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The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of...

This book is a collection of papers presented at the conference New Trends in the History and Philosophy of Mathematics held at the University of Roskilde, Denmark, 6-8 August 1998. The purpose of the meeting was to present some of the new ideas on the study of mathematics, its character and the nature of its development. During the last decades work in history and philosophy of mathematics has led to several new original views on mathematics. Both new methods and angles of study have been introduced, and old views of, say, the nature of mathematical theories and proofs have been challenged. For instance, disciplines as etnohistorical studies of mathematics and the sociology of mathematics h...

This volume contains seventeen papers that were presented at the 2015 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held in Washington, D.C. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of general topics in the history and philosophy of mathematics, this meeting also honored the memories of Jacqueline (Jackie) Stedall and Ivor Grattan-Guinness; celebrated the Centennial of the Mathematical Association of America; and considered the importance of mathematical communities in a special session. These themes and many others are explored in th...

Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century. In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure ...

Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics.

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

Why did Plato put mathematics at the heart of education for the rulers of his ideal city? Why has mathematics played such a central role in Western philosophy? And just how do we acquire knowledge of necessary truths? Three philosophers of international repute tackle these questions. M. F. Burnyeat brings out Plato's distinctive vision of the world as it objectively is: the structures of mathematics are also the structures that express the nature of the human soul and the soul that governs the world. Ian Hacking highlights the phenomena associated with the actual experience of proof, which so impressed philosopher-mathematicians like Descartes and Leibniz and onlookers like Plato and Wittgenstein. Jonathan Bennett explores modal discovery in Locke and Leibniz, and the infallibility of reason in Descartes and Spinoza. The answers offered by these distinguished scholars make a significant contribution to our understanding of some of the great thinkers of the past.