Self-Reference and Rejection

Abstract

The paper consists of two parts. The first contains the paradox of Truth-teller, i.e. a sentence which asserts own truth. The paradox appears when we apply logic of rejection to the Truth-teller sentence. The Truth-teller paradox is symmetric with respect to the Liar paradox. The second part considers a sentence which asserts own provability. This sentence is unprovable on the base of rejection logic. This leads to counterparts of the Gödel incompleteness theorems and other metamathematical results.