Incompleteness and infinity


View Calendar
September 14, 2022 4:30 pm - 5:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

W. Hugh Woodin - Harvard University

A natural speculation is that incompleteness is simply a by-product of infinity. Perhaps one can avoid incompleteness by simply restricting our mathematical scope to the finite. Do we lose anything in this move?

The answer I shall argue, is both yes and no. Along the way I will discuss an entirely new approach to the Godel Incompleteness Theorems which has emerged over the last 15 years. I will also introduce some very large finite numbers which arise naturally from finite combinatorics, and indicate how by invoking these large finite numbers, any number theoretic problem of modern interest can be converted to a finitistic statement.

It is unclear which would be more amazing for these problems of modern interest: This conversion does not always produce an equivalent problem, or that this conversion always does.