Franci Mangraviti & Andrew Tedder, Irregular theories - PhilPapers
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What happens when logic breaks its own rules? This paper explores "irregular theories" — formal systems that reject standard logical theorems, challenging the foundations of how we reason.
Paraconsistent LogicSubstructural LogicDeductive ClosureNon-Classical Logic
Theory Briefing
- Irregular theories are deductively closed sets of sentences that deliberately exclude standard logical theorems, violating classical norms.
- Mangraviti and Tedder map the logical landscape where accepted truths like tautologies are not automatically included, destabilizing inference.
- This challenges the Principle of Explosion and classical consequence relations, opening space for paraconsistent and substructural logics.