Ben, The difference can I think be best illustrated with two hypothetical AGIs. Both are supposed to be learning that "computers are approximately Turing machines". The first, made by you, interprets this constructively (let's say relative to PA). The second, made by me, interprets this classically (so it will always take the strongest set of axioms that it suspects to be consistent).
The first AGI will be checking to see how well the computer's halting matches with the positive cases it can prove in PA, and the non-halting with the negative cases it can prove in PA. It will be ignoring the halting/nonhalting behavior when it can prove nothing. The second AGI will be checking to see how well the computer's halting matches with the positive cases it can prove in the axiom system of its choice, and the non-halting with the negative cases it can prove in PA, *plus* it will look to see if it is non-halting in the cases where it can prove nothing (after significant effort). Of course, both will conclude nearly the same thing: the computer is similar to the formal entity within specific restrictions. The second AGI will have slightly more data (extra axioms plus information in cases when it can't prove anything), but it will be learning a formally different statement too, so a direct comparison isn't quite fair. Anyway, I think this clarifies the difference. --Abram On Wed, Oct 29, 2008 at 1:13 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > >> >> > >> > But the question is what does this mean about any actual computer, >> > or any actual physical object -- which we can only communicate about >> > clearly >> > insofar as it can be boiled down to a finite dataset. >> >> What it means to me is that "Any actual computer will not halt (with a >> correct output) for this program". An actual computer will keep >> crunching away until some event happens that breaks the metaphor >> between it and the abstract machine-- memory overload, power failure, >> et cetera. > > Yes ... this can be concluded **if** you can convince yourself that the > formal model corresponds to the physical machine. > > And to do *this*, you need to use a finite set of finite data points ;-) > > ben > > ________________________________ > agi | Archives | Modify Your Subscription ------------------------------------------- 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
