The Labyrinth Of The Continuum

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.

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.

The writings of German mathematician and philosopher GOTTFRIED WILHELM LEIBNIZ (1646-1716) have had an incalculable impact on modern science and technology, from physics and computers to law and psychology. But not everyone is a fervent fan. At the turn of the 20th century, the great British thinker Bertrand Russell uncovered what he believed was the hypocritical secret to Leibniz's philosophy: a hidden devotion to a logic he did not reveal in his writings. Here, Russell explores Leibniz's work from this perspective, examining the premises of Leibniz's work, the questions raised by his arguments, the validity of Leibniz's proofs, problems with his "philosophy of matter," and much more. First published in 1900, this is a replica of the 1937 second edition, and is complete with the original, extensive appendix of relevant extracts from Leibniz's work, essential for understanding Russell's critique. British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (1872-1970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959).

"Whereas the history of philosophy defines metaphysics as asking the question 'What is Being?'; here is asked 'Where is Being?' What is to be analyzed is indeed part of the tradition of metaphysics to inquire about Being qua being, but here the inquiry is into its structure, its position within the ontological whole. The concept of the 'architectonic' is borrowed from Kant ... In this work, three philosophical structures are chosen for a more extensive examination: the three 'architectonics' are that of Plato's Chora, Aristoteles' continuum, and finally Leibniz's labyrinth"--Back cover.

Anapolitanos critically examines and evaluates three basic characteristics of the Leibnizian metaphysical system: Leibniz's version of representation; the principle of continuity; and space, time, and the phenomenally spatio-temporal. Chapter I discusses representation, especially as it refers to the connection between the real and the phenomenal levels of Leibniz's system. Chapter II examines the principle of continuity, including continuity as a general feature of every level of Leibniz's metaphysics. The position adopted is that the problem of the composition of the continuum played a central role on the development of Leibniz's non-spatial and non-temporal monadic metaphysics. The machinery developed is then used to offer a new interpretation of Leibniz' metaphysics of space and time. The notion of indirect representation is used to construct appropriate models that clarify the nature of the correspondence between the real and the phenomenal levels in the case of the relations `spatially between' and `temporally between', as well as in the cases of spatial and temporal density. Finally, Leibniz's solution to the problem of the continuum is discussed, arguing that it is not entirely satisfactory. A non-anachronistic alternative is proposed, compatible with Leibniz's metaphysics of substance.

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

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.

Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.