Interpreting Gödel: Critical Essays

Interpreting Gödel: Critical Essays

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Cambridge University Press, 8/21/2014
EAN 9781107002661, ISBN10: 1107002664

Hardcover, 288 pages, 22.9 x 15.2 x 2.5 cm
Language: English

The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues.

1. 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.