ABSTRACT
A “propositional function,” is an expression containing one or more undetermined constituents, such that, when values are assigned to these constituents, the expression becomes a proposition. Any mathematical equation is a propositional function. So long as the variables have no definite value, the equation is merely an expression awaiting determination in order to become a true or false proposition. The notion of “cases” or “instances” depends upon propositional functions. Not only the principles of deduction, but all the primitive propositions of logic, consist of assertions that certain propositional functions are always true. A set of notions as to which philosophy has allowed itself to fall into hopeless confusions through not sufficiently separating propositions and propositional functions are the notions of “modality”: necessary, possible, and impossible.
