Theory of KNowledge structures and process

Theory of Knowledge Structures and Processes 8893_9789814522670_TP.indd 12/10/16 8:22 AM World Scientific Series in Information Studies (ISSN: 1793-7876) Series Editor: Mark Burgin (University of California, Los Angeles, USA) International Advisory Board: Søren Brier (Copenhagen Business School, Copenhagen, Denmark) Tony Bryant (Leeds Metropolitan University, Leeds, United Kingdom) Gordana Dodig-Crnkovic (Mälardalen University, Eskilstuna, Sweden) Wolfgang Hofkirchner (ICT&S Center, University of Salzburg, Salzburg, Austria) William R King (University of Pittsburgh, Pittsburgh, USA) Vol Theory of Information — Fundamentality, Diversity and Unification by Mark Burgin Vol Information and Computation — Essays on Scientific and Philosophical Understanding of Foundations of Information and Computation edited by Gordana Dodig-Crnkovic & Mark Burgin Vol Emergent Information — A Unified Theory of Information Framework by Wolfgang Hofkirchner Vol An Information Approach to Mitochondrial Dysfunction: Extending Swerdlow’s Hypothesis by Rodrick Wallace Vol Theory of Knowledge: Structures and Processes by Mark Burgin Sajani - Theory of Knowledge.indd 25-07-16 2:02:32 PM World Scientific Series in Information Studies — Vol Theory of Knowledge Structures and Processes Mark Burgin University of California, Los Angeles, USA World Scientific NEW JERSEY • LONDON 8893_9789814522670_TP.indd • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TA I P E I • CHENNAI • TOKYO 12/10/16 8:22 AM Published by World Scientific Publishing Co Pte Ltd Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Names: Burgin, M S (Mark Semenovich), author Title: Theory of knowledge : structures and processes / Mark Burgin Description: New Jersey : World Scientific, 2016 | Series: World Scientific series in information studies ; Volume | Includes bibliographical references and index Identifiers: LCCN 2015049963 | ISBN 9789814522670 (hc : alk paper) Subjects: LCSH: Knowledge, Theory of Classification: LCC BD161 B865 2216 | DDC 121 dc23 LC record available at http://lccn.loc.gov/2015049963 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Copyright © 2017 by World Scientific Publishing Co Pte Ltd All rights reserved This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA In this case permission to photocopy is not required from the publisher Desk Editors: Dr Sree Meenakshi Sajani/Tan Rok Ting Typeset by Stallion Press Email: enquiries@stallionpress.com Printed in Singapore Sajani - Theory of Knowledge.indd 25-07-16 2:02:32 PM September 27, 2016 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm page v Contents Preface ix Acknowledgments xiii About the Author xv Introduction 1.1 The role of knowledge in the contemporary society 1.2 A brief history of knowledge studies 1.3 Structure of the book 39 Knowledge Characteristics and Typology 2.1 The differentiation and classification of knowledge 2.2 Existential characteristics of knowledge 2.3 Descriptive properties of knowledge and corresponding typology 2.3.1 Dimensions and other characteristics of knowledge 2.3.2 Correctness, relevance, and consistency of knowledge 2.3.3 Confidence in and certainty of knowledge 2.3.4 Complexity and clarity of knowledge 2.3.5 Significance of knowledge 2.3.6 Efficiency of knowledge 2.3.7 Reliability of knowledge v 45 45 77 91 94 96 119 122 131 134 136 September 27, 2016 vi 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm page vi Contents 2.3.8 Abstractness and generality of knowledge 2.3.9 Completeness of knowledge versus precision of knowledge 2.3.10 Meaning of knowledge 2.3.11 Other descriptive properties of knowledge 2.4 Metaknowledge and metadata 137 Knowledge Evaluation and Validation in the Context of Epistemic Structures 3.1 Knowledge in the context of epistemic structures and knowledge scales 3.2 Knowledge evaluation, justification, and testing 3.2.1 Knowledge evaluation 3.2.2 Knowledge validation, justification, and testing 3.3 Local consistency versus global consistency in knowledge representation 139 140 149 151 169 170 215 215 240 263 Knowledge Structure and Functioning: Microlevel or Quantum Theory of Knowledge 4.1 Basic structures of knowledge units on the quantum level — knowledge quanta and semantic links 4.1.1 Quantum theory of knowledge (QTK) 4.1.2 Semantic link network theory (SLNT) and Semantic link theory of knowledge (SLTK) 4.1.3 QTK–SLTK connection 4.2 Signs and symbols as quantum units of knowledge 4.3 Operations with and relations between quantum knowledge units 4.3.1 Properties of and relations between nodes and links in SLN and knowledge quanta in QTK 4.3.2 Operations with extended knowledge quanta 4.3.3 Operations with symbolic knowledge quanta and complete semantic links 307 309 310 329 340 343 358 360 369 380 September 27, 2016 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm vii Contents Knowledge Structure and Functioning: Macrolevel or Theory of Average Knowledge 5.1 Language as a universal tool for knowledge representation 5.1.1 Natural languages 5.1.2 Languages of science and mathematics 5.1.3 Algorithmic and programming languages 5.2 Logic as a tool for knowledge representation and production 5.2.1 Concepts, names, terms, and objects 5.2.2 Statements, queries, and instructions 5.2.3 Logical systems of inference 5.3 Theory of abstract properties 5.4 Semantic networks and ontology 5.5 Scripts and productions 5.6 Frames and Schemas Knowledge Structure and Functioning: Megalevel or Global Theory of Knowledge 6.1 A typology of structures and scientific knowledge 6.2 Nuclear and comprehensive knowledge systems 6.3 Logic-linguistic knowledge system and descriptive knowledge 6.4 Model-representation knowledge system and representational knowledge 6.5 Procedural, axiological and instrumental knowledge systems, and operational knowledge 6.6 Relations between and operations with global knowledge systems 6.7 Hierarchies of knowledge systems Knowledge Production, Acquisition, Engineering, and Application page vii 395 402 403 411 423 428 446 481 491 500 518 527 536 593 595 603 612 617 622 631 636 643 7.1 Knowledge production, learning, and acquisition as basic cognitive processes 644 September 27, 2016 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in viii b2334-fm page viii Contents 7.1.1 Scientific cognition 7.1.2 Intuition as a cognitive instrument 7.1.3 Computers and networks as cognitive tools 7.1.4 Learning 7.1.5 Knowledge creation in organizations 7.2 Knowledge organization and engineering 7.3 Knowledge management and application Knowledge, Data, and Information 658 669 688 696 705 711 714 721 8.1 Epistemic structures and cognitive information 8.2 Structural aspects of knowledge–information duality 8.3 Information as a source of knowledge 8.4 Dynamic aspects of knowledge, data, and information interaction 8.5 Knowledge as a measure of information 722 727 760 766 791 Conclusion 803 Appendix 809 A B C D E Set theoretical foundations Elements of the theory of algorithms Elements of algebra and category theory Numbers and numerical functions Topological, metric and normed spaces 809 819 825 831 833 Bibliography 837 Subject Index 927 September 27, 2016 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm Preface If the extent of knowledge is the hallmark of our civilization, the use to be made of it may be its crisis S Dilon Ripley An investment in knowledge pays the best interest Benjamin Franklin Knowledge has always been important in society and all educated people have always understood importance of knowledge That is why Western philosophers have studied knowledge as an important phenomenon from the time of Plato and Aristotle Thinkers from other countries, such as China and India, also tried to understand the essence of knowledge from ancient times In contemporary society, importance of knowledge is much higher and continues to grow very fast Researchers concluded that knowledge had become the key strategic asset for the 21st century and for every organization Consequently, the necessity in developing the best strategy for identifying, developing, and applying the knowledge assets has become critical Every organization needs to invest in creating and implementing the best knowledge networks, processes, methods, tools, and technologies The growing needs in knowledge and efficient knowledge organization intensified studies of knowledge There are three main directions ix page ix September 27, 2016 19:41 x Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm Preface in these studies: — The philosophical and methodological direction, which comprises epistemology and the methodology of science and mathematics — The area of artificial intelligence (AI), in which knowledge is perceived as the base of intelligence — The field of knowledge management where knowledge is treated as the main asset of companies and organizations AI is typically directed at knowledge representation and processing Epistemology is largely interested in knowledge definition and acquisition (cognition) Knowledge management is mostly concerned with knowledge organization and utilization In addition, knowledge is also explored in psychology, sociology, and linguistics Intensification of studies in area of knowledge brought forth a quantity of books on a variety of issues and problems of knowledge So, why is this book different? It is different because its main goal is to present, organize and synthesize the basic ideas, results, and concepts from these three directions, which are loosely related now, into a unified theory of knowledge and knowledge processes It is called the synthetic theory of knowledge It is multidisciplinary and transdisciplinary at the same time The approach presented in this book provides a new explanation of important relations between knowledge and information demonstrating new kinds of possibilities for knowledge management, information technology, data mining, information sciences, computer science, knowledge engineering, psychology, social sciences, genetics, and education that are made available by the synthetic theory of knowledge Explanation of knowledge essence, structure and functioning is given in this book, as well as answers to the following questions: — How knowledge is related to information and data? — How knowledge is modeled by mathematical and logical structures? page x September 27, 2016 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in Preface b2334-fm page xi xi — How these models are used to better understand and utilize computers and Internet, cognition and education, communication and computation? Knowledge is inseparable from information People acquire knowledge receiving cognitive information At the same time, knowledge, by its essence, contains information and this is the main feature of knowledge This intrinsic unity of knowledge and information forms the base of the synthetic theory of knowledge b2530   International Strategic Relations and China’s National Security: World at the Crossroads This page intentionally left blank b2530_FM.indd 01-Sep-16 11:03:06 AM September 27, 2016 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm Acknowledgments Many wonderful people have made contributions to my efforts with this work I am especially grateful to the staff at World Scientific and especially, Ms Tan Rok Ting, for their encouragement and help in bringing about this publication, as well as to Ms Raghavarshini for diligent preparation of this text for publication I would like to thank the teachers and especially, my thesis advisor, Alexander Gennadievich Kurosh, who helped shape my scientific viewpoint and research style In developing ideas in knowledge theory, I have benefited from conversations and discussions with many friends and colleagues Thus, I am grateful for the interest and helpful discussions with those who have communicated with me on these problems I greatly appreciate advice and help of Andrei Nikolayevich Kolmogorov from Moscow State University in the development of the holistic view on mathematics and its connections with the physical world I have also benefited from the discussions I had with Michael Arbib from USC on schema theory and with Frank Land from the London School of Economics and Political Science on knowledge management Collaboration with Kees de vey Mestdagh from the University of Groningen gave much to the development of the theory of logical varieties as a tool for representing and reasoning with inconsistent knowledge Collaboration with Victor Gladun from Gorsystemotechnika (Kiev) gave much to the development of mathematical modeling of semantic networks Collaboration with Dmitri Gorsky from the Moscow Institute of Philosophy contributed to the xiii page xiii September 27, 2016 xiv 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm Acknowledgments further development of mathematical theory of concepts Collaboration with Vladimir Kuznetsov from the Kiev Institute of Philosophy in the methodology of science contributed to the further development of mathematical models of scientific theories and global knowledge Collaboration with Paul Zellweger from ArborWay Labs and Rex Gantenbein from the University of Wyoming contributed to better understanding of knowledge discovery and representation Credit for my desire to write this book must go to my academic colleagues Their questions and queries made significant contribution to my understanding of knowledge and information I would particularly like to thank many fine participants of the Jacob Marschak Interdisciplinary Colloquium on Mathematics in the Behavioral Sciences at UCLA and especially, Colloquium Director, Michael Intrilligator, for extensive and helpful discussions on problems of knowledge and information that gave me much encouragement for further work in this direction Comments and observations of participants of the Applied Mathematics Colloquium of the Department of Mathematics, Seminar of Theoretical Computer Science of the Department of Computer Science at UCLA, various conferences where I presented these materials and the Internet discussion group on Foundations of Information Science (FIS) were useful in the development of my views on knowledge I would also like to thank the Departments of Mathematics and Computer Science in the School of Engineering at UCLA for providing space, equipment, and helpful discussions page xiv September 27, 2016 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm About the Author Dr Mark Burgin received his M.A and Ph.D in mathematics from Moscow State University, which was one of the best universities in the world at that time, and Doctor of Science in logic and philosophy from the National Academy of Sciences of Ukraine He was a Professor at the Institute of Education, Kiev; at International Solomon University, Kiev; at Kiev State University, Ukraine; and Head of the Assessment Laboratory in the Research Center of Science at the National Academy of Sciences of Ukraine Currently he is working at UCLA, USA Dr Burgin is a member of the New York Academy of Sciences and an Honorary Professor of the Aerospace Academy of Ukraine Dr Burgin is a member of the Science Advisory Committee at Science of Information Institute, Washington He was the Editor-in-Chief of the international journals Integration and Information, as well as an Editor and Member of Editorial Boards of various journals Dr Burgin is doing research, has publications, and taught courses in various areas of mathematics, artificial intelligence, information sciences, system theory, computer science, epistemology, logic, psychology, social sciences, and methodology of science He originated theories such as the general theory of information, theory of named sets, mathematical theory of schemas, theory of oracles, hyperprobability theory, system theory of time, theory of non-Dophantine arithmetics and neoclassical analysis (in mathematics) and made essential contributions to fields such as foundations of mathematics, theory of algorithms and computation, theory of knowledge, theory of intellectual activity, and complexity studies xv page xv September 27, 2016 xvi 19:41 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-fm About the Author He was the first to discover Non-Diophantine arithmetics, the first to axiomatize and build mathematical foundations for negative probability used in physics, finance and economics, and the first to explicitly overcome the barrier posed by the Church-Turing Thesis Dr Burgin has authorized and co-authorized more than 500 papers and 21 books, including “Structural Reality” (2012), “Hypernumbers and Extrafunctions” (2012), “Theory of Named Sets” (2011), “Theory of Information” (2010), “Neoclassical Analysis: Calculus Closer to the Real World” (2008), “Super-recursive Algorithms” (2005), “On the Nature and Essence of Mathematics” (1998), “Intellectual Components of Creativity” (1998), “Fundamental Structures of Knowledge and Information” (1997), “The World of Theories and Power of Mind” (1992), and “Axiological Aspects of Scientific Theories” (1991) Dr Burgin was also the Editor of books page xvi September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Chapter Introduction All men by nature desire knowledge Aristotle There is an abundance of different books and papers treating various problems and studying different issues of knowledge (cf., for example, (Aune, 1967; Polanyi, 1974; Cleveland, 1985; Chisholm, 1989; Bloor, 1991; Burgin, 1997; Boisot, 1998; Choo, 1998; Rao, 1998; Pollock and Cruz, 1999; Bernecker and Dretske, 2000; Bean and Green, 2001; Popper, 2002; Goldman, 2004; Dalkir, 2005; Leydesdorff, 2006; Magnani, 2007; Nguen, 2008; Fantl and McGrath, 2009; Zhuge, 2012)) A lot of ideas, models, and several theories have been suggested in this area The whole area of knowledge related activities consists of three parts: Knowledge studies (theoretical and experimental) Knowledge engineering Knowledge utilization and management The two latter parts belong to knowledge technology — knowledge engineering deals with technology of knowledge production, organization, transformation, management, preservation, capture and acquisition, while knowledge utilization studies how people and organizations use knowledge, developing new techniques and approaches for this purpose page September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes There are three types of knowledge theories: Philosophical theories comprised by the philosophical discipline called epistemology are interested in three fundamental problems: (1) knowledge definition, i.e., trying to find what knowledge is and how to separate knowledge from beliefs; (2) limits of knowledge acquisition, i.e., what it is possible to know; and (3) ways of knowledge creation and acquisition, i.e., how knowledge is obtained Mathematical theories include mathematical logic, which provides means for formal knowledge representation and formation; theory of algorithms, which provides means for knowledge transformation and preservation dealing mostly with procedural or operational knowledge (cf., Chapter 6); and mathematical linguistics, which studies informal knowledge representation and formation Empirical theories are oriented at the practice of knowledge functioning, including theories of many disciplines, such as artificial intelligence, knowledge management, knowledge bases, cognitology, knowledge acquisition, cognitive psychology, cognitive neuroscience, cognitive anthropology, cognitive sociology, education, and the sociology of knowledge Experimental exploration of knowledge emerged in ancient times A brilliant example of such an experimentation is presented in the Plato dialogue Theætetus describing how Sokrates and Theaetetus discuss and investigate the essence and nature of knowledge For a long time, people used mental experiments for knowledge studies With the advance of computers, computer experiment has become crucial in AI and knowledge management Besides, various experiments have been conducted with physical carriers of knowledge For instance, psychologists, educators and sociologists organized various experiments examining how people acquire, store and disseminate knowledge All research in the area of knowledge can be divided into three directions: • Structural analysis of knowledge strives to understand how knowledge is built and what properties it has page September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 page 3 Introduction • Axiological analysis of knowledge aims at explanation of those features that are primary for knowledge as a social and technological phenomenon • Functional analysis of knowledge tries to find how knowledge functions, how it is produced and acquired Structural analysis of knowledge is the main tool for the system theory of knowledge, knowledge bases, and artificial intelligence (AI) Axiological analysis of knowledge is the core instrument for the philosophy of knowledge, psychology, and social sciences, including the sociology of knowledge, which is the study of the relationship between human creativity and the social context within which it arises, of the effects knowledge has on individuals, organizations and societies dealing with broad fundamental questions, of the extent and limits of social influences on cognition, and of the social and cultural foundations of knowledge about the world Functional analysis of knowledge is the key device for epistemology, knowledge engineering, and cognitology 1.1 The role of knowledge in the contemporary society Knowledge is power Francis Bacon To survive and to prosper, people have always needed knowledge Through the ages, philosophers contemplated problems of knowledge and cognition The importance of knowledge has grown all the time and now active knowledge assets become crucial This is true for all levels of society Simply to function in the contemporary society, any individual needs some basic knowledge Many organizations feel obliged to run their business based on efficient knowledge management just to keep up More and more people and organizations are coming to the understanding that the optimal generation, acquisition, and application of knowledge is the key to success Although the role of knowledge in the economy is not new, in recent years, knowledge has gained increased importance, both September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes quantitatively and qualitatively, due to the development and utilization of information processing and communication technologies (Foray, 2004) The main roles of knowledge are (Tuomi, 1999): a resource, a product, and a restriction Indeed, knowledge is clearly the primary resource in the technologically advanced industries, such as the computer, communication and software industries, and other knowledge-intensive industries, such as pharmaceuticals, but it is fast becoming the primary source of wealth in more traditional sectors of the economy as well (Stata, 1989) It is also estimated that knowledge now accounts for approximately three-fourths of the value increase in the manufacturing sector (Stewart, 1997) At the same time, in contrast to many other resources, people can produce knowledge, which now plays the role of a product As a result, importance of knowledge production and creation grows very fast Governments and other organizations invest more and more into knowledge production Knowledge has become an intellectual property, attached to a name or group of names and certified by copyright, or some other form of social recognition, e.g., publication or awarding prizes (Granstrand, 1999) As an economical commodity, knowledge and knowledge production are paid for in the research, communication, and educational areas As the result, knowledge has moved to the social overhead investment of society in the form presented in books, articles, patents or computer programs, written down, printed or recorded at some point for transmission and utilization (Bell, 1973) Our civilization is based on knowledge and information processing In contemporary knowledge-driven economy, organizations ultimately gain their value from intellectual and knowledge-based assets rather than material commodities That is why it is so important to know properties of knowledge and how to work with it For instance, the principal problem for computer science as well as for computer technology is to process not only data but also knowledge Knowledge processing and management make problem solving much more efficient and are crucial (if not vital) for big companies and institutions (Ueno, 1987; Osuga, 1989; Dalkir, 2005) To achieve this goal, it is necessary to make a distinction between knowledge and page September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 5 knowledge representation to know regularities of knowledge structure, functioning and representation, and to develop software (and in some cases, hardware) that is based on theses regularities Many intelligent systems search knowledge spaces, which are explicitly or implicitly predefined by the choice of knowledge representation In effect, the knowledge representation serves as a strong bias People increasingly rely on AI processing systems, which in turn, depend on their software, while information is processed in the search of knowledge Sophisticated safety-critical software is embedded in a diversity of systems across most industry sectors, ranging from automotive and aerospace to energy and maritime (Kandel and Dick, 2005) This situation once more demonstrates importance of knowledge because software is a form of operational knowledge representation At the same time, the National Institute of Standards and Technology (NIST) reported that low quality software costs the U.S economy almost $60 billion per year (Tassey, 2002; Thibodeau, 2002) Besides, only one quarter of software projects are judged a success (Standish Group) Software defects are accepted as inevitable by both the software industry and the long-suffering user community In any other engineering discipline, this defect rate would be unacceptable Moreover, when safety and security are at stake, the extent of current software vulnerability also becomes unsustainable (Croxford and Chapman, 2005) Therefore, validation of operational knowledge in the form of software has become an urgent task for contemporary society In our time, importance of knowledge has grown very fast with the advancement of society Thus, in the 20th century, with the advent of computers, knowledge has become a concern of science As a result, now knowledge is studied in such areas as AI, computer science, dataand knowledge bases, global networks (e.g., the Internet), information science, knowledge engineering, and knowledge management Philosophers also continue their studies of knowledge (Chisholm, 1989) However, knowledge is not an easy concept to understand As Land et al (2007) write, knowledge is understood to be a slippery September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes concept, which has many definitions This is apparent in the many questions philosophers and other thinkers ask themselves about the essence, distinctive characteristics, functions and roles of knowledge in society These questions can vary from theoretical considerations to practical applications For instance, relations between knowledge and information are blurred in contemporary society Some comprehend knowledge as a kind of information (cf., for example, (Osuga and Saeki, 1990; Davenport, 1997; Probst et al., 1999; Gundry, 2001; Stenmark, 2002; Dalkir, 2005)), while others claim that information is a kind of knowledge (cf., for example, (Kogut and Zander, 1992; Tuomi, 1999)) In addition, there are opinions that information and knowledge are essentially different essences (cf., for example, (Davenport and Prusak, 1998; Lenski, 2004; Burgin, 2010)) All basic questions about knowledge are related to the way in which we organize and direct the development and application of knowledge on different levels — from individuals through companies and organizations through the whole society For instance, in many organizations, knowledge management has come to occupy a central place in their functioning It is a role that makes great demands on an organization’s strategic insight, problem solving ability, and successful development As Kalfoglou et al (2004) write, managing knowledge is a difficult and tricky enterprise A wide variety of technologies have to be invoked in providing support for knowledge requirements, ranging from the acquisition, modeling, maintenance, transmission, dissemination, retrieval, reuse, and publishing of knowledge Knowledge is a valuable asset and resource So, any toolset capable of providing support for operating with knowledge would be valuable as its effects can percolate down to all the application domains structured around the domain representation To reflect importance of knowledge, the term knowledge society was coined as a description of the contemporary society by its pivotal characteristic Some researchers suggest that knowledge society is the next stage of the information society In essence, every society has its own knowledge assets However, in our times, knowledge page September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 7 together with information is becoming the key tool not only for further development but also for present survival in conditions of the knowledge economy To describe the role of knowledge in contemporary society, Fritz Machlup (1902–1983) introduced the concept knowledge economy in the book (Machlup, 1962) The knowledge economy is a particular knowledge-driven stage of economical development, based on knowledge, succeeding a phase based on physical assets such as workforce, energy, and matter Knowledge is in the process of taking the place of the workforce and other resources making possible getting better results with less workforce and other resources Knowledge is substance and money substitutable, meaning that knowledge can replace, to some extent, capital, labor, or physical materials Namely, knowledge allows one to use less money, labor, or physical materials than it is possible to without this knowledge As a result, the created wealth is measured less by the output of work itself but more and more by the general level of scientific and technological development (Jaffe and Trajtenberg, 2002) Amidon explained that knowledge about how to produce different products and provide services as well as their embedded knowledge is often more valuable than the products and services themselves or the materials they contain (Amidon, 1997) That is why Machlup (1962) defined knowledge as a commodity, developing techniques for measuring the magnitude of its production and distribution within a modern economy He correctly assumed that all devices involved in knowledge production, dissemination, and utilization have to be taken into account in these measurements A diversity of activities linked to research, education, and services, tend to assume increasing importance in the knowledge economy Besides, the importance of knowledge in economic activity is not confined to the high-tech sectors but also pervades modes of organization of production and commerce in apparently low-tech sectors, which have also been essentially transformed Toffler explains that knowledge is a wealth and force multiplier, in that it augments what is available or reduces the amount of resources needed to achieve a September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes given purpose (Toffler, 1990) Stewart