Heavy duty platonism is of great dialectical importance in the philosophy of mathematics. It is the view that physical magnitudes, such as mass and temperature, are cases of physical objects being related to numbers. Many theorists have assumed HDP’s falsity in order to reach their own conclusions, but they are only justified in doing so if there are good arguments against HDP. In this paper, I present all five arguments against HDP alluded to in the literature and show that they (...) all fail. In doing so, I establish two related truths: HDP has been unfairly ignored, and the arguments which take its falsity as a key premise should be re-assessed. (shrink)

In ‘Ramseyan Humility’ David Lewis argues that a particular view about fundamental properties, quidditism, leads to the position that we are irredeemably ignorant of the identities of fundamental properties. We are ignorant of the identities of fundamental properties since we can never know which properties play which causal roles, and we have no other way of identifying fundamental properties other than by the causal roles they play. It has been suggested in the philosophical literature that Lewis’ argument for Humility is (...) merely an instance of traditional scepticism, to which traditional responses to scepticism are applicable. I agree that in ‘Ramseyan Humility’ Lewis does present an argument to which it is appropriate to consider the applicability of responses to traditional scepticism—he argues that we irredeemably lack the evidence to rule out possibilities in which different properties occupy the causal roles described by our best physical theory. And prima facie this is just the kind of argument responses to traditional scepticism are designed to tackle. However, I will argue that Lewis bolsters this argument with a second. This second argument serves to deepen Lewis’ case and cannot be met with a response to traditional scepticism. For Lewis argues that not only do we lack evidence for which properties play which roles, we lack the ability to grasp any such proposition about role-occupancy. And if we cannot grasp any such proposition we cannot know it. (shrink)

Are the sparse properties drawn from all the levels of nature, or only the fundamental level? I discuss the notion of sparse property found in Armstrong and Lewis, show that there are tensions in the roles they have assigned the sparse properties, and argue that the sparse properties should be drawn from all the levels of nature.

Problems about the accidental properties of properties motivate us--force us, I think--not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us--though this time they probably don't force us--to give up this theory as well, (...) and to identify properties with functions from world, time pairs to extensions. Again, the replacement theory is neutral with respect to a metaphysical dispute that the old theory (arguably) forces us to take a stand on--the dispute over whether objects have temporal parts. It also allows us to give a smoother semantics for predication, to better accommodate our intuitions about which objects temporary properties are properties of, and to make temporally self-locating beliefs genuinely self -locating. (shrink)

I explore two accounts of properties within a dispositional essentialist (or causal powers) framework, the pure powers view and the powerful qualities view. I first attempt to clarify precisely what the pure powers view is, and then raise objections to it. I then present the powerful qualities view and, in order to avoid a common misconception, offer a restatement of it that I shall call the truthmaker view. I end by briefly defending the truthmaker view against objections.

Powers are popularly assumed to be distinct from, and dependent upon, inert qualities, mainly because it is believed that qualities have their nature independently of other properties while powers have their nature in virtue of a relation to distinct manifestation property. George Molnar and Alexander Bird, on the other hand, characterize powers as intrinsic and relational. The difficulties of reconciling the characteristics of being intrinsic and at the same time essentially related are illustrated in this paper and it is argued (...) that the reasons for thinking of powers as essentially relational are based on misguided epistemological consideration. Finally, I present a way of thinking of fundamental properties as primitive natures that we can only understand in virtue of what they do but which we should not think of as being ontologically constituted by these doings. According to this view, properties are both qualities and powers. (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 nominalism with idealism.

Indexicality is a feature of predicates and predicate components (verbs, adjectives, adverbs and the like) as well as of referring expressions. With classic referring indexicals such as 'I' or 'that' a distinctive rule takes us from token and context to some item present in the content which is the semantic correlate of the token. Predicates and predicate components may function in an analogous fashion. For example 'thus' is an indexical adverb which latches onto some manner of performance present in its (...) context. 'John sang thus', said while indicating someone singing discordantly, claims that John sang discordantly. The phenomenon of predicatival indexicality is widespread in English and is expressed in a variety of idioms. Indexical predication plays important epistemological and psychological roles and the notion may have other interesting philosophical applications. (shrink)

If the property _being a methane molecule_ is a universal, then it is a structural universal: objects instantiate _being a methane molecule_ just in case they have the right sorts of proper parts arranged in the right sort of way. Lewis argued that there can be no satisfactory account of structural universals; in this paper I provide a satisfactory account.

