Die Mathematisierung der Erfahrung: Vorgänger zu Carnaps “Aufbau”

Abstract

At present, there is a renewed interest in thoseaspects of Rudolf Carnap's LogischerAufbau der Welt that cannot just be reduced tothe tradition of logical positivism. There is, however,one of these aspects which seems to have beenneglected by the historical analyses of theAufbau's background: what may be called aprogram for the mathematization of sense experience,as developed by Carnap in the most difficult partof his work, Chapter IV/A. It is the program of applying settheory and topology to the reconstruction of phenomenal structures,quite independently of any other general philosophical aim.I claim that there are three forerunners of this program:Henri Poincaré's essayPourquoi l'espace a trois dimensions (1912), Chapter 4of Bertrand Russell's Our Knowledge of the ExternalWorld (1914), and Jean Nicod's La géométriedans le monde sensible (1923). This article provides acomparison of these different instances of theabove-mentioned program.