Mike, That may be the case, but I do not think it is relevant to Valentina's point. How can we mathematically define how an AGI might mathematically define its own goals? Well, that question assumes 3 things:
-An AGI defines its own goals -In doing so, it phrases them in mathematical language -It is possible to mathematically define the way in which it does this I think you are questioning assumptions 2 and 3? If so, I do not think that the theory needs to be able to do what you are saying it cannot: it does not need to be able to generate new branches of mathematics from itself before-the-fact. Rather, its ability to generate new branches (or, in our case, goals) can and should depend on the information coming in from the environment. Whether such a logic really exists, though, is a different question. Before we can choose which goals we should pick, we need some criteria by which to judge them; but it seems like such a criteria is already a goal. So, I could cook up any method of choosing goals that sounded OK, and claim that it was the solution to Valentina's problem, because Valentina's problem is not yet well-defined. The closest thing to a solution would be to purposefully give an AGI a complex, probabilistically-defined, and often-conflicting goal system with many diverse types of pleasure, like humans have. On Tue, Aug 26, 2008 at 2:36 PM, Mike Tintner <[EMAIL PROTECTED]> wrote: > Abram, > > Thanks for reply. This is presumably after the fact - can set theory > predict new branches? Which branch of maths was set theory derivable from? I > suspect that's rather like trying to derive any numeral system from a > previous one. Or like trying to derive any programming language from a > previous one- or any system of logical notation from a previous one. > >> Mike, >> >> The answer here is a yes. Many new branches of mathematics have arisen >> since the formalization of set theory, but most of them can be >> interpreted as special branches of set theory. Moreover, >> mathematicians often find this to be actually useful, not merely a >> curiosity. >> >> --Abram Demski >> >> On Tue, Aug 26, 2008 at 12:32 PM, Mike Tintner <[EMAIL PROTECTED]> >> wrote: >>> >>> Valentina:In other words I'm looking for a way to mathematically define >>> how >>> the AGI will mathematically define its goals. >>> >>> Holy Non-Existent Grail? Has any new branch of logic or mathematics ever >>> been logically or mathematically (axiomatically) derivable from any old >>> one? e.g. topology, Riemannian geometry, complexity theory, fractals, >>> free-form deformation etc etc >>> ________________________________ >>> 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 >> > > > > > ------------------------------------------- > 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 > ------------------------------------------- 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
