Paraconsistent logic

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Paraconsistent logic refers to alternative (non-classical) systems of logic which reject the law of non-contradiction, i.e., that everything must be either true or false but not both. To avoid triviality, it is necessary to also reject the principle of ex contradictione quodlibet, which states that once a contradiction has been asserted, any proposition can be inferred from it.

Paraconsistent logic is proposed as a potential solution to logical paradoxes such as the liar paradox. So when making something such as "The next sentence is false. The previous sentence is true", the contradiction magically disappears because paraconsistent logic asserts that things can be false and true. Does this mental voodoo perhaps destroy the entire point of logic? Not necessarily; some philosophers and scientists assert that true contradictions (dialetheia) exist and therefore should be represented by formal logic. The wave-particle duality of electrons is a common proposed example of a dialethium.

Paraconsistent mathematics refers to attempts to develop mathematics on top of a foundation of paraconsistent logic.

The most notable adherent of paraconsistency in the contemporary philosophical scene is the British-Australian philosopher Graham Priest.

Historically speaking, paraconsistency has been a common theme in Indian logic,[citation needed] especially Jain and Buddhist logic. Whereas classical Western logic would see a statement as either true or false, but not both nor neither, Indian logics have traditionally been accepting of statements being both true and false simultaneously, or neither true nor false. Paraconsistency applies in particular to the both case - although it often allows the neither case as well. Constructivist/intuitionistic logic allows the neither case but not the both case, by denying the law of the excluded middle.


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