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Title: Truth, paradoxes, and partiality : a study on semantic theories of naïve truth
Author: Rossi, Lorenzo
ISNI:       0000 0004 6346 6991
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2015
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This work is an investigation into the notion of truth. More specifically, this thesis deals with how to account for the main features of truth, with the interaction between truth and fundamental linguistic elements such as connectives and quantifiers, and with the analysis and the solution of truth-theoretic paradoxes. In the introductory Chapter 1, I describe and justify the approach to truth I adopt here, giving some general coordinates to contextualize my work. In Part I, I examine some theories of truth that fall under the chosen approach. In Chapter 2, I discuss a famous theory of truth developed by Saul Kripke. Some difficulties of Kripke's theory led several authors, notably Hartry Field, to emphasize the importance of a well-behaved conditional connective in conjunction with a Kripkean treatment of truth. I articulate this idea in a research agenda, which I call Field's program, giving some conditions for its realizability. In Chapter 3, I analyze the main theory of truth proposed by Field to equip Kripke's theory with a well-behaved conditional, and I give a novel analysis of its shortcomings. Field's theory is remarkably successful but is technically and intuitively very complex, and it is unclear whether Field's conditional is a plausible candidate for a philosophically useful conditional. Moreover, Field's treatment of "determinate truth" and his handling of many kinds of paradoxes is not fully satisfactory. In Part II, I develop some new theories that capture the main aspects of the notion of truth and, at the same time, give a philosophically interesting meaning to connectives and quantifiers - in particular, they yield a strong and conceptually significant conditional. The theory proposed in Chapter 4 extends the inductive methods employed in Kripke's theory, showing how to adapt them to non-monotonic connectives as well. There, I also develop and defend a new, theoretically fruitful notion of gappiness. The theory proposed in Chapter 5 (and discussed further in Chapter 6), instead, employs some graph-theoretic intuitions and tools to provide a new model-theoretic construction. The resulting theory, I argue, provides a nice framework to account for the interaction between truth, connectives, and quantifiers, and it is flexible enough to be applicable to several interpretations of the logical vocabulary. Some new technical results are established with this theory as well, concerning the interplay between every Lukasiewicz semantics and some interpretations of the truth predicate, and concerning the handling of determinate truth. Finally, the theory developed in Chapter 5 provides articulate and telling solutions to truth-theoretical paradoxes.
Supervisor: Halbach, Volker ; Williamson, Timothy Sponsor: Arts and Humanities Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Truth ; Logic ; Paradox ; Necessity (Philosophy)