All Godel's Theorem says is that there are statements that can't be proven or disproven within an axiomatic system sufficiently rich enough to represent arithmetic operations. It doesn't say how interesting those statements are. Really, after the novelty has worn off, how important or interesting is the statement "This statement cannot be proven within the current axiomatic system"? Outside of the general implications for mathematics as a field, who cares whether that particular statement can or can't be proven? Just because there is a guarantee that there will always be new things to discover doesn't mean they will be interesting.
On Mon, Mar 18, 2013 at 8:21 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/** > 23050605-2da819ff<https://www.listbox.com/member/archive/rss/303/23050605-2da819ff> > Modify Your Subscription: https://www.listbox.com/** > member/?&id_**secret=23050605-53e85d0d<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
