The Nature of Mathematical KnowledgeOxford University Press, 1984 - 287 páginas This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified. |
Índice
Introduction | 3 |
1 Epistemological Preliminaries | 13 |
2 The Apriorist Program | 36 |
3 Mathematical Intuition | 49 |
4 Conceptualism | 65 |
5 Toward a Defensible Empiricism | 88 |
6 Mathematical Reality | 101 |
7 Mathematical Change and Scientific Change | 149 |
8 Mathematical Changes | 178 |
9 Patterns of Mathematical Change | 193 |
A Case Study | 229 |
| 272 | |
| 281 | |
Otras ediciones - Ver todo
The Nature of Mathematical Knowledge San Diego Philip Kitcher Professor of Philosophy University of California Vista previa restringida - 1983 |
Términos y frases comunes
abstract objects algebraic analysis answer apriorism apriorist apsychologistic argument axioms Bolzano calculus Cantor Cauchy Cauchy's chapter claim collecting complex numbers concept conceptualist constructivist Dedekind Descartes discussion divergent series ematical entities epistemological equation Euler example experience explanation formal Frege functions geometrical given Hence idea ideal subject inference infinite series infinitesimals intuition kind know a priori Leibniz linguistic logic math mathematical apriorism mathematical change mathematical knowledge mathematical practice mathematical reality mathematical statements mathematical truth mathematicians metamathematical views method Mill Arithmetic naïve set theory Newton notion operations paradigm particular perception philosophical philosophy of mathematics Platonist possible principles priori knowledge priori warrants problem proofs proposal questions Quine rational real numbers reference rigor scientific change sentence sequence set of accepted set theory stipulation successor suggest suppose techniques theorems thesis tion transfinite true in virtue understanding virtue of meaning W. V. Quine warrant belief Weierstrass