6 - The Value of a Function

Summary

Gottlob Frege has been called “the founder of modern mathematical logic,” “the father of ‘linguistic philosophy,’” and “one of the founders of analytic philosophy” (Dummett 1973, 665 and 683; Beaney 1996, 1). Frege, like Leibniz, Humboldt, and Mill before him, focuses on a form of language that runs deeper than its apparent grammatical structure, and he specifically follows Leibniz and Mill in isolating logical form. What distinguishes Frege is his mathematical perspective on language. Drawing on mathematics, Frege constructed a language of logic that he believed also served as a basis for understanding the essential components of all languages, whether natural or artificial. Mill reestablished the tie between logical and linguistic studies, but Frege gave this relation a mathematical character that left a lasting mark in the philosophy and science of logic and language. In doing so, Frege also filtered out what might be thought of as the human dimension of language, namely its psychological properties, and consequently Frege has contributed to the concept of language as an autonomous formal system.

Concept Script

Frege's development began with what is also by far his most significant contribution: his work on the language of logic published in 1879 in “an epoch-making little book” called Begriffsschrift, translated as Concept Script or Conceptual Notation (Kneale and Kneale 1962, 436). It has been compared in significance and scope with Aristotle's contribution to logic.