VARIABLES AND THE BIJECTION PRINCIPLE

The constituent α is an open sentence: its tnith value cannot be evaluated since the reference of je or the domain over which χ may r nge is not determined within a. In Standard logic, χ in (l)b is called a variable and is said to be bound by the universal quantifier. Analogically, the term jein (l)a is called a variable, bound by the quantifier phrase everyone. This is not sufficient to define what a variable is, however. By extension from cases like (l)a, the implicit characterization of variables up to (and not including) Chomsky (1981) has been (2):