Pluralism and paradox

The paradoxes are a problem for pluralists about truth. While alethic pluralists have generally set discussion of the paradoxes aside, this chapter argues that paradox issues have direct implications for their view. More specifically, alethic pluralism has bifurcated into two main types: strong and weak. Both accept multiple truth predicates, T1, …, Tn, but weak theories also accept a truth predicate that applies to every true sentence (a universal truth-predicate), which strong theories reject. This chapter shows that both types of theories suffer from paradox-generated inconsistency given certain plausible assumptions. It then outlines a new, consistent way to be a strong alethic pluralist. The trick to avoiding paradox is rejecting infinitary disjunction, something there are already pluralism-independent, paradox-motivated reasons to reject. This chapter concludes by comparing this theory with a Tarskian hierarchical view, and then discuss some directions for future research