. For example, platonism is supposed to come at the cost of a plausible epistemology and ontology. But the hedged claim is often treated as a background assumption. It is motivated by the intuitively stronger one that the platonist (...) can take the semantic appearances at ‘face-value’ while the nominalist must resort to ad hoc and technically problematic machinery in order to explain those appearances away. In this article, I argue that, on any natural construal of ‘face-value’, the platonist, like the nominalist, is not able to take the semantic appearances at face-value. And insofar as the nominalist is forced to resort to ad hoc and technically awkward devices in order to explain those appearances away, the platonist must resort to such devices as well. One moral of the story is that the thesis that platonism affords a better account of the semantic appearances than nominalism – even other things being equal – is not trivial. Another is that we should rethink a widespread methodology in metaphysics. (shrink)

The subject matter of this thesis is analytic ontology. Chapters II and III deal with two versions of trope theory, or moderate nominalism; these are defined as ontologies which recognise properties and relations but no (real) universals. The key notion of both theories, trope, is characterised as an abstract particular. What the abstractness amounts to differs between the two. Yet another difference is that simplicity is an essential trait of a trope according to one theory, but not according to (...) the other. Though exact similarity is said to play an important role in both theories, as it turns out, this does not seem to be the case. The ontology dealt with in chapter IV is a mixture of moderate nominalism concerning qualities and realism concerning relations. In it, quality instances (moments) and universal relations are the ultimate constituents of the universe. While relations and moments are considered to be constituents of states of affairs, which are characterised as objects of higher orders, complexes that are objects of the first order are made up of moments on their own. Among these complexes one finds the ordinary objects. Paradoxically, although relations are necessary for the existence of complex first order objects, relations are not thought to be among the contents of these objects. The main subject of chapter V is a particular version of moderate realism; it is an ontology which is realistic in its recognition of universals and moderate in its recognition of instances of these universals. Instances combine to form complex networks. A theoretically motivated claim is that although each instance has a predicational aspect as well as a universal one, it is simple in the sense of lacking internal predicative structure; though, this claim can be called into question. Keywords: analytic ontology, moderate nominalism, moderate realism, particular, universal, abstract, concrete, abstract particular, abstract universal, concrete particular, concrete universal, trope, moment, complex unity, collection, instance, unit attribute, intensional aspect, predicational aspect, continuous composite, articulated composite. (shrink)

This monograph details a new solution to an old problem of metaphysics. It presents an improved version of Ostrich Nominalism to solve the Problem of Universals. This innovative approach allows one to resolve the different formulations of the Problem, which represents an important meta-metaphysical achievement. In order to accomplish this ambitious task, the author appeals to the notion and logic of ontological grounding. Instead of defending Quine’s original principle of ontological commitment, he proposes the principle of grounded ontological commitment. (...) This represents an entirely new application of grounding. Some metaphysicians regard Ostrich Nominalism as a rejection of the problem rather than a proper solution to it. To counter this, the author presents solutions for each of the formulations. These include: the problem of predication, the problem of abstract reference, and the One Over Many as well as the Many Over One and the Similar but Different variants. This book will appeal to anyone interested in contemporary metaphysics. It will also serve as an ideal resource to scholars working on the history of philosophy. Many will recognize in the solution insights resembling those of traditional philosophers, especially of the Middle Ages. (shrink)

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

The notion of grounding has gained increasing acceptance among metaphysicians in recent years. In this paper, I argue that this notion can be used to formulate a very attractive version of (property) nominalism, a view that I call ‘grounding nominalism’. Simplifying somewhat, this is the view that all properties are grounded in things. I argue that this view is coherent and has a decisive advantage over competing versions of nominalism: it allows us to accept properties as real, (...) while fully accommodating nominalist intuitions. Finally, I defend grounding nominalism against several seemingly troublesome objections. (shrink)

The causal theory of properties is standardly combined with a realist's ontology of universals or tropes. In this paper, I consider an uncharted alternative – a nominalist causal theory of properties. I discuss advantages and disadvantages of the resulting theory of properties, and explore the Rylean understanding of causal powers that emerges.

