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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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Do Paracomplete Solutions Depend on Expressive Limitations?

Do Paracomplete Solutions Depend on Expressive Limitations?

Chapter:
(p.309) 21 Do Paracomplete Solutions Depend on Expressive Limitations?
Source:
Saving Truth From Paradox
Author(s):

Hartry Field (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230747.003.0022

The chapter considers various versions of the charge that paradox has been avoided only by limiting the expressive power of the language. The charge that the language has no ‘exclusion negation’ but only ‘choice negation’ is rejected as incorrect. It is true that the language contains no negation or conditional that obeys all the classical or intuitionist laws, but it is argued that no language can coherently contain such operators. Two ingenious arguments by Wright and Restall, according to which we ought to be able to define intuitionist operators from fairly uncontroversial resources, are considered at length and rejected. In the case of the Restall argument, this involves some considerations about how to understand infinite conjunctions and disjunctions.

Keywords:   Boolean negation, choice negation, exclusion negation, intuitionist negation, intuitionist conditional, Wright, Restall, infinitary disjunction, impredicative, indeterminate

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