  It is interesting to note that \(\mathbf{S5}\) can be formulated equivalently by adding \((B)\) to \(\mathbf{S4}\). The axiom \((B)\) raises an important point about the interpretation of modal formulas. \((B)\) says that if \(A\) is the case, then \(A\) is necessarily possible. One might argue that \((B)\) should always be adopted in any modal logic, for surely if \(A\) is the case, then it is necessary that \(A\) is possible. However, there is a problem with this claim that can be exposed by noting that \(\Diamond \Box A\rightarrow A\) is provable from \((B)\). So \(\Diamond \Box A\rightarrow A\) should be acceptable if \((B)\) is. However, \(\Diamond \Box A\rightarrow A\) says that if \(A\) is possibly necessary, then \(A\) is the case, and this is far from obvious. Why does \((B)\) seem obvious, while one of the things it entails seems not obvious at all? The answer is that there is a dangerous ambiguity in the English interpretation of \(A\rightarrow \Box \Diamond A\). We often use the expression ‘If \(A\) then necessarily \(B\)’ to express that the conditional ‘if \(A\) then \(B\)’ is necessary. This interpretation corresponds to \(\Box(A\rightarrow B)\). On other occasions, we mean that if \(A\), then \(B\) is necessary: \(A\rightarrow \Box B\). In English, ‘necessarily’ is an adverb, and since adverbs are usually placed near verbs, we have no natural way to indicate whether the modal operator applies to the whole conditional, or to its consequent. For these reasons, there is a tendency to confuse \((B): A\rightarrow \Box \Diamond A\) with \(\Box(A\rightarrow \Diamond A)\). But \(\Box(A\rightarrow \Diamond A)\) is not the same as \((B)\), for \(\Box(A\rightarrow \Diamond A)\) is already a theorem of \(M\), and \((B)\) is not. One must take special care that our positive reaction to \(\Box(A\rightarrow \Diamond A)\) does not infect our evaluation of \((B)\). One simple way to protect ourselves is to formulate \(B\) in an equivalent way using the axiom: \(\Diamond \Box A\rightarrow A\), where these ambiguities of scope do not arise.