This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...) discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications. (shrink)

Nelson Goodman’s disparate writings are often discussed and written about only within their own particular discipline, such that the epistemology is discussed in contrast to others’ epistemology, the aesthetics is contrasted with more traditional aesthetics, and the ontology and logic is viewed in opposition to both other contemporary philosophers and to his historical predecessors. This book argues that that is not an adequate way to view Goodman. The book is divided into three sections: The Metaphysics, The Epistemology, The Aesthetics. I (...) demonstrate, firstly, the dependency of his epistemology and aesthetics on his early metaphysical and ontological writings, and secondly, that it is the very application of those metaphysical and ontological positions to the rest of his philosophical writings that is the source of much of which fails to be completely satisfactory in his aesthetics. They are sequential sections within each providing the ground rules for the next section and, furthermore, providing the reasons for limitations on the terms available to the subsequent section(s). Thus the Metaphysics is an explication of Gooodman’s basic nominalist ontology and logic, and it is upon those principles that he builds his epistemology. It is the sum of both the metaphysics and the epistemology, with the nominalist principle as the guiding force, which constructs the aesthetics. At the end of each section, the consequent limitations imposed on his terms and concepts available to him are explicated, such that, by the end of the book, I am able to delineate the constraints imposed upon the aesthetics by both the metaphysics and the epistemology. (shrink)

In my book *Resemblance Nominalism* I argued that the truthmakers of ´a and b resemble each other´ are just a and b. In his "Resemblance Nominalism and counterparts" Alexander Bird objects to my claim that the truthmakers of ´a and b resemble each other´ are just a and b. In this paper I respond to Bird´s objections.

This paper explores the impact of quantification into predicate position on the metaphysics of properties, arguing that two familiar debates about properties are fundamentally altered by recasting them in a second-order setting. Two theories of properties are outlined, differing over whether the existence of properties is expressed using first-order or second-order quantifiers. It is argued that the second-order theory: provides good reason to regard debate about the locations of properties as contentless; resolves debate about whether properties are particulars or universals (...) in favour of universals. (shrink)

This is a study, in two volumes, of one of the longest-standing philosophical problems: the problem of universals. In volume I David Armstrong surveys and criticizes the main approaches and solutions to the problems that have been canvassed, rejecting the various forms of nominalism and 'Platonic' realism. In volume II he develops an important theory of his own, an objective theory of universals based not on linguistic conventions, but on the actual and potential findings of natural science. He thus (...) reconciles a realism about qualities and relations with an empiricist epistemology. The theory allows, too, for a convincing explanation of natural laws as relations between these universals. (shrink)

The paper focuses on Nominalism in history, its application, and its historiographical implications. By engaging with recent scholarship as well as classic works, a survey of Nominalism’s role in the discipline of history is made; such examination is timely, since it has been done but scantily in a purely historical context. In the light of recent theoretical works, which often display aporias over the nature and method of historical enquiry, the paper offers new considerations on historical theory, which (...) in the author’s view may solve some of the contradictions that have surfaced in recent times. The Nominalistic stance is argued against by disputing theorists such as Paul Veyne, who has made a case for Nominalism in history. A brief philosophical section introduces Nominalism in its metaphysical dimension and the discussion is speedily brought to its significance for history. The paper also proposes a solution to the misconstrued yet too often vague application of scientism in history, and offers theoretical grounds that might solve some of the ‘stormy grounds’ historiography finds itself today. Articles by Marcel Gauchet and History and Theory’s Anton Froeyman and Bert Leuridan are engaged with, as well as Murray Murphy’s books on the philosophy of history. Works by Georg Gadamer, Marc Bloch, Benedetto Croce, Hyppolite Taine, and Anthony Grafton crucially inform the discussion and brace the consequential conclusion. (shrink)

The idea of “material plenitude” has been gaining traction in recent discussions of the metaphysics of material objects. My main goal here is to show that this idea may have important dialectical implications for the metaphysics of properties – more specifically, that it provides nominalists with new resources in their attempt to reject an ontology of universals. I will recapitulate one of the main arguments against nominalism – due to David Armstrong – and show how plenitude helps the nominalist (...) overcome the argument. (shrink)

Many philosophers of mathematics are attracted by nominalism – the doctrine that there are no sets, numbers, functions, or other mathematical objects. John Burgess and Gideon Rosen have put forward an intriguing argument against nominalism, based on the thought that philosophy cannot overrule internal mathematical and scientific standards of acceptability. I argue that Burgess and Rosen’s argument fails because it relies on a mistaken view of what the standards of mathematics require.

‘Nominalism’ refers to a family of views about what there is. The objects we are familiar with (e.g. hands, laptops, cookies, and trees) can be characterized as concrete and particular. Nominalists agree that there are such things. But one group of nominalists denies that anything is non-particular and another group denies that anything is non-concrete. These two sorts of nominalism, referred to as ‘nominalism about universals’ and ‘nominalism about abstract objects’, have common motivations in contemporary philosophy.

