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, Gödel); 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.
Autorentext
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.
Inhalt
- Preface
- Part 1: History of Logic
- 1: The Development of Mathematical Logic from Russell to Tarski, 1900-1935
- Oart 2: Foundations of Mathematics
- 2: Hilbert and Bernays on Metamathematics
- 3: Between Russell and Hilbert: Behmann on the foundations of mathematics
- 4: The Russellian influence on Hilbert and his school
- 5: On the constructivity of proofs
- 6: Wittgenstein's constructivization of Euler's proof of the infinitude of primes
- 7: Between Vienna and Berlin: The immediate reception of Gödel's incompleteness theorems
- 8: Essay Review of Gödel's Collected Works (volumes IV and V)
- Part 3: Phenomenology and Mathematics
- 9: Hermann Weyl: Predicativity and an intuitionistic excursion
- 10: Mathematics and Phenomenology: the correspondence between O. Becker and H. Weyl
- 11: Geometry, Physics and Phenomenology: Four letters of O. Becker to H. Weyl
- 12: Das Abenteuer der Vernunft: O. Becker and D. Mahnke on the phenomenological foundation of the exact sciences
- Part 4: Nominalism
- 13: Harvard 1940-1941: Tarski, Carnap and Quine on a finitist language of mathematics for science
- 14: Quine and Tarski on nominalism
- Part 5: The emergence of semantics: truth and logical consequence
- 15: Neurath and Kokoszynska on the semantic conception of truth
- 16: Tarski on models and logical consequence
- 17: Tarski on Categoricity and Completeness: an unpublished lecture from 1940
- 18: Archival Appendix. "On the completeness and categoricity of deductive theories" (1940), By Alfred Tarski.
- Bibliography