A Semantic Situation without Syntax (Non- axiomatizibility of Theories)

Abstract

Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in the subject of axiomatizibility. Based on this claim, having an axiomatic system for Computability Theory is not possible. In fact, the same argument shows that many other theories are non-axiomatizable. (Dare to say: General Theories of Physics and Mathematics).