ABSTRACT
The variable is the most distinctively mathematical of all notions; it is certainly also one of the most difficult to understand. When a given term occurs as term in a proposition, that term may be replaced by any other while the remaining terms are unchanged. The class of propositions so obtained have what may be called constancy of form, and this constancy of form must be taken as a primitive idea. The notion of a class of propositions of constant form is more fundamental than the general notion of class, for the latter can be defined in terms of the former, but not the former in terms of the latter. The terms included in the object denoted by the defining concept of a variable are called the values of the variable: thus every value of a variable is a constant. A variable is not any term simply, but any term as entering into a propositional function.
