 Lewis in his paper discusses several refinements of the correspondence, depending on which conditions are imposed on ordering frames, and further results can be found in Chemla (2011). From a philosophical and foundational perspective, the correspondence may be taken to suggest that the choice between an ordering-first approach and a premise-first approach doesn’t matter. Arguably, however, a premise semantics may be judged more explanatory than one in which the ordering comes first, for two reasons. First of all, from a cognitive perspective, it may be argued that premise semantics is closer to implementing the Ramsey test idea, since an ordering semantics only implicitly refers to the idea of making adjustments to one’s belief set. Secondly, in an o-semantics the question is indeed moot what determines similarity between worlds. Of course, which facts to admit or not in premise semantics is also problematic, but using propositions as an ordering source makes clearer that similarity between worlds is a relative rather than an absolute matter. In recent years, several authors have proposed to further clarify the problem of premise selection in counterfactuals by looking at causal models of reasoning (K. Schulz 2007; Briggs 2012; S. Kaufmann 2013; Santorio 2019).