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<p>We begin with the claim that a paradoxical sentence is a sentence that cannot consistently be true and cannot consistently be false either. We provide two approaches to interpret that claim: a gappy approach that takes paradoxical sentences to be neither true nor false, and a glutty approach that takes paradoxical sentences to be both true and false. We present two systems capable of expressing this semantic understanding. The models that we use ensure that paradoxicality is understood as a bivalent notion—saying of a sentence that it is paradoxical will result in either a true sentence or a false one (not both, not neither). Starting with a reflexive-free gappy logic of paradox, <InlineMediaObject> <ImageObject Color="Color" FileRef="MediaObjects/11229_2026_5574_Figa_HTML.png" Format="PNG" Height="495" Rendition="HTML" Resolution="300" Type="Halftone" Width="725" /> </InlineMediaObject>, we show that this logic can adequately capture paradoxicality and unparadoxicality. Moreover, we show that it is also immune to semantic paradoxes including revenge paradoxes. We then show that a non-transitive glutty logic of paradox, <InlineMediaObject> <ImageObject Color="Color" FileRef="MediaObjects/11229_2026_5574_Figb_HTML.png" Format="PNG" Height="495" Rendition="HTML" Resolution="300" Type="Halftone" Width="725" /> </InlineMediaObject>, escapes problems of overinternalizations of semantic notions and subdues metainferential paradoxes. We end our discussion by showing that the two logics are equivalent—they are two sides of the same coin.</p>

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Classical logic of paradox

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Rashed Ahmad,
  • Jonathan Erenfryd

摘要

We begin with the claim that a paradoxical sentence is a sentence that cannot consistently be true and cannot consistently be false either. We provide two approaches to interpret that claim: a gappy approach that takes paradoxical sentences to be neither true nor false, and a glutty approach that takes paradoxical sentences to be both true and false. We present two systems capable of expressing this semantic understanding. The models that we use ensure that paradoxicality is understood as a bivalent notion—saying of a sentence that it is paradoxical will result in either a true sentence or a false one (not both, not neither). Starting with a reflexive-free gappy logic of paradox, , we show that this logic can adequately capture paradoxicality and unparadoxicality. Moreover, we show that it is also immune to semantic paradoxes including revenge paradoxes. We then show that a non-transitive glutty logic of paradox, , escapes problems of overinternalizations of semantic notions and subdues metainferential paradoxes. We end our discussion by showing that the two logics are equivalent—they are two sides of the same coin.