DIAGONALIZATION AND LOGICAL PARADOXES

Abstract

<p>The purpose of this dissertation is to provide a proper treatment for two groups of logical paradoxes: semantic paradoxes and set-theoretic paradoxes. My main thesis is that the two different groups of paradoxes need different kinds of solution. Based on the analysis of the diagonal method and truth-gap theory, I propose a functional-deflationary interpretation for semantic notions such as ‘heterological’, ‘true’, ‘denote’, and ‘define’, and argue that the contradictions in semantic paradoxes are due to a misunderstanding of the non-representational nature of these semantic notions. Thus, they all can be solved by clarifying the relevant confusion: the liar sentence and the heterological sentence do not have truth values, and phrases generating paradoxes of definability (such as that in Berry’s paradox) do not denote an object. I also argue against three other leading approaches to the semantic paradoxes: the Tarskian hierarchy, contextualism, and the paraconsistent approach. I show that they fail to meet one or more criteria for a satisfactory solution to the semantic paradoxes. For the set-theoretic paradoxes, I argue that the criterion for a successful solution in the realm of set theory is mathematical usefulness. Since the standard solution, i.e. the axiomatic solution, meets this requirement, it should be accepted as a successful solution to the set-theoretic paradoxes.</p>