Structure-preserving representations, constitution, and the relative a priori

Abstract

The aim of this paper is to show that a comprehensive account of the role of representations in science should reconsider some neglected theses of the classical philosophy of science proposed in the first decades of the twentieth century. More precisely, it is argued that the representational accounts of Helmholtz and Hertz, in which the concept of structure-preservation plays an essential role, still deserve attention for contemporary debates. Following Reichenbach, structure-preserving representations provide a useful device for formulating an up-to-date version of a (relativized) Kantian a priori. An essential feature of modern scientific representations is their mathematical character. That is, representations can be conceived as (partially) structure-preserving maps or functions. This observation suggests an interesting but neglected perspective on the history and philosophy of this concept, namely, that structure-preserving representations are closely related to a priori elements of scientific knowledge. Reichenbach's early theory of a relativized constitutive but nonapodictic a priori component of scientific knowledge provides a further elaboration of Kantian aspects of scientific representation. To cope with the dynamic aspects of the evolution of scientific knowledge, Cassirer proposed a re-interpretation of the concept A first version of this paper was presented at the International Conference on Modelling and Representation. How to Make World(s) with Symbols that took place at the University of the Basque Country (UPV/EHU) in Donostia-San Sebastian (Spain) on December 10-12, 2015. My thanks to two anonymous referees for this journal for insightful comments and criticism. The author's work was supported by the research project "Representation and Anticipation: RRI modelling in emerging sciences and technologies" (FFI2015-69792-R), funded by the Spanish Ministry of Economy and Competitiveness, Government of Spain.