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The inclosure scheme and the solution to the paradoxes of self-reference

Abstract

All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give arguments against Priest’s use of IS in favour of dialetheism. IS fails to identify sufficient conditions for having a paradox of self-reference. That means that, even if we identified a problem common to any reasoning satisfying IS, that problem would not explain why some of those reasonings are paradoxical and some others are not. Therefore IS cannot justify by itself the claim that some particular theory offers the best solution to the paradoxes of self-reference. We still need to consider aspects concerning the content and context of occurrence of every paradox.

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Correspondence to Jordi Valor Abad.

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Abad, J.V. The inclosure scheme and the solution to the paradoxes of self-reference. Synthese 160, 183–202 (2008). https://doi.org/10.1007/s11229-006-9109-x

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Keywords

  • Structure of the paradoxes of self-reference
  • Inclosure Scheme
  • Priest
  • Russell
  • Dialetheism