On Sunday, September 23, 2012 9:28:03 PM UTC-5, William Elliot wrote: > On Sun, 23 Sep 2012, Zuhair wrote: > Actually Godel's incompleteness theorems didn't abort Hilbert's > program at all. We can still have a consistent effectively generated > formal system in which ALL "mathematical" statements are provable! How so. If P is an undeciable mathematical statement, then both P and ~P are mathematical statements. Thus such a formal system is inconsistend. > Now this system must be of the nature that all statements in its > language that are not provable in it must not be mathematical. This is > actually not a thing that is hard to contemplate. Of course this calls > beforehand for a strict definition of what "mathematical" is.