calls knowledge the intellectual capital (Stewart, 2002) Many researchers, economists, authors, governments, policymakers, international organizations, and think tanks declare that people now live in a knowledge-based economy as knowledge is the basis for various decisions in different areas, as well as a priceless asset to individuals and organizations Moreover, few concepts introduced by economists have been more successful than that of a knowledgebased economy reflecting a qualitative transition in economic conditions (Foray and Lundvall, 1996; Leydesdorff, 2006a) To represent and study this new situation, the economical triple helix of university–industry–government relations was introduced (Etzkowitz and Leydesdorff, 1995; 1997; 1998; Leydesdorff, 2006; 2006a) Governance is treated as the force that instantiates and organizes systems in the socio-geographical dimension of the model Industry is the main mover of material production and exchange, while academe plays the leading role in the organization of the knowledge production function As a result, knowledge production and exchange becomes an economy in itself (Foray, 2004) and the development of a knowledge base turns out to be essentially dependent on the condition that knowledge production is socially organized and regulated Naturally, the global economy now places much greater value on knowledge production and dissemination activities such as design with an emphasis on Research and Development including patenting, on education and on information effort such as marketing, networking, computation, and communication Information is a source for knowledge, while knowledge is a base for producing and retrieving information Naturally, importance of knowledge grows very rapidly as society becomes more and more advanced As a result, in the 20th century, with the advent of computers, knowledge has become a concern of science and now knowledge is studied in such areas as AI, computer science, data and knowledge bases, global networks (e.g., Internet), information science, knowledge engineering, and knowledge page September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 9 management Philosophers also continue their studies of knowledge (Chisholm, 1989) 1.2 A brief history of knowledge studies Some people drink deeply from the fountain of knowledge Others just gargle Grant M Bright Knowledge has been always important in society That is why the best minds have been concerned with the problem of knowledge from ancient times Studies of knowledge formed one of the pivotal philosophical disciplines, which is called epistemology from Greek words episteme, which means knowledge, and logos, which means cognition, study or reason In other words, epistemology is the philosophical theory of knowledge and cognition In this section, we give a very brief exposition of the epistemological research presenting approaches of some leading philosophers in the history of the human civilization and starting with the most ancient explorations and ideas In Upanishad, which is one of the principal classical texts in Indian culture written from the end of the second millennium B.C.E to the middle of the second millennium C.E., two kinds of knowledge, higher knowledge and lower knowledge, were discerned Later Nyaya school of Hindu philosophy considered four types of knowledge acquisition: perception when senses make contact with an object, inference, analogy, and verbal testimony of reliable persons Inference was used in three forms: a priory inference, a posteriory inference, and inference by common sense In general, theory of knowledge has a long-standing tradition in Indian philosophy with many achievements and interesting insights Let us get some glimpses on this big knowledge field developed in ancient India In his book “Theories of knowledge”, Rao presents eight directions in the philosophical and methodological studies of knowledge in India September 27, 2016 19:40 10 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes (Rao, 1998): — — — — — — — — Samkhya (Yoga) theory of knowledge Vedantins’ theories of knowledge Visistadvaita theory of knowledge Madhva theory of knowledge Mimansaka theories of knowledge Jaina theory of knowledge Buddhist theories of knowledge Logician’s (Nyaya) theory of knowledge The Samkhya (Yoga) theory of knowledge Samkhya, also Sankhya, S¯ am ankhya, ˙ is one of the most khya, or S¯ prominent and one of the oldest directions in Indian philosophy It belongs to the six basic schools of the classical Indian philosophy Bhagavad Gita identifies Samkhya with understanding of knowledge The word Samkhya is based upon the Sanskrit word samkhya which means ‘number’ or ‘perfect knowledge’ An eminent, great sage Kapila (between 8th and 6th B.C.E.) was the founder of the Samkhya philosophy Samkhya may be characterized as a dualistic realism It is dualistic because it advocates two ultimate realities: Prakriti, matter and Purusha, self, spirit or consciousness At the same time, Samkhya is a kind of realism as it considers that both matter and spirit are equally real In addition, Samkhya is pluralistic because it is teaching that Purusha is not one but many Samkhya has a developed theory of knowledge discerning three sources of valid knowledge: perception, inference based on Sankhya syllogism and valid testimony The procedure of knowledge acquisition starts when the sense-organs come in contact with an object causing sensations and impressions to come to the manas (mind) The manas processes these impressions into proper forms and converts them into definite percepts These percepts are carried to the Mahat (intellect) inducing changes in Mahat, and Mahat takes the form of the object, from which these sensations come This transformation page 10 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 11 11 of Mahat is known as vritti or modification of buddhi As Mahat is a physical entity, the process of knowledge formation is not complete Thus, the consciousness of the Purusha (self) transforms Mahat producing in it consciousness of the form of the object, from which these sensations come To better explain this, the following analogy is used A mirror cannot produce an image by itself It needs light to reflect and produce the image and thereby reveal the object In a similar way, Mahat needs the “light” of the consciousness of the Purusha to produce knowledge Besides, Samkhya discerns two types of perceptions: indeterminate (nirvikalpa) perceptions and determinate (savikalpa) perceptions Indeterminate perceptions are like pure sensations or crude impressions containing no knowledge of the form or the name of the object There is only vague awareness about an object Determinate perceptions are the mature form of perceptions obtained from sensations, which have been processed, categorized and interpreted properly In turn, determinate perceptions generate knowledge by inference based on analogy Samkhya is related to Yoga, which is a specific religious system within Hinduism emerging from the older Samkhya system The theoretical part of Yoga, i.e., its philosophy, was derived almost entirely from Samkhya The Vedanta Theory of knowledge Vedanta is one the most prominent and philosophically advanced six basic schools of the classical Indian philosophy According to Balasubramanian (2000), the Vedantic philosophy is as old as the Vedas, since the basic ideas of the Vedanta systems are derived from the Vedas during the Vedic period (1500–600 B.C.E.) The term veda means “knowledge” and the term anta means “end” Thus, Vedanta means complete knowledge of the Veda Originally, Vedanta denoted the Upanishads, a collection of foundational texts in Hinduism considered as the final layer of the Vedic canon By the 8th century, the meaning of Vedanta changed for standing for all philosophical September 27, 2016 12 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes traditions concerned with interpreting the three basic texts of Hinduist philosophy, namely, the Upanishads, the Brahma Sutras, and the Bhagavad Gita There are at least 10 schools of Vedanta as the system of philosophy that further develops the implications in the Upanishads that all reality is a single principle, Brahman, teaching that the believer’s goal is to transcend the limitations of self-identity and achieve unity with Brahman According to the Vedanta Theory of knowledge, Brahman is selfindulgent and knowledge is not different from Brahman Therefore, knowledge is eternal and without beginning However, ignorance also exists until it is destroyed by knowledge Although knowledge is without beginning, the state of knowing is produced by mental modification (Vrtti) of the internal organ (Abhivyanjaka) The Vrtti is four-fold consisting of doubt, definite knowledge, egoism, and recollection Knowledge is produced with the help of two causes, the material cause (Upadana) and the efficient cause (Nimitta) The Vedanta Theory discerned two types of knowledge: the mediate knowledge (Paroksa) and the immediate knowledge (Aparoksa) An example of mediate knowledge is the statement “Brahman is”, while an example of immediate knowledge is the statement “I am Brahman is” (cf., (Rao, 1998)) Here is another example The statement “I see fire” is immediate knowledge, while “I see smoke, so there is fire” is mediate knowledge It might be interesting to compare this knowledge classification with a similar classification of Kant who considered knowledge of two kinds: intuitions as immediate knowledge and concepts as mediate knowledge The Visistadvaita theory of knowledge Visistadvaita is a philosophy of religion, in which the central idea is integration and harmonization of all knowledge, while knowledge, jnaana, is obtained through sense perception, inference, and revelation According to the Upanisads, knowledge comes from Brahman as “he who knows the Brahman attains the highest” This asserts unity page 12 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 13 13 of the threefold system of Vedantic wisdom known as tattva, hita, and purusartha Answering the basic question of epistemology about the origin and possibility of knowledge, Visistadvaita affirms possibility of getting knowledge about reality stating that people can know things as they are Knowledge essentially presupposes a knowing self and an object of thought and is obtained in the process of ascent from the corresponding sensation to the self Namely, this process starts with sensations, which form the raw material of knowledge and become percepts by action of the “a priori” form prescribed by the mind The perceived objects are conceived and arranged by the synthetic mind or understanding which brings together the perceived objects producing judgments Then reason unifies these judgments and forming conception in the self as the synthetic unity of knowledge This shows that knowledge is not a plain synthetic construction, but originates in a process by which things are revealed The objects in nature exist by themselves and are not created by thought, which only reveals them Thus, knowledge is the self-revelation of a real object as a holistic system, while the object is not the copy of the idea, nor is the idea the archetype of the object, neither is deduced from the other The Visistadvaita theory of knowledge assumes the integrity of experience on all its levels and forms, which constitute pratyaksa (perception), anumana (inference), and sastra (scripture) As a result, Visistadvaita is a dualistic philosophy assuming independent existence of the perceiving self, and of the external world that is perceived The Madhva theory of knowledge The Dvaita or “dualist” school of Hindu Vedanta philosophy originated by Sri Madhvacarya, or Madhva (ca 1238–1317), who considered himself an avatara of the wind-god Vayu and taught the fundamental difference between the individual self or Atman and the ultimate reality, Brahman Thus, according to Madhva, there are three orders of reality: (1) the independent ultimate reality, Brahman; September 27, 2016 14 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes and the dependent reality, paratantra, which consists of (2) souls (jivas), and (3) lifeless objects (jada) Madhva’s pluralistic ontology is founded on his realistic epistemology He argues that God and the human soul are separate because our daily experience of separateness from God and of plurality in general is given to people as an undeniable fact, fundamental to our knowledge of all things Madhva considered two means of valid knowledge (Pramana): valid knowledge itself (Kevala Pramana), and the instrument of knowledge (Anupramana) In turn, Anupramana consists of three sources of knowledge: sense perception (Pratyaksha), inference (Anum¯ ana), and testimony of Vedic literature (Aagama) (Sharma, 1994) Further, existence of invalid knowledge acquired by sense perception demands permanent questioning of the knowledge content The Mimansaka theories of knowledge M¯ım¯ am a is a Sanskrit word meaning “revered thought” It is also the s¯ name of one of the six astika (orthodox) schools of Hindu philosophy based on the Vedas Its core tenets are ritualism, anti-asceticism, and anti-mysticism The central aim of the school is explanation of the nature of dharma to maintain the harmony of the universe and provide the personal well-being of the person who follows ritual obligations and prerogatives The Mimamsa school traces the source of the knowledge of dharma neither to sense-experience nor inference, but to verbal cognition (knowledge of words and meanings) In order to understand the correct dharma for specific situations, it is necessary to rely on examples of explicit or implicit commands in the Vedic texts An implicit command must be understood by studying parallels in other, similar passages If one text does not provide details for how a priest should proceed with a particular action, the details must be sought in other, related Vedic texts This preoccupation with precision and accuracy required meticulous examination of the structures of sentences conveying commands, and led to an extensive exegesis of the Vedas and a detailed analysis of semantics page 14 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 15 15 The Mimamsa made notable contributions to Indian thought in the fields of logic and epistemology The Mimamsa doctrine of knowledge affirms that the world is real Mimamsa introduced two additional means of valid knowledge in addition to the four traditional means of perception, inference, comparison and testimony, recognized by other schools of Hinduism They are arthapatti (pre-conception or postulation) and abhava (absence, negation, nonexistence) Mimamsa advanced the unique epistemological theory that all cognition is valid All knowledge is true, until it is superseded by further cognition What is to be proved is not the truth of a cognition, but its falsity Mimamsakas drew on this theory of validity to establish the unchallengeable validity of the Vedas The Jaina theory of knowledge The concept of soul is central in philosophy Knowledge (Jnana) according to Jainas, is the soul’s intrinsic, inherent, inseparable, and inalienable attribute, without which no soul can exist Knowledge plays an important part in the conception of soul and its emancipation As a result, Jain epistemology or Jain theory of knowledge thus becomes vital in Jaina philosophy including the theory of knowledge along with various topics such as psychology, teaching about feelings, emotions, and passions, theory of causation, logic, philosophy of non-absolutism, and the conditional mode of predication (Shah, 1990) Consciousness (Cetana), according to Jainas, is the power of the soul knowledge and operates through understanding (Upyoga) It gets experience in three ways: (1) some experience is the fruit of karma; (2) other experience comes from activity of the soul; and (3) one more kind of experience is knowledge itself (Shah, 1990) According to Jaina thinkers, Cetana (consciousness) culminates in pure and perfect knowledge and knowledge itself has grades and modes In turn, understanding (Upyoga) is divided into two: sensation (Darsana) and Cognition (Jnana) Uma Svati says: “Understanding is the distinguishing characteristic of the soul It is of two sets — Jnana and September 27, 2016 16 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes Darsana The first is of eight kinds and the second, of four” (Shah, 1990) Namely, sensation (Darsana) is of four kinds: • • • • Visual (Cakshusa) Non-visual (Acakshusa) Clairvoyant (Avadhi Dersana) Pure (Kevala) Each piece of knowledge is experienced with reference to its characteristic (Dharma) and its substratum (Dharmin) In addition, Jainas discerned two kinds of knowledge: direct knowledge and indirect knowledge Direct knowledge does not demand the medium of another knowledge in contrast to indirect knowledge According to Jainas, it is possible to obtain indirect knowledge by five techniques: recollection, recognition, Reductio ad Absurdum (Tarka), inference, and syllogism The Buddhist theories of knowledge Being a strict empiricist, Siddhartha Gautama Sakyamuni (the “Buddha” or “awakened one”) believed that people can have knowledge of only those things that can be directly experienced It is impossible to achieve ultimate knowledge until the follies and weakness of human life bring one to despair That is why Buddha famously refused to answer ultimate questions such as “Does the world have a beginning or not?”, “Does God exist?”, and “Does the soul perish after death or not?” Later, Buddhists developed a technique of denying all the logically alternative answers to such questions For instance, the answer to the first question has to be: “No, the world does not have a beginning, it does not fail to have a beginning, it does not have and not have a beginning, nor does it neither have nor not have a beginning” Knowledge in the Buddhist understanding is of prime importance to people One of the principles of Buddhist philosophy instructs that the pleasure of advancing knowledge becomes a duty Theory of knowledge in Buddhism is not treated as relative but is presumed to be perfectly true and absolute page 16 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 17 17 With respect to their ontological assumptions, Buddhist religious directions are separated into four classes (Rao, 1998): — Madhyamika presupposes that the entire world is void, everything is fleeting and all activity goes in the dream state — Yogasaras hold that there are no external objects in the world asserting that the object cognized and the cognizing person are the same — Sautrantikas admit existence of the objective world, which cannot be perceived by senses but it is only inferred — Vaibhastika admits existence of the objective world but rejects existence of objects of inference claiming that only indeterminate knowledge is valid As reasoning is an important procedure in knowledge acquisition, three features of reason are explicated and utilized: — Existence only in the subject (Paksa) — Existence in the homologue (Sapaksa) — Non-existence only in the heterologue (Vipaksa) In addition, reason in the Buddhist theory of knowledge has three types: — Non-cognition (Anupalabdhi) — Cause in itself (Svabhava) — Effect (Karya) Besides, the Buddhist theory of knowledge uses four forms of predication: S is P , e.g., “a square is a rectangle” or “there is a world of ideas” S is not P , e.g., “a square is not a circle” or “there is no world of ideas” S is and is not P , e.g., “a ball that is partially green and partially yellow is green and is not green” or “there is and is no world of ideas” September 27, 2016 18 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes S neither is nor is not P , e.g., “a ball neither is green nor it is not green” or “the world of ideas neither is real nor it is not real” The Buddhists assume that at least one of these alternatives is always true in any meaningful situation and use this assumption for logical classification However, when the question is considered meaningless, all four alternatives are rejected At the same time when the answer is ‘yes’ to each of the alternatives, it was treated as misleading and all four alternatives are also excluded The Logician’s (Nyaya) theory of knowledge In the Logician’s theory of knowledge, knowledge (Buddhi or J˜ n¯ ana) is a special property of the soul, while mind (Manas) is a separate substance (Rao, 1998) Knowledge is obtained by experience (Anubhava) and recollection (Smrti) In turn, experience gives (is) twofold — valid knowledge (Yatharthanubhava or Prama) and invalid knowledge (Ayatharthanubhava or Bhrama) There are four ways for getting valid knowledge (Yatharthanubhava or Prama): — — — — Perception gives perceptual knowledge (Pratyksa) Inference (Anumana) gives inferential knowledge (Anumiti) Analogy (Upamana) gives analogical knowledge (Upamiti) Utilization of language (verbal testimony) gives verbal knowledge (Sabda) According to Gautama, there are four factors involved in direct perception (Pratyksa): — — — — the the the the senses (indriyas) sensual objects (artha) contact of the senses and the objects (sannikarsa) cognition produced by this contact (jnana) In addition, the Nyaya believed that the five sense organs — eye, ear, nose, tongue, and skin — have the five elements — light, ether, earth, water, and air — as their field, with corresponding qualities of color, sound, smell, taste, and touch page 18 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Introduction page 19 19 According to logicians, there are also three ways for getting invalid knowledge (Ayatharthanubhava or Bhrama): — Doubt gives (is) uncertain knowledge (Samsaya) — Wrong reasoning gives invalid knowledge (Viparyaya) — Reductio ad absurdum gives (is) invalid knowledge (Tarka) Tarka includes: — — — — — Faults of self-dependence (Atmasraya) Faults of mutual dependence (Anyonyasraya) Faults of dependence on a cycle (Cakrakasraya) Faults of infinite regress (Anavastha) Statements of undesirable effects (Anistaprasanga) Inference (Anumana) is knowledge from the perceived about the unperceived and this relation may be of three sorts: — the inferred constituent may be the cause of the element perceived — the inferred constituent may be the effect of the element perceived — both may be the joint effects of something else In addition, inference (and the results of inference) has two types: — Inference for one’s own sake (Svartha) — Inference for another’s own sake (Parartha) Verbal testimony (and its results) has two types: — Scriptural testimony (Vaidika) — Non-scriptural testimony (Laukika) Perception (and the results of perception) has two types: — Determinate perception (Nirvikalpaka) — Indeterminate perception (Savikalpaka) September 27, 2016 20 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes In addition, there three kinds of transcendental perception (Alaukika): — Perception in the Samanyalak¸sana supernormal contact — Perception in the Jnanalak¸sana supernormal contact — Perception in the Yogaja (Lak¸sana) supernormal contact In the process of cognition, mind (Manas) mediates between the self and the senses When the mind is in contact with one sense organ, it cannot be so with another It is therefore said to be atomic in dimension The Nyaya assumed that due to the nature of the mind that experiences of people are discrete and linear, although quick succession of impressions may give the appearance of simultaneity It is possible to read more about Indian theories of knowledge in the book (Rao, 1998) In other countries, philosophers also paid considerable attention to the problems of knowledge and cognition In China, Confucius (551–479 B.C.E.) thoroughly considered knowledge and its sources He discerned two kinds of knowledge: one was innate, while the other came from learning According to him, knowledge consisted of two components: knowledge of facts (statics) and skills of reasoning (dynamics) The contemporary methodology of science classifies the first type as a part of the logic-linguistic subsystem, which contains declarative knowledge, while the second type is a part of the procedural subsystem of a developed knowledge system, which contains procedural knowledge (Burgin and Kuznetsov, 1994) For Confucius, to know was to know people He was not interested in knowledge about nature, studied by modern science The philosophy of Confucius had the main impact on Chinese society for many centuries Besides, Chinese philosophers paid much attention to names as carriers (bearers) of knowledge reflecting intrinsic aspects of reality In this respect, Confucius writing about names and their rectification, asserted (Confucius, 1979): “If names be not correct, language is not in accordance with the truth of things If language be not in accordance with the truth of things, affairs cannot be carried on to success page 20 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Introduction page 21 21 When affairs cannot be carried on to success, proprieties and music not flourish When proprieties and music not flourish, punishments will not be properly awarded When punishments are not properly awarded, the people not know how to move hand or foot” One of the basic aims of name rectification was to create a consistent knowledge representation in language that would allow each word to have a consistent and universal meaning, providing accurate knowledge of things and actions, while avoiding confusion of multiple Ways (Dao) Later Xun Zi, also called Hsă un Tzu, (ca 312–230 B.C.E.) continued exploration of names as knowledge representations Xun Zi wrote a tract on the rectification of names, arguing for the rectification of names so, that a ruler could adequately control his people in accordance with Dao (the Way), without being misunderstood Indeed, when misapprehension became easy, then Dao would not effectively be put into action Xun Zi explained (cf., (Watson, 2003)): “When the ruler’s accomplishments are long lasting and his undertakings are brought to completion, this is the height of a good government All of this is the result of being careful to see that men stick to the names which have been agreed upon” Necessity for rectifying names is both political and epistemological On one hand, there is a need to distinguish the higher from the lower in terms of the social rank, while on the other hand, it is necessary to discriminate the different states and qualities of things “When the distinctions between the noble and the humble are clear and similarities and differences [of things] are discriminated, there will be no danger of ideas being misunderstood and work encountering difficulties or being neglected” (cf., (Ding, 2008)) Besides, explaining that understanding right and wrong causes morality to be more unbiased, Xun Zi argued that without universally accepted interpretations of names, knowledge of right and wrong would become hazy According to Xun Zi, the ancient knowledgeable kings chose names that gave correct knowledge of actualities, but later generations confused terminology, coined new names, and thus could no longer differentiate right from wrong September 27, 2016 22 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes Xun Zi assumed that utilization of senses through seeing, hearing, smelling, tasting, and touching is the key source for getting knowledge of distinctions between things and thus, allowing people to give names based on the sameness or difference between various things Consequently, this was the way of producing true knowledge of the world, i.e., true knowledge was achieved through naming Xun Zi also wrote about “things which share the same form but occupy different places, and things which have different forms but occupy the same place” The former, e.g., two identical flutes, should be distinguished as two separate things, although they have the same form and other properties, because they occupy different places At the same time, as one of these identical things, e.g., flutes, is used and becomes damaged or broken over time, it appears to change into something else But even though it seems to become something different, it is still the same things, e.g., flute, and should be regarded as such Another representative of the School of Names Gongsun Long (ca 325–250 B.C.E.) asserted in his work “On Names and Actualities” that because all things in the world come into sight in particular shapes and substances, they are given different names To know if the meaning of a word correctly corresponds to the essence of the thing named by it or not, it is necessary to know the conditions which give rise to it Gongsun Long writes (cf., (Ding, 2008)): “A name is to designate an actuality If we know that this is not this and know that this is not here, we shall not call it [‘this’] If we know that is not that and know that is not there, we shall not call it [‘there’]” In ancient Greece, Plato (427–347 B.C.E.) performed even more profound analysis of the problem of knowledge For instance, in one of Plato dialogues, Theætetus, Socrates and Theaetetus discuss the nature of knowledge and Socrates asks the question that permanently puzzles him: “What is knowledge?” To answer this question, three approaches are suggested At first, the conjecture “knowledge and perception are the same” is proposed Socrates refutes this idea by explaining that it is possible to perceive without knowing and it is possible to know without perceiving For page 22 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 23 23 instance, it is possible to see a text in a foreign language without us knowing it The second hypothesis is that true belief is knowledge Socrates invalidates this idea by giving the following example When a jury believes a defendant is guilty by listening to the prosecutor instead of looking at solid evidence, it cannot be said that jurors know that the accused is guilty even if, in fact, he is The third proposition is that true belief with a rational validation is knowledge However, Socrates also challenges this approach because all interpretations of this definition look inadequate Thus, Socrates demonstrates that all three definitions of knowledge: knowledge as nothing but perception, knowledge as true judgment, and, finally, knowledge as a true judgment with justification, are unsatisfactory In spite of this, according to Cornford (2003), in many of his works, e.g., Meno, Phaedo, Phaedo, Symposium, Republic, and Timaeus, Plato treated knowledge as a justified true belief, and this approach prevailed becoming a stable tradition in philosophy Much later Bertrand Russell in (Russell, 1912; 1948), Edmund Gettier in (Gettier, 1963), Elliot Sober in (Sober, 1991) and some other thinkers gave persuasive examples demonstrating that the definition of knowledge as a justified true belief is not adequate Let us consider an example demonstrating deficiencies of this definition (Russell, 1912; 1948; Scheffler, 1965) A woman looks at a clock at p.m The clock shows p.m So, the woman thinks that it is p.m Thus, she has a belief, which is true and justified by observation of the clock Now suppose that the clock is not going though the woman thinks it is Thus, it seems wrong to hold that she knows that it is p.m Plato was also interested in the problem of knowledge acquisition His idea was that people learn in this life by remembering knowledge originally acquired in a previous life In essence, the soul has all knowledge and knowledge acquisition is recollection of what the soul already knows Plato