The conference on Proof Theory: History and Philosophical Significance held in 1997 at the University of Roskilde, Denmark, tracked the history of proof theory and its role in the analysis of the philosophical foundations of mathematics since Hilbert's original program to its modern, highly articulated form. This volume is a collection of papers presented at the conference. It can be read with profit and pleasure by philosophers, mathematicians, computer scientists and scholars with no professional training in proof theory, provided they have a general knowledge of foundational issues.
Author(s): Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen (eds.)
Series: Synthese Library
Publisher: Springer
Year: 2000
Language: English
Pages: 272
Cover......Page cover.djvu
Front Matter......Page _004.djvu
Contents......Page _005.djvu
Preface......Page _009.djvu
Contributing Authors......Page _011.djvu
Introduction......Page 001.djvu
PART 1. REVIEW OF PROOF THEORY......Page 009.djvu
1. Review of Hilbert's Program and Finitary Proof Theory......Page 011.djvu
2. Results of Finitary Proof Theory via Gentzen's L-Calculi......Page 014.djvu
3. Shifting Paradigms......Page 021.djvu
4. Countably Infinitary Methods (Getting the Most Out of Logic)......Page 025.djvu
References......Page 029.djvu
PART 2. THE BACKGROUND OF HILBERT'S PROOF THEORY......Page 034.djvu
1. Introduction......Page 035.djvu
3. Carl Neumann......Page 039.djvu
4. Paul Volkman......Page 042.djvu
5. Physics and Geometry in Hilbert's Early Courses......Page 044.djvu
6. Grundlagen der Geometrie and its Aftermath......Page 045.djvu
7. Concluding Remarks......Page 050.djvu
Notes......Page 051.djvu
References......Page 052.djvu
David Rowe / The Calm Before the Storm: Hilbert's Early Views on Foundations......Page 055.djvu
1. Hilbert's Early Career......Page 056.djvu
2. Hilbert's Grundlagen der Geometrie......Page 063.djvu
3. Hilbert's Axiomatic Method and Frege's Critique......Page 071.djvu
4. Hilbert's Return to Foundations......Page 083.djvu
Notes......Page 087.djvu
References......Page 088.djvu
1. Introduction......Page 095.djvu
2. Background......Page 096.djvu
3. Mathematical Logic......Page 098.djvu
4. Constructive Number Theory......Page 101.djvu
5. Finitist Proof Theory......Page 103.djvu
6. Remarks and Issues......Page 106.djvu
Notes......Page 108.djvu
References......Page 110.djvu
PART 3. BROUWER AND WEYL ON PROOF THEORY AND PHILOSOPHY OF MATHEMATICS ......Page 115.djvu
1. Mysticism and the Dissertation......Page 117.djvu
2. Issues and Topics in the Dissertation......Page 124.djvu
3. Place and Function of Logic......Page 128.djvu
4. The Introduction of Choice Sequences......Page 135.djvu
5. The Impact of the Grundlagenstreit......Page 144.djvu
Notes......Page 148.djvu
References......Page 149.djvu
1. Introduction......Page 153.djvu
2. Some Comments on the Epistemological Standards of Intuitionism......Page 160.djvu
3. The Problem of Solving the Fan Theorem......Page 161.djvu
4. Epistemological Discussion......Page 166.djvu
5. Historical Discussion......Page 169.djvu
6 . Conclusion......Page 172.djvu
Notes......Page 173.djvu
References......Page 176.djvu
2. Two Different Continuum Concepts, 1918 and 1920/21......Page 195.djvu
3. Space made up from "Infinitesimally Small Parts"......Page 200.djvu
4. Digression: Purely Infinitesimal Geometry and Field Theoretic Matter Explanation......Page 202.djvu
5. "Free Emergence" in a Combinatorially Specifed Framework......Page 204.djvu
6. Problems for Weyl's Semi-Intuitionistic Approach to Manifolds......Page 206.djvu
7. Symbol Systems and "Transcendent"/"Transient" Reality......Page 209.djvu
Notes......Page 212.djvu
References......Page 214.djvu
PART 4. MODERN VIEWS AND RESULTS FROM PROOF THEORY......Page 220.djvu
1. Informal Mathematical Part......Page 221.djvu
2. Metamathematical Part......Page 229.djvu
References......Page 235.djvu
Index......Page 237.djvu
Back Cover......Page untitled job1_2.djvu
Sleeves......Page untitled job1_3.djvu
