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

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Princeton University Press, Feb 11, 2011 - Mathematics - 624 pages
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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).

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.

  

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Contents

CHAPTER 1 Explanations
3
Algebraic Logic and Mathematical Analysis up to 1870
14
Mathematics as Mengenlehre
75
CHAPTER 4 Parallel Processes in Set Theory Logics and Axiomatics 1870s1900s
126
the Formulary of Mathematics
219
From Certainty to Paradoxes 18951903
268
CHAPTER 7 Russell and Whitehead Seek the Principia Mathematica 19031913
333
CHAPTER 8 The Influence and Place of Logicism 19101930
411
Mathematical Logic and Logicism in the 1930s
506
CHAPTER 10 The Fate of the Search
556
CHAPTER 11 Transcription of Manuscripts
574
BIBLIOGRAPHY
594
INDEX
671
Copyright

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About the author (2011)

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."

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