The Architecture of Modern Mathematics: Essays in History and PhilosophyJ. Ferreiros, J. J. Gray This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions. |
Contents
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 | |
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Common terms and phrases
abstract algebraic algebraic topology analysis applications approach argument arithmetic axiomatic axioms called changes claim clear complex concept concerning connection consequence considered consistency construction continuous course Dedekind defined definition described detailed discussion domain elements empirical example existence experience expressed extended fact field formal foundations Frege function fundamental geometry give given groups Hausdorff Hilbert homotopy idea ideal important integers interesting interpretation introduced intuition issues kind knowledge later lecture logical maps mathematicians mathematics means methods natural notion numbers objects particular philosophical physics Poincaré position possible practice present principle problems proof properties prove published pure quantum mechanics question reason reference reflection relations relative remarks Riemann role scientific seems sense sentence simply space structure symbolic Tarski theorem theory thought tion tradition understanding Weierstrass Weyl