Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

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 is a study of a crucial and controversial topic in metaphysics and the philosophy of science: the status of the laws of nature. D. M. Armstrong works out clearly and in comprehensive detail a largely original view that laws are relations between properties or universals. The theory is continuous with the views on universals and more generally with the scientific realism that Professor Armstrong has advanced in earlier publications. He begins here by mounting an attack on the orthodox and (...) sceptical view deriving from Hume that laws assert no more than a regularity of coincidence between instances of properties. In doing so he presents what may become the definitive statement of the case against this position. Professor Armstrong then goes on to establish his own theory in a systematic manner defending it against the most likely objections, and extending both it and the related theory of universals to cover functional and statistical laws. This treatment of the subject is refreshingly concise and vivid: it will both stimulate vigorous professional debate and make an excellent student text. (shrink)

Argues that a set is the mereological whole of the singleton sets of its members (following Lewis's Parts of Classes), and that the singleton set of X is the state of affairs of X's having some unit-making property.

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)

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.

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)

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 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)

Everything we do relies on causation. We eat and drink because this causes us to stay alive. Courts tell us who causes crimes, criminology tell us what causes people to commit them. D.H. Mellor shows us that to understand the world and our lives we must understand causation. The Facts of Causation , now available in paperback, is essential reading for students and for anyone interested in reading one of the ground-breaking theories in metaphysics. We cannot understand the world and (...) our place in it without understanding causation. Yet a complete account of the nature and implications of causation does not exist. D.H Mellor's new book is that account. (shrink)

In this book about metaphysics the author defends a realistic view of universals, characterizing the notion of universal by considering language and logic, the idea of possibility, hierarchies of universals, and causation. He argues that neither language nor logic is a reliable guide to the nature of reality and that basic universals are the fundamental type of universal and are central to causation. All assertions and predications about the natural world are ultimately founded on these basic universals. A distinction is (...) drawn between unified particulars and arbitrary particulars ; unified particulars are the terms of causal relations and thus the real constituents of the world. The world is not made up of events but of unified particulars and basic universals. (shrink)

The world contains objective causal relations and universals, both of which are intimately connected. If these claims are true, they must have far-reaching consequences, breathing new life into the theory of empirical knowledge and reinforcing epistemological realism. Without causes and universals, Professor Fales argues, realism is defeated, and idealism or scepticism wins. Fales begins with a detailed analysis of David Hume's argument that we have no direct experience of necessary connections between events, concluding that Hume was mistaken on this fundamental (...) point. Then, adopting the view of Armstrong and others that causation is grounded in a second-order relation between universals, he explores a range of topics for which the resulting analysis of causation has systematic implications. In particular, causal identity conditions for physical universals are proposed, which generate a new argument for Platonism. The nature of space and time is discussed, with arguments against backward causation and for the view that space and time can exist independently of matter or causal process. Many of Professor Fales's conclusions seem to run counter to received opinion among contemporary empiricists. Yet his method is classically empiricist in spirit, and a chief motive for these metaphysical explorations is epistemological. The final chapters investigate the perennial question of whether an empiricist, internalist and foundational epistemology can support scientific realism. (shrink)