Two Criticisms against Mathematical Realism

Seungbae Park

About author

http://philpapers.org/profile/5452

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

Email: nature@unist.ac.kr

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.


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DOI:

http://dx.doi.org/10.13153/diam.52.2017.1061

Article links:

Default URL: http://www.diametros.iphils.uj.edu.pl/index.php/diametros/article/view/1061
English abstract URL: http://www.diametros.iphils.uj.edu.pl/index.php/diametros/article/view/1061/en

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