'The New Intuitionism'

25 February 2008
15:30
David McCarty
Abstract
Now that the "classical" philosophies that have danced attendance upon intuitionistic mathematics (Brouwer's subjectivism, Heyting's eclecticism, and contemporary anti-realism) are recognized as failures, it is encumbent upon intuitionists to develop new foundations for their mathematics. In this talk, we assay such efforts, in particular, investigations into the various mathematical grounds on the basis of which the law of the excluded third might be proven invalid. It will also be necessary, along the way, to explode certain mistaken ideas about intuitionism, among them the notion that the logical signs of the intuitionists bear meanings different from those attached to the corresponding signs in conventional mathematics. Please let Bruno Whittle (bruno.whittle@philosophy.ox.ac.uk) know if you would like to go out to dinner with the speaker after the seminar.
  • Philosophy of Mathematics