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1Parrochia, D.: Mathematical theory of classification.
In: Knowledge organization. 45(2018) no.2, S.184-201.
(Reviews of concepts in knowledge organization)
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
Themenfeld: Klassifikationstheorie: Elemente / Struktur
2Parrochia, D. ; Neuville, D.: Towards a general theory of classifications.
Basel : Birkhäuser, 2013. XXIII, 304 S.
(Studies in universal logic)
Abstract: This book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind of them: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or not overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothing but a dream. Instead, the authors are essentially put forward a number of key questions. Their aim is rather to reveal the "state of art" of this dynamic field and the philosophy one may eventually adopt to go further. To this end they present some advances made in the course of the last century, discuss a few tricky problems that remain to be solved, and show the avenues open to those who no longer wish to stay on the wrong track. Researchers and professionals interested in the epistemology and philosophy of science, library science, logic and set theory, order theory or cluster analysis will find this book a comprehensive, original and progressive introduction to the main questions in this field.
Inhalt: Philosophical problemsInformation / data structures / Empirical clustering and classic hierarchies / Algebra of trees / Generalized classifications / Topology of generalized classifications / Metaclassification / For an axiomatic theory of classifications / Alternative theories and higher infinite / Postscript.
LCSH: Categories (Philosophy) ; Classification / Mathematics ; Logic, Symbolic and mathematical ; Mathematics / Philosophy
BK: 31.10 Mathematische Logik Mengenlehre ; 31.11 Ordnungen allgemeine mathematische Systeme ; 31.02 Philosophie und Wissenschaftstheorie der Mathematik
DDC: 001.01/2 / dc23
RVK: CC 2600