A Renewed Challenge for Alethic Pluralism. Designation and Generic Truth

Alethic pluralism is a philosophical conception holding that there are many ways of being true. Accordingly, truth consists in different properties in different domains of discourse. This position has been challenged to make sense of validity, understood as necessary truth preservation, when inferences involving sentences from different domains are considered. We exploit the formal construction known as Suszko’s reduction in order to clarify the dispute and show that, despite the defence put forward by some authors, the solution proposed by Beall, based on the notion of designated values, is unavailable to strong pluralism. In particular, we discuss a possible move that may be adopted to resist the philosophical consequences of the reduction, showing that some prominent pluralist proposals currently on the market cannot afford it.