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L ogic An expression containing one or more free variables , such as “X is wise.” This is also called an open sentence . Once the free variable is replaced by a constant, an actual or closed sentence is formed. For instance, if we substitute “Socrates” for X in the above sentential function, we get the closed sentence “Socrates is wise.” Obviously, various sentences of the same type can be formed from such a function. A sentential function can be quantified both existentially (“There is at least one X such that X is wise”) and universally (“For every X, X is wise”). A sentential function is sometimes distinguished from a propositional function , which is what a sentential function denotes, but more often these two expressions are treated as synonymous. “A sentential function, as this technical term is used by logicians, is an expression containing a variable such that a sentence which is either true or false results when a constant is substituted for the variable.” Pap, Elements of Analytic Philosophy ... log in or subscribe to read full text