CMA & DM, FCT, Universidade Nova de Lisboa
Abstract: In the foundations of mathematics, David Hilbert's name is associated, i.a., with the programmatic idea to carry out consistency proofs for formalized mathematical theories. It is well-known that Gödel's Incompleteness Theorems set limits to this programme which can only be exceeded by transcending the finitistic standpoint which was advocated by Hilbert for the time being. In our talk we relate this narrower Hilbert Programm with his original, much wider mathematico-philosophical concerns. We are able to identify a Larger Hilbert Programme which was successful from the beginning of proof theory till this day; these successes justify outright the philosophical status of mathematical logic as foundational base of mathematics.
This talk is dedicated to the memory of Amílcar Sernadas, 1952-2017, who expressed a great admiration for Hilbert and whose work fits squarely in Hilbert's Larger Programme.
This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.