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http://hdl.handle.net/11375/13307
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DC Field | Value | Language |
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dc.contributor.advisor | W., Richard T. | en_US |
dc.contributor.advisor | Griffin, Nicholas | en_US |
dc.contributor.advisor | Hitchcock, David | en_US |
dc.contributor.author | Zhong, Haixia | en_US |
dc.date.accessioned | 2014-06-18T17:03:35Z | - |
dc.date.available | 2014-06-18T17:03:35Z | - |
dc.date.created | 2013-09-09 | en_US |
dc.date.issued | 2013-10 | en_US |
dc.identifier.other | opendissertations/8126 | en_US |
dc.identifier.other | 9229 | en_US |
dc.identifier.other | 4567243 | en_US |
dc.identifier.uri | http://hdl.handle.net/11375/13307 | - |
dc.description.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> | en_US |
dc.subject | 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 | en_US |
dc.subject | Logic and foundations of mathematics | en_US |
dc.subject | Philosophy of Language | en_US |
dc.subject | Logic and foundations of mathematics | en_US |
dc.title | DIAGONALIZATION AND LOGICAL PARADOXES | en_US |
dc.type | dissertation | en_US |
dc.contributor.department | Philosophy | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
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fulltext.pdf | 3.49 MB | Adobe PDF | View/Open |
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