propositional function an operation that, when applied to something as argument (or to more than one thing in a given order as arguments), yields a truth-value as the value of that function for that argument (or those arguments). This usage presupposes that truth-values are objects. A function may be singulary, binary, ternary, etc. A singulary propositional function is applicable to one thing and yields, when so applied, a truth-value. For example, being a prime number, when applied to the number 2, yields truth; negation, when applied to truth, yields falsehood. A binary propositional function is applicable to two things in a certain order and yields, when so applied, a truth-value. For example, being north of when applied to New York and Boston in that order yields falsehood. Material implication when applied to falsehood and truth in that order yields truth. The term ‘propositional function’ has a second use, to refer to an operation that, when applied to something as argument (or to more than one thing in a given order as arguments), yields a proposition as the value of the function for that argument (or those arguments). For example, being a prime number when applied to 2 yields the proposition that 2 is a prime number. Being north of, when applied to New York and Boston in that order, yields the proposition that New York is north of Boston. This usage presupposes that propositions are objects. In a third use, ‘propositional function’ designates a sentence with free occurrences of variables. Thus, ‘x is a prime number’, ‘It is not the case that p’, ‘x is north of y’ and ‘if p then q’ are propositional functions in this sense. C.S.