Incompleteness and infinity
W. Hugh Woodin - Harvard University
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.