tag:blogger.com,1999:blog-6555947.post111046318749950813..comments2020-10-20T22:39:09.892-06:00Comments on The Geomblog: GĂ¶del, Original Sin, and Sausage...Suresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6555947.post-1111185780209072512005-03-18T15:43:00.000-07:002005-03-18T15:43:00.000-07:00So the actual statement is more nuanced. The corre...So the actual statement is more nuanced. The correct statement is that it is possible to construct a statement in a consistent system of logic that essentially says 'this statement cannot be proved'. Now if the system is consistent, it will not prove a false statement. If the statement could be proved, it would be false, which would violate consistency. The only other choice is that the statement is true, but then cannot be proved within the system. <BR/><BR/>The trick is that "true" is relative to the logical system, and is not defined outside it. in fact what Godel basically showed is that there no absolute notion of truth (or no sound and complete logic system) <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>SureshAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1111179988358799782005-03-18T14:06:00.000-07:002005-03-18T14:06:00.000-07:00The popular definition in the review goes somethin...The popular definition in the review goes something like Godel's=there exist true statements that are unproveable<BR/><BR/>This "true but unproveable" seems to come up a lot. Does that make any sense? If something is unproveable in given system of axioms, how is it true? <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A><A HREF="yaroslavvb.blogspot.com" REL="nofollow" TITLE="yaroslavvb at gmail dot com">Yaroslav Bulatov</A>Anonymousnoreply@blogger.com