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Imagining the Real or Realizing the Imaginary: Platonism Versus Imaginism

In: The New Mathematical Coloring Book

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  • Alexander Soifer

    (University of Colorado at Colorado Springs, College of Letters, Arts, and Sciences)

Abstract

Undoubtedly, a vast majority of mathematicians are Platonists. They believe that mathematical objects exist “out there” independently of the human mind, and mathematicians merely discover them. The Platonists believe that a mathematical statement, such as AC, is objectively either true or false – we simply do not know which it is, although in a poll of mathematicians, “AC is true” would win hands down. Likewise, a question, what is the chromatic number of the first Shelah–Soifer graph G, surely, must have a definitive answer; it cannot be “2 or uncountable infinity.” Therefore, for the Platonists either ZFC or ZF+DC+LM is true, we just do not know which. Platonists imagine the real.

Suggested Citation

  • Alexander Soifer, 2024. "Imagining the Real or Realizing the Imaginary: Platonism Versus Imaginism," Springer Books, in: The New Mathematical Coloring Book, edition 2, chapter 0, pages 779-781, Springer.
    • Handle: RePEc:spr:sprchp:978-1-0716-3597-1_67
    DOI: 10.1007/978-1-0716-3597-1_67
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