 The vocabulary of pure quantificational logic contains the usual propositional connectives: \(\lnot\), \(\wedge\), \(\vee\), \(\rightarrow\), and \(\leftrightarrow\). It contains predicate letters of different adicities: one-place predicate letters with or without subscripts, \(P^{1}, Q^{1}, R^{1}, P^{1}_{1}\), …, two-place predicate letters, \(P^{2}, Q^{2}, R^{2}, P^{2}_{1}\), …, and more generally, \(n\)-place predicate letters. Sentence letters are 0-place predicates. There is, in addition to this, an infinite stock of variables with or without subscripts: \(x, y, z, x_1, y_1, z_1\), … , and two quantifiers \(\forall\) and \(\exists\). In a classical framework, we need not treat all these symbols as primitive; we may, for example, treat \(\lnot\), \(\rightarrow\), and \(\forall\) as primitive and provide standard definitions for the other propositional connectives and quantifiers in terms of them. For example, the existential quantifier, \(\exists x A\), may be defined: \(\lnot \forall x\lnot A\).