A certain theory of substance, one that grows out of Aristotelian philosophy but which has adherents today as well, draws a distinction between the features a substance has by instantiating a universal and the features it has by possessing a trope. An adherent of this theory might say that a certain cat is red because it possesses a redness-trope, but that it is a cat because it instantiates the universal CAT. A problem that must be faced by philosophers who hold (...) this sort of view is the following: Which features are which? In other words, which features are the ones had in virtue of trope-possession, and which are the ones had in virtue of instantiation? In this paper I discuss this problem, consider and reject a competing view, and propose my own Aristotelian solution. I also raise and answer an objection. (shrink)

Dispositionality and qualitativity are key notions to describe the world that we inhabit. Dispositionality is a matter of what a thing is disposed to do in certain circumstances. Qualitativity is a matter of how a thing is like. According to the Identity Theory of powers, every fundamental property is at once dispositional and qualitative, or a powerful quality. Canonically, the Identity Theory holds a contentious identity claim between a property’s dispositionality and its qualitativity. In the literature, this view faces a (...) contradiction objection that undermines its merits. We should therefore consider an alternative version that does not embrace the identity claim. My aim is to show that we can enjoy the benefits of the Identity Theory without embracing the identity between the dispositional and the qualitative. I shall argue that a distinction between two senses of dispositionality and qualitativity serves the purpose. I will then discuss three readings of the identity claim that can be formulated in light of such a distinction. I will conclude that even if the identity were to fail in any of the suggested readings, it would be possible to hold an account of fundamental powerful qualities. (shrink)

We outline Ladyman's 'metaphysical' or 'ontic' form of structuralrealism and defend it against various objections. Cao, in particular, has questioned theview of ontology presupposed by this approach and we argue that by reconceptualisingobjects in structural terms it offers the best hope for the realist in thecontext of modern physics.

The ontological debate on the nature of properties is alive as ever. Mainly, they are viewed either as universals or tropes, an alternative with an immediate impact on what events are taken to be. Although much inquiry in philosophy of mind is done without a full awareness of it, some recent works suggest that the choice may have far-reaching consequences on central topics of this discipline, e.g., token physicalism, multiple realisability, mental causation, perception, introspection, self-awareness. This book explores the extent (...) to which this is true with novel contributions by philosophers who have played a major role in bringing to the fore this interplay of foundational metaphysics and philosophical psychology and by other experts in these fields. Contributors : John Heil, Anna-Sofia Maurin, E. Jonathan Lowe, David Robb, Ausonio Marras & Juhani Yli-Vakkuri. (shrink)

I present a formal framework historically faithful to Leibniz's analysis of relational sentences, which: (i) engrafts thematic roles and the non-truth-functional connective insofar as (quatenus) into the monadic fragment of first-order logic; (ii) suggests a plausible ontological picture of thematic roles and relational facts; (iii) supports argument deletion and related inferential patterns that are not taken into account by standard first-order logic.

It is shown that two formally consistent type-free second-order systems, due to Cocchiarella, and based on the notion of homogeneous stratification, are subject to a contingent version of Russell's paradox.

We formulate a Curry-typed logic with fine-grained intensionality within Turner’s typed predicate logic. This allows for an elegant presentation of a theory that corresponds to Fox and Lappin’s property theory with curry typing, but without the need for a federation of languages. We then consider how the fine-grained intensionality of this theory can be given an operational interpretation. This interpretation suggests itself as expressions in the theory can be viewed as terms in the untyped lambda-calculus, which provides a model of (...) computation. (shrink)

Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted at by Armstrong. This (...) is the Operator Theory of instantiation, by which I mean the theory that universals are operators, and that a particular instantiates a monadic universal because the universal operates on the particular, resulting in the state of affairs. On this theory the state of affairs supervenes on the instantiation rather than vice versa. In the second part of the paper I develop this theory of universals as operators, including an account of structural universals, which are useful for accounts of modality and of mathematics. (shrink)

This paper explores the mereology of structural universals, using the structural richness of a non-classical mereology without unique fusions. The paper focuses on a problem posed by David Lewis, who using the example of methane, and assuming classical mereology, argues against any purely mereological theory of structural universals. The problem is that being a methane molecule would have to contain being a hydrogen atom four times over, but mereology does not have the concept of the same part occurring several times. (...) This paper takes up the challenge by providing mereological analysis of three operations sufficient for a theory of structural universals: Reflexive binding, i.e. identifying two of the places of a universal; Existential binding, i.e. the language-independent correlate of an existential quantification; and Conjunction. (shrink)

Structural universals are a kind of complex universal. They have been put to work in a variety of philosophical theories but are plagued with problems concerning their compositional nature. In this article, we will discuss the following questions. What are structural universals? Why believe in them? Can we give a consistent account of their compositional nature? What are the costs of doing so?

