OK ... but are both of these hypothetical computer programs on standard contemporary chips, or do any of them use weird supposedly-uncomputability-supporting chips? ;-)
Of course, a computer program can use any axiom set it wants to analyze its data ... just as we can now use automated theorem-provers to prove stuff about uncomputable entities, in a formal sense... By the way, I'm not sure the sense in which I'm a "constructivist." I'm not willing to commit to the statement that the universe is finite, or that only finite math has "meaning." But, it seems to me that, within the scope of *science* and *language*, as currently conceived, there is no *need* to posit anything non-finite. Science and language are not necessarily comprehensive of the universe.... Potentially (though I doubt it) mind is uncomputable in a way that makes it impossible for science and math to grasp it well enough to guide us in building an AGI ;-) ... and, interestingly, in this case we could still potentially build an AGI via copying a human brain ... and then randomly tinkering with it!! ben On Wed, Oct 29, 2008 at 1:45 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > 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/?&; > Powered by Listbox: http://www.listbox.com > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects." -- Robert Heinlein ------------------------------------------- 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
