Function and Argument

Abstract

Introduction Begriffsschrift was, as the subtitle announced, a formula language of pure thought modeled upon the language of arithmetic . Frege borrowed the notation for functions from arithmetic, and enlarged the realm of applicability of a function beyond the domain of numbers. Then, supplanting the subject/predicate division, which was characteristic of previous logical systems, by a function/argument division, he created a logical notation, a Begriffsschrift – literally, Concept Writing – which would serve to represent thoughts about any objects whatsoever. Like the language of arithmetic, his Begriffsschrift represented thoughts so that the inferential connections between them were molded in the representations themselves. The project was enormously successful. Not only did Frege create modern quantificational logic, but he also provided the theoretical framework for many subsequent philosophical developments in logic as well as in speculative philosophy. As Dummett (1981 a ) correctly remarked, Frege's work shifted the central focus of philosophy from the epistemological issues raised by Descartes back to the metaphysical and ontological issues that were salient after Aristotle. The function/argument analysis Frege (1879) presented was, however, flawed. There was a significant confusion in his operating semantic notion of the content [Inhalt] of a sentence. Frege came to recognize that repairs were needed, and after much hard philosophical work, the theory with which we are now familiar emerged in the early 1890s. It was announced first in Frege (1891), and then elaborated upon in Frege (1892 c ) and Frege (1892 a ).