Contents: Preface VII; Introduction 1; 1. The General Framework 5; 2. Some Standard Systems 61; 3. Systems in General 147; 4. Non-Standard Systems 177; Bibliography 210; General Index 215; Index of Symbols 219-220.

We pose a puzzle for forms and show how it might be solved by appeal to the theory of arbitrary objects. We also discuss how the resulting account of forms relates to issues concerning structural universals and the nature of abstraction.

If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering paradox. (...) I employ a semantics which is infinite-valued, with the values only partially ordered. Can the solution be adapted to naïve set theory? Probably not, but limiting naïve comprehension in set theory is perfectly satisfactory, whereas this is not so in a property theory used for semantics. (shrink)

Lewis has objected to Armstrong's notion of a structural universal on the grounds that it violates the Principle of Uniqueness of Composition, which says that given some parts, there is only one whole that they compose. This paper reviews Armstrong's case for structural universals, and then attempts to reconcile structural universals with PUC by arguing for the existence of arrangement universals. The latter are not only a key to defending structural universals against Lewis' objection, but are in fact essential to (...) Armstrong's conception of structural universals in general. Three objections to my proposal are deflected, and two alternative proposals are shown to be inferior to it. (shrink)

Two grams mass, three coulombs charge, five inches long – these are examples of quantitative properties. Quantitative properties have certain structural features that other sorts of properties lack. What are the metaphysical underpinnings of quantitative structure? This paper considers several accounts of quantity and assesses the merits of each.

Resemblances obtain not only between objects but between properties. Resemblances of the latter sort - in particular resemblances between quantitative properties - prove to be the downfall of a well-known theory of universals, namely the one presented by David Armstrong. This paper examines Armstrong's efforts to account for such resemblances within the framework of his theory and also explores several extensions of that theory. All of them fail.

It is a traditional empiricist doctrine that natural laws are universal truths. In order to overcome the obvious difficulties with this equation most empiricists qualify it by proposing to equate laws with universal truths that play a certain role, or have a certain function, within the larger scientific enterprise. This view is examined in detail and rejected; it fails to account for a variety of features that laws are acknowledged to have. An alternative view is advanced in which laws are (...) expressed by singular statements of fact describing the relationship between universal properties and magnitudes. (shrink)

This paper is an investigation of the general logic of "identifications", claims such as 'To be a vixen is to be a female fox', 'To be human is to be a rational animal', and 'To be just is to help one's friends and harm one's enemies', many of which are of great importance to philosophers. I advocate understanding such claims as expressing higher-order identity, and discuss a variety of different general laws which they might be thought to obey. [New version: (...) Nov. 4th, 2016]. (shrink)

First published in 1985, D. M. Armstrong's original work on what laws of nature are has continued to be influential in the areas of metaphysics and philosophy of science. Presenting a definitive attack on the sceptical Humean view, that laws are no more than a regularity of coincidence between stances of properties, Armstrong establishes his own theory and defends it concisely and systematically against objections. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Marc (...) Lange, illuminating its continuing importance and relevance to philosophical enquiry, this influential work is available for a new generation of readers. (shrink)

This book espouses a theory of scientific realism in which due weight is given to mathematics and logic. The authors argue that mathematics can be understood realistically if it is seen to be the study of universals, of properties and relations, of patterns and structures, the kinds of things which can be in several places at once. Taking this kind of scientific platonism as their point of departure, they show how the theory of universals can account for probability, laws of (...) nature, causation and explanation, and explore the consequences in all these fields. This will be an important book for all philosophers of science, logicians and metaphysicians, and their graduate students. The readership will also include those outside philosophy interested in the interrelationship of philosophy and science. (shrink)

William Jaworski shows how hylomorphism can be used to solve mind-body problems--the question of how thought, feeling, perception, and other mental phenomena fit into the physical world. Hylomorphism claims that structure is a basic ontological and explanatory principle, and is responsible for individuals being the kinds of things they are, and having the powers or capacities they have. From a hylomorphic perspective, mind-body problems are byproducts of a worldview that rejects structure, and which lacks a basic principle which distinguishes the (...) parts of the physical universe that can think, feel, and perceive from those that can't. Without such a principle, the existence of those powers in the physical world can start to look inexplicable and mysterious. But if mental phenomena are structural phenomena then they are uncontroversially part of the physical world. Hylomorphism thus provides an elegant way of solving mind-body problems. (shrink)

