Frege's Philosophy of Mathematics

Frege's Philosophy of Mathematics PDF

Author: William Demopoulos

Publisher: Harvard University Press

Published: 1995

Total Pages: 492

ISBN-13: 9780674319424

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Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.

On the Mathematical Method and Correspondence with Exner

On the Mathematical Method and Correspondence with Exner PDF

Author: Bernard Bolzano

Publisher: Rodopi

Published: 2004

Total Pages: 208

ISBN-13: 9789042017818

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The Prague Philosopher Bernard Bolzano (1781-1848) has long been admired for his groundbreaking work in mathematics: his rigorous proofs of fundamental theorems in analysis, his construction of a continuous, nowhere-differentiable function, his investigations of the infinite, and his anticipations of Cantor's set theory. He made equally outstanding contributions in philosophy, most notably in logic and methodology. One of the greatest mathematician-philosophers since Leibniz, Bolzano is now widely recognised as a major figure of nineteenth-century philosophy. Praised by Husserl as "one of the greatest logicians of all times," he has also been recognised by Michael Dummett as one of the first modern analytic philosophers and by Alberto Coffa as the founder of the "semantic tradition." This volume contains English translations of the essay "On the Mathematical Method," a concise introduction to Bolzano's logic and philosophy of mathematics, as well as substantial selections from his correspondence with Franz Exner, Professor of Philosophy at the Charles University in Prague in the 1830s and 40s. It will be of interest to students of Austrian philosophy, the development of analytic philosophy, the philosophy of language, and the history and philosophy of logic and mathematics.

The Mathematical Philosophy of Bertrand Russell: Origins and Development

The Mathematical Philosophy of Bertrand Russell: Origins and Development PDF

Author: Francisco Rodríguez-Consuegra

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 249

ISBN-13: 3034875339

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by Ivor Grattan-Guinness Until twenty years ago the outline history of logicism was well known. Frege had had the important ideas, until he was eclipsed by Wittgenstein. Russell was important in publicising the former and tutoring the latter, and also for working with Moore in the conversion of British philosophy from neo-Hegelianism to the new analytic tradition in the 1900s, but his own work on logic and especially logicism was very muddled. Around that time Russell, who was still alive, sold his manuscripts to McMaster University in Canada, and interest in his achievements in logic began to develop, especially after his death in 1970. Scholars found thousands of folios of unpublished holograph awaiting their attention, and also hundreds of pertinent letters (both in the Russell Archives and elsewhere in certain recipients' collections). Various facets of his work came to light for the first time, and others -which could have been gleaned from carefully reading of the published sources- gained new publicity from the evidence revealed in manuscripts. Even the technical passage work, which constitutes the unread majority of the Principia mathematica (1910-13) of Russell and Whitehead, began to receive a little respectful scrutiny. It turned out that Russell had done several pioneering things. While indeed often incoherent in reference and content, they comprised major forays into the new mathematical logic, of which he turned out to be a major founder: some are even of interest to modem studies.

Deleuze and the History of Mathematics

Deleuze and the History of Mathematics PDF

Author: Simon Duffy

Publisher: A&C Black

Published: 2013-05-09

Total Pages: 225

ISBN-13: 1441113894

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Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon B.Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seemingly incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.

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