The existence of formally valid paraconsistent logics shows that inferential systems can function without explosion, defeating the claim that contradiction-avoidance is foundational.
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contradiction(Relevant to distinguishing contradictions from false contingent statements in the logic student variant of the preface paradox.)
A statement that is necessarily false in all interpretations; in this context, specifically the negation of a tautology or any falsehood drawn from a list containing only tautologies and contradictions.
paraconsistent logic(Used to challenge the modal inference from □¬p to ¬◇p in Fitch's knowability argument)
A logical system in which contradictions do not entail arbitrary conclusions, and in which a necessarily false statement may be both false and true at some world — making it both necessarily false and possible