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Jc Beall, Graham Priest, Zach Weber, Can u do that?, Analysis, Volume 71, Issue 2, April 2011, Pages 280–285, https://doi.org/10.1093/analys/anr001
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Extract
In his ‘On t and u and what they can do’, Greg Restall (2010) 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 (gappy) or paraconsistent (glutty) 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 (or, dually, untruths), you're either leaving some truths out, or you're letting some untruths in. Truth, in a slogan, is either gappy or glutty.
