Two Criticisms against Mathematical Realism Cover Image

Two Criticisms against Mathematical Realism
Two Criticisms against Mathematical Realism

Author(s): Seungbae Park
Subject(s): History of Philosophy, Philosophical Traditions, Special Branches of Philosophy
Published by: Instytut Filozofii Uniwersytetu Jagiellońskiego
Keywords: Abstract World; Concrete World; Mathematical Realism; Mathematical Object; Tricle

Summary/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.

  • Issue Year: 2017
  • Issue No: 52
  • Page Range: 96-106
  • Page Count: 11
  • Language: English