A Belief Expressionist Explanation of Divine Conceptualist Mathematics

Metaphysica 23 (1):15-26 (2022)
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Abstract

Many have pointed out that the utility of mathematical objects is somewhat disconnected from their ontological status. For example, one might argue that arithmetic is useful whether or not numbers exist. We explore this phenomenon in the context of Divine Conceptualism, which claims that mathematical objects exist as thoughts in the divine mind. While not arguing against DC claims, we argue that DC claims can lead to epistemological uncertainty regarding the ontological status of mathematical objects. This weakens DC attempts to explain the utility of mathematical objects on the basis of their existence. To address this weakness, we propose an appeal to Liggins’ theory of Belief Expressionism. Indeed, we point out that BE is amenable to the ontological claims of DC while also explaining the utility of mathematical objects apart from reliance upon their existence. We illustrate these themes via a case study of Peano Arithmetic.

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David Freeman
University of Cincinnati

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Warrant and proper function.Alvin Plantinga - 1993 - New York: Oxford University Press.
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Go figure: A path through fictionalism.Stephen Yablo - 2001 - Midwest Studies in Philosophy 25 (1):72–102.
Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - Bulletin of Symbolic Logic 8 (4):516-518.
Abstract Expressionism and the Communication Problem.David Liggins - 2014 - British Journal for the Philosophy of Science 65 (3):599-620.

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