conceived it is possible to achieve correct knowledge only through the knowledge of the forms, or ideas (eidos), because what September 27, 2016 24 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes came through our senses is not knowledge of the thing itself but only knowledge of the imperfect changing copy of the form Thus, the only possible way to acquire correct knowledge of the forms was through reasoning as senses could provide only opinion For a long time, philosophers were not able to clearly and consistently explain what Plato forms, or ideas (eidos), are Only at the end of the 20th century, it was discovered that the concept structure provides the scientific representation of Plato forms, while the existence of the world of structures was postulated and proved (Burgin, 1997; 2010; 2012) Another great philosopher Aristotle (384–322 B.C.E.) studied problems of knowledge categorizing knowledge with respect to knowledge domains (objects) and the relative certainty with which one could know those domains (objects) He assumed that certain domains (such as in mathematics or logic) permit one to have absolute knowledge that is true all the time However, his examples of absolute knowledge, such as two plus two is always equal to four or all swans are white, failed when new discoveries were made For instance, the statement two plus two always equals four was disproved when non-Diophantine arithmetics were discovered (Burgin, 1977; 1997c; 2007; 2010c) The statement “all swans are white” was invalidated when Europeans came to Australia and found black swans According to Aristotle, absolute knowledge, e.g., mathematical knowledge, is characterized by certainty and precise explanations However, unlike Plato and Socrates, Aristotle did not demand certainty in everything Some domains, such as human behavior, not permit precise knowledge The corresponding vague knowledge involves expectations, chances, and imprecise explanations Knowledge that falls into this category is related to ethics, psychology, or politics One cannot expect the same level of certainty in politics or ethics that one can demand in geometry or logic In his work Ethics, Aristotle defines the difference between knowledge in different areas in the following way: “we must be satisfied to indicate the truth with a rough and general sketch: when the subject and the basis of a discussion consist of matters which hold good only as a general rule, but not always, the conclusions page 24 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 page 25 25 Introduction reached must be of the same order For a well-schooled man is one who searches for that degree of precision in each kind of study which the nature of the subject at hand admits: it is obviously just as foolish to accept arguments of probability from a mathematician as to demand strict demonstrations from an orator” (Aristotle, 1984) Aristotle was deeply interested in how people got knowledge He identified three sources of knowledge: sensation as the passive capacity for the soul to be changed through the contact of the associated body with external objects, thought as the more active process of engaging in the manipulation of forms without any contact with external objects at all, and desire as the origin of movement towards some goal Developing logic as a tool for knowledge acquisition, Aristotle constructed rules of logical inference The basic rule is called syllogism It has the following form All A are B C is A Therefore, C is B Here is the famous example of a syllogism: All men are mortal Socrates is a man Therefore, Socrates is mortal Treating syllogism as the main tool of knowledge acquisition, Aristotle conceives of knowledge as hierarchically structured by inference He puts this claim forward in the Posterior Analytics (Aristotle, 1984) To have knowledge of a fact, it is not enough simply to be able to repeat the fact, while in many cases, for example, in history, it is impossible to repeat the fact Thus, to have knowledge, it is also necessary to be able to give the reasons why that fact is true Aristotle calls this process demonstration, which is essentially a matter of showing that the fact in question is the conclusion to a valid syllogism Thus, knowledge that is premises for obtaining other knowledge is logically prior to the knowledge that follows from it Eventually, September 27, 2016 26 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes there must be one or several “first principles”, from which all other knowledge follows and which themselves not follow from anything However, if these first principles not follow from anything, then by Aristotle, they cannot count as knowledge because there are no reasons or premises we can give to prove that they are true Aristotle suggests that these first principles are a kind of intuition of the facts and ideas we recognize in experience Aristotle believes that knowledge domains or objects are structured hierarchically Consequently, he treats definition as a process of division and specification For instance, defining whale, we observe that whales are animals, which is the genus to which they belong Then we search for various conditions, which distinguish whales from other animals such as: whales live in water, unlike tigers, and they are very big, unlike mice While true knowledge is derived from knowledge of first principles, actual argument and debate is much less immaculate When two people argue, they not go back to first principles to ground every claim but simply suggest premises they both acquiesce The essence of the debates is to find premises your opponent can agree with and then show that conclusions different from your opponent’s position to follow necessarily from these premises In the Topics, Aristotle classifies the kinds of conclusions that can be drawn from different kinds of premises, while in the Sophistical Refutations, he explores various logical ploys used to trick people into accepting a faulty line of reasoning Thus, we can see that Aristotle strives to organize knowledge in the manner of a well-structured, architectural construction with a firm foundation of unshakable first principles and an upper structure of propositions firmly attached to the foundation by steadfast inference In such a way, the Euclid’s geometry and virtually any axiomatic mathematical system is built It has a foundation of definitions, postulates, and axioms or common notions as first principles and an upper structure of deduced propositions — theorems and lemmas In the first millennium, the distinguished philosopher Abă u Naásr al-Farabi (870950) also studied knowledge and its sources He page 26 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 27 27 defined the highest level of knowledge as theoretical or genuine knowledge, which is the excellence of the theoretical part of the soul and comes from (or is) science (‘ilm) As al-Farabi wrote, for genuine knowledge, certainty is achieved within the soul For the entities that not depend on human production, their existence and determination of what each one of them is and how it is can be accomplished by demonstration of true, necessary, universal and primary premises, securely grasped and naturally known by reasons (Fusul, p 51) As a result, genuine knowledge is indispensable, unchangeable, and universal The highest type of this theoretical knowledge, for al-Farabi, is wisdom (hikmah), which is the knowledge of the ultimate causes of all existing entities (metaphysics) as well as the proximate causes of everything caused (physics) According to al-Farabi, certain knowledge is threefold: — certain knowledge that the thing exists, which is called the knowledge of existence; — certain knowledge of the cause of the thing, which is called knowledge why; — the certain knowledge of the both together The syllogisms used in attaining this threefold epistemic certainty are also three: — syllogisms used to prove only existence of the thing; — syllogisms used to prove only its cause; — syllogisms used to prove the two together Later many outstanding philosophers, such as Thomas Aquinas (1224–1274), Ren´e Descartes (1596–1650), Baruch Spinoza (1632 – 1677), John Locke (1634–1704), George Berkeley (1685–1753), David Hume (1711–1776), Immanuel Kant (1724–1804), Georg Wilhelm Friedrich Hegel (1770–1831), Bertrand Russell (1872–1970), Ludwig Josef Johann Wittgenstein (1889–1951), Michael Polanyi (1891– 1976) and Karl Raimund Popper (1902–1993) studied problems of knowledge September 27, 2016 28 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes The great medieval philosopher Thomas Aquinas assumed that all knowledge of people comes from sense perception writing: “ it is natural to man to attain to intellectual truths through sensible objects, because all of our knowledge originates from the sense.” In its turn, sense perception comes from the actual things themselves, while the human mind does not have inborn ideas At the same time, people possess a natural ability to abstract knowledge When people see an object such as a tree, the actual tree is what the person observes and perceives its reflection by senses The mind knows that what it is seeing corresponds to reality and as a result, an individual attains knowledge about the tree The form of the real object, e.g., a tree, is not generated by the senses, or the mind of the perceiver, but is impressed by the object itself All external knowledge obtained through sense is combined by the common sense, which causes the unifying process of the senses into a single perception, which is then presented to the mind The mind forms a representation sent to the intellect, which generates the universal idea from it by abstraction and names it by a word The great French philosopher Rene Descartes evaluates knowledge in terms of doubt and certainty, distinguishing certain rigorous knowledge (scientia) and knowledge with lesser grades of certainty (persuasio) Descartes posits that doubt and certainty are complementary feelings — when certainty increases, doubt decreases, and vice versa Consequently, according to Descartes, knowledge is conviction based on a reason so strong that it could never be shaken by any stronger reason As a result, knowledge becomes absolute and utterly indefeasible Descartes writes: “ we reject all such merely probable knowledge and make it a rule to trust only what is completely known and incapable of being doubted” (Descartes, 1984) That is why Cartesian methodology of cognition starts with assessing convictions or beliefs by doubting and reasoning in the process of discovering innate truths and obtaining knowledge This page 28 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Introduction page 29 29 method demands not merely to apply doubt to all candidates for knowledge, but to apply doubt collectively to these candidates and describes this process in the following way (Descartes, 1984): “ those who have never philosophized correctly have various opinions in their minds which they have begun to store up since childhood, and which they therefore have reason to believe may in many cases be false They then attempt to separate the false beliefs from the others, so as to prevent their contaminating the rest and making the whole lot uncertain Now the best way they can accomplish this is to reject all their beliefs together in one go, as if they were all uncertain and false They can then go over each belief in turn and re-adopt only those which they recognize to be true and indubitable” Descartes promotes skeptic arguments precisely in acknowledgement that there is a definite reason for the overall doubt, while it is necessary to have valid arguments for truth recognition Note that although Descartes suggests applying doubt universally to all candidates for knowledge, he does not recommend to this with tools for founding knowledge Besides, understanding of cognitive processes by Descartes is similar to Plato’s doctrine of recollection as Descartes writes that cognition seems not so much learning something new as remembering what was known before Descartes also evokes that there are three possible options for the kind of external essences causing sensations: (1) God (2) Material/corporeal substance (3) Other created substance However, Descartes discards options (a) and (c) leaving only the second possibility for sensations The basic Descartes’ principle of doubting any knowledge claim, as well as every attempt at justification of knowledge claims gained much support in traditional epistemology It has been assumed that it is vital to find a bedrock of certain knowledge immune to all possible doubt However, this search did not bring conclusive solutions September 27, 2016 30 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes The great European philosopher Baruch Spinoza called by the name Benedito de Espinosa when he was born and later by the name Benedict de Spinoza also studied problems of knowledge elaborating the triadic typology of knowledge: ✧ The first kind of knowledge is obtained in two ways — from opinion or random experience and from imagination ✧ The second kind of knowledge arises from the intellect, which employs common notions and elaborates adequate ideas of the properties of things ✧ The third kind of knowledge comes from intuition allowing people to have adequate knowledge, and therefore, to get absolute truth about things Treating problems of knowledge, the outstanding British philosopher John Locke, at first, explains the origin of ideas that people have and the use of words to signify them He assumes, being in good agreement with Chinese philosophers, that making of the names of substances is a kind of discovery through an abstract general idea, which is named and then introduced into language By Locke, names of substances are supposed to copy the properties of the substances they refer to After this, Locke gives a simple definition of knowledge writing: “Knowledge then seems to me to be nothing but the perception of the connection and agreement, or disagreement and repugnancy of any of our Ideas In this alone it consists” (Locke, 1975) Thus, genuine knowledge occurs only when people actually are perceiving Locke also considered habitual knowledge, which is related to what was known in the past but is not perceived now Besides, he rejected innate knowledge arguing that otherwise children (and mental defectives) would be the most pure and reliable guides to logical truth Observing the development of knowledge in individual cases, it is possible to see gradual acquisition of the requisite ideas, perception of agreement or disagreement of which forms knowing, although there is self-evident knowledge page 30 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 31 31 Locke’s definition of knowledge as perception of agreement or disagreement of ideas involves two criteria for knowledge acquisition: first, it is necessary to have the requisite ideas and then to perceive the connection, i.e., agreement or disagreement, between them As a result, knowledge has to be relational in structure and propositional in form Locke recognizes four types of knowledge: — Knowledge of identity and diversity, which rests upon recognition of the difference of each idea from any other — Knowledge of relation, which reflects positive non-identical connections among ideas — Knowledge of co-existence, which is based on coincident appearance of qualities — Knowledge of real existence, which presumes some connection between an idea and the real thing it represents In addition, Locke supposes that these types of knowledge can occur in any of three forms: — Intuitive knowledge is a certain and unquestionable perception of identity and relation of any two ideas without the mediation of any other It is the clearest and the most certain of all degrees of human knowledge It accounts for self-evident truths serving as the foundation upon which all other genuine knowledge is built — Demonstrative knowledge is obtained through a series of connections between intermediate ideas by means of reasoning The standard area of demonstrative human knowledge is mathematics, where our possession of distinct ideas of particular quantities yield the requisite clarity, while disciplined reasoning helps to uncover the intermediate links that establish knowledge of identity and relation However, Locke thinks that it is possible to have demonstrative knowledge of moral relations — Sensitive knowledge provides some evidence of the existence of particular objects outside ourselves, although it is not always true that there must exist an external object corresponding September 27, 2016 32 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes to each idea of sensation Locke makes serious reservations about the reliability of our sensitive knowledge of the natural world Another outstanding British philosopher George Berkeley studied problems of knowledge in his Treatise Concerning the Principles of Human Knowledge (1710) The goal was to make an inquiry into the first principles of human knowledge for discovering what had led to doubt, uncertainty, absurdity, and contradiction in philosophy Berkeley claimed that the mind cannot conceive abstract ideas and declared that words, such as names, not signify abstract ideas To the contrary, he stressed that people could only think of particular things that had perceived Thus, names denoted general ideas, not abstract ideas General ideas represent any one of several particular ideas, while existence of an idea of a thing was actually the state of perception of a perceiver Based on this approach, Berkeley came to a conclusion that all motion is relative, which perfectly correlates with contemporary physics Human minds know ideas, not objects Ideas, which constitute knowledge, are brought forth by sensation, thought and imagination When several ideas are associated together, they are comprehended as ideas of one distinct thing, which is then signified by one name Even more, according to Berkeley, the outside world is composed only of ideas because “ideas can only resemble ideas” However, the world possesses logic and regularity given by God Berkeley challenged that even if some things exist outside the human mind, we cannot know this Indeed, knowledge through our senses only gives us knowledge of our senses but not of any of the unperceived things Knowledge through reason does not guarantee that there are, necessarily, unperceived objects while imagination, the third source of knowledge, has proved to produce mostly nonexisting (imaginary) entities For instance, in dreams, people have ideas that not correspond to external objects Another outstanding British philosopher David Hume also tried to solve the enigma of knowledge He claimed that all knowledge page 32 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 33 33 stemmed from sense experience being justified in terms of what was in peoples’ minds Thus, all knowledge consists of impressions and ideas The former are vivid and clear perceptions, while the latter are less vivid and clear copies of impressions Hume contended that it is possible to have knowledge of two kinds — the relations between ideas and matters of fact “Relations between ideas can be known with absolute certainty, and can be known by the “mere operations of thought” In his treatise, Hume cites only mathematics as an example of relations of ideas At the same time, “matters of fact” can never be known with the same degree of certainty, and cannot be known by the mere operations of thought Knowledge of matters of fact is always a posteriori and synthetic as people obtain it by using observation and employing induction and reasoning about what is probable The foundation of this knowledge is what people experience in the present or can remember from the past Knowledge that goes beyond testimony of the senses or the records of our memory rests on causal inference Discussing inference, Hume questions validity of induction arguing that our belief that the future will resemble the past is not based on reason at all Hume was especially interested in different ways used to justify that some belief we had in essence was knowledge maintaining that all knowledge comes from and must be justified by experience For instance, matters of fact are justified by probable arguments and not by deductive reasoning Immanuel Kant is one of the most influential philosophers in the history of Western thought His ideas in metaphysics, epistemology, ethics, and aesthetics have made a profound impact on almost every philosophical movement that followed his work A substantial part of Kant’s philosophy addresses the question “What can we know?” In answering this question, he discerned three parts of theoretical knowledge: — logic, which, according to Kant, gives absolute knowledge and have not changed from the time of Aristotle — arithmetic and geometry, which give the most reliable knowledge September 27, 2016 34 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes — the fundamental principles of natural sciences, which are changing with time giving relative knowledge Besides, Kant defined items of human knowledge as representations, dividing representations into two classes: — Intuitions, which are “immediate” representations — Concepts, which are “mediate” representations These representations could be pure without any relation to experience or empirical, coming from experience Pure intuitions gave perceptions of basic forms, e.g., intuitions of space and time, which turn unorganized sensations into perceptions Pure concepts give their basic forms of conceptual knowledge facilitating understanding and comprising the 12 categories described by Kant in accordance with the Aristotelian logic Being necessary for experience of physical objects, their causal behavior and structural properties, the conceptual categories cannot be circumvented to achieve a mindindependent world Reason, according to Kant, is structured by forms of experience and categories, giving practical and logical arrangement to people’s everyday experience In addition, Kant brought in two kinds of knowledge: — analytic knowledge (analytic representations), which is expressed by self-justifying judgments about properties of objects that exist in these objects by definition, e.g., propositions the predicate concept of which is contained in its subject concept — synthetic knowledge (synthetic representations), which is expressed by judgments about properties of objects that are added to these objects, e.g., propositions, the predicate concept of which is not contained in its subject concept These two kinds were related to two classes of knowledge: — a priori knowledge (representations) known before and independent of experience — a posteriori knowledge (representations) is obtained from experience page 34 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Introduction page 35 35 As a result, Kant discriminated three kinds of knowledge: • analytical a priori knowledge, which is exact and certain but mostly uninformative as it expounds only what is contained in definitions; • synthetic a posteriori knowledge, which conveys information about what is learned from experience, but it is subject to the errors of the senses; • synthetic a priori knowledge, which is uncovered by pure intuition and is both exact and certain, for it expresses the necessary conditions that the mind imposes on all objects of experience According to Kant, mathematics and philosophy give synthetic a priori knowledge Kant explains that analytic knowledge is a priori knowledge, while synthetic knowledge is sometimes a posteriori knowledge and sometimes a priori knowledge For instance, the statement “Any natural number is larger than or equal to one” is analytic because this property is contained in the definition of natural numbers, which start with one and are built by consecutive addition of one At the same time, the statement “Any natural number is either prime or compound” is synthetic As the majority of philosophers, Kant assumed that knowledge was characterized by propositions or statements Analytic propositions are true by nature of the meaning of the words involved in the sentence, while synthetic statements only tell people something about the world Thus, the truth or falsehood of synthetic statements comes from something outside of their linguistic content However, Kant does not demand coincidence of analytic and a priori knowledge explaining that elementary mathematics, e.g., arithmetic, is synthetic and a priori because its statements provide new knowledge, but knowledge that is not derived from experience This becomes part of his main argument for transcendental idealism, in which the possibility of experience depends on certain necessary conditions called a priori forms, which organize comprehension of the world of experience September 27, 2016 36 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes It is possible to suggest that knowledge of basic arithmetic does not demand any empirical experience to know that + = 4, which is essentially analytic However, Kant disproves this explaining that if the number in this calculation is examined, there is nothing to be found in it by which the number can be inferred Thus, it is selfevident, and undeniably a priori, but at the same time, it is synthetic It is interesting that this might be true for arithmetic as an empirical science When axioms of arithmetic, e.g., Peano axioms (cf., for example, (Shoenfield, 2001)), were constructed, arithmetic propositions that were not axioms became analytic and a posteriori This became even more transparent with the discovery of non-Diophantine arithmetics (Burgin, 1977; 1997c; 2007; 2010c) Moreover the whole mathematics is, in a definite sense, an empirical science where experiments, mostly mental experiments, play the leading role (Burgin, 1998) Consequently, the majority of mathematical propositions, even many axioms, are a posteriori by their nature In the 20th century, Bertrand Russell also studied problems of knowledge His views are exposed in the article (Russell, 1926) He writes, “the question how knowledge should be defined is perhaps the most important and difficult” of all problems related to knowledge “This may seem surprising”: he continues, — at first sight, it might be thought that knowledge might be defined as belief which is in agreement with the facts The trouble is that no one knows what a belief is, no one knows what a fact is, and no one knows what sort of agreement would make a belief true” According to Russell, theory of knowledge is partly logical, partly psychological and we can add, partly algorithmic Connection between these parts is not very pronounced Taking precision and certainty as the basic characteristics of knowledge, Russell assumes that they have different degrees, or in modern terms, precision and certainty are fuzzy properties In essence, there is no absolutely precise knowledge or knowledge with absolute certainty — all knowledge is more or less uncertain and more or less vague Often vague knowledge seems more reliable than precise knowledge, but is less useful Russell believes that one of the aims of science is to increase page 36 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Introduction page 37 37 precision without diminishing certainty although it is incorrect to restrict understanding of knowledge to what has the highest degree of both precision and certainty It is interesting that Russell treats data as a kind of knowledge, namely, immediate knowledge Indeed, he writes: “the separation into data and inferences belongs to a well-developed stage of knowledge, and is absent in its beginnings” (Russell, 1926) At the same time, he assumes that all knowledge is represented by propositions and is obtained by observations (data) and inference (inferred knowledge) Traditionally, two sorts of data are considered: one physical, derived from the senses, the other mental, derived from introspection Russell suggests that the difference between the physical and the mental belongs to inferences and constructions and not to data Russell also distinguishes two kinds of inference, deduction and induction Deduction, as he maintains, is obviously of great practical importance, since it embraces the whole of mathematics Inductive inferences are essential to the conduct of life Russell implies that “we have to accept merely probable knowledge in daily life, and theory of knowledge must help us to decide when it really is probable, and not mere animal prejudice” In addition, Russell also writes about analogy as a way of inference Interestingly, that parallel to conventional inference, Russell acknowledges animal inference explaining why there are grounds for doing this Studying knowledge, the outstanding Austrian philosopher Ludwig Wittgenstein asserts that some statements, such as “here is a hand” or “the world has existed for more than five minutes”, look like empirical propositions saying something factual about the world and open to doubt However, in essence, they are similar to logical propositions because they function in language, which makes possible for empirical propositions to make sense This compels us to take such propositions for granted to allow us to speak about things in the external world According to Wittgenstein, a proposition has no meaning unless it is placed within a particular context September 27, 2016 38 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes It is not the goal of Wittgenstein to refute skeptical doubts about the existence of an external world Instead, he tries to circumvent them by explaining that the doubts, as they are understood in philosophy, not what they are meant to By ascribing logical nature to certain fundamental propositions, Wittgenstein explicates their structural role in communication and behavior of people For instance, the statement “Here is a hand” is an implicit definition of the word hand by showing an example In addition, this statement indicates how the word hand is used rather than making an empirical claim about the presence of a hand Doubts aimed at such propositions destroy language and its utilization Communication and rational thought are only possible, provided there is some sort of common ground Although skeptical doubts are sensible in rational debate, doubting too much undermines rationality and as a consequence, very foundation for doubt In addition, similar to many Chinese philosophers mentioned above, Wittgenstein explores how words acquire meaning However, in contrast to them, Wittgenstein derives meaning from usage and not vice versa In doing this, he asserts that one should look to real language to answer questions about the meaning of words Wittgenstein demonstrates that many philosophical problems arose from philosophers’ redefining words and then applying their own definitions to promote their ideas and to defeat their opponents Wittgenstein does not try to define knowledge but suggests looking at the way the word knowledge is used in natural languages He apprehends knowledge as an instance of a family resemblance reconstructing the concept of knowledge as a cluster conception that comprises relevant features but cannot be adequately captured by any precise definition Wittgenstein also discusses the distinction between sense-data and reality indicating that people learn what a tree is by being shown trees and not by being given tree sense-data According to him, the tree sense-data are irrelevant in this case and not bear on anything useful