Paraconsistent naïve truth theories and Curry paradox

Naïve truth, T(x), is a predicate that applies to all of the sentences of the language and also for every sentence A of the language, T(˹A˺)↔A holds. Tarski for avoiding the liar paradox and trivializing of the language (theory) forced to withdraw from defining the naïve notion of truth and he defined truth of every language in a metalanguage. Proponents of paraconsistency claim that by accepting paraconsistent logics we can retain the naïve truth predicate. A logic would be called paraconsistent if contradiction does not entail everything. But there is another paradox, the Curry paradox, which is related to conditionals and without using EFQ can trivialize naïve theories of truth. In this paper I will argue that although if we add arithmetic and naïve truth predicate to paraconsistent logics we would have a non-trivial theory, but for low deductive power, losing some prospected properties of naïve truth predicate and leaking of inconsistency to pure arithmetic parts, these logics will be unjustifiable.