Imagining the Real or Realizing the Imaginary: Platonism Versus Imaginism

Alexander Soifer
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Alexander Soifer: University of Colorado at Colorado Springs, College of Letters, Arts, and Sciences

Chapter Chapter 67 in The New Mathematical Coloring Book, 2024, pp 779-781 from Springer

Abstract: 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.

Date: 2024
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DOI: 10.1007/978-1-0716-3597-1_67

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