In this chapter, I evaluate various conceptions of distance. Of the two most prominent, one takes distance relations to be intrinsic, the other extrinsic. I recommend pluralism: different conceptions can peacefully coexist as long as each holds sway over a distinct region of logical space. But when one asks which conception holds sway at the actual world, one conception stands out. It is the conception of distance embodied in differential geometry, what I call the Gaussian conception. On this conception, all (...) fundamental facts about distance are “local” facts.” But there is a problem: the Gaussian conception, notwithstanding its mathematical and physical credentials, appears metaphysically suspicious on Humean grounds. In the final section, I suggest that the Gaussian conception can be given a sound metaphysical footing in terms of non-standard analysis. (shrink)

As is well known, Aristotelian natural philosophy, and many other systems of natural philosophy since, have relied heavily on teleology and teleological causation. Somehow, the purpose or end of an obj ect can be used to predict and explain what that object does: once you know that the end of an acorn is to become an oak, and a few things about what sorts of circumstances are conducive to the attainment of this end, you can predict a lot about the (...) sprouting of the acorn and the subsequent behaviour of the piece of vegetation that results. Once you know that a rock seeks to move towards the centre of the Earth, you gain some insight into why it falls when released, and why it deforms the carpet or foot that it lands on. Once you know that the rabbit seeks to preserve itself, you can predict it will run from the fox. And so on. There are at least three features of Aristotle’s teleology, and more generally of an Aristotelian frame of mind about teleology, that may induce suspicion. One is that an end can serve as a "cause": as well as the sort of causation we all recognize, efficient causation, there are other forms, one of which is teleological causation. However, this can look less odd if we think of causes as things that figure in "because" answers to "why" questions. Whether or not self-preservation, or the rabbit’s continued existence, or something similar, causes the rabbit to run, the reply "because it seeks to continue in existence" certainly makes sense as an answer, or part of an answer, to a question about why it ran from the fox. (At present we are only. (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.

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)

This book combines physics, history, and philosophy in a radical new approach to introducing the philosophy of physics.

In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and ...

A modest proposal concerning laws, counterfactuals, and explanations - - Why be Humean? -- Suggestions from physics for deep metaphysics -- On the passing of time -- Causation, counterfactuals, and the third factor -- The whole ball of wax -- Epilogue : a remark on the method of metaphysics.

John Hawthorne is widely regarded as one of the finest philosophers working today. He is perhaps best known for his contributions to metaphysics, and this volume collects his most notable papers in this field. Hawthorne offers original treatments of fundamental topics in philosophy, including identity, ontology, vagueness, and causation. Six of the essays appear here for the first time, and there is a valuable introduction to guide the reader through the selection.

This book espouses an innovative 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)

In this short text, a distinguished philosopher turns his attention to one of the oldest and most fundamental philosophical problems of all: How it is that we are able to sort and classify different things as being of the same natural class? Professor Armstrong carefully sets out six major theories—ancient, modern, and contemporary—and assesses the strengths and weaknesses of each. Recognizing that there are no final victories or defeats in metaphysics, Armstrong nonetheless defends a traditional account of universals as the (...) most satisfactory theory we have.This study is written for advanced students, but as Armstrong goes considerably beyond his earlier work on this topic, it will interest professional scholars as well. Carefully plotted and clearly written, Universals is both a paradigm of exposition and a case study on the value of careful analysis of fundamental issues in philosophy. (shrink)

This paper forms part of a wider campaign: to deny pointillisme, the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. (...) A companion paper argues against pointillisme about -geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of "Newtonian" ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics. Introduction The wider campaign 2.1 Connecting physics and metaphysics 2.1.1 Avoiding controversy about the intrinsic–extrinsic distinction 2.1.2 Distinction from three mathematical distinctions 2.2 Classical mechanics is not pointilliste, and can be perdurantist 2.2.1 Two versions of pointillisme 2.2.2 Two common claims 2.2.3 My contrary claims 2.3 In more detail... 2.3.1 Four violations of pointillisme 2.3.2 For perdurantism Velocity as intrinsic? 3.1 Can properties represented by vectors be intrinsic to a point? 3.2 Orthodox velocity is extrinsic but local 3.2.1 A question and a debate 3.2.2 The verdict 3.3 Against intrinsic velocity 3.3.1 A common view—and a common problem 3.3.2 Tooley's proposal and his arguments 3.3.3 Tooley's further discussion "Shadow velocities": Lewis and Robinson 4.1 The proposal 4.2 Criticism: the vector field remains unspecified 4.3 Avoiding the presupposition of persistence, using Hilbert's symbol 4.4 Comparison with Robinson and Lewis. (shrink)

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

Despite heroic efforts, philosophers have found it increasingly difficult to evade discussion of metaphysical topics. Take the philosophy of mind. Take, in particular, the mind-body problem in its latest guise: the problem of causal relevance. If mental properties are not reducible to physical properties, how can we reconcile the role such properties seem to have in producing bodily motions that constitute actions with the apparent fact that the very same motions are entirely explicable on the basis of purely physical properties (...) of purely physical events in the nervous system? Familiar approaches to the problem include appeals to “supervenient causation,” to “higher-level” laws governing putatively higher-level entities and events, and to “realizing” relations that make room in objects for overlapping properties. (shrink)

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.

