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<p>Gap theory and glut theory are two dominant strategies in the treatment of paradoxes. The paper shows they can be profitably combined. Given the Liar’s sentence ‘L’ which says ‘‘not L’ is true’, there are reasons to say that ‘L and not L’ is true, but this does not mean that ‘L’ as such or ‘not L’ are separately true. We have two untrue sentences (‘L’ and ‘not L’) for a true conjunction (‘L and not L’): two gaps for one glut. This interpretation satisfies the program of <i>conjunctive paraconsistency</i>, a consequence relation whereby ‘p and not p’ does not prove ‘q’ (whatever), since Simplification fails: the two conjuncts cannot be asserted, assumed or accepted separately. The paper shows how this strategy works in case of Liar-like paradoxes.</p>

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Two gaps for one glut: A combined solution of paradoxes

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Franca d’Agostini

摘要

Gap theory and glut theory are two dominant strategies in the treatment of paradoxes. The paper shows they can be profitably combined. Given the Liar’s sentence ‘L’ which says ‘‘not L’ is true’, there are reasons to say that ‘L and not L’ is true, but this does not mean that ‘L’ as such or ‘not L’ are separately true. We have two untrue sentences (‘L’ and ‘not L’) for a true conjunction (‘L and not L’): two gaps for one glut. This interpretation satisfies the program of conjunctive paraconsistency, a consequence relation whereby ‘p and not p’ does not prove ‘q’ (whatever), since Simplification fails: the two conjuncts cannot be asserted, assumed or accepted separately. The paper shows how this strategy works in case of Liar-like paradoxes.