The Palgrave Centenary Companion to Principia Mathematica

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 Wole?ski, Jagiellonian University, Krakow, Poland

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 : ?! versus ?;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