In "Über Sinn und Bedeutung", Frege limits his discussion of the sense/reference distinction to "complete expressions" such as names purporting to pick out some object and whole propositions. However, in other works, Frege makes it quite clear that the distinction can also be applied to "incomplete expressions", which include functional expressions and grammatical predicates. These expressions are incomplete in the sense that they contain an "empty space", which, when filled, yields either a complex name referring to an object, or a complete proposition. Thus, the incomplete expression "the square root of ( )" contains a blank spot, which, when completed by an expression referring to a number, yields a complex expression also referring to a number, e.g., "the square root of sixteen". The incomplete expression, "( ) is a planet" contains an empty place, which, when filled with a name, yields a complete proposition. According to Frege, the references of these incomplete expressions are not objects but functions. Objects (Gegenstände), in Frege's terminology, are self-standing, complete entities, while functions are essentially incomplete, or as Frege says, "unsaturated" (ungesättigt) in that they must take something else as argument in order to yield a value. The reference of the expression "square root of ( )" is thus a function, which takes numbers as arguments and yields numbers as values. The situation may appear somewhat different in the case of grammatical predicates. However, because Frege holds that complete propositions, like names, have objects as their references, and in particular, the truth-values the True or the False, he is able to treat predicates also as having functions as their references. In particular, they are functions mapping objects onto truth-values. The expression, "( ) is a planet" has as its reference a function that yields as value the True when saturated by an object such as Saturn or Venus, but the False when saturated by a person or the number three. Frege calls such a function of one argument place that yields the True or False for every possible argument a "concept" (Begriff), and calls similar functions of more than one argument place (such as that denoted by "( ) > ( )", which is doubly in need of saturation), "relations".
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