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 (DC), 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 (BE). 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.
Acknowledgments
We heartily thank (in alphabetical order) James Anderson, Paul Balaguer, Paul Gould, David Liggins, Noah Weaver, and Greg Welty for extremely helpful correspondence while pondering the issues addressed in this article.
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Articles in the same Issue
- Frontmatter
- Original Papers
- Quantum Entanglement Undermines Structural Realism
- A Belief Expressionist Explanation of Divine Conceptualist Mathematics
- A Short Argument against Truthmaker Maximalism
- The Evil That Free Will Does: Plantinga’s Dubious Defense
- The Dead Past Dilemma
- The Role of Logic in Metaphysical Theorizing
- Reducing Constitution to Composition
- On Armstrong’s Radical Absolutism
- Objective Facts
Articles in the same Issue
- Frontmatter
- Original Papers
- Quantum Entanglement Undermines Structural Realism
- A Belief Expressionist Explanation of Divine Conceptualist Mathematics
- A Short Argument against Truthmaker Maximalism
- The Evil That Free Will Does: Plantinga’s Dubious Defense
- The Dead Past Dilemma
- The Role of Logic in Metaphysical Theorizing
- Reducing Constitution to Composition
- On Armstrong’s Radical Absolutism
- Objective Facts