  In Frege’s analysis, the verb phrase ‘loves’ signifies a binary function of two variables: \(L((\:),(\:))\). This function takes a pair of arguments \(x\) and \(y\) and maps them to The True if \(x\) loves \(y\) and maps all other pairs of arguments to The False. Although it is a descendent of Frege’s system, the modern predicate calculus analyzes loves as a two-place relation (written: \(Lxy\)) rather than a function; some objects stand in the relation and others do not. The difference between Frege’s understanding of predication and the one manifested by the modern predicate calculus is simply this: in the modern predicate calculus, relations are taken as basic, and functions are defined as a special case of relation, namely, those relations \(R\) such that for any objects \(x\), \(y\), and \(z\), if \(Rxy\) and \(Rxz\), then \(y=z\). By contrast, Frege took functions to be more basic than relations. His logic is based on functional application rather than predication; a binary relation is analyzed as a binary function that maps a pair of arguments to a truth-value.  Thus, a 3-place relation like gives would be analyzed in Frege’s logic as a function that maps arguments \(x\), \(y\), and \(z\) to an appropriate truth-value depending on whether \(x\) gives \(y\) to \(z\); the 4-place relation buys would be analyzed as a function that maps the arguments \(x\), \(y\), \(z\), and \(u\) to an appropriate truth-value depending on whether \(x\) buys \(y\) from \(z\) for amount \(u\); etc.