Abram,
> To re-explain: We might construct generalizations of AIXI that use a > broader range of models. Specifically, it seems reasonable to try > models that are extensions of first-order arithmetic, such as > second-order arithmetic (analysis), ZF-set theory... (Models in > first-order logic of course could be considered equivalent to > Turing-machine models, the current AIXI.) Description length then > becomes description-length-in-language-X. But, any such extension is > doomed to a simple objection: > > (1) We humans understand the semantics of formal system X. > (2) The undefinability theorem shows that formal system X cannot > understand its own semantics. > > That is what needs an explanation. It doesn't, because **I see no evidence that humans can understand the semantics of formal system in X in any sense that a digital computer program cannot** Whatever this mysterious "understanding" is that you believe you possess, **it cannot be communicated to me in language or mathematics**. Because any series of symbols you give me, could equally well be produced by some being without this mysterious "understanding". Can you describe any possible finite set of finite-precision observations that could provide evidence in favor of the hypothesis that you possess this posited "understanding", and against the hypothesis that you are something equivalent to a digital computer? I think you cannot. So, your belief in this posited "understanding" has nothing to do with science, it's basically a kind of religious faith, it seems to me... '-) -- Ben G ------------------------------------------- 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
