What is of interest to us here is that in categorial grammars determiners such as ‘a’ and verbs are thought of as functions, but they can differ from one another in terms of whether they take arguments on their right or on their left. In the set theoretic concept of function as a set of ordered pairs, functions are thought of just in terms of their correlating arguments with values. A function, as it is understood in categorial grammar has more structure than this. This is an interesting generalization of the notion of a function as it is used in logic. We can see that it also has important links to the concept of a propositional function, especially as it is used in Montague semantics.