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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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What Is To Be Done?

What Is To Be Done?

Chapter:
(p.231) 15 What Is To Be Done?
Source:
Saving Truth From Paradox
Author(s):

Hartry Field (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230747.003.0016

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.

Keywords:   Tarski schemas, intersubstitutivity, deMorgan algebras, conditionals, determinacy operators, hierarchy theorem, vagueness

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