- Title Pages
- Dedication
- Epigraph
- Preface
- Introduction
- 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
- 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
- 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
- 19 Validity, Truth‐Preservation, and the Second Incompleteness Theorem
- 20 Other Paradoxes
- 21 Do Paracomplete Solutions Depend on Expressive Limitations?
- 22 Determinateness, Hyper‐Determinateness, and Super‐Determinateness
- 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
- References
- Index
Adding a Conditional? Curry and Lukasiewicz
Adding a Conditional? Curry and Lukasiewicz
- Chapter:
- (p.83) 4 Adding a Conditional? Curry and Lukasiewicz
- Source:
- Saving Truth From Paradox
- Author(s):
Hartry Field (Contributor Webpage)
- Publisher:
- Oxford University Press
This chapter discusses the Lukasiewicz continuum-valued semantics as a way of improving upon the Kleene semantics as the basis for an account of truth. It is shown that it gives a very nice treatment of the paradoxes within a quantifier-free fragment of the language, but that it breaks down when quantifiers are added. This account will nonetheless serve as something of a model for the view to be advocated later, and so a number of issues that will arise later are discussed here. These include the Curry paradox, the meaning of semantic values, and the notion of determinate truth.
Keywords: continuum-valued semantics, Curry paradox, semantic value, determinate truth
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- Title Pages
- Dedication
- Epigraph
- Preface
- Introduction
- 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
- 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
- 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
- 19 Validity, Truth‐Preservation, and the Second Incompleteness Theorem
- 20 Other Paradoxes
- 21 Do Paracomplete Solutions Depend on Expressive Limitations?
- 22 Determinateness, Hyper‐Determinateness, and Super‐Determinateness
- 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
- References
- Index
