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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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Introduction to Supervaluational Approaches to Paradox

Introduction to Supervaluational Approaches to Paradox

Chapter:
(p.156) 10 Introduction to Supervaluational Approaches to Paradox
Source:
Saving Truth From Paradox
Author(s):

Hartry Field (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230747.003.0011

This chapter examines the simplest supervaluationist fixed points, and the ‘internal’ fixed-point theories based on them. These are not gap theories; they are ‘weakly classical’ theories in that they preserve the implications of classical logic but not certain meta-rules. Most dramatically, they do not allow for reasoning by cases. Two notions of validity are distinguished (strong and weak), and the framework of deMorgan semantics and Boolean semantics is introduced and discussed.

Keywords:   supervaluation fixed points, weakly classical theories, meta-rules, reasoning by cases, conditional proof, truth rules, validity, deMorgan algebras, Boolean algebras

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