 A consequence of the definitions of state-descriptions for a language and L-truth is that each atomic sentence and its negation turn out to be true at some, but not all, state-descriptions. Hence, if \(p\) is atomic both \(\Diamond p\) and \(\Diamond \neg p\) are L-true. Hence, Lewis’s rule of Uniform Substitution fails (if \(p\wedge \neg p\) is substituted for \(p\) in \(\Diamond p\) we derive \(\Diamond(p\wedge \neg p)\), which is L-false, not L-true). This is noticed by Makinson (1966a) who argues that what must be done is reinstate substitutivity and revise Carnap’s naïve notion of validity (as logical necessity) in favor of a schematic Quinean notion (“A logical truth … is definable as a sentence from which we get only truths when we substitute sentences for its simple sentences” Quine 1970: 50) that will not make sentences like \(\Diamond p\) valid. Nonetheless, Carnap proves the soundness and completeness of propositional S5, which he calls “MPC” for “modal propositional calculus”, following Wajsberg. The proof however effectively employs a schematic notion of validity.