Realism in mathematics
Clarendon Press, 11 ott 1990 - 204 pagine
Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics.
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analogous argued arithmetic assumption axiom of choice axiom of constructibility Benacerraf Benacerraf-style Borel sets Cantor causal theory cell-assemblies Chapter Chihara claim collection consider continuum hypothesis correspondence countable Dedekind Enderton epistemological equinumerous evidence example existence experience extrinsic fact Field finite Frege numbers functions Godel Hebb hereditarily finite sets idea indispensability arguments infinite intuitive beliefs iterative hierarchy justification knowledge large cardinal Lebesgue Lebesgue measurable logical Maddy Martin mathematical entities mathematical objects mathematical realism mathematicians measurable cardinals monist Moschovakis Moschovakis 1980 natural numbers natural science Neumann ordinals nominalist notion number properties number theory ontology particular perceive perceptual beliefs perfect subset philosophical physical objects physical stuff physicalistic Platonism Platonist predicate principle problem projective determinacy projective sets Putnam question Quine Quine/Putnam real numbers reliable Resnik role scientific sect sense set theoretic realism sets of reals sort statements structure suggests theorists things triangle true truth various well-ordering Zermelo