The Nature of Mathematical KnowledgeOxford University Press, USA, 21 apr 1983 - 300 pagina's 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. |
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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 history of mathematics 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 Newton notion Ontology 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 true in virtue understanding virtue of meaning W. V. Quine warrant belief Weierstrass