On the Concepts of Function and Dependence

Abstract

This paper briefly traces the evolution of the function concept until its modern settheoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is misconceived, and that two different notions of dependence are actually involved in the classic and the modern viewpoints, namely effective and functional dependence. The former contains the latter, and seems to conform more to our pre-formal conception of dependence. The idea of effective dependence is further investigated in connection with the notions of function content and intensionality. Finally, the relevance of the distinction between the two kinds of dependence to mathematical practice is considered.

Keywords

• Function Concept
• Variable Dependence
• Philosophy of Mathematics
• History of Mathematics