31 Jul
2015
31 Jul
'15
8:35 p.m.
Yet, G??del uses "provability" to create new sentences, and simply opens up that bag of sentences, and throws in these new ones. It has always been accepted, but this in fact breaches the lativity principle, which indeed is not respected in logic.
The point is that the provability predicate doesn't require new syntax but can be formulated already with a modicum of arithmetic (that's what has become known as "Goedelization"). It would be a different issue with a "truth" predicate which cannot be expressed in the language (known as Tarski's theorem). Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]