 Frege thus in a first step extended the familiar notion of a numerical function to functions on singular objects in general and, moreover, introduced a new kind of singular objects that can serve as arguments and values of functions on singular objects, the truth values. In a further step, he considered propositional functions taking functions as their arguments. The quantifier phrase ‘every city’, for example, can be applied to the predicate ‘is a capital’ to produce a sentence. The argument of the second-order function denoted by ‘every city’ is the first-order propositional function on singular objects denoted by ‘is a capital’. The functional value denoted by the sentence ‘Every city is a capital’ is a truth value, the False.