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<p>The idea of a <i>paraconsistent computability theory</i> has been proposed as a way to work effectively with inconsistent sets of numbers. The viability of such a theory, though—the very coherence of the idea of an ‘inconsistent recursive relation’—has been called into doubt, most recently in&#xa0;(Choi, Synthese 200(5):418, 2022). In this paper we remove some doubt, by setting out a simple model of (naïve) set theory in <b>LP</b>, showing how to compute inconsistent sets in terms of extensions and antiextensions, and establishing further representability results. This suggests a way that a longstanding and apparently impossible-to-answer question—<i>how can inconsistency be computed?</i>—can be answered.</p>

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Inconsistent sets and how to compute them

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Fernando Cano-Jorge,
  • Zach Weber

摘要

The idea of a paraconsistent computability theory has been proposed as a way to work effectively with inconsistent sets of numbers. The viability of such a theory, though—the very coherence of the idea of an ‘inconsistent recursive relation’—has been called into doubt, most recently in (Choi, Synthese 200(5):418, 2022). In this paper we remove some doubt, by setting out a simple model of (naïve) set theory in LP, showing how to compute inconsistent sets in terms of extensions and antiextensions, and establishing further representability results. This suggests a way that a longstanding and apparently impossible-to-answer question—how can inconsistency be computed?—can be answered.