for people The possibility of illusion is there, of course, but there are criteria for deciding what constitutes an illusion These page 38 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 39 39 criteria work for most people Those for whom they fail are called “mad” and are widely disregarded However, according to contemporary psychological and neurophysiological theories, an individual sees a tree only if she receives tree sense-data through her senses However, the reception of sensedata is not enough To see a tree as a tree, the brain has to correctly process sense-data, building a relevant image and assigning the correct name “tree” to this image Besides, it is possible to know what a tree is by observing not trees but their images, e.g., pictures or movies with trees After images of trees are stored in the memory, an individual can see a tree in her dreams In this case, the brain simulates acceptance of sense-data from a physical tree or from its picture 1.3 Structure of the book There’s only one solution: look at the map Umberto Eco, Foucalt’s Pendulum The map is not the territory, and the name is not the thing named Alfred Korzybski The main goal of this book is to achieve a synthesized understanding of the complex, multifaceted phenomenon called knowledge by building a synthetic theory of knowledge, which allows systematizing and binding together existing approaches to knowledge in one unified theoretical system However, we not try to represent all approaches and directions of knowledge studies in a complete form or even to give all important results of this area Our goal is to give an introduction to the main approaches and directions, explaining their basics and demonstrating how they can be comprehended in the context of the general theory of knowledge Besides, references are given to sources where an interested reader can find more information about these approaches and September 27, 2016 40 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes directions of knowledge studies The goal is to present a broad picture of contemporary knowledge studies, provide a unifying theory of knowledge and synthesize all existing approaches in an amalgamated structure of ideas, constructions, methods, and applications That is why in Chapter 1, we explain the leading role of knowledge in the contemporary society and describe a brief history of knowledge studies in different countries and cultures exhibiting not only the development of knowledge studies in Western countries but also achievements of the Eastern civilizations in the fields of logic and epistemology Chapter studies properties of knowledge and its classifications Usually, knowledge is studied in the context of beliefs (cf., for example, (Gettier, 1963; Pollock, 1974; Pollock and Cruz, 1999; Dretske, 2000)) In this book, we treat knowledge in the more general setting, namely, in the context of epistemic structures Knowledge items are epistemic structures Beliefs are epistemic structures associated with descriptive knowledge However, beliefs are related only to declarative or descriptive knowledge while there are also other epistemic structures, to which knowledge is intrinsically attached In particular, there is operational knowledge and representational knowledge To understand knowledge, it is important to know that there are various types, sorts, and kinds of knowledge That is why we start Chapter (Section 2.1) with exposition and exploration of diverse classifications, taxonomies and typologies of knowledge In Section 2.2, different approaches to knowledge characterization are discussed and analyzed from the perspective of the existential characteristics of knowledge In Section 2.3, dimensions of knowledge are described and investigated Section 2.4 contains knowledge about metaknowledge and metadata, where metaknowledge is knowledge about knowledge, while metadata provide information about data However, it is necessary to not only know properties of knowledge but also be able to evaluate and justify these properties This is the main topic of Chapter 3, where Section 3.1 tells the reader about knowledge evaluation and Section 3.2 narrates knowledge justification issues It is especially significant to appraise and justify consistency of knowledge That is why in Section 3.3, we explain page 40 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 41 41 how to work with knowledge that has been traditionally considered inconsistent giving an overview of existing approaches to this problem and an exposition of some parts of the theory of logical varieties This section is based on the papers (Burgin and de Vey Mestdagh, 2011; 2015) In the next part of the book, we separate and study three key levels of knowledge: the microlevel, macrolevel, and megalevel (Burgin, 1997) Chapter describes the microlevel, or the quantum level of knowledge, its structures, properties, and processes This level contains “bricks” and “blocks” of knowledge that are used for construction of other knowledge systems We call such minimal “bricks” knowledge quanta and study them in Section 4.1 Two fundamental theories of the knowledge quanta are presented — the Quantum Theory of Knowledge (QTK) created by Burgin (1995a; 1997; 2004) and the Semantic Link Network Theory (SLNT) developed by Zhuge (2002; 2004; 2010; 2012) Relations between these two theories are established “Blocks” of knowledge are identified with structured quantum knowledge items and we consider such quantum knowledge items as signs and symbols discussing different approaches and models in Section 4.2 Operations with and relations between knowledge quanta and other quantum knowledge units representing dynamics and structural organization of the quantum level of knowledge are constructed and explored in Section 4.3 On the macrolevel, or the level of average knowledge, considered in Chapter 5, researchers study knowledge representation used by people and artificial systems for practical purposes Section 5.1 explains utilization of languages, such as natural, mathematical, programming, and scientific languages, for knowledge representation, preservation, and processing Section 5.2 presents means of logics, which are used for knowledge representation, validation, preservation, and processing, while Section 5.3 describes elements of the theory of abstract properties, which is a synthesis of logic and qualitative physics providing even more powerful means for knowledge representation, validation, acquisition, preservation and processing Next three sections of Chapter are dedicated to September 27, 2016 42 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch01 Theory of Knowledge: Structures and Processes knowledge representation in AI Semantic networks and ontology are the topics of Section 5.4 Scripts and productions are exposed in Section 5.5 Frames and schemas are studied in Section 5.6 with the emphasis on the new direction in this area called mathematical schema theory On the megalevel, or the global level of knowledge, researchers consider the immense knowledge systems such as mathematics, physics, biology, advanced mathematical, and physical theories Chapter contains an exposition of the global level of knowledge describing structure and organization of such knowledge systems Knowledge production, acquisition, engineering and application are studied in Chapter Section 7.1 analyzes knowledge production and acquisition as basic cognitive processes Section 7.2 is concerned with problems of knowledge organization and engineering Section 7.3 treats issues of knowledge application and management Relations between information and knowledge are studied in Chapter Section 8.1 presents structural aspects of knowledge–information duality exploring different opinions about the triad Data–Information–Knowledge Section 8.2 considers relations between epistemic structures and cognitive information Dynamic aspects of knowledge, data, and information interaction are the main concern of Section 8.3 Section 8.4 analyzes information as a source of knowledge, while Section 8.5 investigates knowledge as a measure of information in the context of mathematical stratum of the general theory of information The last Chapter contains some conclusions and directions for future research Exposition of material is aimed at different groups of readers Those who want to know more about history of knowledge studies and get a general perspective of the current situation in this area can skip proofs and even many theoretical results given in the strict mathematical form At the same time, those who have a sufficient mathematical training and are interested in formalized knowledge theories can skip preliminary deliberations and go directly to the sections that contain mathematical exposition Thus, a variety of readers will be able to find interesting and useful issues in this book page 42 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Introduction b2334-ch01 page 43 43 if each reader chooses those topics that are of interest to her or to him It is necessary to remark that the research in the area of knowledge studies and application is extremely active, while knowledge is related almost to everything Consequently, it is impossible to include all ideas, issues, directions, and references to materials that exist in this area, for which we ask the reader’s forbearance September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Chapter Knowledge Characteristics and Typology In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual Galileo Galilei 2.1 The differentiation and classification of knowledge There is a strong tendency to reduce the many to the few, the complex to the simple, the various to the uniform Richard Pring For millennia, philosophers, who were the first to study the problems of knowledge, have asserted that knowledge is a kind of beliefs reducing all knowledge to declarative or descriptive knowledge and actively imposing this opinion on all others Even now, the majority of philosophers believe in this declaration For instance, such experts in contemporary philosophical theories of knowledge as John Pollock and Joseph Cruz write: “Epistemology might better be called “doxastology”, which means the study of beliefs” (Pollock and Cruz, 1999) However, this understanding was challenged At first, physicists discovered operational knowledge It was Nobel laureate Percy Williams Bridgman (1882–1961), who insisted that conceptual knowledge is, in essence, operational He wrote that “any concept 45 page 45 September 27, 2016 46 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes [is] nothing more than a set of operations; the concept is synonymous with the corresponding set of operations” (Bridgman, 1927) Many scientists, especially, physicists and psychologists, became enthusiasts of this methodological approach bringing into being operationalism, also called operationism, as a direction in methodology of science based on the idea that to know the meaning of a concept is to have a method of measurement for it (Bridgman, 1936; 1959; Boring et al., 1945; Chang, 2009) Behaviorist psychologists, such as Edwin Boring (1886–1968), Stanley Smith Stevens (1906–1973), and Edward Chace Tolman (1886–1959), became ardent adherents of operationalism They used operationalism as a weapon in their fight against more traditional psychologists (Feest, 2005) Nevertheless, despite the initial popularity of Bridgman’s approach, by the middle of the 20th century, the common attitude among philosophers and philosophically-minded scientists towards operationalism was strongly critical (Chang, 2009), although operational knowledge was explicitly used by logical positivism in its verification theory of meaning (Frank, 1956) Another kind of knowledge — representational knowledge — was elucidated in methodology of science Namely, the structuralist direction represented scientific knowledge in the form of a scientific theory as a system of models (Sneed, 1971; Stegmă uller, 1976; 1979; Balzer et al., 1987) The computational approach treats scientific knowledge in the form of a scientific theory as complex data structures in computational systems, which contain organized packages of rules (operational knowledge), concepts (representational knowledge), and problem solutions (operational and descriptive knowledge) (Thagard, 1988) Lobovikov included questions and problems (erotetic knowledge) into scientific knowledge in the form of a scientific theory (Lobovikov, 1984) Pearce and Rantala combined representational and descriptive knowledge in their model of a scientific theory (Pearce and Rantala, 1981) page 46 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 47 47 Later the structure-nominative direction in methodology of science included descriptive, representational knowledge and operational knowledge as specific components of general knowledge systems in general and scientific theories in particular (Burgin and Kuznetsov, 1988; 1989; 1991; 1992; 1993; 1994; Balzer et al., 1991; Burgin, 2011) Namely, in the structure-nominative model of scientific knowledge, operational knowledge constitutes the pragmaticprocedural subsystem, while representational knowledge constitutes the model-representing subsystem (Burgin and Kuznetsov, 1988; 1989; 1991; 1992a; 1992b; 1994) In addition, operational knowledge also called procedural knowledge, has become popular in knowledge management (Valente and Rigallo, 2002; 2003) Some philosophers also made a distinction between “know-that” as descriptive/declarative knowledge and “know-how” as operational/procedural knowledge In general, they interpreted operational/procedural knowledge as knowledge that is manifested in the use of a skill, whereas descriptive/declarative knowledge as explicit knowledge of a fact (Fantl, 2012) Although there is a discussion whether ancient Greeks considered “know-how” as a specific kind of knowledge, it is assumed that Gilbert Ryle was the first philosopher to treat “know-how” as knowledge distinguishing it from propositional knowledge or “know-that.” He identified “know-how” with a disposition whose “exercises are observances of rules or canons or the application of criteria” (Ryle, 1949) His main argument was that it was possible to have lots of knowledge-that, without possessing any knowledge-how In addition, he insisted that “knowledge-how is a concept logically prior to the concept of knowledge-that” (1971/1946) Later in her analysis of behavior from the epistemological perspective, Katherine Hawley came to the conclusion that “know-how” was a matter of successful actions plus warrant (Hawley, 2003) In a similar way, Thorkelson (2008) writes: “What is knowledge? The time-worn and widely criticized philosophical definition is “justified true belief ” (Gettier, 1966; Goldman, 1967; Lewis, 1996); for anthropological purposes it suffers from three major September 27, 2016 48 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes problems centered especially around the term “belief.” First, the definition reduces knowledge to propositional knowledge, “knowing-that,” thus occluding other knowledge types like practical “know-how” (knowledge embodied in routinized dispositions), affective states (knowledge embodied in emotion and sentiment), and phenomenological acquaintance (conferred, for instance, by sensory experience or artistic representation).” Although many philosophers started to understand that knowledge-how and knowledge-that are distinct kinds of knowledge and consequently, procedural knowledge is non-propositional, others tried to reduce procedural knowledge to propositions For instance, Bruce Kogut and Udo Zander write: “Procedural knowledge consists of statements that describe a process, such as the method by which inventory is minimized” (Kogut and Zander, 1992) Some educators also rejected reduction of knowledge to descriptive knowledge and especially, to propositions or beliefs For instance, Scheffler (1965) discerns “know-that” as descriptive knowledge and “know-how” as operational knowledge There are also an extreme comprehensions of operational knowledge For instance, Nonaka and Takeuchi (1995) assume that all knowledge is about action as any knowledge must be used to some end Thus, methodological and sociological analysis shows that there are three basic categories of knowledge: ∗ Representational knowledge about an object is representations of this object by knowledge structures, such as models and images, e.g., when Bob has an image of his friend Ann, it is representational knowledge about Ann ∗ Descriptive knowledge also called declarative knowledge or sometimes propositional knowledge is knowledge about properties and relations of the objects of knowledge, e.g., “a swan is white”, “a lion is an animal” or “three is larger than two” However, objectively, declarative knowledge is only a kind of descriptive knowledge, while propositional knowledge is a kind of declarative knowledge page 48 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 49 49 ∗ Operational knowledge also called procedural knowledge consists of rules, procedures, algorithms, etc., and serves for organization of behavior of people and animals, for control of system functioning and for performing actions A more exact categorization shows that procedural knowledge is a kind of operational knowledge Note that in the literature, there is no agreement as to the definition of operational (procedural) knowledge For instance, Lewicki et al (1987) equate procedural knowledge either with cognitive skills or with processing rules At the same time, Kogut and Zander claim that operational (procedural) knowledge consists of statements that describe the process (Kogut and Zander, 1992) In addition, each basic category consists of three subcategories ∗ Representational knowledge can represent statics or/and dynamics, while dynamics knowledge, in turn, is divided into two more exact categories — representation of functions or of processes ∗ Descriptive knowledge can be either informal, e.g., linguistic, i.e., represented by texts in natural languages; or semiformal such as the conventional mathematical language; or formal, e.g., logical, i.e., represented by logical expressions (formulas) ∗ Operational knowledge can be either procedural, e.g., in the form of instructions, algorithms, programs, plans and scenarios; or instrumental, e.g., descriptions of tools of operations, operators and performers; or axiological, e.g., in the form of goals, tasks, values, estimates, norms or judgments Moreover, the basic categories of knowledge contain other subcategories For instance, existential knowledge, i.e., knowledge about existence of the object of knowledge, is a kind of descriptive knowledge because existence and its characteristics are properties of the object Representational knowledge also comprises structural knowledge, which is basic to problem solving in creation of plans and strategies, setting conditions for different procedures, and in determining structures of different systems September 27, 2016 50 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Differentiation of knowledge into three types allows solving the problem of relations between art and knowledge Different thinkers have been seriously puzzled by the following situation (cf., for example, (Pring, 1976; Reid, 1985; Bender, 1993; John, 1998)) On one hand, art definitely gives knowledge On the other hand, if we assume that knowledge is only descriptive, e.g., in the form of logical propositions, then we all know that art goes beyond descriptions not speaking about logical propositions For instance, each proposition in logic has its negation but as Pring writes, what conceivably could be the negation of the Mona Lisa (Pring, 1976) As a result of this confusion, philosophers even suggested “to reconceive knowledge in such a way that we may eventually come to understand how it can be gained non-propositionally” (Worth, 2010) In contrast to this, art can convey representational and operational knowledge Indeed, on the one hand, art is representation of different things It can imitate (represent or reflect) states of the external world — nature, people, society, etc., as well as the inner state of the artist “Art as a representation of outer existence (admittedly “seen through a temperament”) has been replaced by art as an expression of humans’ inner life” (Worth, 2010) In such a way, art gives representational knowledge On the one hand, art can teach people providing models of different actions, behavior, and attitudes In such a way, art gives operational knowledge It is interesting that descriptive and representational knowledge have operational representations, descriptive and operational knowledge have representational (model) representations and representational and operational knowledge have descriptive representations For instance, productions (cf., Section 5.5) give operational representation of descriptive (declarative) knowledge in the form of conditional propositions Algorithms serve as models of processes and actions giving operational representation of representational (model) knowledge Programs in declarative programming languages (cf., Section 5.1.3) give descriptive representation of algorithms as a form of operational knowledge Propositions and predicates as forms of descriptive knowledge have model representations in the structuralist model (reconstruction) of a scientific theory (cf., Chapter 6), as page 50 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 51 51 well as in the possible-world semantics, also called Kripke semantics (Kripke, 1963) Processing of different types of knowledge in the human brain involves corresponding types of memory Namely, declarative memory and procedural memory are two major parts of the long-term memory Experimental evidence for a distinction between declarative memory and procedural memory was demonstrated by Milner (1962) Declarative memory (descriptive memory) is the memory that stores declarative knowledge, such as knowledge of facts and events It is also called explicit memory because knowledge it accumulates is explicitly stored and retrieved Procedural memory (operational memory) is the memory that stores procedural (operational) knowledge in the form of skills and knowledge how to things, such as the utilization of things or movements of the body Procedural memory is also called implicit memory, because knowledge it accumulates is typically acquired through repetition and practice and used without explicit and conscious awareness Cohen and Squire (1980) coined the term procedural memory for storing and using skills and procedures These parts of long-term memory involve different regions of the brain and function in a different manner Declarative memory uses the hippocampus, entorhinal cortex and perirhinal cortex as the coding system and is mostly situated in the temporal cortex Procedural memory uses the cerebellum, putamen, caudate nucleus and the motor cortex as the coding system and is situated in different parts of the brain For instance, learned skills such as driving are stored in the putamen, while instinctive procedures such as sleeping are stored in the caudate nucleus and the cerebellum is involved with timing and coordination of body skills In addition, researchers demonstrated that declarative memory can be further sub-divided into episodic memory and semantic memory (Tulving, 1972) Episodic memory is the memory of experiences and specific events in time in a serial form, from which we can reconstruct the actual events that took place at any given point in our lives September 27, 2016 52 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Semantic memory is a structured representation of general factual knowledge, such as facts, meanings, concepts and knowledge about the external world Knowledge in semantic memory often is abstract and relative It is possible to suggest that representational knowledge is related to eidetic memory As we know, there is a big variety of properties and characteristics of knowledge, as well as many different types and kinds of knowledge To organize this huge diversity into a system, it is worthwhile to classify knowledge with respect to various criteria These criteria are based on five types of attributes: — — — — — Characteristics of knowledge and its representations Features of processes that are related to knowledge Parameters of systems that produce or/and use knowledge Properties of the knowledge domain Traits of the knowledge carriers Here are some examples The most popular feature of knowledge is truthfulness, which takes two values True and False in the classical interpretation In fuzzy logics, truthfulness, takes values in the interval [0, 1] where the value means absolutely false and the value means absolutely true Truthfulness of knowledge depends both on of characteristics, knowledge and its representations and on the properties of the knowledge domain It is necessary to remark that from ancient times, many researchers have thought that knowledge and information cannot be false assuming that being true is an inherent characteristic of knowledge They believe that if a belief is false, then it is not knowledge as knowledge is a justified true belief Other thinkers admit that knowledge can be true and can be false For instance, in his description of the World 3, Popper (1972; 1979) asserted that this world contains all the knowledge and theories of the world, both true and false Thus, Popper assumed existence of false knowledge Burgin (2010) gives a detailed explanation why information and hence knowledge can be false page 52 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 53 53 An important feature of knowledge from the perspective of related processes is complexity, for example, complexity of acquisition, complexity of integration or complexity of learning We see that complexity of knowledge depends on such processes as knowledge acquisition, knowledge integration or learning There are different types of professional knowledge, for example, professional knowledge of a lawyer, professional knowledge of an architect or professional knowledge of a physicist There is knowledge about specific domains, for example, mathematical, physical, biological, or sociological knowledge It is possible to consider four kinds of knowledge based on information characteristics introduced by Collins (1993): Symbol-type knowledge Embodied knowledge Embrained knowledge Encultured knowledge Symbol-type knowledge is represented by symbols and can be transferred without loss on flashcards, hard drives, CD-ROM drives, floppy disks, and so forth Embodied knowledge depends on properties and functioning of the human body For instance, embodied knowledge of the notion chair depends on the ability to put the body in the sitting position on a chair Embodied knowledge is a kind of embedded knowledge In this context, a general understanding treats embedded knowledge as the knowledge that is set in processes, products, culture, routines, artifacts, or structures (Horvath, 2000; Gamble and Blackwell, 2001) Knowledge is embedded either formally, for example, through a management initiative to formalize a certain useful technique, or informally as the organization uses or people behavior Embrained knowledge depends on the physical characteristics of the brain For instance, Collins (1993) explains, there are kinds of knowledge dependent on the way neurons are interconnected or on the chemistry the brain or on the formation of solid shapes in the brain September 27, 2016 54 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Encultured knowledge depends on the social environment For instance, natural languages are the model example of encultured knowledge Thus, the right way to use a language, e.g., to speak, is the sanction of a social group but not of a separate individual and those who not remain in contact with the social group will soon cease to know how to speak properly according to the rules of the group Researchers also consider three kinds of knowledge, which form a representational classification: Symbolic knowledge is represented by symbols Subsymbolic knowledge is constructed from knowledge elements that are not symbols Wired knowledge is a part of a physical system Let us consider some examples Example 2.1.1 Images on the screen of a computer or TV are units of representational knowledge These images are formed from pixels (points of different colors and brightness) on the screen Thus, these images are units of subsymbolic representational knowledge Example 2.1.2 An algorithm in the form of a computer program is a unit of symbolic operational knowledge, while an algorithm implemented in the hardware of a computer is a unit of wired operational knowledge Application of the representational knowledge classification allows researchers to solve some methodological problems For instance, in the theory of computations, many think that computations of neural networks are not algorithmic because they assume that algorithms can be only symbolic However, algorithms as a kind of operational knowledge can be not only symbolic but also wired, and a neural network is just a wired algorithm This understanding is supported by the fact that artificial neural networks are modeled by conventional computers where these networks are represented by conventional symbolic algorithms in the form of computer programs page 54 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 55 55 It is possible to consider three important types of knowledge related to information characteristics suggested by Banathy (1995): Referential knowledge has meaning in the system R Non-referential knowledge has meaning outside the system R, e.g., knowledge that reflects mere observation of R State-referential knowledge reflects an external model of the system R, e.g., knowledge that represents R as a state transition system Philosophers usually consider two kinds of knowledge, which form a cognitive classification: • A priori knowledge, which is known independently of experience For instance, Kant interpreted a priori knowledge as a “transcendental” form of knowledge coming from “rational insight” • A posteriori knowledge is knowledge that people get from experience that can be of two types: ◦ Empirical experience, which is accumulated from practical activity, e.g., experimentation, giving empirical knowledge ◦ Theoretical experience, which is accumulated from mental activity, e.g., thinking, giving theoretical knowledge Separating knowledge with respect to the knower, i.e., to the system that has knowledge, we come to the system classification: — Personal knowledge — Communal knowledge — Network knowledge Michael Polanyi (1891–1976) explicated two sorts of personal knowledge (Polanyi, 1966; 1974): Explicit knowledge is codified knowledge, such as knowledge found in documents Tacit knowledge is intuitive, hard to define knowledge that is mostly experience based September 27, 2016 56 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes This accessibility classification is extremely popular within business and knowledge management where the following descriptions of these sorts of knowledge were elaborated Explicit knowledge can be articulated in formal language and records, communicated by people or through information technology and stored Tacit (or implicit) knowledge is personal knowledge embedded in individuals based on their experience and involving such intangible factors as personal emotions, beliefs, procedures, perspectives, goals