> Mike Archbold, > > It seems you've made a counterargument without meaning to. > > "When we make this transition, it seems to me that the shift is so radical > that it is impossible to justify making the step, because as I mentioned > it involves a surreptitious shift from quantity to quality." > > I maintain that the jump is justified. To me it is like observing the > sequence "1, 2, 4, 8, 16, 32..." and concluding that each number is > twice the previous. It is a jump from several quantities to a single > quality. >
Fair enough. I think what we are saying is that in the transition of quantity to quality -- as in your example -- is a kind of "appeal to the infinite," ie., is an instance of hypercompuation? That does have a Godel sound to it, as I understand it, we appeal beyond the data in question although I have only seen Godel's writings (not read them). I read more of the paper. I like the part about the Zeus Machine. Cool. I guess I am a bit more aligned to the philosophy side than the Turing-Godel-computational side of the house. In my studies as I mentioned of Hegel's Logic, there is a constant interplay between quantity and quality, given as measure -- measure here being the result of quantity and quality intermixing. I guess measure in this sense is roughly equivalent to hypercomputation if I have my Godels and Hegels lined up in a row. Hegel's philosophy was of course totally predicated on the mind which as I said he held to be infinite. Although, we have to be careful in so much as there exist multiple definitions of the infinite. Mike Archbold > On Tue, Jun 17, 2008 at 4:35 PM, Vladimir Nesov <[EMAIL PROTECTED]> > wrote: >> On Tue, Jun 17, 2008 at 11:38 PM, Abram Demski <[EMAIL PROTECTED]> >> wrote: >>> V. N., >>> What is inhuman to me, is to claim that the halting problem is no >>> problem on such a basis: that the statement "Turing machine X does not >>> halt" only is true of Turing machines that are *provably* non-halting. >>> And this is the view we are forced into if we abandon the reality of >>> the uncomputable. >>> >> >> Why, you can also mark up the remaining territory by "true" and >> "false", these labels just won't mean anything there. Set up to sets, >> T and F, place all true things in T, all false things in F, and all >> unknown things however you like, but don't tell anybody how. Some >> people like to place all unknown things in F, their call. >> Mathematically it can be convenient, but really, even of "computable" >> things you can't really compute that much, so the argument is void for >> all practical concerns anyway. >> >> -- >> Vladimir Nesov >> [EMAIL PROTECTED] >> >> >> ------------------------------------------- >> agi >> Archives: http://www.listbox.com/member/archive/303/=now >> RSS Feed: http://www.listbox.com/member/archive/rss/303/ >> Modify Your Subscription: http://www.listbox.com/member/?&; >> Powered by Listbox: http://www.listbox.com >> > > > ------------------------------------------- > agi > Archives: http://www.listbox.com/member/archive/303/=now > RSS Feed: http://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: > http://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=106510220-47b225 Powered by Listbox: http://www.listbox.com
