The concept of number

Abstract

“The Concept of Number”, by Ernst Cassirer, istheChapter 2 ofhisfirstsystematicwork, the “SubstanzbegriffundFunktionsbegriff: Untersuchungenüber die Grundfragen der Erkenntniskritik“, originallypublished in German in 1910. The translation to English, in 1953, by Marie Collins Swabeyand William Curtis Swabey, under the title “Substance and Functionand Einstein's Theory of Relativity”, despite of its importance for having broadcasted the work, losts in its title the work’s essence: the opposition between “concept-substance” and “concept-function”, or better, between “substantial-concept” and “functionalconcept”. Cassirer owns alongside with a “theory of symbolical forms” a “theory of culture”. These theories are “theories of conceptual formation” and they are in charge of diverse studies of case developed by Cassirer in “SubstanzbegriffundFunktionsbegriff”. The 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 Chapter 2 of the book “ZurTheorie der Begriffsbildung” (On the theory of the conceptual formation).