and values People can know about something but be unable to explain the process that led to their knowledge and even explain what they know Tacit knowledge is difficult to articulate, communicate and store, although it can be communicated through face-toface contact and storytelling According to Polanyi, tacit knowledge that underlies explicit knowledge being more fundamental in that all knowledge is either tacit or it was initially rooted in tacit knowledge, which cannot be objective Tacit knowledge located exclusively in the human mind constitutes the invisible part of organizational knowledge including organizational culture, experience, feelings, confidence, relationships being the principal driving force of the organization Thus, it is possible to compare the organizational knowledge base to an iceberg, the explicit knowledge is the visible part of this iceberg, codified and classified knowledge integrated into documents, procedures and business processes, and codified in informational systems However, Botha et al (2008) pointed out that tacit and explicit knowledge should be seen as a spectrum (the accessibility spectrum) rather than as two separate points Tacit and explicit knowledge are the endpoints of the accessibility spectrum Thus, knowledge is mostly a mixture of tacit and explicit elements rather than being one or the other Taking into account this issue, it is possible to formalize the accessibility spectrum defining a measure of knowledge explicitness with the scale from to In this scale, the measure of tacit knowledge will be 0, while the measure of explicit knowledge will be Logical tools for adequate description, valid transformation and effective generation of explicit and implicit knowledge are developed page 56 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 57 57 in (Burgin and Rybalov, 2003) As explicit and implicit knowledge contain propositions that can be inconsistent for two reasons: (1) due to utilization of different systems of knowledge generation, e.g., strong entailment in one case and weak entailment in the other, and (2) because of application of these mechanisms to different parts of new knowledge depending on level of conflict the latter generated Thus, there is no consistent classical calculus that can generate both explicit and implicit knowledge Therefore, the logical representation of explicit and implicit knowledge together forms a non-trivial logical variety (Burgin, 1997) Here we slightly extend the accessibility classification considering three following sorts of personal knowledge: — Externally explicit or articulated (codified) knowledge — Internally explicit (unarticulated) knowledge — Tacit (incommunicable) knowledge Two latter categories form implicit knowledge in contrast to explicit knowledge In this extended accessibility classification, internally explicit knowledge is situated in the accessibility spectrum between externally explicit knowledge and tacit knowledge People very often have internally explicit but unarticulated knowledge This is well known to teachers, who habitually encounter situations when their students can apply definite rules to solve problems but cannot explain and sometimes even repeat these rules There are also three gradations of implicit knowledge: — Instincts are a form of operational knowledge — Unconscious knowledge belongs to the knower but the knower is not aware of it — Conscious but explicitly inexpressible knowledge — the knower knows that she/he has this knowledge but cannot explicitly express it The following situations apparently demonstrate the difference between unconscious knowledge and conscious but explicitly inexpressible knowledge Imagine students in a class who are September 27, 2016 58 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes performing arithmetical operations with numbers Always there are students who correctly use the commutative law in their calculations However, some of them this without remembering this law They have unconscious knowledge of this law Other students this remembering this law, but if the teacher asks them to formulate the law, they would be unable to this They have conscious but explicitly inexpressible knowledge of this law Finally, there are students who have externally explicit knowledge of the commutative law There are three gradations of explicit knowledge: — Personal knowledge — Shared knowledge — Personalized (internalized) knowledge When an engineer invents some new device, her knowledge about this device is personal If she writes a paper or tells a colleague about it, her knowledge about this device becomes shared For the colleague who hears this new device and understands, this knowledge becomes personalized (internalized) In addition, there is a carrier-based classification suggested in (Nonaka and Takeuchi, 1995): — — — — Individual knowledge Group knowledge Organizational knowledge Knowledge of a group of organizations or super-organizational knowledge Amalgamating three latter classes into one class, we obtain the following classification: — Personal knowledge — Public knowledge One more knowledge classification is considered in (Ekinge and Lennartsson, 2000): — Individual knowledge — Shared knowledge — Objectified knowledge page 58 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 59 59 As it is sometimes happens in science, the same word tacit is used for denoting different concepts because it is also used in the following classification also suggested by Polanyi — Focal knowledge is about the object or phenomenon that is in focus — Tacit knowledge is the general background knowledge used as a tool to handle or improve what is in focus The focal and tacit dimensions are complementary Tacit knowledge varies from one situation to another It functions as a background knowledge assisting in accomplishing a task which is in focus By the level of externalization, knowledge is broken up into three classes: Personal knowledge is knowledge that belongs to an individual Shared knowledge is knowledge that is shared by a group of individuals External knowledge is knowledge that does not belong to an individual For instance, knowledge of what a person is going to during the day is personal Knowledge of mathematics is shared knowledge For a non-mathematician, knowledge of category theory is external knowledge By the level of internalization, knowledge is divided into three categories: Subconscious knowledge is knowledge of an individual such that the individual is not aware of its existence Implicit knowledge is knowledge of an individual such that the individual is aware of its existence but cannot express it, e.g., verbalize it Explicit knowledge is knowledge of an individual such that the individual can express it, e.g., verbalize it Aristotle’s very influential three-fold classification of disciplines as theoretical, productive, or practical is used as the base for classification of forms of knowledge in (Smith, 1999) September 27, 2016 60 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes — Theoretical knowledge is pursuing truth for its own sake — Productive knowledge is knowledge for making things — Practical knowledge displays in ability of making judgments and decisions Theoretical knowledge is related to the form of thinking appropriate to theoretical activities, which according to Aristotle, is contemplative involving meditating over facts and ideas that the person already possesses (knows) Productive knowledge and enquiry is used in productive disciplines for performing an action or operation Aristotle associated this form of thinking and doing, with the work of craftspeople or artisans Practical knowledge was originally associated with ethical and political life Their purpose was the cultivation of wisdom and knowledge involving decision-making and human interaction For instance pure mathematics is theoretical knowledge, toolmaking procedures are productive knowledge, and social work training methods are practical knowledge Piaget (1967/1971) identified three kinds of knowledge: Physical knowledge consists of facts about the features of something such as “the window is transparent,” “the crayon is white,” “the cat is grey” and “the air was cold and dry yesterday.” Physical knowledge directly reflects the objects and can be obtained by exploring objects and noticing their qualities Social knowledge consists of names and conventions made up by people Here are some examples: “The name of this dog is Bounty,” “New Year is on January 1,” or “It is polite to say thank you for a gift.” Social knowledge may be arbitrary and is knowable by being told or demonstrated by other people, found in books, journals, and on the Internet Logico-mathematical knowledge, according to Piaget, consists of relations and structures Logico-mathematical knowledge is constructed by each individual, inside his or her own head or learned from people, books, journals, and the Internet page 60 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 61 61 There is also a problem-oriented knowledge classification • Know-what is the fundamental form of knowledge, e.g., people/ group/organizations know what they know (perhaps through their formal education) but not necessarily know when and how to apply the knowledge to solve problems • Know-how is the ability to solve various problems • Know-why is explanatory knowledge enabling individuals to move a step beyond know-how and create opportunities to deal with unknown interactions and unseen situations Sveiby (1997) analyzes two types of knowledge: • Agentive knowledge is mostly oriented towards using the body as a tool • Intellective knowledge is oriented towards using the mind as a tool In the domain of religion and mysticism, usually two types of knowledge are considered: • Esoteric knowledge is preserved and/or understood by a small group of those specially initiated, or of rare or unusual interest • Exoteric knowledge is, to the contrary, open to everybody although it does mean that anybody can understand it By its representation of the domain (object), knowledge has three types: — Exact knowledge — Fuzzy or vague knowledge — Indeterminate knowledge including probabilistic knowledge To understand the difference between these types of knowledge, let us consider the following examples Imagine we take an urn with ten balls If all balls in the urn are definitely blue and we know this, then we have exact knowledge that if we take one ball from the urn at random, then it will be a blue ball If the color of the balls is between blue and green, then because there is no strict boundary between blue and green, we have fuzzy knowledge that if we take one ball from the urn at random, then it will be a blue ball If five balls in the urn are definitely blue, five balls in the urn are definitely red September 27, 2016 62 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes and we know this, then we have probabilistic knowledge that if we take one ball from the urn at random, then it will be a blue ball, namely, we assume that the probability will be 1/2 Probabilistic knowledge is knowledge for which only the probability of being correct (true) is given On one hand, this is contrary to the established through millennia approach to knowledge, which has to be always true On the other hand, probability theory was created by Blaise Pascal (1623–1662) and Pierre de Fermat (1601–1665) in an attempt to describe uncertain knowledge in mathematical terms However, the crucial incursion of probabilistic knowledge happened with the advent of quantum mechanics, which persuasively demonstrated that in many situations, people could have only probabilistic knowledge about nature This changed understanding of the role of probabilistic knowledge The chief proponent of the new approach was Hans Reichenbach (1891–1953) He assumed that probability is the pillar of knowledge systems and without this understanding, the structure of the world cannot be correctly represented and interpreted because, according to Reichenbach, knowledge about the future cannot be as accurate as knowledge about past events (Reichenbach, 1949) Consequently, knowledge about the future is inevitably probabilistic Moreover, descriptions of the past events also are not completely accurate and thus, they demand probabilistic representation In essence, all knowledge can be only probabilistic in such a way that for each knowledge unit, there is the probability of being true or correct It is interesting that mathematics, which is traditionally treated as the most exact discipline because, as many think, mathematical proofs establish, in some sense, absolute knowledge, is also coming to probabilistic knowledge Namely, some mathematicians suggest using probabilistic proofs of mathematical results In this case, a theorem is asserted as true only with some high probability p (cf., for example, (Bass and Burdzy, 1989; Alon and Spencer, 2000)) Traditionally probability is considered as a function that takes values in the interval [0, 1] although each value of this function is also called the probability of an event All conventional interpretations of probability support this assumption about the range of probability, while all popular formal descriptions, e.g., axioms for probability, page 62 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 63 63 such as Kolmogorov’s axioms, canonize this premise However, scientific research and practical problems brought researchers to the necessity to use more wide-ranging concepts of probability in general and negative probabilities, in particular Negative probabilities have been extensively used in physics (Dirac, 1930; 1942; 1974; Heisenberg, 1931; Wigner, 1932; Pauli 1943; 1956; Feynman, 1950) and mathematical finance (Jarrow and Turnbull, 1995; Duffie and Singleton, 1999; Forsyth et al., 2001; Haug, 2004; Burgin and Meissner, 2011; 2012), their mathematical theory is developed in (Bartlett, 1945; 1986; Allen, 1976; Burgin, 2009; 2010; Khrennikov, 2009) Applications of negative probability show that it has been useful for knowledge evaluation in physics and mathematical finance However, negative probability could be a useful tool for representation, exploration and utilization of probabilistic declarative and representational knowledge in general and not only in these areas This possibility is based on the existence of opposite knowledge, namely, if a statement r contains some knowledge, than it is natural to assume that the statement r (not r) contains opposite knowledge Let us take a statement r and assume that it is true with the probability p(r) In classical logic, the Law of Excluded Middle tells us that when r is not true, then the negation r of r is true This implies the equality p( r) = − p( r) However, in real life, there is often a possibility when different options exist in the case when r is not true For instance, it is possible that r is not defined for some objects Thus, the probability p( r) is not uniquely defined by the probability p(r) In this situation, it is beneficial to use probabilities that can take both positive and negative values treating r as the statement opposite to r Then a negative value of the probability p(r) can be interpreted as positive probability for the opposite statement r It is possible to read more about interpretation of negative probability in (Burgin, 2010e) Probabilistic operational knowledge is represented by probabilistic algorithms and automata, while more general indeterminate operational knowledge is represented by non-deterministic algorithms and automata A non-deterministic algorithm is an algorithm where the result and/or the way the result is obtained depend on chance Examples of September 27, 2016 64 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes non-deterministic algorithms are non-deterministic finite automata or non-deterministic Turing machines (Burgin, 2005) In turn, non-deterministic algorithms are examples of non-deterministic operational knowledge A probabilistic algorithm also called randomized algorithm is an algorithm where the result and/or the way the result is obtained depend on chance with the known probability Examples of probabilistic algorithms are probabilistic finite automata or probabilistic Turing machines (Burgin, 2005) Probabilistic algorithms are examples of probabilistic operational knowledge There is also a domain-oriented classification: — General knowledge — Domain-specific knowledge Note that general and domain-specific knowledge are the endpoints of the knowledge domain spectrum Pollock and Cruz (1999) divide knowledge into several areas: — — — — — — Perceptual knowledge is knowledge from perception A priori knowledge is what is known independently of experience Moral knowledge is knowledge of ethical principles Memorized knowledge is knowledge from the memory Inductive knowledge is knowledge of inductive generalizations Knowledge of other minds Here are some more classifications of knowledge Reif (1997) use the following classification of knowledge: — — — — — — — General knowledge Procedural interpretation knowledge Declarative knowledge Procedural knowledge Special knowledge Compiled knowledge Coherent knowledge page 64 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 65 65 Reif and Allen (1992) use the following classification of knowledge: — — — — — — — — General knowledge Main interpretation knowledge Definitional knowledge Ancillary knowledge Supplementary knowledge Case-specific knowledge Entailed knowledge Concept knowledge To categorize knowledge, Wiig (1993) constructs a threedimensional classification The first is the possession dimension with three categories: — Public knowledge — Shared knowledge — Personal knowledge The second is the dynamic dimension with two categories: — Active knowledge — Passive knowledge The third is the typological dimension with four categories: — — — — Factual knowledge Conceptual knowledge Expectational knowledge Methodological knowledge To categorize knowledge, Boisot (1998) constructs a threedimensional classification The first is the codification dimension with two categories: — Codified knowledge — Uncodified knowledge The second is the abstraction dimension with two categories: — Abstract knowledge — Concrete knowledge September 27, 2016 66 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes The third, diffusion dimension has two categories: — Diffused knowledge — Undiffused knowledge Ueno et al (1987) consider two types of knowledge: — Factual knowledge (facts) — Knowledge for decision-making (rules) van Dijk (2004) introduces several classifications of knowledge The social classification: — — — — Personal knowledge Interpersonal knowledge Social (group) knowledge Cultural knowledge The hierarchical classification: — Specific/particular knowledge — General knowledge The ontological classification: — — — — — — Real knowledge Concrete knowledge Abstract knowledge Fictitious knowledge Historical knowledge Future knowledge The confidence classification: — Absolutely certain knowledge — More or less certain knowledge Tuomi (1999) suggested an eight-fold bidirectional classification of knowledge, which is presented in Table 2.1 and has eight classes of knowledge page 66 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 67 67 Table 2.1 The eight-fold bidirectional classification of knowledge Dynamic typology Acquisition typology Self-referential, i.e., active, knowledge Stockpiled (or sediment), i.e., passive, knowledge Ontogenetic, i.e., learned, knowledge Cognitive knowledge Habitual knowledge Phylogenetic, i.e., transgenerational, knowledge Socio-cultural knowledge Instinctive knowledge Tuomi (1999) remarks that habits, i.e., habitual knowledge and its expression in behavior, bridge the mind and body by imbedding meaning into the body Besides, in contrast to active knowledge, passive (sediment) knowledge does not change or changes very slowly On the individual level, passive (sediment) knowledge is wired into the structure of the personality, while on the organizational (social) level, it is embedded in the organizational (respectively, social) practice De Jong and Ferguson-Hessler (1996) use the following classification of knowledge: — Situational knowledge is knowledge about situations as they typically appear in a particular domain — Procedural knowledge contains actions and operations that are valid within a domain helping problem solver to make transitions from one problem state to another — Conceptual knowledge is static knowledge about facts, principles, and concepts that apply within a domain — Strategic knowledge helps organizing problem-solving processes providing a general plan of solution activities In addition, De Jong and Ferguson-Hessler (1996) define levels of knowledge introducing the hierarchical classification: — Surface or superficial knowledge — Deep or deep-level knowledge There are different approaches to discern surface and deep-level knowledge The accessibility hardship differentiates these types in the September 27, 2016 19:40 68 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes following way: — Surface or superficial knowledge is easily accessible knowledge — Deep or deep-level knowledge is knowledge that is hard to obtain For instance, according to the accessibility hardship, knowledge that the Sun gives light is surface knowledge, while knowledge that the Sun radiates its energy due to thermonuclear processes is deep knowledge The representability trait sets these two types apart on the different foundation: — Surface or superficial knowledge is knowledge about outward attributes of the knowledge object (domain) — Deep or deep-level knowledge is knowledge about imperative properties of the knowledge object (domain) For instance, according to the representability trait, knowledge that the Earth is big is surface knowledge, while knowledge that the Earth is a planet is deep knowledge One of the criteria for knowledge classification is the nature of the carrier of knowledge According to this criterion, we have the following types: digital knowledge, printed knowledge, written knowledge, symbolic knowledge, molecular knowledge, quantum knowledge, and so on For instance, digital knowledge is represented by digits, printed knowledge is contained in printed texts, and quantum knowledge is contained in quantum systems Another criterion is the type of the system that acquires information used in knowledge formation According to this criterion, we have the following types: visual knowledge, auditory knowledge, olfactory knowledge, cognitive knowledge, genetic knowledge, and so on For instance, according to neuropsychological data, 80% of all information that people get through their senses is visual information, 10% of all information is auditory information, and only 10% of information that people get through other senses One more criterion for knowledge classification is the specific domain this knowledge is about According to this criterion, we have the following types: physical knowledge biological knowledge, genetic page 68 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 69 69 knowledge, social knowledge, physiological knowledge, ethic knowledge, esthetic knowledge, weather knowledge, car knowledge, emotional knowledge (in the sense of (Sanders, 1985; Keane and Parrish, 1992; George and McIllhagga, 2000; Bosmans and Baumgartner, 2005; Knapska et al., 2006)), author knowledge, political knowledge, health care knowledge, quality knowledge, geological knowledge, economical knowledge, stock market knowledge, and so on One more criterion is the area to which knowledge is applied This criterion determines orientations of knowledge It is possible to discern the following orientations of knowledge: ∗ Cognitive knowledge provides information about different objects and domains ∗ Procedural knowledge serves for organization of behavior of people and animals, functioning of various systems and performing actions ∗ Educational knowledge helps learning and becoming educated ∗ Pragmatic knowledge serves for gaining something ∗ Economic knowledge serves for getting profit Machlup (1992) introduced five types of knowledge: ◦ practical knowledge; ◦ intellectual knowledge, which includes knowledge related to general culture and knowledge that satisfies of intellectual curiosity; ◦ pastime knowledge, i.e., knowledge that satisfies non-intellectual curiosity or the desire for light entertainment and emotional stimulation; ◦ spiritual and religious knowledge; ◦ unwanted knowledge, which is accidentally acquired and aimlessly retained Kesh and Ratnasingam (2007) use the following knowledge classification: • Declarative knowledge as know-about; • Procedural knowledge as know-how; • Individual knowledge as knowledge created and inherent in the individual; September 27, 2016 70 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes • Social knowledge as knowledge created and inherent in the collective actions of the group; • Conditional knowledge know-when; • Relational knowledge know-with; • Pragmatic knowledge as useful knowledge of an organization Knowledge usually has gradations in its orientation Let us consider some of them Cognitive levels of knowledge about an object A reflect the intent of knowledge These levels, or grades, are ordered from the lowest to highest: Knowledge about existence of the object A, which includes naming when this knowledge is explicit Knowledge as a description of the object A and/or of what is related to the object A, which includes knowledge of properties of A and/or of what is related to A Knowledge as understanding (of a description) of properties of the object A and/or of what is related to the object A Knowledge as holistic understanding of the object A Knowledge as an ability to explain properties of the object A and/or of what is related to the object A Knowledge as an ability to explain the structure of the object A Knowledge as an ability to explain the object A as a system with its internal and external connections As an example of levels of knowledge, we can take knowledge about such an object as the Earth At first, people only knew that there was something where they lived, that is, the Earth (the first level) Then they found some properties of the Earth by observation (the second level) For instance, they found that different plants grow on the Earth and different animals live on the Earth Later people began to understand some properties of the Earth (the third level) For instance, they understood how to use soil to grow useful plants and how seasons are changing However, holistic understanding of the Earth was achieved only when it was demonstrated that the Earth is a planet, which rotates around the Sun (the fourth level) Later page 70 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 71 71 scientists explained some properties of the planet Earth (the fifth level) For instance, it was explained why the Earth rotates around the Sun Finding the configuration of the Solar System brought the knowledge about the external structure of the Earth, while geological studies explained (to some extent) the inner structure of the Earth (the sixth level) However, the seventh level is not yet achieved as science still does not have a good explanation of the Earth as a multifaceted system, which includes ecological, geological, and physical (not only mechanical) explanations It is possible to compress cognitive levels of knowledge into three epistemological gradations of knowledge: — Xerox knowledge is knowledge without understanding — Understandable knowledge is knowledge that is understood by its owner — Explainable knowledge is knowledge that its owner can explain to others Relation to the knowledge domain, i.e., the domain this knowledge is about, gives us one more classification: • Complete knowledge completely describes its domain • Partial knowledge only partially describes its domain • Irrelevant knowledge does not at all describe its domain Operational levels of knowledge about an object A reflect the potency of knowledge These levels are also ordered from the lowest to highest: Knowledge as an ability to perceive the object A, which usually includes naming Knowledge as an ability to something with the object A Knowledge as an ability to use the object A for some purpose For instance, at first, people were able to perceive electricity in the form of a lightning (the first level) Then they invented the lightning rod to divert lightning from people and buildings (the second level) Later they learned how to use electricity (the third level) and as September 27, 2016 72 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes we know, now electricity is one of the material pillars of the human civilization Relations between knowledge and a given system Q determine three important types of knowledge: — knowledge K is accessible for Q if Q has access to K, — knowledge K is available for Q if Q can get (obtain) K, — knowledge K is acceptable for Q if given K, the system Q can accept K There is essential difference between these classes For instance, even if a person has access to some knowledge, it does not mean that this person can get this knowledge Imagine you come to a library that has one million books You know that knowledge you need is in some of these books but you not know in which one If you not have contemporary search tools to get this knowledge and can only read books to find it, then it will not be available to you You cannot read all million books Here is one more example Knowledge about Lebesgue integration, which is a high-level mathematical concept with a developed theory, is accessible to anybody who has a book on Lebesgue integration but it is available only to those who know mathematics Some laws of physics, e.g., Heisenberg’s uncertainty principle, state that there is knowledge about physical reality unavailable to anybody Some mathematical results, e.g., Găodels incompleteness theorems, claim that there is knowledge about mathematical structures unavailable to anybody In computer science, it is proved (cf., for example, (Sipser, 1997; Burgin, 2005)) that for a universal Turing machine, knowledge whether this machine halts given arbitrary input is unavailable As we know, when a person can get some knowledge, it does not mean that this person accepts this knowledge Imagine you read about some unusual event in a newspaper, but you not believe that it is possible Then knowledge about this event is available to you, but you cannot accept it because you not believe that it is possible There are many historical examples of such situations For millennia, mathematicians tried to directly prove that it is possible to deduce the fifth postulate of the Euclidean geometry page 72 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 73 73 from the first four postulates Being unable to achieve this, mathematicians were becoming frustrated and tried some indirect methods Girolamo Saccheri (1667–1733) tried to prove a contradiction by assuming that the first four postulates were valid, while the fifth postulate was not true (Burton, 1997) To this, he developed an essential part of what is now called a non-Euclidean geometry Thus, he was able to become the creator of the first non-Euclidean geometry However, Saccheri was so sure that the only possible geometry is the Euclidean geometry that at some point, he claimed a contradiction and stopped further reasoning Actually, his contradiction was only applicable in Euclidean geometry Of course, Saccheri did not realize this at the time and