The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

Ivor Grattan-Guinness

Published by Princeton University Press 2001

The Search for Mathematical Roots, 1870-1940

Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

Ivor Grattan-Guinness

https://doi.org/10.1515/9781400824045

Overview
Contents

About this book

While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913).
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This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI.

Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials.

Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

Author / Editor information

I. Grattan-Guinness is Professor of the History of Mathematics and Logic at Middlesex University. Founder of the journal History and Philosophy of Logic and past President of the British Society for the History of Mathematics, he has authored or edited numerous books, including The Norton History of Mathematics, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, and Convolutions in French Mathematics, 1800-1840.

Reviews

"I know of no comparably comprehensive treatment of the history of this important period in modern logic. There is a large body of historical literature that is in need of just the kind of synthesis and masterly overview that this work provides. Though most people recognize mathematics as a principal motivating force behind the development of modern logic, the influences on and from mathematics have been largely ignored or minimized. The Search for Mathematical Roots acts as a guide through that challenging mathematical thicket."—Albert C. Lewis, chief editor of The History of Mathematics from Antiquity to the Present

"Ivor Grattan-Guinness provides a marvelous, comprehensive overview of the history of efforts to come to an understanding of mathematical logic and its relation to mathematics in the period 1870-1940. Given its rich detail and inclusion of under-appreciated figures who deserve to be better known, this is an especially important and useful book."—Joseph Dauben, author of George Cantor: His Mathematics and Philosophy of the Infinite

"Grattan-Guiness's uniformly interesting and valuable account of the interwoven development of logic and related fields of mathematics . . . between 1870 and 1940 presents a significantly revised analysis of the history of the period. . . . [His] book is important because it supplies what has been lacking: a full account of the period from a primary mathematical perspective."---James W. Van Evra, Isis

"Ivor Grattan-Guinness, Recipient of the Kenneth O. May Medal and Prize for contributions to the History of Mathematics, awarded by the International Commission for the History of Mathematics"

Topics

Frontmatter Publicly Available Download PDF	i
CONTENTS Publicly Available Download PDF	v
CHAPTER 1. Explanations Requires Authentication Unlicensed Licensed Download PDF	3
CHAPTER 2. Preludes: Algebraic Logic and Mathematical Analysis up to 1870 Requires Authentication Unlicensed Licensed Download PDF	14
CHAPTER 3. Cantor: Mathematics as Mengenlehre Requires Authentication Unlicensed Licensed Download PDF	75
CHAPTER 4. Parallel Processes in Set Theory, Logics and Axiomatics, 1870s–1900s Requires Authentication Unlicensed Licensed Download PDF	126
CHAPTER 5. Peano: the Formulary of Mathematics Requires Authentication Unlicensed Licensed Download PDF	219
CHAPTER 6. Russell’s Way In: From Certainty to Paradoxes, 1895–1903 Requires Authentication Unlicensed Licensed Download PDF	268
CHAPTER 7. Russell and Whitehead Seek the Principia Mathematica, 1903–1913 Requires Authentication Unlicensed Licensed Download PDF	333
CHAPTER 8. The Influence and Place of Logicism, 1910–1930 Requires Authentication Unlicensed Licensed Download PDF	411
CHAPTER 9. Postludes: Mathematical Logic and Logicism in the 1930s Requires Authentication Unlicensed Licensed Download PDF	506
CHAPTER 10. The Fate of the Search Requires Authentication Unlicensed Licensed Download PDF	556
CHAPTER 11. Transcription of Manuscripts Requires Authentication Unlicensed Licensed Download PDF	574
BIBLIOGRAPHY Requires Authentication Unlicensed Licensed Download PDF	594
INDEX Requires Authentication Unlicensed Licensed Download PDF	671

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