# Two Criticisms against Mathematical Realism

*Diametros*52:96-106 (2017)

**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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References found in this work BETA

The Indispensability of Mathematics.Colyvan, Mark

Realism, Mathematics and Modality.Field, Hartry

From a Logical Point of View.Quine, W. V.

Mathematics as a Science of Patterns.Resnik, Michael D.

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Citations of this work BETA

Can Mathematical Objects Be Causally Efficacious?Park, Seungbae

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2017-06-30

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