Topological Ontology and Logic of Qualitative quantity

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philosophy or philosophical topology, in particular the “inaparent” category and method of qualitative quantity in the logic and ontology, and in the cultural phenomenology as well. The aim of this research paper is first to introduce in philosophy the term of “topological ontology” 4 and in turn to demonstrate how contemporary upper ontologies and human computer stidies may still benefit from the philosophical tradition, in particular from the core categories in philosophical logic and ontology such as quality and quantity in their paradoxical coexistence in the topological cobordism of Hegel’s fourfold of infinities: /. the bad qualitative infinity; 2/. the good qualitative infinity; 3/. the bad quantitative infinity; 4/. the good quantitative infinity implemented as: 1. Quantitative quantity; 2. Quantitative quality; 3. Qualitative quality; 4. Qualitative quantity, will give us new understanding about the evolution of contemporary capital, market and globalization. This paper provide philosophical discussion on the critical categiries and methods for ontology such as quality and quantity with the aim to open new horizon for an applied philosophy in areas related with the upper ontologies, such as computer science, AI, knowledge-based systems, lingustics and semiotics. The categories of quality and quantity are critical categories in logic and ontology and the recent research demonstrates their development. This development of the categories of quality and quantity follows the developments and shift of ontology from the philosophy to the areas such as the mentioned above with the focus on the human computer stidies, with the believe that the topological notion of qualitative quantity as logic and ontology will enhance the opportunity to contribute to development of research on theories, methods and technology regarding the design and use and evaluation of complex human-computer systems. The topological ontology of qualitative quantity here is proposed in the sense and from the point of view of AI as an “explicit specification of conceptualization” and agreement aout shared conceptualization. The goal of this paper is to introduce the topological ontology of qualitative quantity in the conceptual frameworks for modeling domain knowledge; content-specific protocols for communication among inter-operating agents; and -Borislav Dimitrov, Cultural Phenomenology of Law and Topological Approach to Law, (2012): http://ariadnetopology.org/1PDF.pdf Borislav Dimitrov, “A Topological Approach to Audit Dynamics and Auditing Research –Cultural Phenomenology of Audit and Auditing research” (2011): http://ariadnetopology.org/5.html. Borislav Dimitrov, “A Topological Approach to Audit Dynamics and Auditing Research –Cultural Phenomenology of Audit and Auditing research” (2011): http://ariadnetopology.org/5.html. 4 Topological ontology is quite foreign for philosophy but well at home in human-computer studies. The term “topological ontology” appears and can be found in the server of the KACTUS project at http://hcs.science.uva.nl/projects/NewKACTUS/library/lib/topology.html KACTUS stands for modelling Knowledge About Complex Technical systems for multiple USe. It is an European ESPRIT project (ESPRIT Project 8145)aiming at the development of a methodology for the reuse of knowledge about technical systems during their life-cycle. This implies using the same knowledge base for design, diagnosis, operation, maintenance, redesign, instruction, et cetera. Reuse will be achieved by giving these knowledge bases an explicit structure (ontology). KACTUS aim is to model knowledge about complex technical systems for multiple use. The project has started at January 1st 1994 and runs for 30 months. The prject consortium includes the partners as Gap Gemini Innovation, Integral Solution Limited, Cap Programator, Delos S.p.A, Fincarntieri, Iberdrola, Labein, Lloyd’s Register, RPK University in Karlsuhe, Statiol, Sintef Automatic Control, SWI University of Amsterdam. The strategic objectives of the KACTUS project are Efficiency via Method Integration, Competitive Advantage by Creation of an Ontological Basis and Interoperability by Modelling and Information Exchange. Projects and Publications on the subject of topological ontology could are available on the ONTOLINGUA SERVER http://ontolingua.stanford.edu (Library of Ontologies Table of Contents) with the Reference Documents, List of Ontologies (http://www-ksl.stanford.edu/knowledgesharing/ontologies/html/index.html#theory-list) Topological ontology is one of the main concerns of Human-Computer Studies Laboratory, a part of the Informatics Institute, which is a part of the Faculty of Science of the University of Amsterdam. 2
