The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900…

Paperback | January 7, 2014

byPaolo Mancosu

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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'sprogram, 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 onthe 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.

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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'sprogram, constructivity, Wittgenstein, Godel); ...

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.

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Format:PaperbackDimensions:632 pages, 9.61 × 6.69 × 0.68 inPublished:January 7, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198701519

ISBN - 13:9780198701514

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Table of Contents

PrefacePart 1: History of Logic1. The Development of Mathematical Logic from Russell to Tarski, 1900-1935Part 2: Foundations of Mathematics2. Hilbert and Bernays on Metamathematics3. Between Russell and Hilbert: Behmann on the foundations of mathematics4. The Russellian influence on Hilbert and his school5. On the constructivity of proofs6. Wittgenstein's constructivization of Euler's proof of the infinitude of primes7. Between Vienna and Berlin: The immediate reception of Godel's incompleteness theorems8. Essay Review of Godel's Collected Works (volumes IV and V)Part 3: Phenomenology and Mathematics9. Hermann Weyl: Predicativity and an intuitionistic excursion10. Mathematics and Phenomenology: the correspondence between O. Becker and H. Weyl11. Geometry, Physics and Phenomenology: Four letters of O. Becker to H. Weyl12. Das Abenteuer der Vernunft: O. Becker and D. Mahnke on the phenomenological foundation of the exact sciencesPart 4: Nominalism13. Harvard 1940-1941: Tarski, Carnap and Quine on a finitist language of mathematics for science14. Quine and Tarski on nominalismPart 5: The emergence of semantics: truth and logical consequence15. Neurath and Kokoszynska on the semantic conception of truth16. Tarski on models and logical consequence17. Tarski on Categoricity and Completeness: an unpublished lecture from 194018. Archival Appendix. "On the completeness and categoricity of deductive theories" (1940), By Alfred Tarski.Bibliography

Editorial Reviews

"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