Analysis 71 (2):280-285 (2011)

Zach Weber
University of Otago
Jc Beall
University of Notre Dame
In his ‘On t and u and what they can do’, Greg Restall presents an apparent problem for a handful of well-known non-classical solutions to paradoxes like the liar. In this article, we argue that there is a problem only if classical logic – or classical-enough logic – is presupposed. 1. Background Many have thought that invoking non-classical logic – in particular, a paracomplete or paraconsistent logic – is the correct response to the liar and related paradoxes. At the most basic level, the target non-classical idea is that some expressions, like ‘all and only the true propositions’, do not behave as we would expect from classical logic. Non-classical theorists argue that the class of all and only the truths is either incomplete or inconsistent: when you truly speak of all and only truths , you're either leaving some truths out, or you're letting some untruths in. Truth, in a slogan, is either gappy or glutty. Non-classicality is not a glib or easy-way-out response to the paradoxes. Innocuous-seeming notions can turn out to be philosophically substantial. Moreover, apparently correct forms of reasoning can turn out to be incorrect. To take a example, a glut theorist must hold that the following argument form is not in general valid. Either p is true or q is true. But p is untrue. So q is true. This argument form may strike our ears as acceptable. But if p is a truth value glut, then the inference fails to preserve truth. According to glut theorists, the inference breaks down in inconsistent contexts: if the subject matter involves gluts, then the inference is to be rejected. And the liar paradox, according to such theorists, shows that truth is exactly the kind of subject matter that yields inconsistency. In the …
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/analys/anr001
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 53,586
Through your library

References found in this work BETA

Curry's Paradox.Robert K. Meyer, Richard Routley & J. Michael Dunn - 1979 - Analysis 39 (3):124 - 128.
On T and U, and What They Can Do.G. Restall - 2010 - Analysis 70 (4):673-676.
Curry's Paradox.Robert K. Meyer & Alonso Church - 1979 - Analysis 39 (3):124.

Add more references

Citations of this work BETA

Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.

Add more citations

Similar books and articles

True and False–as If. Ch. 12 of G. Priest, Jc Beall and B. Armour-Garb.Jc Beall - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The Law of Non-Contradiction : New Philosophical Essays. Oxford University Press.
Letters to Priest and Beall.David Lewis - 2004 - In The Law of Non-Contradiction. Oxford University Press. pp. 176-177.
Review of Priest, Towards Non-Being. [REVIEW]J. C. Beall - forthcoming - Notre Dame Philosophical Reviews.
Letters to Beall and Priest.David Lewis - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The Law of Non-Contradiction : New Philosophical Essays. Oxford University Press. pp. 176--177.
End of Inclosure.Jc Beall - 2014 - Mind 123 (491):829-849.
Relevant Restricted Quantification.J. C. Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall - 2006 - Journal of Philosophical Logic 35 (6):587-598.
Too Good to Be “Just True”.Marcus Rossberg - 2013 - Thought: A Journal of Philosophy 2 (1):1-8.
Jc Beall: Spandrels of Thruth.Zach Weber - 2010 - Bulletin of Symbolic Logic 16 (2).
Logical Pluralism, Meaning-Variance, and VerbalDisputes.Ole Thomassen Hjortland - 2013 - Australasian Journal of Philosophy 91 (2):355-373.
Why Priest's Reassurance is Not Reassuring.Jc Beall - 2012 - Analysis 72 (3):517-525.


Added to PP index

Total views
137 ( #66,844 of 2,348,743 )

Recent downloads (6 months)
1 ( #512,546 of 2,348,743 )

How can I increase my downloads?


My notes