A Study of The Tarsklan Hierarchy of Languages

Abstract

<p>Alfred Tarski 's formulation of the hierarchy of languages was intended to prevent semantic paradoxes from occurring in a formal language, and thus to preserve consistency. This thesis attempts to explain how Tarski accomplishes this, and to identify logical problems which occur in the hierarchy. Chapter one outlines the parameters of study. Chapter two outlines a simple version of the hierarchy of languages. Chapter three provides an exegesis of 'The Concept of Truth in Formalized Languages', explaining the notion of "essential richness", which is central to understanding how paradoxes are avoided by Tarski. Chapter four introduces problems relating to infinite regress, and a direct, general definition of truth is presented using Tarski's own notation. Questions relating to expressibility and proving consistency are addressed in chapter five. In the appendix, a weakness in Tarski's attempt to reduce semantic concepts to non-semantic concepts is shown using his own definitions and notation.</p>