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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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Paraconsistent Dialetheism and Soundness

Paraconsistent Dialetheism and Soundness

Chapter:
(p.376) 26 Paraconsistent Dialetheism and Soundness
Source:
Saving Truth From Paradox
Author(s):

Hartry Field (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230747.003.0027

Priest has argued that his dialetheic theories declare themselves sound and in this regard are better than non-dialetheic theories. This chapter shows this to be unfounded. Indeed, dialetheic theories cannot on pain of triviality declare modus ponens to be truth-preserving, and those that accept excluded middle declare it not to be. Moreover, Priest's favored dialetheic theories say that modus ponens doesn't preserve truth even when applied to premises we accept. In this respect, they do worse than glut theories in classical logic and weakly classical theories. This however is not a problem for all dialetheic theories.

Keywords:   dialetheism, Priest, truth-preservation, modus ponens, incompleteness theorems

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