0

I have been looking at Tarski's work and asked a question here:

Can truth be defined by a 'same-level' language according to Tarski's undefinability theorem?

I am trying to refine my question as follows: if a 'meta-language' L* is meta- only as far as one predicate is concerned, can the truth of that predicate in the lower language L be proven? Or is it essential that L* contains all of L (plus more), to prove the truth of something in L?

magnolia1
  • 159
  • Not clear... you say "the truth of that predicate"; I think it must be "the truth-predicate". – Mauro ALLEGRANZA Jul 18 '18 at 12:50
  • I guess I mean the truth of one single statement, without having to prove the truth of the entire language L. – magnolia1 Jul 18 '18 at 13:49
  • 1
    Truth of a single statement $S$ can be expressed without any met-language; just say $S$. – Andreas Blass Jul 18 '18 at 16:30
  • But then I’m missing something important. When would a meta-language be needed? Can’t every truth be expressed within L then? – magnolia1 Jul 18 '18 at 19:50
  • also, @AndreasBlass wouldn't this run into trouble with a statement like the liar's paradox? – magnolia1 Jul 19 '18 at 09:45
  • 1
    Truth of any single statement of $L$ can (trivially) be expressed in $L$. The general notion of truth for $L$-sentences cannot be expressed in $L$ (Tarski's theorem). The liar paradox is essentially the proof of Tarski's theorem. A (fairly) general notion of truth is needed in order to produce the liar sentence ("This sentence is false"), and that's why such a general notion of truth can't exist. – Andreas Blass Jul 19 '18 at 11:27

0 Answers0