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Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the Gödel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches.
Part One examines Tarski's, Kripke's, and Lukasiewicz's theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to "revenge problems" are addressed. Finally, Part Five deals with dialetheic approaches to the paradoxes: approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists' claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle.
PART ONE: A Selective Background
1: Chapter 1: Self-Reference and Tarski's Theorem
2: Validity and the Unprovability of Soundness
3: Kripke's Theory of Truth (Strong Kleene Version)
4: Adding a Conditional? Curry and Lukasiewicz
5: Interlude on Vagueness, and the Paradoxes of König and Berry
PART TWO: Broadly Classical Approaches
6: Introduction to the broadly classical options
7: Truth-Value Gaps in Classical Theories
8: Truth-value Gluts in Classical Theories
9: A Second Interlude on Vagueness
10: Introduction to Supervaluational Approaches to Paradox
11: A Survey of Supervaluational and Revision-Rule Theories
12: Are Supervaluational and Revision Theories Self-Undermining?
13: Intersubstitutivity and the Purpose of Truth
14: Stratified and Contextual Theories
Stratified and Contextual Theories
15: What Is To Be Done?
16: Fixed Points and Revision Rules for Conditionals
17: More on Revision-theoretic Conditionals
18: What Has Been Done
PART FOUR: More on Paracomplete Solutions
19: Validity, Truth-Preservation and the Second Incompleteness Theorem
20: Other Paradoxes
21: Do Paracomplete Solutions Depend on Expressive Limitations?
22: Determinateness, Hyper-determinateness, Super-Determinateness and Revenge
PART FIVE: Paraconsistent Dialetheism
23: Determinateness, Stratification, and Revenge
24: An Introduction to Paraconsistent Dialetheism
25: Some Dialetheic Theories
26: Paraconsistent Dialetheism and Soundness
27: Hyper-determinacy and Revenge
"one of the most impressive works on semantic paradoxes to have appeared in recent years [...] written with great clarity and meticulous rigour, the difficulty of the issues dealt with [...] The book, a must-read for everyone interested in semantic paradoxes (or in philosophical logic more generally), develops a highly-sophisticated theory of truth that aims at solving the resilient problems posed by the Liar Paradox [...] The book is a valuable source of inspiration [...] . It will certainly shape the discussion on semantic paradoxes in the years to come."
– José Martínez Fernández and Jordi Valor Abad, Notre Dame Philosophical Reviews
"Field is St George on a white charger (as portrayed by Raphael on the cover), come to save what he can of a theory of truth (the damsel) from the damage wreaked by the Liar paradox, König's paradox, Curry's paradox, and others (the dragon)."
– Stephen Read, Mind