For the purposes of mathematics the general notion of logic 'propositional function' may be used to define a concept which we may wish to regard as a mathematical function. The term function will be restricted to entities which satisfy the conditions imposed. These conditions may be regarded as axioms. They imply certain elementary properties of functions which we may call theorems, although it seems legitimate to raise the question: Are these propositions in logic or mathematics? The symbolism, and methodology are those of mathematics. The significance is so broad that the subject as a whole may be regarded as at least meta-mathematical if not entirely in the domain of logic. It will be assumed that there is a theory of classes, and certain properties of classes essential to the development of the theory of functions will be stated as need for them arises.
Proceedings of the Iowa Academy of Science
© Copyright 1947 by the Iowa Academy of Science, Inc.
Chittenden, E. W.
"On the General Theory of Functions,"
Proceedings of the Iowa Academy of Science, 54(1), 207-210.
Available at: https://scholarworks.uni.edu/pias/vol54/iss1/27