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.
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)
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)
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)
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.
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)
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.
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)
The object of this paper is to provide a solution to Nelson Goodman's Imperfect Community difficulty as it arises for Resemblance Nominalism, the view that properties are classes of resembling particulars. The Imperfect Community difficulty consists in that every two members of a class resembling each other is not sufficient for it to be a class such that there is some property common to all their members, even if `x resembles y' is understood as `x and y share some (...) property'. In the paper I explain and criticise several solutions to the difficulty. Then I develop my own solution, which is not subject to the objections I make to the other solutions, and which accords completely with the basic tenets of Resemblance Nominalism. (shrink)
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)
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)
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)
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)
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.
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)
Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
‘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)
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.
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)
In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this (...) reasoning generalizes to other philosophically problematic entities. The moral is that puzzle avoidance fails to motivate deflationary nominalism. (shrink)
Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with the cost of not taking mathematical theories literally. Jody Azzouni's _Deflating Existential Consequence_ has recently challenged this conclusion by formulating a nominalist view that lacks this cost. In this paper, we argue that, as it stands, Azzouni's proposal does not yet succeed. It faces a dilemma to the effect that either the view is not (...) nominalist or it fails to take mathematics literally. After presenting the dilemma, we suggest a possible solution for the nominalist. (shrink)
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)
We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.
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.
In this paper I draw a connection between Kuhn and the empiricist legacy, specifically between his thesis of incommensurability, in particular in its later taxonomic form, and van Fraassen's constructive empiricism. I show that if it is the case the empirically equivalent but genuinely distinct theories do exist, then we can expect such theories to be taxonomically incommensurable. I link this to Hacking's claim that Kuhn was a nominalist. I also argue that Kuhn and van Fraassen do not differ as (...) much as might be thought as regards the claim that observation is theory laden. (shrink)
This paper by Theodore de Laguna presents and argues for the deflationary theory of truth. The paper was first published in French in 1922. The version published here is the original, English version of the paper and has been edited by Joel Katzav.
The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...) difficulties while still being able to put abstraction principles to a foundational use. (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.
One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case (...) for two alleged nominalist views: Field’s fictionalism, and Frank Arntzenius and Cian Dorr’s geometricalism. Central to our competing approach to nominalism is a distinction between terms that refer to objects and ones that instead code empirical phenomena while being referentially empty. We next contrast our approach to nominalism, which uses this term-grained distinction between coding and referring, with approaches that instead attempt to make a sentence-grained distinction between mathematical and non-mathematical content. We show the latter approach fails to be responsive to objections raised by van Fraassen. In the end, only one last approach to nominalism is left standing. 1 Introduction2 Troubles for Mathematical Fictionalism2.1 A distinction2.2 Field’s programme2.3 Parts of nominalistically acceptable entities are nominalistically acceptable2.4 Structural assumptions: How far can these be pushed?2.5 Cases of indispensable theories where the mathematical posits are known not to be real2.6 How does science distinguish between the indispensable structural presuppositions taken to be real and those that aren’t?2.7 Do physicists distinguish between mathematical posits and non-mathematical posits?2.8 Mathematical coding versus genuine metaphysics. Case study: Fields2.9 The upshot3 Troubles for Topologism4 Contrasts: Kitcher, Maddy, Sober, and van Fraassen4.1 Sober’s approach4.2 Maddy’s approach4.3 Kitcher’s approach4.4 Where do we go from here?4.5 Van Fraassen’s objection to Maddy’s approach to ontological commitment5 Conclusion. (shrink)
The concept of population thinking was introduced by Ernst Mayr as the right way of thinking about the biological domain, but it is difficult to find an interpretation of this notion that is both unproblematic and does the theoretical work it was intended to do. I argue that, properly conceived, Mayr’s population thinking is a version of trope nominalism: the view that biological property-types do not exist or at least they play no explanatory role. Further, although population thinking has (...) been traditionally used to argue against essentialism about biological kinds, recently it has been suggested that it may be consistent with at least some forms of essentialism—ones that construe essential properties as relational. I argue that if population thinking is a version of trope nominalism, then, as Mayr originally claimed, it rules out any version of essentialism about biological kinds. (shrink)
It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path (...) to easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism. (shrink)
This paper focuses on a central aspect of the “picture theory” in the Tractatus – the “identity requirement” – namely the idea that a proposition represents elements in reality as combined in the same way as its elements are combined. After introducing the Tractatus' views on the nature of the proposition, I engage with a “nominalist” interpretation, according to which the Tractatus holds that relations are not named in propositions. I claim that the nominalist account can only be maintained by (...) rejecting the “identity requirement.” I then consider an opposite – “realist” – interpretation, according to which Tractarian names include names of properties and relations. I argue that, although it can accommodate the “identity requirement,” the realist interpretation falls short of providing a correct interpretation of the Tractatus' conception of a name. I conclude by presenting an alternative account (to both nominalism and realism) of the Tractatus' conception of a name. (shrink)
In this essay I first outline contemporary Platonism about musical works – the theory that musical works are abstract objects. I then consider reasons to be suspicious of such a view, motivating a consideration of nominalist theories of musical works. I argue for two conclusions: first, that there are no compelling reasons to be a nominalist about musical works in particular, i.e. that nominalism about musical works rests on arguments for thoroughgoing nominalism, and, second, that if Platonism fails, (...) fictionalism about musical works is to be preferred to other nominalist ontologies of musical works. (shrink)