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The Worlds of PossibilityModal Realism and the Semantics of Modal Logic$
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Charles S. Chihara

Print publication date: 2001

Print ISBN-13: 9780199246557

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780199246557.001.0001

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Anti-Realism in Mathematics

Anti-Realism in Mathematics

(p.291) 9 Anti-Realism in Mathematics
The Worlds of Possibility

Charles S. Chihara

Oxford University Press

This chapter discusses the implications of the modal theory developed in this book in terms of mathematics. It focuses on Mathematical Realism, because its own position regarding the ontology of mathematics can only be appreciated by way of contrast with the metaphysical doctrines it rejects. Mathematical Realism is the view that mathematical objects exist and that mathematical terms, such as five, and the null set, refer to these mathematical objects. It should be noted, however, that Mathematical Realists do not always insist that all the standard mathematical terms refer.

Keywords:   metaphysics, mathematics, modal theory, Mathematical Realism, anti-realism, ontology, vagueness argument

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