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MENTAL MODEL · M13253

Paraconsistent Logic

Paraconsistent Logic
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Updated 2026-09-10

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INTRODUCTION

English translation pending.

CORE DEFINITION

A consequence relation is explosive if any contradiction A and not A entails an arbitrary conclusion B, which is the principle known as ex contradictione quodlibet. Classical logic and most standard non-classical logics such as intuitionistic logic are explosive; paraconsistent logic is precisely a consequence relation that is not explosive, so that contradictions can be tolerated without trivializing a theory.

SCAFFOLDING EFFECT

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- Contain contradiction: keep a local conflict local instead of letting the whole theory collapse. - Preserve information: accommodate conflicting material first and clean it up later rather than discarding it outright. - Audit explosion: check whether an argument smuggles in an irrelevant conclusion through the explosion principle.

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Explosion arises from disjunction introduction combined with disjunctive syllogism: from A we get A or B, and with not A we get B. Paraconsistent logic restricts disjunctive syllogism or adopts many-valued or relevant semantics, so that truth values may be in surplus without being deficient: a contradiction is confined to its locality and no longer makes the whole theory entail anything whatever.

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Source support: Explicit

  • link
    plato.stanford.eduhttps://plato.stanford.edu/entries/logic-paraconsistent/ZH · Explicit
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