 The addition of B9 makes it impossible to interpret \(\Rightarrow\) as material implication, since in the case of material implication it can be proved that for any propositions \(p\) and \(q, ((p\rightarrow q)\vee(p\rightarrow \neg q))\) (1932: 179). From B9 Lewis proceeds to deduce the existence of at least four logically distinct propositions: one true and necessary, one true but not necessary, one false and impossible, one false but not impossible (1932: 184–9).