
Author 
Message 
anticorncob28


Joined: Thu May 05, 2016 10:31 pm Posts: 38 Location: Nebraska, USA

According to GĂ¶del's first imcompleteness theorem, any selfconsistent system has a statement that is independent of the system. I don't understand how this is true. Take the real numbers. There are several constructions of the real numbers, and they all demonstrably describe a unique system up to isomorphism. How then can there exist a statement P about the real numbers which can be neither proven nor disproven? Then you can invent two real number systems, one in which P is true and one in which P is false. But that can't be the case if the two real number constructions are isomorphic.
_________________ "Climate change is the canvas on which the history of the 21st century will be painted." Mark Lynas, Six Degrees: Our Future on a Hotter Planet





GiantEvil


Original Member
Joined: Sat Aug 06, 2011 10:19 am Posts: 786

_________________ It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence. W. K. Clifford






Users browsing this forum: No registered users and 0 guests 
You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum


