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https://hdl.handle.net/2142/71564
Description
Title
This Is the Title of This Thesis
Author(s)
Aoyama, Hiroshi
Issue Date
1988
Department of Study
Philosophy
Discipline
Philosophy
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Philosophy
Abstract
This thesis is a study of the Liar paradox and the notion of truth and consists of two parts, a philosophical part and a technical part.
In the philosophical part (Ch. 1-Ch. 3), the Liar paradox and a solution to it are considered. Ch. 1 presents an overview of logical and semantical paradoxes, including the Liar paradox. Ch. 2 presents some discussions of Kripke's solution to the Liar paradox and it is argued that although Kripke's view that the Liar sentence is neither true nor false is reasonable, he does not present a serious consideration of the question of what the primary bearers of truth are. This question has recently been discussed in detail by Barwise and Etchemendy. Ch. 3 presents some discussions of their work on the Liar paradox. It is argued that their view that the Liar sentence expresses a proposition is not acceptable and then a solution to the paradox (i.e., the Liar sentence does not express a proposition in any situation) is presented and defended.
In the technical part (Ch. 4-Ch. 6), some formal systems of logic containing truth predicate symbols are studied. Ch. 4 presents a consistency proof for an extension of Gentzen's sequent calculus LK in which Tarski's biconditional A $\equiv$ T ('A') holds for every sentence A of the system, where T is a truth predicate symbol and ''are quotation marks. Ch. 5 contains the strong completeness theorems for classical first-order systems in which Tarski's biconditional holds for each sentence of the system. The same kind of strong completeness theorem is presented in Ch. 6 for a formal system based on Kleene's strong three-valued logic which contains a truth predicate and the equality symbol =.
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