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Saving Truth From Paradox$
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Hartry Field

Print publication date: 2008

Print ISBN-13: 9780199230747

Published to Oxford Scholarship Online: May 2008

DOI: 10.1093/acprof:oso/9780199230747.001.0001

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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
DOI:10.1093/acprof:oso/9780199230747.003.0023

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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