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Palgrave Macmillan

The Palgrave Centenary Companion to Principia Mathematica

ISBN 9781137344625
Publication Date November 2013
Formats Hardcover Ebook (EPUB) Ebook (PDF) 
Publisher Palgrave Macmillan
Series History of Analytic Philosophy

This collection of fifteen new essays marks the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell. The papers study the influence of PM on the development of symbolic logic in the twentieth century, Russell's philosophy of logic and his program of reducing mathematics to logic, the distinctive theory of logical types that provides a response to the paradoxes of logic that Russell and others discovered around 1900, as well as the details of some of the mathematical theories in the three volumes of symbolic proofs.

Nicholas Griffin is Director of the Bertrand Russell Centre at McMaster University, Hamilton, Ontario, Canada, where he holds a Canada Research Chair in Philosophy. He has written widely on Russell, is the author of Russell's Idealist Apprenticeship and the general editor of The Collected Papers of Bertrand Russell.

Bernard Linsky is Professor of Philosophy at the University of Alberta, Canada. He is the author of Russell's Metaphysical Logic and The Evolution of Principia Mathematica: Russell's Manuscripts and Notes for the Second Edition and editor (with Guido Imaguire) of On Denoting: 1905-2005.

Note on Citations
Introduction: Nicholas Griffin and Bernard Linsky
PART I: THE INFLUENCE OF PM
1. Principia Mathematica: The First Hundred Years; Alasdair Urquhart
2. David Hilbert and Principia Mathematica; Reinhard Kahle:
3. Principia Mathematica in Poland; Jan Wolenski
PART II: RUSSELL'S PHILOSOPHY OF LOGIC AND LOGICISM
4. From Logicism to Metatheory; Patricia Blanchette
5. Russell on Real Variables and Vague Denotation; Edwin Mares
6. The Logic of Classes and the No-Class Theory; Byeong-uk Yi
7. Why There Is No Frege–Russell Definition of Number; Jolen Galaugher
PART III: TYPE THEORY AND ONTOLOGY
8. Principia Mathematica: φ! versus φ;Gregory Landini
9. PM's Circumflex, Syntax and Philosophy of Types; Kevin Klement
10. Principia Mathematica, the Multiple-Relation Theory of Judgment and Molecular Facts; James Levine
11. Report on Some Ramified-Type Assignment Systems and Their Model-Theoretic Semantics; Harold Hodes
12. Outline of a Theory of Quantification; Dustin Tucker
PART IV: MATHEMATICS IN PM
13. Whatever Happened to Group Theory?; Nicholas Griffin
14. Proofs of the Cantor–Bernstein Theorem in Principia Mathematica; Arie Hinkis
15. Quantity and Number in Principia Mathematica: A Plea for an Ontological Interpretation of the Application Constraint; Sébastien Gandon

Patricia Blanchette, University of Notre Dame, Indiana, USA
Jolen Galaugher, University of Iowa, USA
Sébastien Gandon, Université Blaise Pascal, Clermont, France
Arie Hinkis lives in Israel and is the author of Proofs of the Cantor–Bernstein Theorem. A Mathematical Excursion
Harold T. Hodes, Cornell University, USA
Reinhard Kahle, Universidade Nova de Lisboa, Portugal
Kevin C. Klement, University of Massachusetts, Amherst, USA
Gregory Landini, University of Iowa, USA
James Levine, Trinity College, Dublin, Ireland
Edwin Mares, Victoria University of Wellington, New Zealand
Dustin Tucker, Colorado State University, Fort Collins, Colorado, USA
Alasdair Urquhart, Professor Emeritus, University of Toronto, Canada
Byeong-uk Yi, University of Toronto, Canada
Jan Woleński, Jagiellonian University, Krakow, Poland

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