In this note, I show how to construct Liar-like and Curry-like paradoxes in a framework Graham Priest has been considering recently, in which he tries to solve the paradoxes by giving up the rule of modus ponens (detachement) instead of the rules of ex falso and contraction. The Curry-like paradox presents a serious challenge to the detachment-free framework because it threatens to trivialize the system, just as Curry's original paradox does for the more standard paraconsistent approach to the paradoxes.