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Philosophy of MathematicsStructure and Ontology$
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Stewart Shapiro

Print publication date: 2000

Print ISBN-13: 9780195139303

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0195139305.001.0001

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Object and Truth

Object and Truth

A Realist Manifesto

(p.36) 2 Object and Truth
Philosophy of Mathematics

Stewart Shapiro (Contributor Webpage)

Oxford University Press

Several varieties of realism are distinguished. Working realism is a methodological thesis that sanctions the inferences and principles suggested by traditional realism: excluded middle, the axiom of choice, impredicative definition, and general extensionality. Working realism is consistent with antirealist philosophical positions. Realism in ontology, sometimes called “platonism”, is the philosophical view that mathematical objects exist independent of the mind, language, or form of life of the mathematician. Realism in truth value is the view that mathematical assertions have objective truth values independent of the mind, language, or form of life of the mathematician. The relations between these realism are articulated, and the results are related to Quine's ontological, epistemological, and semantic themes.

Keywords:   antirealism, axiom of choice, excluded middle, extensionality, impredicative definition, object, objectivity, ontology, Platonism, Quine, realism, truth value

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