MATHEMATICS

Talking About the Sentences that Talk About Themselves!

Saeed Salehi , University of Tabriz & IPM

14:00 - 16:00

Talking about oneself is natural in natural languages. But it can be ambiguous or can cause difficulties in formal languages. For example, the following sentence Ax Ey (x=2y ˅ x=2y+1) says that every number is either odd or even. But how can a sentence talk about itself? Gödel had the opinion that if the biconditional φ ↔ Ψ(#φ) holds, where #φ is the Godel code of φ, then φ says about itself that it has the Ψ property. In this talk, we will discuss on this interpretation and will give some mathematical arguments for some philosophical discussions on the truth or falsity of Gödelean sentences of arithmetical theories. By definition, a sentence γ is a Gödelean sentence of theory T when the biconditional γ ↔ ¬ PrT(#γ) is provable in T where PrT(x) is the provability predicate of T.