- 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

# Determinateness, Hyper‐Determinateness, and Super‐Determinateness

# Determinateness, Hyper‐Determinateness, and Super‐Determinateness

- Chapter:
- (p.325) 22 Determinateness, Hyper‐Determinateness, and Super‐Determinateness
- Source:
- Saving Truth From Paradox
- Author(s):
### Hartry Field (Contributor Webpage)

- Publisher:
- Oxford University Press

This chapter is about whether we can make sense of a notion of hyper-determinacy that will transcend the hierarchy of iterations of the determinacy operators and restore paradox. To investigate this, we need to be more rigorous about how the transfinite iterations of the operator are defined. It turns out that one can in a sense define operators that ‘iterate beyond the allowable hierarchies’, but that they don't lead to new paradoxes because they don't behave like we would expect an iteration of a determinacy operator to behave. This is connected to König's paradox. It is argued that the use of higher order resources would not affect the conclusion.

*Keywords:*
determinately, transfinite iteration, hierarchy, ordinal notation, hyper-determinateness, second order logic, quasi-impredicative, super-determinateness, König's paradox

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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