he died thinking he had proved Euclid’s fifth postulate from the first four Thus, knowledge about non-Euclidean geometries was available but not acceptable to Saccheri As a result, he missed an opportunity to obtain one of the most outstanding results in the whole mathematics A more tragic situation due to biased comprehension involved such outstanding mathematicians as Niels Henrik Abel (1802–1829) and Carl Friedrich Gauss (1777–1855) As history tells us (Bell, 1965), there was a famous long-standing problem of solvability in radicals of an arbitrary fifth-degree algebraic equation Abel solved this problem proving impossibility of solving that problem in a general case In spite of being very poor, Abel himself paid for printing a memoir with his solution This was an outstanding mathematical achievement That is why Abel sent his memoir to Gauss, the best mathematician of his time Gauss duly received the work of Abel and without deigning to read it he tossed it aside with the disgusted exclamation “Here is another of those monstrosities!” Moreover, people often not want to hear truth because truth is unacceptable to them For instance, the Catholic Church suppressed knowledge that the Earth rotates around the Sun because people who were in control (the Pope and others) believed that this knowledge contradicts to what was written in the Bible Relations between these three types of knowledge show that any available knowledge is also accessible However, not any accessible knowledge is available and not any acceptable knowledge is available September 27, 2016 74 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes or accessible For instance, there are many statements that a person can accept but they are inaccessible for this person A simple example gives theory of algorithms It is known that given a word x and a Turing machine T , it is impossible, in general, to find whether T accepts x or not using only recursive algorithms (cf., for example, (Burgin, 2005)) Thus, knowledge about acceptance of x by T is acceptable to any computer scientist because this knowledge is neutral At the same time, this knowledge is in principle inaccessible by recursive algorithms for infinitely many words Exploring accessibility, we find that it is possible to have access to some knowledge to a different extent For instance, imagine that you need two books A and B The first one, A, is in your library at your home You can go to the shelf where the book is and take it any time you want At the same time, the second book, B, is only in the library of another city You can get it, but only by the interlibrary exchange Thus, both books are accessible, but the first one is much easier to retrieve This shows that accessibility is a property of knowledge, which can be estimated (measured) and used in the knowledge quality assessment As knowledge may be available to a different extent, availability is a graded property of knowledge, which can be estimated (measured) and used in the knowledge quality assessment There are different levels at which knowledge may be acceptable For instance, knowledge about yesterday’s temperature is acceptable as knowledge, while knowledge about tomorrow’s temperature is acceptable only as a hypothesis Thus, acceptability is a graded, fuzzy, or linguistic property (Zadeh, 1973) of knowledge, which can be estimated (measured) and used in the knowledge quality assessment (cf., Section 6.2) In addition, it is possible to distinguish conditional counterparts of accessible, available, and acceptable knowledge — knowledge K is conditionally accessible for Q if Q has access to a carrier of K; — knowledge K is conditionally available for Q if Q can get (obtain) a carrier of K; page 74 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 75 75 — knowledge K is conditionally acceptable for Q if given K, the system Q can accept a carrier of K To see the difference between accessible knowledge and conditionally accessible knowledge, imagine a book in English For a person E who knows English and has the book, knowledge in this book is accessible At the same time, for a person D who does not know English and has the book, knowledge in this book is only conditionally accessible There are different conditions for accessibility One condition is that D learns English Another condition is that D finds an interpreter One more condition assures that, that the book is translated from English to the language D knows To see the difference between available knowledge and conditionally available knowledge, imagine a book in English on Lebesgue integration For a person D who knows English, basic calculus and can get this book, knowledge in it is available At the same time, for a person C whose knowledge of mathematics is very low but she can buy this book, knowledge in it is only conditionally available Location characteristics generate the following classification of knowledge: — Individual knowledge is knowledge to which only one person has access — Group knowledge is knowledge to which only people from a certain group have access — Public knowledge is knowledge accessible to everybody Modalities reflect definite aspects of knowledge There are three existential modalities of knowledge: — Existential knowledge reflects what is, i.e., the existing state of the knowledge domain — Potential knowledge reflects what can be, i.e., possible state of the knowledge domain — Compulsory knowledge reflects what must be, i.e., the necessary state of the knowledge domain September 27, 2016 76 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes There are three confidential modalities of knowledge: — Assertoric knowledge affirms the content of an epistemic structure meaning that the epistemic structure is knowledge, which asserts something about its domain (object) — Hypothetic knowledge conjectures the content of an epistemic structure suggesting that an epistemic structure may be knowledge — Erotetic knowledge inquires about the content of an epistemic structure expressing lack of knowledge and having the form of a question, problem or puzzle For instance, an assertoric proposition asserts that something is (or is not) the case, in contrast to a hypothetic proposition, which asserts the possibility of something being (or not being) the case, or to an apodeictic proposition, which assert that something is (or is not) necessarily the case, e.g., something is necessarily or selfevidently true or false Note that the division of propositions into these three classes is rather subjective depending on the opinion For instance, for some people, e.g., for the majority of philosophers and mathematicians, the proposition “two plus two always equals four” is apodeictic For other people, e.g., for the majority of physicists, this proposition is assertoric, while for those who know about non-Diophantine arithmetics studied in (Burgin, 1977; 1997g; 2007; 2010c) this proposition is hypothetic Researchers also used other names for these types of knowledge For instance, LaDuke called erotetic knowledge by the name antiknowledge (LaDuke, 2002) There are three temporal modalities of knowledge, which reflect directions in knowledge time-orientation: — Knowledge about the future has anticipation modality — Knowledge about present has current modality — Knowledge about the past has bygone modality It is easy to comprehend these modalities for descriptive knowledge For instance, propositions stating something about the past, page 76 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 77 77 e.g., “Yesterday was cold”, have bygone modality Propositions stating something about present, e.g., “Today is warm”, have current modality Propositions stating something about the future, e.g., “According to the weather prognosis, tomorrow will be hot”, have anticipation modality Note that knowledge with any modality can be true or false although knowledge with anticipation modality is more often false in comparison with two other modalities as people rarely have the ability to predict future However, operational and representational knowledge also have temporal modalities For instance, taking operational knowledge, we see that now the majority of quantum algorithms (Deutsch, 1985) have anticipation modality because there are no quantum computers, which can perform these algorithms At the same time, algorithms for counting using abacus have bygone modality, while algorithms used in contemporary operating systems have current modality Taking representational knowledge, we see that, for example, the Ptolemaic model of the Solar system has bygone modality, while the Copernican model of the Solar system has current modality 2.2 Existential characteristics of knowledge Knowledge is an unending adventure at the edge of uncertainty Jacob Bronowski Existence is an important property of anything Properly inquiring whether an object A exists, it is necessary to define or at least, to describe this object Thus, discussing existence of knowledge, we need to explain what knowledge is and here we come to a big problem From ancient times, as we have seen in the previous chapter, philosophers and other researchers have tried to build a comprehensive definition of knowledge and still different opinions exist causing a lot of controversy in this area There were many suggestions but in spite of this, the diversity of essences called knowledge evades any exact and comprehensive definition In spite of many unsuccessful efforts to figure out the unique definition of knowledge, there are various descriptions of knowledge, some of which are essentially disparate September 27, 2016 19:40 78 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes For instance, Froehlich writes, “for some philosophers, validated, true information is that which coheres with other truths (coherence theory of truth) For others, what corresponds to reality (correspondence theory of truth) For others, it is what works or is functional (pragmatic theory of truth) At any event it is always contextual” (cf., ((Zins, 2007)) Even larger diversity of understandings and interpretations is reflected in dictionaries and encyclopedias For instance, in the Webster’s Revised Unabridged Dictionary (1998), knowledge is defined as: A dynamic process: (a) (b) (c) (d) (e) (f) the act or state of knowing; clear perception of fact, truth, or duty; certain apprehension; familiar cognizance; learning; cognition An object: (a) that which is or may be known; (b) the object of an act of knowing; (c) a cognition An object: (a) (b) (c) (d) (e) (f) that which is gained and preserved by knowing; instruction; acquaintance; enlightenment; scholarship; erudition A property: (a) that familiarity which is gained by actual experience; (b) practical skill; as, a knowledge of life As a domain: (a) scope of information; (b) cognizance; (c) notice; as, it has not come to my knowledge page 78 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 79 79 In the Oxford English Dictionary, knowledge is defined as: (i) expertise, and skills acquired by or education; the theoretical or subject, (ii) what is known in a particular information, (iii) awareness or familiarity gained situation a person through experience practical understanding of a field or in total; facts and by experience of a fact or In monographs on knowledge engineering (Osuga et al., 1990), we find the following definitions: Knowledge is a result of cognition Knowledge is a formalized information, to which references are made or which is utilized in logical inference The most popular approach in artificial intelligence is to define knowledge functionally as it was suggested by Allen Newell (1927– 1992) It means that if an external observer O can ascribe to some system A, e.g., to an agent, definite goals and if O witnesses that A is behaving so as to achieve these goals in systematic, rational mode, i.e., according to the principle of rationality, the observer O assumes that A has knowledge (Newell, 1982) One of the problems with this methodology is that as it is demonstrated in (Burgin and Krymsky, 1985), there is no one unique concept of rationality — different people and different systems interpret rationality in their own way It implies that rationality is relative and what seems rational to one person can be completely irrational to another one This makes the functional definition of knowledge essentially dependent on the observer and instead of unification, it generates a multiplicity of concepts of knowledge Herbert Simon (1916–2001) suggested that the development of information technology changes the meaning of the term “to know.” While traditional meaning is to have knowledge in ones memory, now it is understood as to have knowledge where to find the necessary knowledge (Simon, 1971) September 27, 2016 80 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes All approaches to knowledge discussed above give some general ideas about knowledge but these definitions, or better, to say, descriptions, are not sufficiently constructive even to unmistakably distinguish knowledge from knowledge representation and from information The following example demonstrates differences between knowledge and knowledge representation Some event may be described in several articles written in different languages, for example, in English, Spanish, and Chinese, but by the same author These articles convey the same semantic information and contain the same knowledge about the event However, representation of this knowledge is different As in the case with information, there is also a distinction between knowledge representation and knowledge carrier For instance, an individual can be a carrier of knowledge but representation of this knowledge is only in his brain That is why here we not strive to obtain an encompassing precise definition of knowledge There are many books and papers, in which this goal is pursued As an example, we can take such an interesting and well-written book as (Pollock and Cruz, 1999) In contrast to this, we follow the steps of scientists, who build models of studied phenomena instead of explanation of what these phenomena are in layman terms Thus, our goal is to build efficient and flexible models of knowledge on different levels of its existence To achieve this goal, we implement the pragmatic approach to knowledge, which is adopted in artificial intelligence (AI) where there is often no “attempt to define knowledge in the philosophical or even the popular view” (Fayyad et al., 1996) That is, we not try to give a complete characterization of knowledge precisely discerning it from other epistemological structures Our goal is to describe knowledge structure, acquisition, behavior, relations, and utilization Many researchers assume that in contrast to data and information, knowledge, exists only in some knowledge system, such as an individual, society, or a knowledge base Consequently, we apply the observer-oriented approach to knowledge Namely, we not try to exactly define knowledge in general or to describe it in an absolute manner In contrast to this, we presume that an observer page 80 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 81 81 (user or knower) characterizes and utilizes some epistemic structures as knowledge That is, dealing with epistemic structures, an observer makes use of an assembly K of knowledge properties as a knowledge criterion labeling epistemic structures that satisfy criteria from the assembly K by the name knowledge (Chisholm, 1989; Pollock and Cruz, 1999) Criteria (properties) from the arrangement K are called existential characteristics of knowledge because to find whether knowledge with respect to K exists, we need to find an object that satisfies these criteria For instance, Fayyad et al (1996) write “we can consider a pattern to be knowledge if it exceeds some interestingness threshold ” However, in (Burgin, 1989a, 2010), it is assumed that these criteria are subjective and can be different for different individuals and different societies For instance, what was treated as knowledge three millennia ago, e.g., that the Sun rotates around the Earth, now is often considered as being a misconception In a similar way, Fayyad et al (1996) write “knowledge is purely user oriented and domain specific and is determined by whatever functions and thresholds the user chooses.” Let us look at some examples of knowledge criteria (existential characteristics of knowledge) It is possible to consider the following assembly K of knowledge properties as an objective knowledge criterion: To be a belief To be true To be justified This criterion corresponds to the time-worn and widely criticized philosophical definition of knowledge as a “justified true belief” (Russell, 1912; 1948; Gettier, 1966; Goldman, 1967; Lewis, 1996) As Thorkelson shows, this definition suffers from three major problems centered especially around the term “belief” (Thorkelson, 2008) First, this definition reduces knowledge to propositional knowledge, “knowing-that.” As a result, other types of knowledge such as operational knowledge in the form of practical “know-how” (knowledge embodied in actions, behaviors, and procedures), as well as September 27, 2016 82 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes representation knowledge in the form of affective states (knowledge embodied in emotion and sentiment) and phenomenological acquaintance (conferred, for instance, by sensory experience or artistic representation) are excluded Second, insofar as “belief” is considered as a mental state of the individual, the definition directs towards an egocentric rather than socio-centric theory of knowledge (Silverstein, 2004) Third, since a belief is an isolated, singular entity, it is possible to think of knowledge as an unordered aggregate of isolated epistemic items, e.g., propositions, instead of as a coordinated, though not necessarily total epistemic system Scheffler (1965) suggests the following criteria of descriptive/ declarative knowledge: To be a belief To be supported by an adequate evidence To efficiently treat descriptive/declarative knowledge, it is also possible to use the following assembly K of knowledge properties as a subjective knowledge criterion: To be a belief To be believed (assumed) as being true To be believed (assumed) as being justified Here is one more similar assembly K of knowledge properties, which can be used as a knowledge criterion: To be a belief To give correct information about the knowledge object (domain) To give exact information about the knowledge object (domain) However, knowledge criteria not need to include the condition of being a belief For instance, operational knowledge, as a rule, has the form of instructions and not of beliefs Consequently, it is possible to use other knowledge criteria such as “to be useful,” “to be correct” or “to be constructive.” The observer-oriented approach makes it possible to solve some paradoxes related to knowledge For instance, let us imagine that page 82 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 83 83 two millennia ago somebody was asked what the Sun was doing Historical sources allow us to presume that he or she would tell: The Sun is giving light and is rotating around the Earth (2.1) Contemporary knowledge supports the first statement but rejects the second one as according to the present-day celestial mechanics, the Earth rotates around the Sun It means that what people considered as knowledge two millennia ago, now is treated as a misconception This example and many others bring people to the skeptical view on knowledge, which claims that it is impossible to have knowledge or to correctly discern knowledge from other epistemic structures However, the observer-oriented approach to knowledge gives a different answer to this riddle It says that the statement (2.1) was a temporal subjective knowledge about the Sun In our approach, we distinguish three basic types of observers: internal observers and two kinds of external observers — real external observers and abstract external observers An external observer can be either a real system (real external observer), such as a scientist, or an abstract system (abstract external observer), such as a scientific theory An internal observer is a knowing system (knower), i.e., the system such as a reader of a book or a computer that stores knowledge Usually, an observer is treated as a physical system that in the same way, i.e., physically, interacts with the observed object Very often, an observer is interpreted as a human being However, here we use a broader perspective, allowing an abstract system also to be an observer because in our case the observed object is knowledge, i.e., it is an abstract system itself In addition, it is necessary to understand that interaction between abstract systems involves representations of these systems and the performing system, which perform interaction and is usually physical An interesting approach to knowledge posits it as a process of knowing For instance, Polanyi (1974) regards knowledge as both September 27, 2016 84 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes static “knowledge structure” or “knowledge item” and dynamic “knowing” When people discuss something, they usually either suppose that what they discuss exists or try to show that it does not exist It means that existence is treated as a dualistic possibility — either something exists or it does not exist However, this is very inexact and in many cases even wrong because there are different kinds, types, and modes of existence (Burgin, 2012) For instance, does a fictional hero of some novel exist? Many think that he does not exist but a more correct answer is that this fictional hero exists as a mental entity but does not exist as a material object This kind of existence was considered by Alexius Meinong (1853– 1920) in his analysis of language He assumed that language, when properly understood, is a guide to ontology and this ontology permits two kinds of existence: genuine existence of physical objects and generalized existence of objects in imagination, e.g., fictional characters, square circles, and golden mountains To have a complete picture of reality, we come to the conclusion that forms of existence are determined by the world stratification and structuration (Burgin, 2012) Taking the structuration determined by the Existential Triad of the world (Burgin, 1997; 2010), which stems from the long-standing tradition in philosophy and is presented in Figure 2.1, we come to the three existential forms — material/ physical existence, mental existence, and structural existence In this stratification, the Physical (material) World is interpreted as the physical reality studied by natural sciences (cf., for example, (Born, 1953)), the Mental World encompasses different levels of mentality, and the World of Structures consists of various forms and types of structures World of Structures Physical World Mental World Figure 2.1 The existential triad of the world page 84 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 85 85 Usually people comprehend the Mental World as individual mentality Science extended this picture exploring the Mental World on three levels, all of which are included in the Mental World of the Existential Triad: • The first level treats mentality of separate individuals and is the subject of psychological studies As in the case of physical reality, now psychology knows a lot about mentality/psyche of people It is necessary also to remark that in the same way as physics does not study the physical reality as a whole but explores different parts, levels and aspects of it, psychology also separates and investigates different parts and aspects of the individual mental reality, such as intelligence, emotions, conscience, or unconscious However, there are components of individual mentality that yet lay beyond the studies of contemporary psychology • The second level deals with group mentality of various groups of people and is the subject of social psychology, which bridges sociology and conventional psychology In particular, this level includes group conscience, which incorporates collective memory (Durkheim, 1984), collective intelligence (Brown and Lauder, 2000; Nguen, 2008a) and is projected on the collective unconscious in the sense Jung (see (Jung, 1969)) by the process of internalization • The third level encompasses mental issues of society as a whole Social mentality includes social memory, social intelligence, and social conscience Social psychology also studies some features of this level However, these three levels not exhaust the whole Mental World In fact, the Mental World from the Existential Triad comprises higher (than the third) levels of mentality although they are not yet studied by science (Burgin, 1997; 2010) It is possible to relate higher levels of the Mental World to the spiritual mystical worlds described in many religious esoteric teachings Some thinkers, following Descartes, consider the individual mental world as independent of the physical world Others assume that individual mentality is completely generated by physical systems of the organism, such as the nervous system and brain as its part However, September 27, 2016 86 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes in any case, the mental world is different from the physical world and constitutes an important part of our reality Psychological experiments and theoretical considerations show that the Mental World is stratified into three spheres: cognitive or intellectual sphere, affective or emotional sphere and effective or regulative sphere This stratification is based on the extended theory of triune brain and the concept of the triadic mental information (Burgin, 2010) The Mental World has elements and components, which are similar to elements and components of the Physical World In a natural way, the Mental World has its mental space, mental objects (structures), and mental representations (Burgin, 1998a) It is also necessary to explain that the World of Structures directly corresponds to Plato’s World of Ideas/Forms because ideas or forms might be associated with structures Indeed, on the level of ideas, it is possible to link ideas or forms to structures in the same way as atoms of modern physics may be related to atoms of Democritus and Leucippus Only recently, modern science came to a new understanding of Plato ideas, representing the global world structure as the Existential Triad of the world, in which the World of Structures is much more comprehensible, exact, and explored in comparison with the World of Ideas/Forms When Plato and other adherents of the World of Ideas/Forms were asked what idea or form was, they did not have a satisfactory answer In contrast to this, many researchers have been analyzing and developing the concept of a structure (Ore, 1935; 1936; Bourbaki, 1948; 1957; 1960; Bucur and Deleanu, 1968; Corry, 1996; Burgin, 1997; 2010; 2011; 2012; Landry, 1999; 2006) It is possible to find the most thorough analysis and the most advanced concept of a structure in (Burgin, 2012) As a result, in contrast to Plato, mathematics and science has been able to elaborate a sufficiently exact definition of a structure and to prove existence of the world of structures, demonstrating by means of observations and experiments, that this world constitutes the structural level of the world as a whole Informally, a structure is a collection of symbolic (abstract) objects and relations between these objects Each system, phenomenon or process in nature, technology or society has some page 86 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 87 87 structure These structures exist like material things, such as tables, chairs, or buildings do, and form the structural level of the world When it is necessary to learn or to create a system or to start a process, it is done, as a rule, by means of knowledge of the corresponding structure Structures mould things in their being and comprehension If we say that structures exist only embodied in material things, then we have to admit that material things exist only in a structured form, i.e., matter (physical entities) cannot exist independently of structures For instance, atomic structure influences how the atoms are bonded together, which in turn helps one to categorize materials as metals, ceramics, and polymers and permits us to draw some general conclusions concerning the mechanical properties and physical behavior of these three classes of materials Even chaos has its structure and not a unique one The three worlds from the Existential Triad are not separate realities: they interact and intersect Individual mentality is based on the brain, which is a material thing, while in the opinion of many physicists mentality influences physical world (see, for example, (Herbert, 1987)) At the same time, our knowledge of the physical world essentially depends on interaction between mental and material worlds (see, for example, (von Bayer, 2004)) Moreover, our mentality influences the physical world and can change it We can see how ideas change our planet, create many new things and destroy existing ones Even physicists, who research the very foundation of the physical world, developed the, so-called, observer-created reality interpretation of quantum phenomena A prominent physicist, Wheeler, suggests that in such a way it is possible to change even the past He stresses (Wheeler et al., 1983) that elementary phenomena are unreal until observed In addition, there is a projection of the Mental World into the Physical World in the form of creations of human mentality (creativity), such as books, movies, magazines, newspapers, cars, planes, computers, and computer networks This projection determines the Extended Mental World, which consists of the Mental World and its projection The Extended Mental World correlates with the World from the General Popper Triad of the world September 27, 2016 88 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Structural and material worlds are even more intertwined Actually, no material thing exists without a structure Even chaos has its chaotic structure Structures make things what they are For instance, it is possible to make a table from different material: wood, plastics, iron, aluminum, etc What all these tables have in common is not their material; it is specific peculiarities of their structure In a similar way, according to Poincar´e (1908), space is in reality amorphous, and it is only the things in space that give it a structure (form) As some physicists argue, physics studies not physical systems as they are but structures of these systems, or physical structures In some sciences, such as chemistry, and areas of practical activity, such as engineering, structures play the leading role For instance, the spatial structure of atoms, chemical elements, and molecules determines many properties of these chemical systems Contemporary physics treats the physical world as a net of interacting components (systems), where there is no physical meaning to the state of an isolated object A physical system (or, more precisely, its contingent state) is represented by the net of relations with the surrounding objects it retains As a result, the physical structure of the world is identified with such a global net of system relationships As North (2009) writes, physics is supposed to be telling us about the nature of the world, while physical theories are formulated in a mathematical language, using mathematical structures, which