Sam Alexander : Well-foundedness of machine knowers

Posted by , part of the Louise Hay Logic Seminar.

At

Sept. 15, 2011, 3 p.m.

In

SEO 1227

Abstract

We give an introduction to machine knowledge, and show that a truthful machine which has basic reasoning and arithmetic abilities can possibly know itself to be truthful, or know its own Godel number, but not both. We then discuss well-foundedness of machine knowers: Is there an infinite sequence of truthful machines, each of which knows the Godel number and the truthfulness of the next? We show that this is not possible, assuming the machines are capable of comprehending recursive ordinals.