Home – Home – Jornals – Philosophy of Sciences 2026 number 3

Within possible-world semantics, an object can have different properties in different worlds. This allows us to consider an object as it is in world w, as it is in world w', and so on, i.e. to associate objects with worlds. In turn, this makes it possible to consider relations between objects where each object is associated with a certain world - cross-world relations. If we want first-order modal logic based on possible-world semantics to represent cross-world relations, its models must involve a cross-world interpretation of predicates, i.e. an interpretation that assigns extensions of predicates not to individual worlds, but to tuples of worlds. Some authors hold that cross-world relations are reducible to standard (intra-world) relations, which makes the cross-world interpretation of predicates redundant. The paper provides an argument in favor of the hypothesis that cross-world relations are not reducible to intra-world ones. The argument consists in pointing to the variety of cross-world relations that we speak about in natural language and to the variety of corresponding contexts. In particular, it is shown that cross-world relations are naturally used in comparing theories.