On Mon, Mar 18, 2013 at 9:21 PM, just camel <[email protected]> wrote:
> Neither the Halting Problem nor Goedel's incompleteness theorem say that > there will always be new things to discover? They do say you could learn new things about a 'closed system' because there are infinite "theorems" about non-decidable problems that could be made. That means that the system is not actually closed. Furthermore, the problem cannot be associated with a 'level' of abstraction. When we talk about inductive problems are we actually talking about the creation of new logical theorems? No, although they may be new to us. That suggests that we did not start out talking about complete systems in the first place. So while I was a little dubious about Russell's statement, there is an argument that incompleteness implies infinite inductive potential or something like that. Jim Bromer On Mon, Mar 18, 2013 at 9:21 PM, just camel <[email protected]> wrote: > Neither the Halting Problem nor Goedel's incompleteness theorem say that > there will always be new things to discover? Could you elaborate on that? > Being unable to predict/proof things within system A does not say anything > about whether you can actually discover new stuff ad infinitum? Just > because I can not disproof the existence of God or turtles carrying the > cosmos on their shoulders does not mean that I will discover anything? If > we are living in a perfect simulation the system will not allow you to find > out anything about the entity running those simulations for example. If you > can not access anything outside of your framework than you will have a hard > time discovering new things and Goedel's theorem will still hold true. > > On 03/14/2013 01:52 PM, Russell Wallace wrote: > >> The answer turns out to be no, not as a matter of opinion, but as a >> matter of mathematical proof: check out Godel's theorem, the Halting >> Problem etc. No matter how much you know, there will always be new >> discoveries to make. >> > > > > ------------------------------**------------- > AGI > Archives: > https://www.listbox.com/**member/archive/303/=now<https://www.listbox.com/member/archive/303/=now> > RSS Feed: https://www.listbox.com/**member/archive/rss/303/** > 10561250-470149cf<https://www.listbox.com/member/archive/rss/303/10561250-470149cf> > Modify Your Subscription: https://www.listbox.com/** > member/?&id_**secret=10561250-b8cb8eb9<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/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