William of Ockham is a towering figure in the history of philosophy and he is commonly seen as the most important nominalist thinker of the Middle Ages. His nominalism basically consists in three theses: there are no universals in the external world, no relations either, and no quantities considered as distinct entities. This book provides an introduction to Ockham's defence of these positions and to what they amount to in metaphysics, semantics, and epistemology. It thus displays the outlines of (...) a rich and carefully crafted nominalist system that is still of great philosophical interest today. All along in so doing, it situates Ockham's thought with respect to several salient contemporary debates in philosophy. (shrink)

A challenger of traditions and boundaries A pivotal figure in 20th-century philosophy, Nelson Goodman has made seminal contributions to metaphysics, epistemology, aesthetics, and the philosophy of language, with surprising connections that cut across traditional boundaries. In the early 1950s, Goodman, Quine, and White published a series of papers that threatened to torpedo fundamental assumptions of traditional philosophy. They advocated repudiating analyticity, necessity, and prior assumptions. Some philosophers, realizing the seismic effects repudiation would cause, argued that philosophy should retain the familiar (...) framework. Others considered the arguments compelling, but despaired of doing philosophy without the framework. Goodman disagreed with both factions. Rather than regretting the loss of structure, he capitalized on the opportunities that arise when the strictures of tradition are loosened. Available individually by volume 1. Nominalism, Constructivism, and Relativism in the Work of Nelson Goodman (0-8153-2609-2) 296 pages 2. Nelson Goodman's New Riddle of Induction (0-8153-2610-6) 312 pages 3. Nelson Goodman's Philosophy of Art (0-8153-2611-4) 284 pages 4. Nelson Goodman's Theory of Symbols and its Applications (0-8153-2612-2) 344 pages. (shrink)

ABSTRACT: Sellars formulated his thesis of 'psychological nominalism' in two very different ways: (1) most famously as the thesis that 'all awareness of sorts…is a linguistic affair', but also (2) as a certain thesis about the 'psychology of the higher processes'. The latter thesis denies the standard view that relations to abstract entities are required in order to explain human thought and intentionality, and asserts to the contrary that all such mental phenomena can in principle ‘be accounted for causally' (...) without any use of normative terms in the explanation. Recent 'Hegelian Sellarsians' such as Rorty, McDowell, and Brandom have argued that the holistic, normative themes in (1) support various non-realist or rather (German) 'idealist but common-sense realist' outlooks. By contrast, Sellars' own defenses of (2) reveal psychological nominalism itself to be a naturalistic empiricism intended to sustain the normative-holistic themes in (1) within an exhaustively scientific naturalist conception of reality. (shrink)

Probably there is no position in Goodman’s corpus that has generated greater perplexity and criticism than Goodman’s “nominalism”. As is abundantly clear from Goodman’s writings, it is not “abstract entities” generally that he questions—indeed, he takes sensory qualia as “basic” in his Carnap-inspired constructional system in Structure—but rather just those abstracta that are so crystal clear in their identity conditions, so fundamental to our thought, so prevalent and seemingly unavoidable in our discourse and theorizing that they have come to (...) form the generally accepted framework for the most time-honored, exact, sophisticated, refined, central, and secure branch of human knowledge yet devised, mathematics itself! Of all the abstracta to question, why sets? Of course, Goodman gave his “reasons”, the unintelligibility of “generating” an infinitude of “constructed objects” automatically from any given object or objects. But critics have been quick to point out that set theory is intended not as a theory of what can be “generated” or “constructed” from given objects in any literal sense but rather as a theory of a certain realm of objects independently existing in their own right. “Construction” is a metaphor. (shrink)

Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of mathematical statements in terms of possible linguistic constructions. The chapter responds directly to a recent study of nominalism by Gideon Rosen and John Burgess, and develops a reply to the Quine-Putnam indispensability argument for the existence of mathematical objects.

There are a number of different versions of Reductive Nominalism, versions distinguished by the way in which each accounts for facts about having and sharing properties. This chapter discusses three broad varieties of Reductive Nominalism: Predicate Nominalism, Class Nominalism, and Resemblance Nominalism. Class Nominalism identifies properties with classes or sets. Resemblance Nominalists come in two sub‐varieties, depending on whether they take the resemblance relation to hold between particular properties (called 'tropes') or particular things that (...) have properties (ordinary particulars). Trope Theory comes in two varieties depending on whether one plumps for universals. It should not be difficult to see that Extreme Resemblance Nominalism is faced with Class Nominalism's extensionality problems, both the problem of contingent predication and the co‐extensive property problem. Resemblance Nominalists can reply by insisting on a distinction between a priori or conceptual equivalence and metaphysical equivalence. The chapter focuses on the extensionality problems for Class Nominalism. (shrink)