Crítica, Revista Hispanoamericana de Filosofía, Volume 32, number 95, agosto 2000
Una teoría combinatoria de las representaciones científicas
[A Combinatory Theory of Scientific Representations]
Andoni Ibarra
Unidad de Filosofía de la Ciencia
Universidad del País Vasco/CSIC

Thomas Mormann
Departamento de Lógica y Filosofía de la Ciencia
Universidad del País Vasco

Abstract: The aim of this paper is to introduce a new concept of scientific representation into philosophy of science. The new concept -to be called homological or functorial representation- is a genuine generalization of the received notion of representation as a structure preserving map as it is used, for example, in the representational theory of measurement. It may be traced back, at least implicitly, to the works of Hertz and Duhem. A modern elaboration may be found in the foundational discipline of mathematical category theory. In contrast to the familiar concepts of representations, functorial representations do not depend on any notion of similarity, neither structural nor objectual one. Rather, functorial representation establish correlations between the structures of the representing and the represented domains. Thus, they may be said to form a class of quite "non-isomorphic" representations. Nevertheless, and this is the central claim of this paper, they are the most common type of representations used in science. In our paper we give some examples from mathematics and empirical science. One of the most interesting features of the new concept is that it leads in a natural way to a combinatorial theory of scientific representations, i.e. homological or functorial representations do not live in insulation, rather, they may be combined and connected in various ways thereby forming a net of interrelated representations. One of the most important tasks of a theory of scientific representations is to describe this realm of combinatorial possibilities in detail. Some first tentative steps towards this endeavour are done in our paper.

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