 Stalnaker’s semantics uses a “selection function”, F, which selects, for any proposition \(A\) and any world \(w\), a world, \(w'\), the nearest (most similar) world to \(w\) at which \(A\) is true. “If \(A, B\)” is true at \(w\) iff \(B\) is true at F\((A, w)\), i.e. at \(w'\). “If \(A, B\)” is true simpliciter iff \(B\) is true at the nearest \(A\)-world to the actual world. (However, we do not know which world is the actual world—there are many candidates compatible with our knowledge. To be sure that if \(A, B\), we need to be sure that whichever world \(w\) is a candidate for actuality, \(B\) is true at the nearest \(A\)-world to \(w\).) If \(A\) is true, the nearest \(A\)-world to the actual world is the actual world itself, so in this case “If \(A, B\)” is true iff \(B\) is also true. The selection function does substantive work only when \(A\) is false.