In this book, Arthur gives fresh interpretations of Gottfried Leibniz's theories of time, space, and the relativity of motion, based on a thorough examination of Leibniz's manuscripts as well as his published papers. These are analysed in historical context, but also with an eye to their contemporary relevance. Leibniz's views on relativity have been extremely influential, first on Mach, and then on Einstein, while his novel approach to geometry in his analysis situs inspired many later developments in geometry. Arthur expounds the latter in some detail, explaining its relationship to Leibniz's metaphysics of space and the grounding of motion, and defending Leibniz's views on the relativity of motion against charges of inconsistency. The brilliance of his work on time, though, has not been so well appreciated, and Arthur attempts to remedy this through a detailed discussion of Leibniz's relational theory of time, showing how it underpins his theory of possible worlds, his complex account of contingency, and his highly original treatment of the continuity of time, providing formal treatments in an appendix. In other appendices, Arthur provides translations of previously untranslated writings by Leibniz on analysis situs and on Copernicanism, as well as an essay on Leibniz's philosophy of relations. In his introductory chapter he explains how the framework for the book is provided by the interpretation of Leibniz's metaphysics he defended in his earlier Monads, Composition, and Force (OUP 2018, winner of the 2019 annual JHP Book Prize for best book in the history of philosophy published in 2018).

Leibniz's monads have long been a source of fascination and puzzlement. If monads are merely immaterial, how can they alone constitute reality? In Monads, Composition and Force, Richard T. W. Arthur takes seriously Leibniz's claim of introducing monads to solve the problem of the composition of matter and motion. Going against a trend of idealistic interpretations of Leibniz's thought, Arthur argues that although monads are presupposed as the principles making actual each of the infinite parts of matter, bodies are not composed of them. He offers a fresh interpretation of Leibniz's theory of substance in which monads are enduring primitive forces, corporeal substances are embodied monads, and bodies are aggregates of monads, not mere appearances. In this reading the monads are constitutive unities, constituting an organic unity of function through time, and bodies are phenomenal in two senses; as ever-changing things they are Platonic phenomena and as pluralities, in being perceived together, they are also Democritean phenomena. Arthur argues for this reading by describing how Leibniz's thought is grounded in seventeenth century atomism and the metaphysics of the plurality of forms, showing how his attempt to make this foundation compatible with mechanism undergirds his insightful contributions to biological science and the dynamical foundations he provides for modern physics.

Richard Arthur's Natural Deduction provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern ""informal logic"" with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. In this new edition, more exercises have been added and others have been updated and replaced. Also included are some clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration.

This book gathers together for the first time an important body of texts written between 1672 and 1686 by the great German philosopher and polymath Gottfried Leibniz. These writings, most of them previously untranslated, represent Leibniz's sustained attempt on a problem whose solution was crucial to the development of his thought, that of the composition of the continuum. The volume begins with excerpts from Leibniz's Paris writings, in which he tackles such problems as whether the infinite division of matter entails "perfect points," whether matter and space can be regarded as true wholes, whether motion is truly continuous, and the nature of body and substance. Comprising the second section is Pacidius Philalethi, Leibniz's brilliant dialogue of late 1676 on the problem of the continuity of motion. In the selections of the final section, from his Hanover writings of 1677-1686, Leibniz abandons his earlier transcreationism and atomism in favor of the theory of corporeal substance, where the reality of body and motion is founded in substantial form or force. Leibniz's texts (one in French, the rest in Latin) are presented with facing-page English translations, together with an introduction, notes, appendixes containing related excerpts from earlier works by Leibniz and his predecessors, and a valuable glossary detailing important terms and their translations.

It is commonly held that there is no place for the 'now' in physics, and also that the passing of time is something subjective, having to do with the way reality is experienced but not with the way reality is. Indeed, the majority of modern theoretical physicists and philosophers of physics contend that the passing of time is incompatible with modern physical theory, and excluded in a fundamental description of physical reality. This book provides a forceful rebuttal of such claims. In successive chapters the author explains the historical precedents of the modern opposition to time flow, giving careful expositions of matters relevant to becoming in classical physics, the special and general theories of relativity, and quantum theory, without presupposing prior expertise in these subjects. Analysing the arguments of thinkers ranging from Aristotle, Russell, and Bergson to the proponents of quantum gravity, he contends that the passage of time, understood as a local becoming of events out of those in their past at varying rates, is not only compatible with the theories of modern physics, but implicit in them.