Hi guys, I took a couple hours on a red-eye flight last night to write up in more detail my argument as to why uncomputable entities are useless for science:
http://multiverseaccordingtoben.blogspot.com/2008/10/are-uncomputable-entities-useless-for.html Of course, I had to assume a specific formal model of science which may be controversial. But at any rate, I think I did succeed in writing down my argument in a more clear way than I'd been able to do in scattershot emails. The only real AGI relevance here is some comments on Penrose's nasty AI theories, e.g. in the last paragraph and near the intro... -- Ben G On Tue, Oct 28, 2008 at 2:02 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > Mark, > > That is thanks to Godel's incompleteness theorem. Any formal system > that describes numbers is doomed to be incomplete, meaning there will > be statements that can be constructed purely by reference to numbers > (no red cats!) that the system will fail to prove either true or > false. > > So my question is, do you interpret this as meaning "Numbers are not > well-defined and can never be" (constructivist), or do you interpret > this as "It is impossible to pack all true information about numbers > into an axiom system" (classical)? > > Hmm.... By the way, I might not be using the term "constructivist" in > a way that all constructivists would agree with. I think > "intuitionist" (a specific type of constructivist) would be a better > term for the view I'm referring to. > > --Abram Demski > > On Tue, Oct 28, 2008 at 4:13 PM, Mark Waser <[EMAIL PROTECTED]> wrote: > >>> Numbers can be fully defined in the classical sense, but not in the > > > > constructivist sense. So, when you say "fully defined question", do > > you mean a question for which all answers are stipulated by logical > > necessity (classical), or logical deduction (constructivist)? > > > > How (or why) are numbers not fully defined in a constructionist sense? > > > > (I was about to ask you whether or not you had answered your own question > > until that caught my eye on the second or third read-through). > > > > > > > ------------------------------------------- > 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
