A Semantic Without Syntax 1

TL;DR

This paper explores a new semantic approach to classical paradoxes like the liar paradox, arguing that some semantic situations cannot be captured by any syntactical logical system, and questions the axiomatizability of theories like physics.

Contribution

It introduces a novel semantic perspective on paradoxes and demonstrates that certain theories, including physics, may be inherently non-axiomatizable.

Findings

Semantic situations beyond syntactical support

Axiomatizability of physics is questionable

Proposes a new perspective on logical paradoxes

Abstract

Here, by introducing a version of "Unexpected hanging paradox" 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 that. In the end, we propose a claim as a question. Based on this claim, having an axiomatic system for computability theory is not possible. In fact we will show that the method applied here could yields us as a generalized result, some Theories like Physic is not axiomatizable.