Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

In a revolutionary new book, a theoretical physicist attacks the foundations of modern scientific theory, including the notion of time, as he shares evidence of ...

Collaboration on the First Edition of Spacetime Physics began in the mid-1960s when Edwin Taylor took a junior faculty sabbatical at Princeton University where John Wheeler was a professor. The resulting text emphasized the unity of spacetime and those quantities (such as proper time, proper distance, mass) that are invariant, the same for all observers, rather than those quantities (such as space and time separations) that are relative, different for different observers. The book has become a standard introduction to relativity. (...) The Second Edition of Spacetime Physics embodies what the authors have learned during an additional quarter century of teaching and research. They have updated the text to reflect the immense strides in physics during the same period and modernized and increased the number of exercises, for which the First Edition was famous. Enrichment boxes provide expanded coverage of intriguing topics. An enlarged final chapter on general relativity includes new material on gravity waves, black holes, and cosmology. The Second Edition of Spacetime Physics provides a new generation of readers with a deep and simple overview of the principles of relativity. (shrink)

John Earman and John Norton have argued that substantivalism leads to a radical form of indeterminism within local spacetime theories. I compare their argument to more traditional arguments typical in the Relationist/Substantivalist dispute and show that they all fail for the same reason. All these arguments ascribe to the substantivalist a particular way of talking about possibility. I argue that the substantivalist is not committed to the modal claims required for the arguments to have any force, and show that this (...) naturally leads to an alteration in the way determinism is characterized for local spacetime theories. (shrink)

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

Recently Carolyn Brighouse and Jeremy Butterfield have argued that David Lewis's counterpart theory makes it possible both to believe in the reality of spacetime points and to consider general relativity to be a deterministic theory, thus avoiding the ‘hole argument’ of John Earman and John Norton. Butterfield's argument relies on Lewis's own counterpart-theoretic analysis of determinism. In this paper, I argue that this analysis is inadequate. This leaves a gap in the Butterfield–Brighouse defence against the hole argument.

This volume provides a balanced set of reviews which introduce the central topics in the philosophy of time. This is the first introductory anthology on the subject to appear for many years; the contributors are distinguished, and two of the essays are specially written for this collection. In their introduction, the editors summarize the background to the debate, and show the relevance of issues in the philosophy of time for other branches of philosophy and for science. Contributors include J.M.E. McTaggart, (...) Arthur N. Prior, D.H. Mellor, Sydney Shoemaker, Graeme Forbes, Lawrence Sklar, Michael Dummett, David Lewis, W.H. Newton-Smith, and Anthony Quinton. (shrink)