 Paradoxes of strict implication similar to those of material implication arise too. Given that strict implication \((p\Rightarrow q)\) is defined as \(\neg \Diamond(p\wedge \neg q)\), it follows that an impossible proposition implies anything, and that a necessary proposition is implied by anything. Lewis argues that this is as it ought to be. Since impossibility is taken to be logical impossibility, i.e., ultimately a contradiction, Lewis argues that from an impossible proposition like \((p\wedge \neg p)\), both \(p\) and \(\neg p\) follow. From \(p\) we can derive \((p\vee q)\), for any proposition \(q\). From \(\neg p\) and \((p\vee q)\), we can derive \(q\) (1932: 250). The argument is controversial since one can argue that the principle \((p\Rightarrow(p\vee q))\) should not be a theorem of a system aiming to express ordinary implication (see, e.g., Nelson 1930: 447). Whatever the merits of this argument, those who disagreed with Lewis started to develop a logic of entailment based on the assumption that entailment requires more than Lewis’s strict implication. See, for example, Nelson 1930, Strawson 1948, and Bennett 1954. See also the SEP entry on  relevance logic.