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E-raamat: Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

(University of California Berkeley)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 09-Jan-2014
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780191021992
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 09-Jan-2014
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780191021992

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Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Godel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

Arvustused

This book contains an enormous amount of material that historians will wish to consult. Mancosu convincingly demonstrates that there is a great deal more that we can still learn about the origins of modern mathematical logic. * Michael Potter, Philosophia Mathematica *

PART I MATHEMATICAL LOGIC, 1900-1935
Introduction
2(3)
1 The Development of Mathematical Logic from Russell to Tarski, 1900-1935
5(117)
Richard Zach
Calixto Badesa
PART II FOUNDATIONS OF MATHEMATICS
Introduction
122(3)
2 Hilbert and Bernays on Metamathematics
125(34)
Addendum
155(4)
3 Between Russell and Hilbert: Behmann on the Foundations of Mathematics
159(17)
4 The Russellian Influence on Hilbert and His School
176(23)
5 On the Constructivity of Proofs: A Debate among Behmann, Bernays, Godel, and Kaufmann
199(18)
6 Wittgenstein's Constructivization of Euler's Proof of the Infinity of Primes
217(15)
Mathieu Marion
7 Between Vienna and Berlin: The Immediate Reception of Godel's Incompleteness Theorems
232(8)
8 Review of Godel's Collected Works, Vols. IV and V
240(16)
PART III PHENOMENOLOGY AND THE EXACT SCIENCES
Introduction
256(3)
9 Hermann Weyl: Predicativity and an Intuitionistic Excursion
259(18)
10 Mathematics and Phenomenology: The Correspondence between
277(31)
O. Becker
H. Weyl
T. Ryckman
11 Geometry, Physics, and Phenomenology: Four Letters of
308(38)
O. Becker
H. Weyl
T. Ryckman
12 "Das Abenteuer der Vernunft": O. Becker and D. Mahnke on the Phenomenological Foundations of the Exact Sciences
346(12)
PART IV TARSKI AND QUINE ON NOMINALISM
Introduction
358(3)
13 Harvard 1940-1941: Tarski, Carnap, and Quine on a Finitistic Language of Mathematics for Science
361(26)
14 Quine and Tarski on Nominalism
387(25)
PART V TARSKI AND THE VIENNA CIRCLE ON TRUTH AND LOGICAL CONSEQUENCE
Introduction
412(3)
15 Tarski, Neurath, and Kokoszynska on the Semantic Conception of Truth
415(25)
16 Tarski on Models and Logical Consequence
440(29)
Addendum
463(6)
17 Tarski on Categoricity and Completeness: An Unpublished Lecture from 1940
469(16)
18 Appendix: "On the Completeness and Categoricity of Deductive Systems" (1940)
485(8)
Notes 493(78)
Bibliography 571(40)
Index 611
Paolo Mancosu is Professor of Philosophy at University of California Berkeley. His main interests are in logic, history and philosophy of mathematics, and history and philosophy of logic.