implies that mathematics is somehow telling us about the physical make-up of the world Plato postulated independent existence of his world of ideas, and it was demonstrated that it is possible to consider structures as scientific counterparts of Plato ideas (Burgin, 2011) Thus, it is natural to ask the question whether structures exist without matter Here we are not going into detailed consideration of this fundamental problem It is important that as a coin has two sides, material things always have two aspects — substance and structure Like atoms studied by contemporary physics were prefigured by ancient thinkers, such as Democritus from Abdera (460–370 B.C.E.) and Leucippus of Miletus (ca 480 – ca 420 B.C.E.), the Existential page 88 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 89 89 Triad also has several precursors suggested by various thinkers such as Plato, Aristotle, Popper, or Gă odel John Locke also suggested a similar triadic stratification of the world and knowledge about the world He wrote: “All that can fall within the compass of human understanding, being either, first, the nature of things, as they are in themselves, their relations, and their manner of operation: or, secondly, that which man himself ought to do, as a rational and voluntary agent, for the attainment of any end, especially happiness: or, thirdly, the ways and means whereby the knowledge of both the one and the other of these is attained and communicated; I think science may be divided properly into these three sorts.” (Locke, 1690) This gives us the structures presented in Figures 2.2 and 2.3 Naturally, the structure of science, according to Locke, is structurally isomorphic to his structure of the World Note that Locke triads are similar (but not exactly) to the Existential Triad The difference is that: (1) nature is only a part of the physical world, e.g., people and machines are elements of the physical world but not belong to nature; (2) signs are only one kind of structures; and (3) although mentality is a pivotal characteristics of human beings, not only human beings have mentality, while a human being cannot be reduced to her/his mentality World of Signs Nature Human beings Figure 2.2 The Locke triad of the world Doctrine of Signs Natural sciences Social sciences and Humanities Figure 2.3 The Locke triad of science September 27, 2016 90 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes According to the existential stratification of reality, knowledge exists as structure in the world of structures but has many representations in two other worlds Namely, there are different physical representations of knowledge, e.g., printed texts in books and journals, written algorithms, software of computer and networks, written manuscripts or states of the computer memory in knowledge bases There are also mental representations of knowledge in the mentality (mind) of people and in the mentality of society However, even having correct knowledge representation, the knowing system (knower) does not always possess knowledge Indeed, imagine a situation when you have a book written in a language you not know, e.g., in Hindu or Japanese This book can have a lot of knowledge but you not possess this knowledge because you cannot read the book Thus, knowledge exists but is not accessible to you This and other examples show that there are many modes, modalities, kinds, types, gradations, and dimensions of existence (Burgin, 2012) However, when existence is treated as a property, it usually means that some object exists, at least, as a mental entity, i.e., it has a name (sometimes several names) and different ascribed properties Although we can ask the question whether there is a material object that has these properties For instance, after Dirac in 1930’s suggested a new particle — positron, the majority of physicists believed that such a particle did not exist However, after several years existence of positron was proved by experiments Knowing is frequently related to existence Very often people assume that what they not know does not exist This exhibits the subjective form of existence, that is, existence in mentality of people For instance, for a long time, people did not know that the Solar system has such a planet as Neptune Consequently, this planet did not exist for them although it existed as a celestial body, i.e., it had physical existence Moreover, existence is a property not only of material things but also of theoretical constructs For a long time, mathematicians did not know about negative numbers Consequently, negative numbers did not exist for them Even after negative numbers had been discovered in the East, namely, in China and India, and then brought to Europe, many European mathematicians tried to argue page 90 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 91 91 that negative numbers did not exist (Martinez, 2006) In a similar way, some notable mathematicians of the 19th century insisted that irrational numbers did not exist (Burton, 1997) For a long time, it was assumed that knowledge is something that exists only in the mentality of people Some researchers believe that this is the crucial difference between knowledge and information, which exists in anything However, the technological development changed the situation Indeed, because knowledge is vital to the whole existence of people, various artificial tools have been invented for knowledge acquisition, storage, transmission, and transformation Among other things, people invented and developed oral and written languages, papyrus, clay tablets, paper, printing, books, and computers This brought an understanding that knowledge also existed not only in people’s mentality but also in various physical things but not in all in contrast to information As a result, researchers started to explore knowledge in artificial systems only after computers came into being and the research area called AI emerged Later when knowledge became crucial for organizations, researchers began studying knowledge not only on the level of individual mentality but also in the group (collective) mentality, performing research in social epistemology and knowledge management One of the important results of this research was explication of distinctions between tacit knowledge, which exists in individual mentality, and explicit knowledge, which usually belongs both to individual mentality and to collective mentality 2.3 Descriptive properties of knowledge and corresponding typology Beware of false knowledge; it is more dangerous than ignorance Bernard Shaw Descriptive properties (characteristics) of knowledge can be formally described by a function assigning values from the property scale to knowledge items or by an abstract property (cf., Chapter and (Burgin, 1985)) For instance, truthfulness is a descriptive property with the scale {True, False} Note that it is possible to represent September 27, 2016 92 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes relations between knowledge items as abstract properties (Burgin, 2010) Relational properties (characteristics) of knowledge characterize relations of knowledge items, e.g., represented by texts or computer files, to physical or mental objects (systems) For instance, the denotation theory of meaning is based on relations between knowledge items and objects they denote (Russell, 1905; Ryle, 1957; Parkinson, 1968) In other words, relational characteristics of knowledge are molded by relations between knowledge and systems that are related to knowledge Contextual properties (characteristics) of knowledge are properties of objects related to knowledge It is possible also to formally describe them by a function assigning values from the property scale to these objects or by an abstract property (cf., Chapter and (Burgin, 1985)) Internal characteristics of knowledge are innate to knowledge as a structural phenomenon We start with the structure of knowledge, which is the basic integral characteristic of knowledge Note that we make a distinction between a knowledge structure and the structure of knowledge A knowledge structure is one or several knowledge items in their structural form, while the structure of knowledge is a structural description of knowledge organization displaying its internal and external relations in a general form, that is, relations that are innate to knowledge in general To find the structure of knowledge, we observe that the indispensable trait of knowledge indicates that each element or system of knowledge refers to some object domain because knowledge is always knowledge about something It means that for any knowledge system (element) K, there is a domain D of real or abstract objects and K describes the whole D or its part Note that it is possible to treat a domain as one object In such a way, we come to the following diagram, which is a specific case of named sets (cf., Appendix) representation Knowledge Item K Object (Domain) D reflection (2.2) page 92 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 page 93 93 Knowledge Characteristics and Typology Diagram (2.2) is also related to Diagram (2.3) because knowledge is a cognitive representation of knowledge objects and knowledge domains, which is intrinsically related to their symbolic representations Besides, cognitive representation is often symbolic Object (Domain) D Cognitive (symbolic) representation of D (2.3) For instance, a symbolic representation of an object A may be a sentence in a natural language (English, Spanish, or French), a logical formula, a mathematical expression and so on Thus, according to this new approach, the statement “People live on the Earth” is not knowledge per se It is a cognitive structure, which becomes knowledge only when it is connected to the object (system) that consists of people and the celestial body called the Earth However, Diagram (2.2) does not give a complete structure of knowledge because knowledge does exist by itself but belongs to a knowledgeable system or a knower This gives us Diagram (2.4) Knower (knowledgeable system) knowing possession (2.4) representation Knowledge item K Domain D The structures of knowledge presented by Diagrams (2.2)–(2.4) reflect the surface level of knowledge organization An exposition of further details about knowledge organization and structure is given in Chapters 4–6 We discern the following kinds of knowledge systems: — Knowledge item is a knowledge system that is contemplated separately of other knowledge systems — Knowledge unit is a knowledge item that is used for constructing other knowledge systems and treated as a unified entity — Knowledge quantum is a minimal, in some sense, knowledge unit — Knowledge element is an element of a knowledge system (structure) September 27, 2016 94 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes By definition, any knowledge unit is also a knowledge item but the converse is not always true To understand the difference between a knowledge unit and a knowledge item, let us look at some examples Knowledge in one story (novel) is a knowledge unit Knowledge in several unrelated stories (novels) is a knowledge item Knowledge about one person is a knowledge unit Knowledge about several unrelated persons is a knowledge item However, knowledge about members of one family is a knowledge unit All of the above are knowledge structures or knowledge systems Here we utilize two meanings of the term knowledge system: Knowledge system as a concise representation of knowledge Knowledge system as a structure consisting of knowledge elements and relations between them An example of a knowledge item: “This book is about knowledge Its title is “Theory of Knowledge: Structures and Processes.” It has many pages It has nine chapters.” An example of a knowledge unit: “This book is about knowledge.” This statement is also a knowledge quantum An example of a knowledge element: “a book” At the same time, there are also composite knowledge elements, e.g., “an interesting book.” 2.3.1 Dimensions and other characteristics of knowledge Dimensions are basic descriptive characteristics of epistemic structures in general and knowledge in particular Each dimension has page 94 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 95 95 different gradations or/and modalities Some of these gradations are discrete, while others can be considered as continuous It is possible to discern the following dimensions of epistemic structures (of knowledge): The correctness dimension reflects adequacy of to its object or domain representation by the knowledge item The confidence dimension reflects confidence of the knower (knowledge user) in the knowledge item property estimation, including certainty of the knower (knowledge user) in knowledge item correctness as its component The validation dimension reflects confirmation of confidence of the knower (knowledge user) in the knowledge item property estimation, including justification of the correctness estimation of a knowledge item The complexity dimension reflects complexity of a knowledge item including several components such as clarity The significance dimension reflects value and significance of a knowledge item The efficiency dimension reflects the role of a knowledge item in achieving some goals The reliability dimension reflects reliability of a knowledge item The abstractness/generality dimension reflects the level of abstraction of a knowledge item, as well as the degree of generalization achieved by a knowledge item The completeness/exactness dimension reflects completeness of a knowledge item with respect to its object (domain), as well as exactness with which a knowledge item reflects/represents its object (domain) 10 The meaning dimension reflects meaning of a knowledge item The first three dimensions are the separation dimensions as these traits have been traditionally used to separate knowledge from other epistemic structures, e.g., from beliefs (cf., Section 2.2) The next six dimensions are the feature dimensions The 10th dimension is the integration dimension as it can include any other dimension and is the primary feature for knowledge utilization September 27, 2016 96 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Each dimension integrates specific knowledge properties usually containing these properties as its components There are also other characteristics of knowledge Novelty shows the extent to which the content is original, or its relation to other works, e.g., whether it repeats, duplicates, adds to, or contradicts the previous work Knowledge domain is what this knowledge is about It is expressed as the subject matter as well as named or implied persons, places, institutions, devices, etc Specificity or depth refers to depth of coverage or degree of detail of the knowledge in a message Amount of knowledge has many different meanings and measures One of such measures is the number of characters, pages or other physical characteristics of a text, which is a carrier of knowledge Another measure of knowledge amount is the Hartley–Shannon entropy (Burgin, 2010) One more estimate for knowledge amount is the recipient’s sense of number of known facts or ideas although there is not yet a formal measure for this Algorithmic complexity gives a possibility to measure amount of knowledge about constructive objects (Burgin, 2010) 2.3.2 Correctness, relevance, and consistency of knowledge Here we give the most general definition of correctness treating it as a relational property In essence, correctness reflects relation of knowledge to some system C of correctness conditions Definition 2.3.1 A knowledge system (unit) K is correct with respect to a system C of conditions or simply C -correct if it satisfies all conditions from C Definition 2.3.2 Conditions from the system C are called components of C -correctness Let us consider some examples Example 2.3.1 Let us look at such procedural/operational knowledge as programs (BK) This knowledge informs computer what to page 96 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 97 97 or how to perform computations Correctness becomes a critical issue in software and hardware production and utilization as a result of the increased social and individual reliance upon computers and computer networks A study of the National Institute of Standards found that only software defects resulted in $59.5 billion annual losses (Tassey, 2002; Thibodeau, 2002) It is possible to find a detailed analysis of the concept software correctness and the most comprehensive development of this concept in (Burgin and Debnath, 2006; 2007) There are different forms of software correctness, such as functional, descriptive, procedural, temporal, and resource correctness Example 2.3.2 Let us contemplate propositional knowledge, i.e., knowledge expressed by propositions in some logical language This may be, the most popular form of knowledge representation (cf., (Bar-Hillel and Carnap, 1952; 1958; Halpern and Moses, 1985)) Then a knowledge system is usually represented by a propositional calculus Traditionally, it is assumed that such knowledge is correct if this calculus is consistent Software correctness introduced in (Burgin and Debnath, 2006) is one more example of knowledge correctness as a software system is a representation of operational knowledge Consistency of descriptive knowledge in the sense of (Nuseibeh et al., 2001) is also an example of knowledge correctness Existence of various correctness conditions results in a variety of correctness types Types of correctness: — Truth — Correlation — Consistency In addition, correctness of knowledge may be higher or lower For instance, the system K can satisfy only of conditions from C or some conditions can be satisfied only partially As a result, correctness is, in essence, a gradual, often fuzzy, property because in many cases, conditions from the set C can be satisfied only partially This shows that it is possible to introduce different measures of correctness, which are September 27, 2016 98 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes functions on knowledge items that can take numerical values, vector values, or even values in a partially ordered set This brings us to degrees of correctness, which turn correctness into a fuzzy property or more generally, into an abstract property (cf., (Burgin, 1985) and Chapter 6) Let us take a system of conditions C and consider a measure m of condition satisfaction by knowledge items Definition 2.3.3 A knowledge system (unit) K is correct to the degree n with respect to a system C of conditions if the measure m of satisfaction of conditions from C is equal to n Note that n may be not only a number but also a vector when we separately consider correctness components or an element from a partially ordered set Let us consider some examples Example 2.3.3 Let us consider propositional knowledge, i.e., knowledge represented by propositions Defining correctness of propositions, it is possible to take into consideration three aspects of propositions — syntactic, semantic, and pragmatic aspects For each of these aspects, we take one criterion of knowledge correctness The syntactic criterion of correctness c1 : The proposition has the form of a syntactically correct English sentence The semantic criterion of correctness c2 : The proposition is true, e.g., true in the sense of classical logic The pragmatic criterion of correctness c3 : The proposition has a model in the real world This allows us to formally define knowledge correctness taking as the system C = {c1 , c2 , c3 } of correctness conditions and evaluate some propositions We denote the weight of a proposition p relative to the correctness criterion ci by wi (p), i = 1, 2, page 98 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 99 99 Proposition p1 : ≥ Correctness weights: w1 (p1 ) = because it is not a syntactically correct English sentence w2 (p1 ) = because it is true that ≥ w3 (p1 ) = because the conventional (Diophantine) arithmetic is a model for p1 Proposition p2 : A bear is an animal Correctness weights: w1 (p2 ) = because it is a syntactically correct English sentence w2 (p2 ) = because it is true that a bear is an animal w3 (p2 ) = because the set of all animals is a model for p2 Proposition p3 : In 2000, the King of France was blue w1 (p3 ) = because it is a syntactically correct English sentence w2 (p3 ) = because it is not true that in 2000, the King of France was blue w3 (p3 ) = because there is no model for p3 in the real world Thus, we have three elements of a weighted knowledge space (cf., Section 3.1): (p1 ; 0, 1, 1) (p2 ; 1, 1, 1) (p3 ; 1, 0, 0) Note that Example 2.3.3 shows that the most popular attribute of knowledge — truth — is only one kind of knowledge correctness Example 2.3.4 Let us consider operational knowledge, i.e., knowledge represented by automata or algorithms September 27, 2016 100 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes The model criterion of correctness c1 : The automaton A is a Turing machine (Burgin, 2005; or Section 2.3) The termination criterion of correctness c2 : The automaton A is defined for all words in its alphabet This allows us to formally define knowledge correctness taking as the system C = {c1 , c2 } of correctness conditions and evaluate some propositions We denote the weight of an automaton A as an operational knowledge relative to the correctness criterion ci by wi (p), i = 1, Automaton A1 is a deterministic finite automaton (Burgin, 2005) Correctness weights: w1 (A1 ) = because it is not a Turing machine w2 (A1 ) = because any deterministic automaton A is defined for all words in its alphabet (Burgin, 2005) Automaton A2 is a universal Turing machine (Burgin, 2005) Correctness weights: w1 (A2 ) = because it is a Turing machine w2 (A2 ) = because a universal Turing machine is defined for all words in its alphabet Thus, we have two elements of a weighted knowledge space (cf., Section 3.1): (A1 ; 0, 1) (A2 ; 1, 1) Definition 2.3.1 allows us to introduce three modalities of knowledge correctness: — Description modality of knowledge correctness reflects how well this knowledge represents or describes its domain — Attribution modality of knowledge correctness reflects how well this knowledge is connected to the domain that this knowledge is attributed to page 100 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 101 101 — Logical modality of knowledge correctness reflects how well this knowledge satisfies some logical rules, such as, for example, absence of contradictions Description and attribution modalities are definitely relational properties of knowledge because they depend on relations between knowledge and some domains Logical modality can be relational property of knowledge in some cases and can be internal property of knowledge For instance, such a component of logical modality as (inner) consistency is an internal property of knowledge systems, while consistency of one knowledge system with respect to another knowledge system is a relational property of knowledge systems Each of knowledge correctness modalities has its components Accuracy, exactness and precision are components of the description modality of knowledge correctness Definition 2.3.4 Accuracy of descriptive knowledge reflects to what extent the given description is sufficient and does not include unnecessary issues For instance, if a man is tall and thin, then the proposition “He is a big man” is less accurate than the proposition “He is a tall man.” Usually informal descriptions are less accurate than formal descriptions For instance, the proposition “His height is seven feet” is more accurate than the proposition “He is a tall man.” Definition 2.3.5 Accuracy of representational knowledge shows to what extent the given representation is sufficient and does not include unnecessary features For instance, the Copernican model of the Solar system is more accurate than the Ptolemaic model of the Solar system Definition 2.3.6 Accuracy of operational knowledge shows to what extent the given procedures, tools, goals, norms are sufficient and necessary for reaching the desired goal For instance, a car mechanic has more accurate operational knowledge about cars than an average person September 27, 2016 102 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Note that knowledge represented by a statement can be clear but not accurate, as in the case of the statement “The weight of a dog is between one and one thousand pounds.” Definition 2.3.7 Precision of descriptive and representational knowledge reflects whether it is possible to give more details or if a knowledge item could be more specific For instance, representation of real numbers has different levels of exactness or precision For floating point numbers, there are three commonly used levels of precision: single precision, double precision and long double, or extended, precision (Sauer, 2006) In the single precision representation, the exponent of a number has bits and the mantissa of a number has 23 bits In the double precision representation, the exponent of a number has 11 bits and the mantissa of a number has 52 bits In the long double precision representation, the exponent of a number has 15 bits and the mantissa of a number has 64 bits Definition 2.3.8 Precision of operational knowledge shows how close it allows to approach the desired goal For instance, two ways of number truncation are usually used — chopping and rounding (Sauer, 2006) By construction, rounding gives more precise results than chopping Note that knowledge represented by a statement can be both clear and accurate, but not precise, as in the case “Bob is overweight” because we not know how overweight Bob is — one pound or 500 pounds Definition 2.3.9 Exactness of descriptive and representational knowledge shows how a knowledge item matches the knowledge domain, i.e., whether a descriptive knowledge item describes and representational knowledge represents a larger or a smaller domain in comparison with its assigned domain and the extent of the existing difference For a long time, philosophers assumed that knowledge is always absolutely true and completely exact However, a little by little, page 102 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 103 103 new generations of researchers has begun to understand that knowledge can be only partially true and moderately exact The first idea to mathematical treatment of partially true and moderately exact knowledge dates back at least to the middle of the 19th century when George Boole aimed to reconcile the classical logic, which tends to express complete knowledge or complete ignorance, and probability theory as an extension of the classical logic such as it tends to express partial or/and imprecise knowledge or ignorance (Boole, 1854) His approach represented subjective interpretation of probabilities because people often not have enough information to assign definite numbers to probabilities of given events Keynes formulated and applied an explicit interval estimate approach to probability, further developing the theory of imprecise probability and describing its applications (Keynes, 1921) However, probability represents only one aspect knowledge vagueness and inexactness To reflect these properties of knowledge in a better way, researchers developed fuzzy set theory, which has become one of the most popular mathematical approaches to problems of uncertainty and imprecision is fuzzy set theory Fuzzy sets were introduced by Lofti Asker Zadeh in 1965 and approximately at the same time, Salii (1965) defined a more general kind of structures called L-relations, which were studied by him in an abstract algebraic context Fuzzy relations, which are used now in different areas, such as decision-making (Kuzmin, 1982) and clustering (Bezdek, 1978), are special cases of L-relations when L is the unit interval [0, 1] The aim of Zadeh was to get better mathematical models for reallife systems and processes, as well as better techniques for human reasoning and decision-making, than the conventional set theory allowed by constructing a more realistic set theory To achieve this goal, Zadeh considered generalizations of sets that allow graded membership of their elements Thus, he assumes that elements can have different grades of membership in a set His main argument was that “classes of objects encountered in real physical world not have precisely defined criteria of membership” (Zadeh, 1965) This approach also reflects situations in which our knowledge about membership is incomplete Fuzzy set theory replaces the two-valued membership September 27, 2016 104 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes function used for sets with a real-valued membership function As a result, membership may be treated as a probability, or as a degree of truthfulness In a similar way, it is possible to assign a real value to assertions as an indication of their degree of truthfulness To represent imprecise, vague, inexact or fuzzy knowledge, Lofty Zadeh also suggested using linguistic variables as a second-level structure based on fuzzy sets (Zadeh, 1973) To understand knowledge correctness, let us consider its components and facets Relevance, domain interpretability and domain describability are components of the attribution modality of knowledge correctness Relevance of knowledge is a pivotal component of knowledge correctness, which has three basic types: • Knowledge K is domain relevant if it is related to the domain (object) it is attributed to • Knowledge K is problem relevant if it is related to the problem under consideration • Knowledge K is goal relevant if it is useful in achieving a definite goal Definition 2.3.10 The domain relevance of a knowledge item shows the extent to which this knowledge item is related to some issue of a considered domain or how does that bear on the issue As relations can be stronger or weaker, domain relevance may be higher or lower For instance, if the domain is a forest in the U.S., then knowledge about the river near this forest is more relevant to this domain than knowledge about some river in Australia To represent these distinctions in the quantitative form, it is possible to introduce different measures of domain relevance, the scale of which can be either the two-element set {0, 1} or the interval [0, 1] or the set of all non-negative real numbers True knowledge about a domain A can be irrelevant to a domain B, which is not related to A For instance, knowledge about elementary particles is irrelevant to music or art Knowledge of geometry is irrelevant to moral issues page 104 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 105 105 Definition 2.3.11 The problem relevance of a knowledge item shows the extent to which this knowledge item is related to some problem As relations can be stronger or weaker, problem relevance may be higher or lower To represent these distinctions in the quantitative form, it is possible to introduce different measures of problem relevance, the scale of which can be either the two-element set {0, 1} or the interval [0, 1] or the set of all non-negative real numbers Definition 2.3.12 The goal relevance of a knowledge item shows the extent to which this knowledge item is helpful (useful) in achieving some goal As in the case of other types of relevance, it is possible to introduce different measures of domain relevance, the scale of which can be the two-element set {0, 1} or the interval [0, 1] or the set of all nonnegative real numbers For instance, if the goal is to know weather in Los Angeles, then