A sieve for entailments

The validity of an entailment has nothing to do with whether or not the components are true, false, necessary, or impossible; it has to do solely with whether or not there is a necessary connection between antecedent and consequent. Hence it is a mistake (we feel) to try to build a sieve which will strain out entailments from the set of material or strict implications present in some system of truth-functions, or of truth-functions with modality. Anderson and Belnap (1962, p. 47).