pp 1–13 | Cite as

On Paradoxes in Normal Form

  • Mattia Petrolo
  • Paolo PistoneEmail author


A proof-theoretic test for paradoxicality was famously proposed by Tennant: a paradox must yield a closed derivation of absurdity with no normal form. Drawing on the remark that all derivations of a given proposition can be transformed into derivations in normal form of a logically equivalent proposition, we investigate the possibility of paradoxes in normal form. We compare paradoxes à la Tennant and paradoxes in normal form from the viewpoint of the computational interpretation of proofs and from the viewpoint of proof-theoretic semantics.



The funding was provided by Agence Nationale de la Recherche (Grant No. ANR-14-FRAL-0002).


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Authors and Affiliations

  1. 1.CNRSUniversité Paris 1 Panthéon-SorbonneParisFrance
  2. 2.Dipartimento di Matematica e FisicaUniversità Roma TreRomeItaly

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