Validity, paradox, and the ideal of deductive logic

In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press (2007)
Abstract
I express my dissatisfaction with the common ways to treat the semantic paradoxes. Not only do they give rise to revenge paradoxes, they ignore the wisdom contained in the ordinary reaction to paradoxes. I instead propose an account that vindicates the ordinary reaction to paradox by putting the blame on us philosophers. It is the wrong conception of what a valid inference is, one that is central to “the ideal of deductive logic” that gives rise to the problem. The solution outlined gives us a new way to accept defeat in light of the paradoxes: the arguments that lead to them are based on valid forms of reasoning, but their conclusions are nonetheless rationally rejected.
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