 He gives a defense of material implication, and shows how to define negation in terms of implication and a special symbol for absurdity. In the next section (§3) he treats what he calls, following the Schoolmen, the “first-intentional logic of relations”. It is here that he coins the term “quantifier”; the propositional matrix of a quantified formula he calls its “Boolian”. In this section the quantifiers range only over the individuals of the universe; the “first-intentional logic” is thus first-order. Here, too, he was the first to discuss the rules for transforming a quantified formula into prenex normal form. The following section (§4) is headed “second-intentional logic”. There is a clear demarcation from the first-intentional logic of §3. Here the quantifiers are permitted to range over predicates; and he uses his new notation to state the modern second-order definition of identity: two objects are identical just in case they satisfy the same predicates.