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http://hdl.handle.net/11375/13307
Title: | DIAGONALIZATION AND LOGICAL PARADOXES |
Authors: | Zhong, Haixia |
Advisor: | W., Richard T. Griffin, Nicholas Hitchcock, David |
Department: | Philosophy |
Keywords: | Diagonalization; Logical Paradoxes; Semantic Paradoxes; Set-theoretic Paradoxes; The Liar Paradox; The Revenge of the Liar; The Heterological Paradox; Berry's Paradox; Definability; Representational Predicates; Truth-gap Theory; Deflationary Theory of Truth;Logic and foundations of mathematics;Philosophy of Language;Logic and foundations of mathematics |
Publication Date: | Oct-2013 |
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> |
URI: | http://hdl.handle.net/11375/13307 |
Identifier: | opendissertations/8126 9229 4567243 |
Appears in Collections: | Open Access Dissertations and Theses |
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