The Liar Paradox: A Consistent and Semantically Closed Solution

Abstract

This thesis develops a new approach to the formal de nition of a truth predicate that allows a consistent, semantically closed defiition within classical logic. The approach is built on an analysis of structural properties of languages that make Liar Sentences and the paradoxical argument possible. By focusing on these conditions, standard formal dfinitions of semantics are shown to impose systematic limitations on the definition of formal truth predicates.

The alternative approach to the formal definition of truth is developed by analysing our intuitive procedure for evaluating the truth value of sentences like "P is true". It is observed that the standard procedure breaks down in the case of the Liar Paradox as a side effect of the patterns of naming or reference necessary to the definition of Truth as a predicate. This means there are two ways in which a sentence like "P is true" can be not true, which requires that the T-Schema be modified for such sentences.

By modifying the T-Schema, and taking seriously the effects of the patterns of naming/ reference on truth values, the new approach to the definition of truth is developed. Formal truth definitions within classical logic are constructed that provide an explicit and adequate truth definition for their own language, every sentence within the languages has a truth value, and there is no Strengthened Liar Paradox. This approach to solving the Liar Paradox can be easily applied to a very wide range of languages, including natural languages. Show more