Two Criticisms against Mathematical Realism

Seungbae Park

About author

Seungbae Park, Ph.D.
Associate Professor
Division of General Studies
Ulsan National Institute of Science and Technology
Ulju-gun, Ulsan 44919
Republic of Korea



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.

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