Williamson has advocated for necessitism over contingentism, arguing that even for neutral expressions, i.e. modal formulations consistent with either hypothesis, necessitism is more expressive in the standard semantics for (second-order) quantified modal logic. Fritz has formalized and refined this claim in the context of generalized quantifiers: he argues that this distinction in expressibility hinges on the quantifer. Here Lauro will introduce an alternative semantics formulated by Antonelli, characterize Fritz's argument in these new terms, and by re-examining his equivalence theorem, demonstrate that the standard semantics are crucial to obtaining Williamson's result. Hence it follows that one cannot be instrumentalist regarding the semantics in modal ontology. 

 

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