Neil Tennant proposed a proof-theoretic criterion for distinguishing genuine paradoxes from mere inconsistencies, characterizing a paradox as the derivation of an unacceptable conclusion, such as absurdity ( \(\bot\) ), through a natural deduction that employs id est inferences and generates an infinite reduction sequence. Critics like Schroeder-Heister and Tranchini have argued that the criterion is overly inclusive, as exemplified by the Ekman case, which satisfies the criterion without formalizing a genuine paradox—a case Tennant termed the ‘Ekmanesque Predicament.’ To address overgeneration, Tennant proposed an additional condition that all elimination rules are to be stated in generalized form. However, Schroeder-Heister and Tranchini contended that Tennant’s solution was inadequate, claiming that the key to resolving the issue lies in establishing a criterion for acceptable reductions. This paper broadens the scope of the Ekmanesque predicament to include both overgeneration and undergeneration, demonstrating that the problem remains unresolved. Undergeneration occurs when derivations fail to meet the proof-theoretic criterion yet still formalize genuine paradoxes, such as the liar paradox. First, the paper explores how Tennant’s additional condition leads to undergeneration by examining two derivations of the liar-one utilizing the rule for Classical Reductio and the other employing the generalized elimination rule for equality. It concludes that merely proposing a criterion for acceptable reductions cannot resolve the Ekmanesque predicament, as accepting or rejecting particular reduction procedures, such as Ekman-type reductions, fails to address both overgeneration and undergeneration. Neither Tennant’s criterion nor Schroeder-Heister and Tranchini’s alternative capture genuine paradoxes; a more refined approach is needed.
