universal instantiation also called universal quantifier elimination. (1) The argument form ‘Everything is f; therefore a is f’, and arguments of this form. (2) The rule of inference that permits one to infer that any given thing is f from the premise that everything is f. In classical logic, where all terms are taken to denote things in the domain of discourse, the rule says simply that from (v)A[v] one may infer A[t], the result of replacing all free occurrences of v in A[v] by the term t. If non-denoting terms are allowed, however, as in free logic, then the rule would require an auxiliary premise of the form (Du)u % t to ensure that t denotes something in the range of the variable v. Likewise in modal logic, which is sometimes held to contain terms that do not denote ‘genuine individuals’ (the things over which variables range), an auxiliary premise may be required. (3) In higher-order logic, the rule of inference that says that from (X)A[X] one may infer A[F], where F is any expression of the grammatical category (e.g., n-ary predicate) appropriate to that of X (e.g., n-ary predicate variable). G.F.S.