Parrochia, D.: Mathematical theory of classification (2018)
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- Abstract
- One of the main topics of scientific research, classification is the operation consisting of distributing objects in classes or groups which are, in general, less numerous than them. From Antiquity to the Classical Age, it has a long history where philosophers (Aristotle), and natural scientists (Linnaeus), took a great part. But from the nineteenth century (with the growth of chemistry and information science) and the twentieth century (with the arrival of mathematical models and computer science), mathematics (especially theory of orders and theory of graphs or hypergraphs) allows us to compute all the possible partitions, chains of partitions, covers, hypergraphs or systems of classes we can construct on a domain. In spite of these advances, most of classifications are still based on the evaluation of ressemblances between objects that constitute the empirical data. However, all these classifications remain, for technical and epistemological reasons we detail below, very unstable ones. We lack a real algebra of classifications, which could explain their properties and the relations existing between them. Though the aim of a general theory of classifications is surely a wishful thought, some recent conjecture gives the hope that the existence of a metaclassification (or classification of all classification schemes) is possible
