  Faced with the limitations of classical logic, Sylvan joined in the project of refining C.I. Lewis’s strict implication to overcome various paradoxes of the conditional. (See the encyclopedia entry on indicative conditionals.) For, according to the classical account of material implication \(\supset\), for any three random declarative sentences \(p\), \(q\), \(r\) you find on the Internet, \( (p \supset q) \lor (q \supset r) \) is valid (to take just one example; see Routley et al. 1982, 6–7). One diagnosis of the problem here is that all these conditionals, of the form ‘if \(p\) then \(q\)’, display irrelevance: the antecedent \(p\) need not have anything “to do with” the consequent \(q\), whereas correct natural language conditionals (so the argument goes) always respect some kind of relevant connection. The problem may be resolved by turning to an appropriate relevant logic.