 Frege’s Begriffsschrift develops a formal system, which includes axioms for quantification over individual objects and concepts. For Frege, objects are the appropriate values for singular variables, and a concept is what is referred to by a predicate. Notice that despite Frege’s use of the term, concepts, for him, are nothing like mental constructs, but rather objective constituents of the world. In particular, concepts are functions, which map objects into truth values. Since a predicate like “is extended” is true of some objects and false of others, Frege takes the concept being extended to assign truth to an object if, and only if, it is extended.