Abstract

"The Concept of Number", by Ernst Cassirer, is the second chapter of his first systematic work, the "Substanzbegriff und Funktionsbegriff: Untersuchungen über die Grundfragen der Erkenntniskritik", originally published in German in 1910. The translation to English, in 1953, by Marie Collins Swabeyand William Curtis Swabey, under the title "Substance and Function and Einstein's Theory of Relativity", despite its importance for having widely disseminated the work, loses in its title the work's essence: the opposition between "concept-substance" and "concept-function", or rather, between "substantial-concept" and "functional-concept". Cassirer possesses along with a "theory of symbolical forms" a "theory of culture". These theories are "theories of conceptual formation" and they are in charge of various case studies developed by Cassirer in “Substanzbegriff und Funktionsbegriff”. Chapter 2, now translated, is a reading of the historical development of the concept of number under the view of a general theory of the concept that he presents in the second chapter of the book “Zur Theorie der Begriffsbildung” (On the theory of the conceptual formation).