Description
Book SynopsisIn this groundbreaking volume, leading philosophers and mathematicians explore almost every aspect of Kurt Gödel's work on the foundations and philosophy of mathematics. It will be invaluable to students, historians, logicians and philosophers who wish to understand the current thinking on Gödel's intellectual legacy.
Trade Review'These essays explore most aspects of Gödel's legacy, including his conceptions of intuition and analyticity, the Completeness theorem, the set-theoretic multiverse and the current state of mathematical logic.' Graham Hoare, The Mathematical Gazette
'In sum, this is a collection of stimulating essays, mathematically as well as philosophically. They are not exactly easy reading and require familiarity, at least in broad strokes, with Gödel's mathematical work and his central philosophical ideas (as well as their evolution and historical context). The patient reader will be rewarded by a deeper understanding of both.' Wilfried Sieg, Isis
Table of Contents1. Introduction: Gödel and analytic philosophy: how did we get here? Juliette Kennedy; Part I. Gödel on Intuition: 2. Intuitions of three kinds in Gödel's views on the continuum John Burgess; 3. Gödel on how to have your mathematics and know it too Janet Folina; Part II. The Completeness Theorem: 4. Completeness and the ends of axiomatization Michael Detlefsen; 5. Logical completeness, form, and content: an archaeology Curtis Franks; Part III. Computability and Analyticity: 6. Gödel's 1946 Princeton bicentennial lecture: an appreciation Juliette Kennedy; 7. Analyticity for realists Charles Parsons; Part IV. The Set-Theoretic Multiverse: 8. Gödel's program John Steel; 9. Multiverse set theory and absolutely undecidable propositions Jouko Väänänen; Part V. The Legacy: 10. Undecidable problems: a sampler Bjorn Poonen; 11. Reflecting on logical dreams Saharon Shelah.
