 Veltman (1976) and Kratzer (1981b) approached counterfactuals from a perspective closer to Goodman (1947): counterfactuals involve explicitly adjusting a body of premises, facts or propositions to be consistent with the counterfactual’s antecedent, and checking to see if the consequent follows from the revised premise set—in a sense of “follow” to be articulated carefully. Since facts or premises hang together, changing one requires changing others that depend on it. The function of counterfactuals is to allow us to probe these connections between facts. While D. Lewis (1981) proved that the Kratzer (1981b) analysis was a special case of similarity semantics, subsequent refinements of premise semantics in Kratzer (1989, 1990, 2002, 2012) and Veltman (2005) evidenced important differences. Kratzer (1989: 626) nicely captures the key difference: