- Title Pages
- 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
What Is To Be Done?
What Is To Be Done?
- (p.231) 15 What Is To Be Done?
- Saving Truth From Paradox
Hartry Field (Contributor Webpage)
- Oxford University Press
This chapter sets the goal: a theory without excluded middle with ‘naïve truth and satisfaction’, that is, satisfying the full Tarski schemas and Intersubstitutivity Principle. A semantic framework is sketched, involving a deMorgan valued semantics with an additional operator for the conditional. There are different ways to fill out the framework — Lukasiewicz semantics is one of them — and the trick will be to find one in which the goal of naïve truth and satisfaction can be achieved. In all ways to fill out the framework, we can define a determinateness operator, and iterate it through the transfinite. But to achieve ‘naïvety’, this hierarchy can never collapse. This is also required if the theory is to be useful for vagueness.
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