Topoi 38 (3):605-617 (2019)

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Abstract
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.
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DOI 10.1007/s11245-018-9543-7
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Investigations Into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.

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