aradox.' Sainsbury regards a sentence (or a formula) with special characteristics a paradox. However, Tennant's criterion for paradoxicality TCP understands a paradox as a derivation (or an argument) which might have an unacceptable conclusion from the acceptable premises by the acceptable inference rules. As Sainsbury's characterization of a paradox is connected to three solutions, we may have a proof-theoretic solution to the paradoxes on the perspectives of TCP. Tennant (1982) proposes TCP as a criterion for genuine paradoxes and regards it as a conjecture namely that for any derivation D, D formalizes a genuine paradox iff D is a T-paradox. Focussing on normalizability, Tennant (2017, pp. 286–287) suggests a similar conjecture which is linked to his criterion for paradoxicality. How ... are we to solve the paradoxes? It is not from this study to venture any new suggestions beyond those of Tennant (1982) and Tennant (1995). Those works provided ... proofs, formalized as natural deductions, for all the major paradoxes ... . They showed that all these ... proofs ... cannot be converted into normal form. The original proof-theoretic thesis stands: Genuine paradoxes are those whose associated proofs of absurdity, when formalized as natural deductions, cannot be converted into normal form. This conjecture provides a proof-theoretic criterion for the identification of genuine paradoxes ... . The conjectures can be his diagnoses of genuine paradoxes. If the conjectures are true, every derivation of genuine paradoxes, such as T-paradoxes, generates a non-terminating reduction sequence and so is not normalizable. His diagnoses, if true, provide a prooftheoretic solution to the paradoxes. 132 As an anti-realist and a constructivist, Tennant (2015, p. 578) believes that 'every truth is knowable, and its truth consists in the existence of a(n in principle) surveyable truthmaker, also called a (canonical) proof.' Moreover, he thinks that a (constructive) proof must be convertible into normal form, and so he suggests the 