News for hackers. Stuff that matters.

A comment on In Mathematics, Mistakes Aren’t What They Used to Be (2015). Parent comment

Re:In Mathematics, Mistakes Aren’t What They Used to Be (2015) by marcelluspye on Saturday August 27, 2016 @04:07PM (#12373939)
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.

[ Parent | on HN ]
Re:In Mathematics, Mistakes Aren’t What They Used to Be (2015) by kxyvr on Saturday August 27, 2016 @04:34PM (#12374050)
Slightly 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) Basically, it's actually kind of hard to define what true means and Tarski goes through a long discussion trying to pin it down.
[ Parent | on HN ]