 First, he rejected Stalnaker’s presupposition that there is a most similar p-world to actuality. He thought there might be many worlds which are equally similar to actuality, with no p-world being more similar. Using the metric analogy suggested above, these worlds all fall on a common ‘sphere’ of worlds, where the centre of this sphere is the actual world. In such a case, Lewis held that p □→ q is true if and only if all the p-worlds on this sphere are q-worlds. One immediate consequence of this is that Conditional Excluded Middle, i.e., (p □→ q) ∨ (p □→ ~q) is not a theorem of counterfactual logic for Lewis, as it was for Stalnaker.