  If we replace a complete name appearing in a sentence by a placeholder, the result is an incomplete expression that signifies a special kind of function which Frege called a concept. Concepts are functions which map every argument to one of the truth-values. Thus, ‘\((\:) \gt 2\)’ denotes the concept being greater than \(2\), which maps every object greater than \(2\) to The True and maps every other object to The False. Similarly, ‘\((\:)^2 = 4\)’ denotes the concept that which when squared is identical to \(4\). Frege would say that any object that a concept maps to The True falls under the concept. Thus, the number \(2\) falls under the concept that which when squared is identical to \(4\). In what follows, we use lower-case expressions like \(f(\:)\) to talk generally about functions, and upper-case expressions like \(F(\:)\) to talk more specifically about those functions which are concepts.