On Thu, Oct 16, 2008 at 1:35 AM, Matt Mahoney <[EMAIL PROTECTED]> wrote: > Goedel and Turing showed that theorem proving is equivalent to solving the > halting problem. So a simple measure of intelligence might be to count the > number of programs that can be decided. But where does that get us? Either > way (as as set of axioms, or a description of a universal Turing machine), > the problem is algorithmically simple to describe. Therefore (by AIXI) any > solution will be algorithmically simple too.
This doesn't follow. Per Chaitin, you can't prove a 20 pound theorem with 10 pounds of axioms, even if the formal system being discussed is algorithmically simple. More to the point, a program that can prove interesting theorems before the sun burns out, will be much more complex than the axiom system. ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