From the operation of the universe to DNA, the brain and the economy, natural and social frequently describe their activity as being concerned with discovering mechanisms. Despite this fact, for much of the twentieth century philosophical discussions of the nature of mechanisms remained outside philosophy of science. The Routledge Handbook of Mechanisms and Mechanical Philosophy is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising over (...) thirty chapters by a team of international contributors the _Handbook_ is divided into four parts: Historical Perspectives on Mechanisms The Nature of Mechanisms Mechanisms and the Philosophy of Science Disciplinary Perspectives. Within these sections central topics and problems are examined, including the rise of mechanical philosophy in the seventeenth century; mechanisms as parts and wholes and their interactive powers; mechanisms and laws and regularities; how mechanisms are discovered and explained; dynamical systems theory; and disciplinary perspectives from physics, chemistry, biology, biomedicine, ecology, neuroscience and the social and political sciences. Essential reading for students and researchers in philosophy of science and philosophy the _Handbook _will also be of interest to those in related fields, such as metaphysics, philosophy of psychology and history of science. (shrink)

Are there any universal entities? Or is the world populated only by particular things? The problem of universals is one of the most fascinating and enduring topics in the history of metaphysics, with roots in ancient and medieval philosophy. This collection of new essays provides an innovative overview of the contemporary debate on universals. Rather than focusing exclusively on the traditional opposition between realism and nominalism, the contributors explore the complexity of the debate and illustrate a broad range of positions (...) within both the realist and the nominalist camps. Realism is viewed through the lens of the distinction between constituent and relational ontologies, while nominalism is reconstructed in light of the controversy over the notion of trope. The result is a fresh picture of contemporary metaphysics, in which traditional strategies of dealing with the problem of universals are both reaffirmed and called into question. (shrink)

Metaphysics and science have a long but troubled relationship. In the twentieth century the Logical Positivists argued metaphysics was irrelevant and that philosophy should be guided by science. However, metaphysics and science attempt to answer many of the same, fundamental questions: What are laws of nature? What is causation? What are natural kinds? -/- In this book, Markus Schrenk examines and explains the central questions and problems in the metaphysics of science. He reviews the development of the field from the (...) early modern period through to the latest research, systematically assessing key topics including -/- dispositions, counterfactual conditionals, laws of nature, causation, natural kinds, essence, necessity. -/- With the addition of chapter summaries and annotated further reading, Metaphysics of Science is a much-needed, clear and informative survey of this exciting area of philosophical research. It is essential reading for students and scholars of philosophy of science and metaphysics. (shrink)

Fifteen philosophers offer new essays exploring the metaphysics of relations from antiquity to the present day. They address topics as diverse as ancient and medieval reasons for scepticism about polyadic properties; recent attempts to reduce causal and spatiotemporal relations; recent work on the directionality of relational properties; powers ontologies and their associated problems; whether the most promising interpretations of quantum mechanics posit a fundamentally relational world; and whether the very idea of such a world is coherent. From those who question (...) whether there are relational properties at all, to those who hold they are a fundamental part of reality, The Metaphysics of Relations covers a broad spectrum of positions on the nature and ontological status of relations, from antiquity to the present day. (shrink)

What does reality encompass? Is it exclusively physical, or does it include mental and 'abstract' aspects? What are the elements of being, reality's raw materials? John Heil offers stimulating answers to these questions framed in terms of a comprehensive metaphysics of substances and properties inspired by Descartes, Locke, and their successors.

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

Bob Hale presents a broadly Fregean approach to metaphysics, according to which ontology and modality are mutually dependent upon one another. He argues that facts about what kinds of things exist depend on facts about what is possible. Modal facts are fundamental, and have their basis in the essences of things--not in meanings or concepts.

Expressions in a language, whether words, phrases, or sentences, have meanings. So it seems reasonable to suppose that there are meanings that expressions have. Of course, it is fashionable in some philosophical circles to deny this.

The treatise attempts to approach and deal with some of the most fundamental problems facing anyone who wishes to uphold some version of the so-called theory of tropes. Three assumptions serve as a basis for the investigation: tropes exist, only tropes exist, and a one-category trope-theory along these lines should be developed so that the tropes it postulates are able to serve as truth-makers for all kinds of atomic propositions. Provided that these assumptions are accepted, it is found that the (...) trope-theorist will have to deal with two important problems. First, some atomic propositions seem to require universal truth-makers. Second, some atomic propositions seem to require concrete truth-makers. As tropes are abstract particulars, it follows that the trope-theorist, in order to fulfil assumption, must provide an account of exactly how he or she could construct universality and concreteness from his or her basic stock of tropes. In the treatise such constructions are attempted and some basic problems with such constructions are revealed. Although these problems are serious enough it is argued that it is nevertheless possible to deal with these basic issues while staying squarely within the boundaries of a one-category trope-ontology. (shrink)

In this book, Linda Wetzel examines the distinction between types and tokens and argues that types exist (as abstract objects, since they lack a unique ...