Gottlob Frege: Basic Laws of Arithmetic

The German philosopher and mathematician Gottlob Frege (1848-1925) was the father of analytic philosophy and to all intents and purposes the inventor of modern logic. Basic Laws of Arithmetic, originally published in German in two volumes (1893, 1903), is Freges magnum opus. It was to be the pinnacle of Freges lifes work. It represents the final stage of his logicist project the idea that arithmetic and analysis are reducible to logic and contains his mature philosophy of mathematics and logic. The aim of Basic Laws of Arithmetic is to demonstrate the logical nature of mathematical theorems by providing gapless proofs in Frege's formal system using only basic laws of logic, logical inference, and explicit definitions. The work contains a philosophical foreword, an introduction to Frege's logic, a derivation of arithmetic from this logic, a critique of contemporary approaches to the real numbers, and the beginnings of a logicist treatment of real analysis. As is well-known, a letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that his basic law V, governing the identity of value-ranges, leads into inconsistency. Frege discusses a revision to basic law V written in response to Russells letter in an afterword to volume II. The continuing importance of Basic Laws of Arithmetic lies not only in its bearing on issues in the foundations of mathematics and logic but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work. Philip Ebert and Marcus Rossberg present the first full English translation of both volumes of Freges major work preserving the original formalism and pagination. The edition contains a foreword by Crispin Wright and an extensive appendix providing an introduction to Frege's formal system by Roy T. Cook.

Table of Contents:
Introduction by Crispin Wright Translators' Introduction Frege: Basic Laws of Arithmetic, volumes I and II. Translators' Notes Bibliography Appendix by Roy T. Cook Index

About the Author :
Philip A. Ebert received his PhD from the University of St Andrews in 2006 and was a Post Doctoral Fellow at the Arché Centre from 2005-2007. Since 2007 he has worked at the University of Stirling. ; Marcus Rossberg received his PhD from the University of St Andrews in 2006 and was a Post Doctoral Fellow at the Arché Centre from 2005-2008. Since 2008 he has worked at the University of Connecticut.

Review :
The book will be an indispensable tool for further research on Frege. [T]his beautifully designed and nicely manufactured book is a bargain. Everybody who is interested in Frege's logic and philosophy as well as in the philosophy of logic and mathematics in general should own it. Ebert's and Rossberg's truly reliable, precise and congenial translation of Frege's Grundgesetze is a masterpiece and a milestone in Frege scholarship. I have no doubt that this marvellous book will greatly stimulate current Frege research especially in the Anglosphere. [T]he new translation is of high quality and the accompanying editorial material very helpful ... This version of BL looks terrific, is helpful in various scholarly respects, and will have a big impact, I am sure. I want to congratulate the translators and editors, especially Ebert and Rossberg, on a major achievement. There is no doubt that this English edition will become a basicwork in international Frege scholarship in general and the standard reference for neologicist programs in particular. The translation and editing were undertaken on the highest level