Can closure be saved? The hardest paradoxes for closure revisited

Recent years saw the emergence of what some have called the hardest paradoxes for closure to date. These hybrid paradoxes combine features of the lottery and the preface paradox in a way that (i) puts pressure on the claim that justification is closed under conjunction (henceforth, simply closure) but (ii) resists familiar closure-preserving solutions previously put forward in response to the original paradoxes. This gives rise to the following question: can closure be saved from the new hybrid paradoxes and, if so, how? This paper puts forward what is likely to be the most promising (general) strategy for solving the new paradoxes in a way that’s compatible with closure, considers the most prominent attempts to implement this strategy, but argues that they are ultimately unsuccessful. Hence, it’s concluded that the case against closure still stands. The paper also corrects some misconceptions about the nature of the hybrid paradoxes and weighs in on the question of what really is the hardest paradox for closure.