The Foundations of Arithmetic
The Foundations of Arithmetic

Author: Gottlob Frege

Publisher: Northwestern University Press

Published: 1980-12

Total Pages: 144

ISBN-13: 0810106051

DOWNLOAD EBOOK

The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.

From Frege to Gödel
From Frege to Gödel

Author: Jean van Heijenoort

Publisher: Harvard University Press

Published: 1967

Total Pages: 684

ISBN-13: 9780674324497

DOWNLOAD EBOOK

Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege’s Begriffsschrift—which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory—begins the volume, which concludes with papers by Herbrand and by Gödel.

Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals)
Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals)

Author: Donald Gillies

Publisher: Routledge

Published: 2013-01-11

Total Pages: 115

ISBN-13: 113672107X

DOWNLOAD EBOOK

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.

Fixing Frege
Fixing Frege

Author: John P. Burgess

Publisher: Princeton University Press

Published: 2005-07-25

Total Pages: 276

ISBN-13: 9780691122311

DOWNLOAD EBOOK

Gottlob Frege's attempt to found mathematics on a grand logical system came to grief when Bertrand Russell discovered a contradiction in it. This book surveys consistent restrictions in both the old and new versions of Frege's system, determining just how much of mathematics can be reconstructed in each.

Gottlob Frege: Foundations of Arithmetic
Gottlob Frege: Foundations of Arithmetic

Author: Gottlob Frege

Publisher: Routledge

Published: 2020-07-24

Total Pages: 129

ISBN-13: 1000154424

DOWNLOAD EBOOK

Part of theLongman Library of Primary Sources in Philosophy, this edition of Frege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for undergraduates.

Frege
Frege

Author: Michael Dummett

Publisher: Harvard University Press

Published: 1991

Total Pages: 364

ISBN-13: 9780674319356

DOWNLOAD EBOOK

No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.