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Mathematics without Numbers
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Mathematics without Numbers: Towards a Modal-Structural Interpretation

Geoffrey Hellman

Abstract

Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc. Structures are understood as comprising objects, whatever their nature, standing i ... More

Keywords: classical mathematics, Geoffrey Hellman, indefinite extendability, large cardinal axioms, mereology, modal logic, nominalism, philosophy of mathematics, Platonism, set theory, structuralism, Zermelo–Fraenkel

Bibliographic Information

Print publication date: 1993 Print ISBN-13: 9780198240341
Published to Oxford Scholarship Online: November 2003 DOI:10.1093/0198240341.001.0001

Authors

Affiliations are at time of print publication.

Geoffrey Hellman, author
University of Minnesota
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