To be a little clearer on my hand-wringing, here is a section where Bringsjord et al argue that belief in the Singularity is not rational:
> A > (P1) There will be AI (created by HI). > (P2) If there is AI, there will be AI+ (created by AI). > (P3) If there is AI+, there will be AI++ (created by AI+). > ) > There will be AI++ (= S will occur). > [...] > Our certainty in > the lack of certainty here can be established by showing, formally, that the > denial > of (P1) is consistent, since if not-(P1) is consistent, it follows that (P1) > doesn’t > follow from any of the axioms of classical logic and mathematics (for example, > from a standard axiomatic set theory, such as ZF). How then do we show that > not- > (P1) is consistent? We derive it from a set of premises which are themselves > consistent. To do this, suppose that human persons are information-processing > machines more powerful than standard Turing machines, for instance the > infinite- > time Turing machines specified and explored by Hamkins and Lewis (2000), that > AI (as referred to in A) is based on standard Turing-level information > processing, > and that the process of creating the artificial intelligent machines is > itself at the > level of Turing-computable functions. Under these jointly consistent > mathematical > suppositions, it can be easily proved that AI can never reach the level of > human > persons (and motivated readers with a modicum of understanding of the mathe- > matics of computer science are encouraged to carry out the proof). So, we know > that (P1) isn’t certain. Note the "for instance" of the ∞ time Turing machines, which itself seems to refer to a stable output in the long run that is taken as a non-halting output ... maybe kindasorta like the decimal format of 1/7 ... or Nick's conception of reality 8^D. I keep thinking, with no decision in sight so far, that Wolpert and Benford's attempt to resolve Roko's Basilisk is related, that there's some underlying set-up that makes the whole controversy dissolve. You'll note the higher-order nature of AI+ and AI++. And if there are some higher-order operators that simply don't operate over potential infinities, what are they? And can we simply define our way out of it, as in defining 1/0 ≡ 0? On 8/3/20 10:02 AM, uǝlƃ ↙↙↙ wrote: > > I know I've posted this before. I don't remember it getting any traction with > y'all. But it's relevant to my struggles with beliefs in potential vs actual > infinity: > > Belief in the Sinularity is Fideistic > https://link.springer.com/chapter/10.1007%2F978-3-642-32560-1_19 > > Not unrelated, I've often been a fan of trying identify *where* an argument > goes wrong. And because this post mentions not only 1/0, but Isabelle, Coq, > Idris, and Agda, I figured it might be a good follow-up to our modeling > discussion on Friday, including my predisposition against upper ontologies. > > 1/0 = 0 > https://www.hillelwayne.com/post/divide-by-zero/ -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
