proof-theoretic principle for constructive mathematics. The following principle is a cornerstone of proof-theoretic foundations for constructive mathematics: For every proof Π that we may provide for a mathematical theorem φ , it must be possible, in principle, to transform Π, via a finite sequence of applicable reduction procedures, into a canonical proof of φ , that is, a proof of φ that is in normal form, so that none of the reduction procedure is applicable to it. (Tennant, 2015, p. 579) Though he proposes the proof-theoretic principle for constructive mathematics, the principle can be extended to a general case. He appears to think that any derivation representing a proof of the true statement must be, in principle, able to be brought into (full) normal form. Also, when Tennant (1982) proposes his earlier criterion, TCPE , he stresses the importance of normalizability as below: The general loss of normalizability, confined as it is according to [TCPE] to just the paradoxical part of the semantically closed language, is a small price to pay for the protection it gives against paradox itself. Logic plays its role as an instrument of knowledge only insofar as it keeps proofs in sharp focus, through the lens of normality. Normali[z]ability, in the context of semantically closed languages, is not to be pressed as a general pre-condition for the very possibility of talking sense; rather, normality of proof is to be pressed as a general pre-condition for the very possibility of telling the truth. (Tennant, 1982, p. 284) Provided that there is a requirement that every derivation representing a proof of the true statement should be, in principle, reducible to a (full) normal derivation, the requirement 133 can block T-paradoxes and be a proof-theoretic solution to the paradoxes. Even though Tennant did not explicitly propose the requirement as the proof-theoretic solution, from TCP, we may interpret the following principle as a plausible proof-theoretic solution to the paradoxes. The Requirement of a (Full) Norm