Radicals of Constructivity: Nelson and Griss on Intuitionism with Dr. Thomas Macaulay Ferguson

Wednesday, August 30, 2023

12:00pm EST

Carnegie 113

 Abstract: Brouwer's program of intuitionistic mathematics has been a remarkably fruitful field, influencing not only pure mathematics but the philosophy of language (through e.g. Dummett), computer science (via e.g. Curry-Howard correspondences), and the foundations of mathematics (in e.g. HoTT). This whole enterprise was based on Brouwer's understanding of constructions as exhibited in the Brouwer-Heyting-Kolmogorov interpretation of logical vocabulary. But several of Brouwer's contemporaries argued for more restrictive notions of constructivity, including David Nelson and G.F.C. Griss. I will discuss some historical background of these mathematicians' underappreciated programs and discuss new work in which the two positions can be reconciled.