tag:blogger.com,1999:blog-34016406.post4503519796391782309..comments2013-11-22T13:42:57.303-08:00Comments on Tales from dekrypt: On Hilbert's sixth problemPauliehttp://www.blogger.com/profile/06424849610575275694noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-34016406.post-8631981098800069352013-11-22T13:42:57.303-08:002013-11-22T13:42:57.303-08:00A) Your assertion that ZF must contain some theor...A) Your assertion that ZF must contain some theorems which annot be proved is rather sloppy. A theorem is a proposition which can be proved. You meant to say that ZF contains some propositions which cannot be proved, and whose negations cannot be proved either. This is incompleteness.<br /><br />B) Goedel's Incompleteness Theorem has nothing to do with whether Physics can be axiomatised. It might have something to do with whether Theoretical Physics can ever be complete. But it might not. After all, Theoretical Physics does not have to include all of ZF. Set theory might go way beyond physical reality, so that Theoretical Physics would not actually contain all of mathematics, and thus Goedel's theorem would not apply. In fact, Goedel also proved a completeness theorem: First order Logic is complete. Now, why would a physicist want second-order quantifiers? So, who knows.<br /><br />C) Forget Boolean algorithms and Turing Machines. No algorithm can be exactly modelled by a physical machine: there is always some noise. E.g., no square wave, and hence no string of bits, can be completely reliably produced in the real world, and if it could be produced, the information in it, the «signal», still could not be reliably extracted in an error-free fashion by any finite physical apparatus.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-34016406.post-65929862993216340952009-09-02T18:41:39.844-07:002009-09-02T18:41:39.844-07:00Hilbert's Sixth has been solved.
www.Einstein...Hilbert's Sixth has been solved.<br /><br />www.EinsteinGravity.comALhttp://www.blogger.com/profile/15745443491036975295noreply@blogger.com