agreements about the representation of particular domain theories. In the knowledge sharing context, topological ontology of qualitative quantity deserve own place into the form of definitions of representational vocabulary. The new area of interdependence between the quality and quantity is open now for rethinking and reconceptualization. In Qualitative Spatial Representation in the field of Qualitative Spatial Reasoning, the term “qualitative quantitative space” emerged and the concept of “qualitative quantity” is vitally accepted and utilized. 5 Qualitative quantity seen in Poincare’s topology and his development of the qualitative theory of differential equations is enhanced by the new science of Mereotopology, which began with theories A.N. Whitehead articulated in several books and articles he published between 1916 and 1929. Mereotopology is a branch of metaphysics, and ontological computer science, a firstorder theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. The Qualitative quantity is the base cathegory and phenomenom of Qualitative research /QR/, due to the aim of QR to utilise methods that seek to discern the quality — as opposed to the quantity — of its subject. Qualitative quantity is critical in Spatial-temporal reasoning applicable in computer science as Visual thinking and Visual music, Visual statistic /the series of works by David James Krus/. Ontology in philosophy means theory of existence. Ontology tries to explain what is being and how the world is configured by introducing a system of critical categories to account things and their intrinsic relations. The origin of philosophical ontology is Aristotle’s metaphysics and his theory of categories, intelligible universals extending across all domains. According to Aristotle the world is organized via types/universals/categories which are hierarchically organized. The historical line goes from Aristotle trough the Medieval scholastics, such as Aquinas, Scotus, Ockham, from Descartes and Kant to Brentano’s rediscovery of Aristotle to Ednund Husserl, the inventor of formal ontology as a discipline distinct from formal logic, who showed how philosophy and science had become detached from the ‘life world’ of ordinary experience, claiming that the methods of philosophy and of science are one and the same. The historical line of ontology is continued by Wittgenstein, Vienna Circle (Schlick, Neurath, Gödel, Carnap, Gustav Bergmann), British Ordinary Language philosophy (Speech Act Theory of J. L. Austin), Quine’s ontological commitment, Analytical metaphysics of Chisholm, Lewis, Armstrong, Fine, Lowe. This line ends with the beginnings of a rediscovery of metaphysics as first philosophy. 1. Topological backgroung of Edmund Husserl’s Ontology – Topological, Mereological and Mereotopological Part-Whole Reasoning Edmund Husserl’s formal ontology is the natural environment of topology and topological background of Husserl’s work. Husserl's “Logical Investigations” (1900/01) contain a formal theory of part, whole and dependence that is used by Husserl to provide a framework for the analysis of mind and language of just the sort that is presupposed in the idea of a topological foundation for cognitive science. 6 One of the most sophisticated scientists and researcher who strongly support the idea of topological Husserl 7 is Barry Smith, Professor of Philosophy, Neurology and Computer Science and Director of the National Center for Ontological Research at the University at 5 See: A. G. Cohn, Qualitative Spatial Representation and Reasoning Techniques, Division of Artificial Intelligence, School of Computer Studies, University of Leeds.- Note 1.’footnote’ about “qualitative quantity”. 6 Barry Smith, Topological Foundations of Cognitive Science, a revised version of the introductory essay in C. Eschenbach, C. Habel and B. Smith (eds.), Topological Foundations of Cognitive Science, Hamburg: Graduiertenkolleg Kognitionswissenschaft, 1994, the text of a talk delivered at the First International Summer Institute in Cognitive Science in Buffalo in July 1994.: http://ontology.buffalo.edu/smith/articles/topo.html And Barry Smith, (ed.) 1982 Parts and Moments. Studies in Logic and Formal Ontology, Munich: Philosophia.) 3
Page 1: Topological Ontology and Logic of Q
Page 5 and 6: Science” (Wissenschaftslehre), Bo
Page 7 and 8: Leśniewski's student Alfred Tarski
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Page 25 and 26: series of Measure Relations” /b/,
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Page 41 and 42: This is not to say, however, that t
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Page 45 and 46: concept of spatiality. But they did
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The term “social topology” is u
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of Leonard Euler and later with the
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To Meet the Other is to have the id
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Topological Ontology and Logic of Qualitative quantity

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