Precis of my book by this title, for a symposium.

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

This dissertation explores the concepts of naturalness, intrinsicality, and duplication. An intrinsic property is had by an object purely in virtue of the way that object is considered in itself. Duplicate objects are exactly similar, considered as they are in themselves. The perfectly natural properties are the most fundamental properties of the world, upon which the nature of the world depends. In this dissertation I develop a theory of intrinsicality, naturalness, and duplication and explore their philosophical applications. Chapter 1 introduces (...) the notions, gives a preliminary survey of some proposed conceptual connections between the notions, and sketches some of their proposed applications. Chapter 2 gives my background assumptions and introduces notational conventions. In chapter 3 I present a theory of naturalness. Although I take ‘natural’ as a primitive, I clarify this notion by distinguishing and explicating various conceptions of naturalness. In chapter 4 I give a theory of various notions related to naturalness, especially intrinsicality and duplication. I show that ‘intrinsic’ and ‘duplicate’ are interde nable, and then give analyses of these and other notions in terms of naturalness. If, as I think likely, naturalness cannot be analyzed, then what is the proper response? David Lewis suggests: accept naturalness as a primitive. I am sympathetic to this proposal, but not to the form Lewis gives it: chapter 5 contains an argument against Lewis’s theory of naturalness. In chapter 6 I reject the idea that naturalness is analyzable in terms of immanent universals. I focus on the work of D. M. Armstrong. I also criticize Armstrong’s arguments against transcendent universals. (shrink)

is the thesis that everything supervenes upon the spatiotemporal distribution of local intrinsic qualities. A recent threat to HS, originating in thought experiments by Armstrong and Kripke, claims that the mere possibility of rotating homogeneous discs proves HS false. I argue that the rotating disc argument (RDA) fails. If I am right, Humeans needn't abandon or alter HS to make sense of rotating homogeneous discs. Homogeneous discs, as necessarily understood by RDA, are not the sorts of things in which we (...) should believe. These discs do not belong in our ontology - not because there is a problem with their homogeneity, but (surprisingly) because there is a problem with their rotation. RDA is shown to be a kind of parody of classic arguments for spatial substantivalism. (shrink)

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). (...) A companion paper argues against pointillisme in mechanics, especially about velocity; it focusses on Tooley, Robinson and Lewis. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time. But both the debate and my arguments carry over to relativistic, and even quantum, physics. (shrink)

A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...) unsupported assumptions concerning existence of physical objects (e.g. that any two actual objects have an actual sum). The theory T Q supports and illustrates a form of naturalistic Platonism, for which claims concerning the existence and properties of universals form part of natural science, and the distinction between accidental generalizations and laws of nature has a basis in the second-order structure of the world. (shrink)

David Lewis's work is of fundamental importance in many areas of philosophical inquiry and there are few areas of Anglo-American philosophy where his impact has not been felt. Lewis's philosophy also has a rare unity: his views form a comprehensive philosophical system, answering a broad range of questions in metaphysics, philosophy of mind, philosophy of language, philosophy of action and many other areas. This breadth of Lewis's work, however, has meant that it is difficult to know where to start in (...) Lewis's work and a casual reader may often miss some of the illuminating connections between apparently quite disparate pieces of Lewis's work. This book aims to make this body of work more accessible to a general philosophical readership, while also providing a unified overview of the many contributions Lewis has made to contemporary Anglo-American philosophy. The book can be divided into four parts. The first part examines Lewis's metaphysical picture - one of the areas where he has had the greatest impact and also the framework for the rest of his theories. The second section discusses Lewis's important contributions in the philosophy of mind, language and meaning. The third part explores some of Lewis's work in decision theory, metaethics and applied ethics, areas where his work in not necessarily as widely appreciated, but in which he has done a range of work that is both accessible and important. The final section focuses on Lewis's distinctive philosophical method, perhaps one of his most significant legacies, which combines naturalism with "common-sense" theorizing. (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.

This paper examines a doctrine which David Lewis has called 'Humean Supervenience' (hereafter 'HS'), and a problem which certain imaginary cases seem to generate for HS. They include rotating perfect spheres or discs, and flowing rivers, imagined as composed of matter which is perfectly homogeneous right down to the individual points. Before considering these examples, I shall introduce the doctrine they seem to challenge.

In physics, objects are often assigned vector characteristics such as a specific velocity. How can this be understood from a metaphysical point of view – is assigning an object a vector characteristic to attribute it an intrinsic property? As a short review of Newtonian, special relativistic and general relativistic physics shows, if we wish to assign some object a vector characteristic, we have to relate it to something – call it S. If S is to be different from the original (...) object – and I argue for this assumption – then having the specific vector characteristic is not an intrinsic property under different readings of “intrinsic”. For instance, I argue that lonely objects with different orientations do not constitute metaphysically distinct possibilities. There are, however, difficulties in applying the loneliness test, and they concern the role of the space‐time. (shrink)

§30. Significance of Desargues's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 CHAPTER VI. PASCAL'S THEOREM. §31. ...