Can Priest's Dialetheism Avoid Trivialism?

Priest's dialetheism is the view that some sentences, called dialetheiae, are both true and false. A crucial problem of di- aletheism is that of avoiding trivialism, i.e. the consequence that all sentences are dialetheiae. In the present paper we want to discuss Priest's strategy for avoiding Curry's paradox, from which trivialism follows. Besides, we will formulate a new version of Curry's paradox, using a notion of nave deducibility, which, in our opinion, should be accepted by Priest himself.