Abstract

There are many versions of the Liar Paradox. J. Agassi names 13 of them. But the most important one is related to Tarski’s theorem that the truth predicate is non-definable for systems that are sufficient for the formalisation of elementary arithmetic of natural numbers. Let S be such a system. We assume that S is consistent and that the syntax of S has been arithmetized as understood by G¨odel. Let E be any sentence of S. E ∗ is the symbol of the G¨odel number of E. If formula A belongs to the language of system S, then formula E is a constant point for formula A if and only if S ⊢ E → A. It can be proved that every formula A ∈ S has a constant point in S.