The Architecture of Modern Mathematics: Essays in History and PhilosophyJosé Ferreirós Domínguez, Jeremy Gray Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics. |
Contents
Introduction | 1 |
REINTERPRETATIONS IN THE HISTORY AND PHILOSOPHY OF FOUNDATIONS | 45 |
EXPLORATIONS INTO THE EMERGENCE OF MODERN MATHEMATICS | 157 |
ALTERNATIVE VIEWS AND PROGRAMS IN THE PHILOSOPHY OF MATHEMATICS | 261 |
CODA | 369 |
| 397 | |
| 433 | |
| 439 | |
Other editions - View all
The Architecture of Modern Mathematics:Essays in History and Philosophy ... J. Ferreiros,J. J. Gray No preview available - 2006 |
Common terms and phrases
abstract Alexandroff algebraic analytic argument arithmetic axiomatic axioms Bernays Brouwer Cantor Cavaillès claim complex analysis concept consistency proofs construction Dedekind defined definition discussion domain elements ematics empirical epistemological Euclidean geometry example fact Ferreirós fibrations finite finitist formal foundations Frege function fundamental Gauss given Göttingen Grundlagen Hausdorff Hilbert history of mathematics homology homomorphism homotopy groups homotopy theory idea ideal divisors integers interpretation intuition isomorphism Kant Kantian Kronecker lecture logical consequence manifolds maps math mathem mathematical knowledge mathematical practice mathematicians means metaphysical methodological methods modern mathematics Mongré natural numbers Noether non-Euclidean geometry notion number theory numbers objects philosophical philosophy of mathematics physics Poincaré possible principle problems projective geometry proof properties pure question real numbers relations Riemann role scientific sense sentence set theory set-theoretic space structure symbolic Tarski theorem theory of ideals tion topology tradition understanding Weierstrass Weyl