Philosophical problems

pp. 1-22

in: Daniel Parrochia, Pierre Neuville, Towards a general theory of classifications, Berlin, Springer, 2013

Abstract

In principle, a general theory of classifications should have to say, first, what is a classification, or even what it must be. So, in a textbook or in a monograph, we should have to begin with some rigorous definition of the notion of "classification". From this mathematical standpoint, a good method would be to take some weak structure, for instance a 'system of classes' or a "hypergraph" in the sense of Berge (Graphes et hypergraphes, 1970), and, by adding restrictive properties, to construct richer structures (for instance: covers, partitions, hierarchy of partitions…), for getting at the end a more precise view of the notion available in some special fields of knowledge. However, using such a method would imply that we already know for what we are searching, i.e. the means of unifying the whole domain of classifications.