The Liar Paradox: A Consistent and Semantically Closed Solution

1 This thesis develops a new approach to the formal denition of a truth predicate that allows a consistent, semantically closed denition 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 denitions of semantics are shown to impose systematic limitations on the denition of formal truth predicates. The alternative approach to the formal denition 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 eect of the patterns of naming or reference necessary to the denition 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 modied for such sentences. By modifying the T-Schema, and taking seriously the eects of the patterns of naming/ reference on truth values, the new approach to the denition of truth is developed. Formal truth denitions within classical logic are constructed that provide an explicit and adequate truth denition 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. The work contained in this Thesis is my own and, unless otherwise attributed, is not the result of any joint eort or research. Acknowledgement. Firstly, I would like to thank Peter Roeper for his time, eort, patience and attention to detail. His willingness to pause and take time to consider and think through all of my ideas, even the worst ones, has been greatly appreciated. While our discussions tended to go round in circles, he succeeded in bringing order and rigour to my work which I would have struggled to achieve otherwise. I am very grateful to Ingolf Max, and the other academics at the Institut für Logik und Wissenschaftstheorie at the University of Leipzig, for their time and support during my stay there. I learnt a lot and my ideas matured signicantly in the stimulating environment they have created. I am also very grateful to Brian Garrett, Daniel Stoljar, Margaret Brown and many others …