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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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Validity and the Unprovability of Soundness

Validity and the Unprovability of Soundness

Chapter:
(p.42) 2 Validity and the Unprovability of Soundness
Source:
Saving Truth From Paradox
Author(s):

Hartry Field (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230747.003.0003

This chapter gives an initial discussion of the relation between validity and necessary truth-preservation. It argues that the so-called ‘soundness theorems’ of first order logic are misnamed, and that the soundness of first order logic is not provable (even ‘rule-circularly’) in standard set theory.

Keywords:   validity, truth-preservation, soundness, rule circularity, finite axiomatizability

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