Postscript (on material consequence)

The supposed “missing premisses” attributed to arguments are generally not premisses at all but rather statements of a rule that would license the inference as it stands. Such substantive rules of inference cannot be underwritten by substitutional or model-theoretic conceptions of consequence. They need to be understood in terms of schemata. A schema is valid if and only if the generalization corresponding to it is true or analogously acceptable in both actual and counterfactual cases, even thought there might be a case where its antecedent is true and there might be a case where its consequent is untrue. Thus an argument’s conclusion follows from its premisses if and only if a counterfactual-supporting covering generalization of the argument is non-trivially acceptable The kernel of truth in the missing premisses approach is that one sometimes needs to make explicit the universe of discourse over which a variable in an inference-licensing covering generalization ranges.