2 ms·
Well, for one thing, you have to define 'true'. The incompleteness theorems don't have anything to do with what's 'true', they have to do with what's 'derivable
by marcelluspye 10y ago
Well, for one thing, you have to define 'true'. The incompleteness theorems don't have anything to do with what's 'true', they have to do with what's 'derivable'.
It's a consequence of the completeness theorem that every consistent theory has a model. Furthermore, in any incomplete system whereby a Godel sentence is useful, there are necessarily models that differ on the satisfaction of the Godel sentence.
- kxyvr 10y agoSlightly off topic, but your comment reminded me of Tarski's paper The Semantic Conception of Truth and the Foundations of Semantics (http://www.jfsowa.com/logic/tarski.htm http://www.jfsowa.com/logic/tarski.htm) Basically, it's actually kind of hard to define what true means and Tarski goes through a long discussion trying to pin it down.