  In Frege’s term logic, all of the terms and well-formed formulas are denoting expressions. These include: (a) simple names of objects, like ‘\(2\)’ and ‘\(\pi\)’, (b) complex terms which denote objects, like ‘\(2^2\)’ and ‘\(3 + 1\)’, and (c) sentences (which are also complex terms). The complex terms in (b) and (c) are formed with the help of ‘incomplete expressions’ which signify functions, such as the unary squaring function ‘\((\:)^2\)’ and the binary addition function ‘\((\:) + (\:)\)’. In these functional expressions, ‘\((\:)\)’ is used as a placeholder for what Frege called the arguments of the function; the placeholder reveals that the expressions signifying function are, on Frege’s view, incomplete and stand in contrast to complete expressions such as those in (a), (b), and (c). (Though Frege thought it inappropriate to call the incomplete expressions that signify functions ‘names’, we shall sometimes do so in what follows, though the reader should be warned that Frege had reasons for not following this practice.) Thus, a mathematical expression such as ‘\(2^2\)’ denotes the result of applying the function \((\:)^2\) to the number \(2\) as argument, namely, the number \(4\). Similarly, the expression ‘\(7 + 1\)’ denotes the result of applying the binary function \(+((\:),(\:))\) to the numbers \(7\) and \(1\) as arguments, in that order.