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.
