In what sense is the no-no paradox a paradox?

Cook regards Sorenson's so-called 'the no-no paradox' as only a kind of 'meta-paradox' or 'quasi-paradox' because the symmetry principle that Sorenson imposes on the paradox is meta-theoretic. He rebuilds this paradox at the object-language level by replacing the symmetry principle with some 'background principles governing the truth predicate'. He thus argues that the no-no paradox is a 'new type of paradox' in that its paradoxicality depends on these principles. This paper shows that any theory (not necessarily meeting Cook's background principles) is inconsistent with the T-schema instances for the no-no sentences, plus the T-schema instance for a Curry sentence associated with the symmetry of the no-no sentences. It turns out that the no-no paradox still depends on the problematic instances of the T-schema in a way that the liar paradox does. What distinguishes the no-no paradox is the T-schema instance for the above Curry sentence, which encodes Sorensen's symmetry principle at the object-language level. [ABSTRACT FROM AUTHOR]