The Price of Mathematical Scepticism - OCIE Seminar in History and Philosophy of Mathematics

Explore a thought-provoking lecture on mathematical philosophy that delves into the consequences of doubting fundamental mathematical concepts. Examine the argument that skepticism about mathematical reality comes at a significant cost, particularly when questioning the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice. Discover how these doubts may lead to questioning the consistency of third-order arithmetic in both classical and intuitionistic versions. Engage with the philosophical view that mathematical beliefs stem from intuitions that must be either fully accepted or doubted, not partially embraced. Participate in the "bivalence questionnaire" designed to help reflect on personal mathematical intuitions and beliefs. Investigate a spectrum of mathematical positions, including ultrafinitism, finitism, countabilism, sequentialism, particularism, and totalism, each maintaining the advocated belief alignment. Gain insights from this Orange County Inland Empire (OCIE) Seminar in History and Philosophy of Mathematics, presented by Paul Levy from the University of Birmingham, based on his paper published in Philosophia Mathematica.