tag:blogger.com,1999:blog-11295132.post112559987355358709..comments2016-10-18T06:55:32.586-07:00Comments on A Neighborhood of Infinity: Alternative LogicDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-11295132.post-1135107690014660442005-12-20T11:41:00.000-08:002005-12-20T11:41:00.000-08:00This comment has been removed by a blog administrator.Basiballihttp://www.blogger.com/profile/10654346740140334878noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1129973921220926062005-10-22T02:38:00.000-07:002005-10-22T02:38:00.000-07:00And perhaps the most interesting fact about the tw...And perhaps the most interesting fact about the two types of completeness is that second order logic has the one that first-order doesn't have, but not the one that it does!Kennyhttp://www.blogger.com/profile/12226268498253877151noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1129826601710818122005-10-20T09:43:00.000-07:002005-10-20T09:43:00.000-07:00Ah yes...when I wrote that article I was a bit con...Ah yes...when I wrote that article I was a bit confused about 'completeness' and was trying hard to figure out how the two different notions were the same thing. Later I realised they aren't. Very confusing until someone explicitly points it out - as the books I was looking at failed to do.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1129793824657314652005-10-20T00:37:00.000-07:002005-10-20T00:37:00.000-07:00Nice post! There's a typo where you talk about Bu...Nice post! There's a typo where you talk about Bush's possibilities and say "not not" instead of "but not" (I think). And your aside about completeness seems to conflate the notion Godel showed didn't hold in the Incompleteness Theorems with the one he showed did hold in the Completeness Theorem. (ie, not every true statement is provable, but every consequence of any premises can in fact be derived from those premises - it's just that no set of premises is enough to get all the truths of arithmetic).<BR/><BR/>Anyway, I definitely have to check out quantum logic now!Kennyhttp://www.blogger.com/profile/12226268498253877151noreply@blogger.com