Two Criticisms against Mathematical Realism

Diametros 52:96-106 (2017)
Authors
Seungbae Park
Ulsan National Institute Of Science And Technology
Abstract
Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an object that changes its shape from a triangle to a circle, and then back to a triangle with every second.
Keywords Abstract World  Concrete World  Mathematical Object  Mathematical Realism  Tricle
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DOI 10.13153/diam.52.2017.1061
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Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy:00-00.

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