Mathematical Truth without Reference
Meaning and Identity in Analytic Philosophy
Colin McCullough-Benner
University of Connecticut Department of Philosophy
Published 2014-12-10
https://doi.org/10.15388/Problemos.2014.0.4926
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Keywords

Mathematics
platonism
anti-realism
non-referential semantics
compositionality
ontological commitment

How to Cite

McCullough-Benner C. (2014). Mathematical Truth without Reference. Problemos, 70-77. https://doi.org/10.15388/Problemos.2014.0.4926

Abstract

According to a canonical argument for mathematical platonism, if we are to have a uniform semantics which covers both mathematical and non-mathematical language, then we must understand singular terms in mathematics as referring to objects and understand quantifiers as ranging over a domain of such objects, and so treating mathematics as literally true commits us to the existence of (mind-independent, abstract) mathematical objects. In this paper, I argue that insofar as we can provide a uniform semantics for the better part of ordinary, non-mathematical language, we can provide a uniform semantics covering both mathematical and non-mathematical language without thereby committing ourselves to the existence of mathematical objects.
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