knowledge about weather in Santa Monica is more relevant to this goal than knowledge about weather in New York A knowledge item represented by a statement can be clear, accurate, and precise, but not relevant to the question at issue For instance, students often think that the amount of effort they put into a course should be used in raising their grade in a course Often, however, the “effort” does not measure the quality of student learning, and when this is so, effort is irrelevant to their appropriate grade (Elder and Paul, 2009) It means that if the goal of a student is to get good knowledge or a high grade, then the operational knowledge of how to apply student’s effort can be weakly goal relevant or even goal irrelevant Relevance of knowledge influences knowledge correctness in general because if a knowledge unit K is irrelevant to some issue K of the domain D of its attribution, then this knowledge cannot be treated as correct with respect to the issue K It is possible to consider relevance as a binary property with only two values — relevant and irrelevant However, a more exact representation of this property treats relevance as a fuzzy property allowing different degrees of relevance September 27, 2016 106 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Let us consider two other components of the attribution modality of knowledge correctness Definition 2.3.13 Domain interpretability of knowledge reflects how an item of knowledge can be interpreted in the domain this knowledge is attributed to The third component of the attribution modality of knowledge correctness is not the same for different types of knowledge Definition 2.3.14 Domain descriptability of descriptive knowledge reflects how well this knowledge can describe the domain (object) it is attributed to For instance, the statement “The Mars has two satellites” has higher domain descriptability than the statement “The Mars has satellites.” Definition 2.3.15 Domain representability of representational knowledge reflects how well this knowledge can represent the domain (object) it is attributed to For instance, when the domain (object) of knowledge is number π, then the number 3.14159 has higher domain representability (i.e., gives a better approximation) than the number 3.14 Definition 2.3.16 Domain applicability of operational knowledge reflects how well this knowledge can be applied to the domain (object) it is attributed to For instance, when the domain of knowledge consists of computations, then knowledge in the form of Turing machines has higher domain applicability than knowledge in the form of finite automata, while knowledge in the form of inductive Turing machines has higher domain applicability than knowledge in the form of Turing machines (Burgin, 2005) The logical modality of knowledge correctness also has three components Namely, consistency, provability, and testability are components of the logical modality of knowledge correctness Consistency is an important relational characteristic of a knowledge system The traditional approach to knowledge consistency page 106 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 107 107 implies separation (and elimination) elements of knowledge that are called contradictions For instance, a standard example of a logical contradiction is the expression p∧ p where p is a proposition, e.g., the expression “It is a table and it is not a table” is contradictory by the rules of classical logic However, as we have seen in Chapter and will see in Chapter 6, Indian logic accepts statements of the form “S is and is not P ,” which are unacceptable, for example, in Aristotle’s syllogistics It is interesting to know that in the 20th century, fuzzy logic also made such statements logically correct (Bandemer and Gottwald, 1996) For instance, a ball that is partially green and partially yellow is green and is not green Studying system consistency in logic and beyond, researchers came to the conclusion that consistency is not an absolute property quality as in classical logic but is a relative property of various systems, including logical systems The most general definition of consistency is given in (Nuseibeh et al., 2001) Namely, at first, a system C of consistency conditions is determined in a class of systems K Then we have the following concept Definition 2.3.17 A system R from K is consistent (inconsistent) with respect to C if satisfies (does not satisfy) all conditions from C The most popular example of consistency is logical consistency when a system of propositions or predicates is consistent when it does not allow inference (deduction) of expressions A and A A weaker kind of consistency is weak logical consistency when a system of propositions or predicates is consistent when it does not contain expressions A and A In logical calculi and in logics, weak logical consistency coincides with logical consistency Here we are mostly interested in consistency of knowledge systems When we are dealing with propositional knowledge, the most popular is the conventional consistency, the basic condition for which is absence of contradictions Another reason for exclusion of contradiction is the situation when any false statement (contradiction) implies any other statement in classical logics As a result, people September 27, 2016 108 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes always considered contradictions as abhorrent irregularities of thinking, which have to be eliminated from correct thinking and valid logic However, as we have seen before, what is a contradiction by classical criteria can provide useful knowledge As, a result, a new kind of logical consistency — paraconsistency — was introduced in the 20th century by weakening conditions of logical consistency (Priest et al., 1989) Namely, a logic is paraconsistent if and only if its logical consequence relation is not explosive Here explosiveness means that using axioms and consequence relations of the logic, it is possible to deduce any formula, e.g., proposition, in the language of this logic Paraconsistent logics accommodate inconsistency in a manner that treats inconsistent information and inconsistent knowledge as informative There are different systems of paraconsistent logics, e.g., discussive logics, non-adjunctive systems, preservationism, adaptive logics, logics of formal inconsistency, many-valued logics, and relevant logics As it is possible to have several consistency conditions and/or some of the conditions can be satisfied only partially, in general, consistency and inconsistency are fuzzy properties In general, consistency is a particular case of correctness Namely, comparing Definitions 2.3.1 and 2.3.17, we see that correctness becomes consistency when correctness conditions actually are consistency conditions However, consistency in general and logical consistency, in particular, is only one type of correctness There are also other types such as provability and testability Provability as a component of the logical modality of knowledge correctness reflects how and to what extent it is possible to prove, e.g., support by evidence or infer, correctness of a given knowledge item For instance, we can assume that a system of statements, e.g., a formal theory, is correct only when it is consistent and it is possible to prove its consistency From this point of view, any sufficiently powerful mathematical theory U , i.e., a theory that includes the formal arithmetic, is not correct by itself because by the second Gă odel’s incompleteness theorem, it is impossible to prove consistency of U page 108 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 109 109 using only means from the theory U Nevertheless, the theory U may be internally incorrect but externally correct if there are other means to prove its consistency Testability as a component of the logical modality of knowledge correctness reflects how and to what extent it is possible to estimate, e.g., support by evidence or infer correctness of a given knowledge item Testability is essentially important for operational knowledge For instance, it is possible to treat a computer program as a potentially correct operational knowledge item if it is possible to test it finding and correcting all deficiencies In this case, the possibility of deficiency correction is also a correctness condition An important type of knowledge correctness is truthfulness There are different ways to introduce truthfulness of knowledge All of them involve two types of truthfulness functions: domain-oriented, reference-oriented, and attitude-oriented According to the first approach, we have the following model of truthfulness A system T , or as it is now fashionable to call it now, an agent A that has knowledge K about the domain (object) D is considered Then the truthfulness K means that (condition from C) the description that K gives for D is true Thus, the truthfulness tr(K, D) of the knowledge K about the domain D is a function of two variables that takes two values — true and false In addition, the function tr(T , D) gives conditions for differentiating knowledge from similar structures, such as beliefs, descriptions or fantasies Knowledge truthfulness, or domain related correctness, shows absence of distortions in knowledge representation of its domain Thus, truthfulness is closely related to accuracy of knowledge, which reflects how close is given knowledge to the absolutely exact knowledge However, truthfulness and accuracy of knowledge are different properties For instance, statements “π is approximately equal to 3.14” and “π is approximately equal to 3.14159” are both true, i.e., their truthfulness is equal to At the same time, their accuracy is different The second statement is more accurate than the first one We see that conventional truthfulness can indicate only two possibilities: complete truth and complete falsehood September 27, 2016 110 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes To measure truthfulness in a better way, we utilize a measure tr of truthfulness of knowledge in the system T Such a measure, allows one to develop the comprehensive approach to true knowledge However, in many situations, it is impossible to verify (or validate) truthfulness or falsehood and we come to three basic types of knowledge: — correct knowledge, — incorrect knowledge, — unverified knowledge To formalize these concepts, let us take a number k from the interval [0, 1] Definition 2.3.18 (a) A portion of knowledge I is called true or genuine knowledge about D with respect to a measure cor if cor (I, TA ) > (b) A portion of knowledge I is called true or genuine to the degree k knowledge about D with respect to a measure cor if cor (I, TA ) > k This definition looks natural and adequately works in many situations However, there are some problems with it Imagine that information that gives correct knowledge about some domain (object) D comes to A but it does not change the knowledge system TA because correct knowledge about D already exists in TA In this case, cor(I, TA ) = cor (I(TB ), TA ) — cor(TB , TA ) = This implies that it is necessary to distinguish relative, i.e., relative to a knowledge system TA , knowledge correctness and absolute correction To define absolute correction, we take a knowledge system T 0D that has no a priori knowledge about the domain (object) D Definition 2.3.19 A portion of knowledge I is called purely true knowledge about D with respect to a measure cor if cor(I, T0D ) > It is necessary to understand that it is not a simple task to find such a knowledge system T0D that has no a priori knowledge about the domain (object) D Besides, truthfulness depends on other properties of the knowledge system T0D , e.g., on algorithms that page 110 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 111 111 are used for conversion of received information into knowledge It is possible to get true information, which eventually transformed into incorrect knowledge For instance, during the Cold War, witty people told the following joke “Russia challenged the United States to a foot race Each country sent their fastest athlete to a neutral track for the race The American athlete won The next day, the major Soviet newspaper “Pravda”, which means truth in Russian, published an article with the following title: Russia takes second in international track event, while the United States comes in next to last.” We see that literally the article of “Pravda” is true, but people’s a priori knowledge makes them to assume a big race with many participants and in such a way, they get a wrong impression and false knowledge if they did not know how many participants was in the race It is possible to treat truthfulness and correctness as linguistic variables in the sense of (Zadeh, 1973) For instance, we can separate such classes as highly correct/true knowledge, sufficiently correct/true knowledge, weakly correct/true knowledge, weakly false knowledge, and highly false knowledge From this point of view, we come to three fuzzy types of knowledge: — true or genuine knowledge, — partially true knowledge, — false knowledge However, it is possible to separate these types of knowledge in a more general situation, utilizing the concept of knowledge measure There are different ways to this Analyzing different publications, we separate two classes of approaches: relativistic definitions and universal definitions The latter approach is subdivided into objectdependent, reference-dependent, and attitude-dependent classes At first, we consider the relativistic approach to this problem September 27, 2016 112 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes To have genuine knowledge in the conventional sense, we take such measure m as correctness of knowledge or such measure as validity of knowledge or of knowledge acquisition Let us specify the relativistic approach in the case of cognitive knowledge, taking a measure m that reflects such property as truthfulness Thus, to get more exact representation of the convenient meaning of the term true knowledge, we consider only cognitive knowledge and assume that true cognitive knowledge gives true knowledge, or more exactly, make knowledge truer than before However, it is necessary to understand that the truth of knowledge and the validity of its acquisition are not always the same For instance, the truth of knowledge represented by propositions and the validity of reasoning are distinct properties, while there are relations between them (cf., for example, (Suber, 2000)) This relationship is not entirely straightforward It is not true that truth and validity, in this sense, are utterly independent because the impossibility of “case zero” (a valid argument with true premises and false conclusion) shows that one combination of truth-values is an absolute bar to validity According to the classical logic, when an argument has true premises and a false conclusion, it must be invalid In fact, this is how we define invalidity However, in real life, people are able to take a true statement and to infer something false An example of such a situation gives the Cold War Joke considered in this section To formalize the concept of knowledge truthfulness, we use the model developed in (Burgin, 2004) and described in Chapter According to this model, general knowledge K about an object F has the structure represented by Diagram (2.5) and high level of validation g W L t p U C f (2.5) page 112 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 113 113 This diagram has the following components: (1) some class U containing an object F ; (2) an intrinsic property that is represented by an abstract property T = (U, t, W ) with the scale W , which is defined for objects from U (cf., Chapter 5); (3) some class C of names, which includes a name “F ” of the object F ; (4) an ascribed property that is represented by an abstract property P = (C, p, L) with the scale L, which is defined for names from C (cf., Chapter 5); (5) the correspondence f assigns names from C to objects from U where in general case, an object has a system of names or more generally, conceptual image (Burgin and Gorsky, 1991) assigned to it; (6) the correspondence g assigns values of the property P to values of the property T In other words, the correspondence g relates values of the intrinsic property to values of the ascribed property For instance, when we consider a property of people such as height (the intrinsic property), in measuring the height, we can get only an approximate value of the real height, or height with some precision (the ascribed property) In more detail, the basic structure of knowledge is discussed and described in Chapter According to the attitude-dependent approach, we have the following definitions Definition 2.3.20 General knowledge T about an object F for a system R is the entity that has the structure represented by Diagram (2.5) that is estimated (believed) by the system R to represent with high extent of confidence true relations Consequently, we come to three main types of knowledge about some object (domain): — objectively true knowledge, — objectively neutral knowledge, — objectively false knowledge September 27, 2016 114 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Taking some object domain D and tr as the measure m in Definition 2.3.3, we obtain unconditional concepts of true and false knowledge Definition 2.3.21 A portion of knowledge I is called objectively true knowledge about D if tr(I, D) > To adequately discuss a possibility of false knowledge existence from a methodological point of view, it is necessary to take into account three important issues: multifaceted approach to reality, historical context, and personal context Thus, we come to the following conclusion First, there is a structural issue in this problem Namely, the dichotomous approach, which is based on classical two-valued logic, rigidly divides any set into two parts, in our case, true and false knowledge As a result, the dichotomous approach gives a very approximate image of reality Much better approximation is achieved through the multifaceted approach based on multivalued logics, fuzzy reasoning, and linguistic variables Second, there is a temporal issue in this problem Namely, the problem of false knowledge has to be treated in the historical or, more exactly, temporal context, i.e., we must consider time as an essential parameter of the concept Indeed, what is treated as true in one period of time can be discarded as false knowledge in another period of time Third, there is a personal issue in this problem, i.e., distinction between genuine and false knowledge often depends on the person who estimates this knowledge For instance, for those who not know about non-Diophantine arithmetics (Burgin, 1997d; 2001b; 2010c), + is always equal to At the same time, for those who know about non-Diophantine arithmetics, it becomes possible that + is not equal to In light of the first issue of our discussion about false knowledge, we can see that in cognitive processes, the dichotomous approach, which separates all objects into two groups, A and not A, is not efficient Thus, if we take the term “false knowledge”, then given page 114 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 115 115 a statement, it is not always possible to tell if it contains genuine or false knowledge To show this, let us consider following statements: “π “π “π “π “π is is is is is equal equal equal equal equal to to to to to 3.” 3.1.” 3.14.” 3.1415926535.” (4/3)2 ” According to the definition of pi and our contemporary knowledge that states that pi is a transcendent number, all these statements contain false knowledge In practice, they are all true but with different exactness For example, the statement (4) is truer than the statement (1) Nevertheless, in the ancient Orient, the value of pi was frequently taken as and people were satisfied with this value (Eves, 1983) Archimedes found that pi is equal to 3.14 For centuries, students, and engineers have used 3.14 as the value for pi and had good practical results Now calculators and computers allow us to operate with much better approximations of pi, but nobody can give the exact decimal value of this number Importance of the temporal issue is demonstrated by the following example from the history of science that helps to better understand the situation with false knowledge Famous Greek philosophers Leucippus (fl 445 B.C.E.) and Democritus (460–360 B.C.E.) suggested that all material bodies consist of small particles, which were called atoms “In reality,” said Democritus, “there are only atoms and the void.” We can ask the question whether this idea about atoms contains genuine or false knowledge From the point of view of those scientists who lived after Democritus but before the 15th century, it contained false knowledge This was grounded by the fact that those scientists were not able to look sufficiently deep into the matter to find atoms However, the development of scientific instruments and experimental methods made it possible to discover microparticles such that have been and are called atoms Consequently, now it is a fact, September 27, 2016 116 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes which is accepted by everybody, that all material bodies consist of atoms As a result, now people assume that the idea of Leucippus and Democritus contains genuine or true knowledge This shows how people’s comprehension of what is genuine knowledge and what is understood as false knowledge changes with time Lakatos (1976) and Kline (1980) give interesting examples of similar situations in the history of mathematics, while Cartwright (1983) discusses analogous situations in the history of physics All these examples demonstrate that it is necessary to consider false knowledge as we use negative numbers, as well as not to discard false knowledge as we not reject utility of such number as History of mathematics demonstrates that understanding that is a number and a very important number demanded a lot of hard intellectual efforts from European mathematicians when Arab mathematicians brought to them knowledge about from India Going to the third point of the discussion about false knowledge related to the personal issue, let us consider other examples from the history of science as here we are studying knowledge by scientific methods In his lectures on optics, Isaac Newton (1642–1727) developed a corpuscular theory of light According to this theory, light consists of small moving particles Approximately at the same time, Christian Huygens (1629–1695) and Robert Hook (1635–1703) built a wave theory of light According to their theory, light is a wave phenomenon Thus, it was possible to ask the question who among them, i.e., was it Newton or Huygens and Hook, gave genuine knowledge and who gave false knowledge For a long time, both theories were competing As a result, the answer to our question depended whether the respondent knew physics and was an adherent of the Newton’s theory or of the theory of Huygens and Hook However, for the majority of people who lived at that time both theories did not provide knowledge because those people did not understand physics A modern physicist believes that both theories contain genuine knowledge So, distinction between genuine and false knowledge in some bulk of knowledge depends on the person who estimates this knowledge page 116 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 117 117 Existence of false knowledge is recognized by the vast majority of people, but some theoreticians insist that false knowledge is not knowledge There is persuasive evidence supporting the opinion that false knowledge exists For instance, readers find a lot of false or inaccurate knowledge in newspapers, books, and magazines Recent studies found a considerable amount of inaccurate knowledge on the Internet (Hernon, 1995; Connell and Triple, 1999; Bruce, 2000; Berland et al., 2001) The new and truly wonderful medium, the Internet, unfortunately has one glaring downside Namely, along with all the valid knowledge it provides, the Internet also contains much misleading knowledge, false knowledge, and outright hype This is also true for the fields of science and science criticism Certainly many so-called “discussion groups” and informal “book review” sites are good examples of the blind leading the blind (Fallis, 2004) On an Internet blog, the author of this book once encountered an assertion of one of the bloggers that there was a critique of a book A in a paper D Finding the paper D, the author did not come across any such a critic in it and was very surprised even thinking about such a possibility because the paper D had been published in 2003, while the book A had been published only in 2005 Another example of the situation when “the blind leads the blind” we can take the critique of the professor P aimed at the book B Indeed, this critique was irrelevant and contained essential logical and factual mistakes However, being asked if he read the book he criticized, P answered that he did not need to that because he saw an article by the same author and understood nothing Naturally, in this situation, his critique was an example not only of incompetent but also indecent behavior because using Internet and other contemporary means of communication, professor P transmitted this false knowledge to those who read his writings on this topic Thus, we see that the problem of false knowledge is an important part of knowledge studies and we need more developed scientific methods to treat these problems in an adequate manner To have genuine knowledge relevant to usual understanding, we take such measure as correctness of knowledge or such measure as September 27, 2016 118 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes validity of knowledge Thus, we can call cognitive knowledge false when it decreases validity of knowledge it gives Definition 2.3.8 shows that we have false knowledge when its acceptance makes our knowledge less correct For instance, let us consider people who lived in ancient Greece and accepted ideas of Leucippus and Democritus that all material bodies consist of atoms Then they read Aristotle’s physics that eliminated the idea of atoms Because we now know that the idea of atoms is true, Aristotle’s physics decreased true knowledge about such an aspect of the world as the existence of atoms and thus, gave false knowledge about atoms We can ask the question whether this idea contains true or false knowledge From the point of view of those scientists who lived after Democritus but before the 15th century, it contained false knowledge This was grounded by the fact that those scientists were not able to go sufficiently deep into the matter to find atoms We see that false knowledge is also knowledge because it has a definite impact on the infological system Only this impact is negative It is necessary to understand that the concept of false knowledge is relative, depending on the chosen measure Let us consider the following situation A message M comes, telling something completely incorrect Thus, it will be wrong knowledge with respect to a semantic measure of knowledge (cf., Chapter 4) At the same time, if all letters in the message M were transmitted correctly, it will contain genuine knowledge with respect to the (statistical) Shannon’s measure of information (cf., Chapter 3) It is interesting that there is no direct correlation between false knowledge and meaningless knowledge Bloch in his book “Apology of History” (1949) gives examples when false knowledge was meaningful for people, while genuine knowledge was meaningless for them Moreover, a knowledge unit can be true knowledge with respect to another measure and false knowledge with respect to the third measure For instance, let us consider some statement X made by a person A It can be true with respect to what A thinks Thus, knowledge in X is genuine with respect to what A thinks (i.e., according to the measure m2 that estimates correlation between the statement page 118 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 119 119 X and beliefs of A) The statement X can be false with respect to the real situation Thus, knowledge in X is false with respect to the real situation (i.e., according to the measure m3 that estimates correlation between the statement X and reality) At the same time, knowledge in X can be pseudo knowledge from the point of view of the person D who does not understand it (i.e., according to the measure m1 that estimates correlation between the statement X and knowledge of D) The opposite property to correctness is incorrectness Definition 2.3.22 (a) A knowledge system K is incorrect with respect to a system C of conditions if it violates at least one condition from C (b) A knowledge system K is strongly incorrect with respect to a system C of conditions if it violates all conditions from C For instance, taking the following system of conditions for formal logics C = {(1) a logic L is not trivial, i.e., it is not empty and does not contain all formulas from the logical language; (2) a logic L does not contain expressions of the form A& A}, we see that any classical logic is incorrect with respect to C if and only if it is strongly incorrect with respect to C (Shoenfield, 2001) However, there are paraconsistent logics that are incorrect with respect to C validating the second condition from C but not strongly incorrect with respect to C because they still may satisfy the first condition from C (Priest et al., 1989) 2.3.3 Confidence in and certainty of knowledge Confidence is an essentially psychological characteristic of knowledge, which shows the extent to which an individual or a group strongly believes (is convinced) that some epistemic structures are knowledge In a more general interpretation, confidence, as a knowledge characteristic, reflects the knower’s (knowledge user) mental state of being without doubt about estimation of the epistemic structure, e.g., knowledge item, property For instance, a person can be confident that her belief, e.g., belief that the Venus is a planet of September 27, 2016 120 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes the Solar system or that Venus is a goddess, is knowledge, i.e., it is true We can see that these two beliefs are essentially different To reflect these differences, it possible to call conventional confidence by the name psychological confidence and consider another type of confidence called epistemic confidence, which reflects epistemological status of knowledge items, i.e., whether they are indeed knowledge items and not other epistemic structures It is useful to distinguish three kinds of psychological confidence — internal, external, and exterior confidence Internal confidence is confidence of an individual or a group in epistemic structures of the same individual or group For instance, self-confidence is having confidence in oneself or more exactly, confidence in own abilities and qualities, which are certain epistemic structures External confidence is confidence of an individual or a group in epistemic structures of another individual or group Exterior confidence is confidence of an individual or a group in epistemic structures stored in some knowledge carrier, such as a book, journal, or knowledge base Certainty is a more restricted characteristic of knowledge, reflecting higher levels of confidence Thus, it is a psychological characteristic of the knower (knowledge user) For instance, it can be certainty of the knower (knowledge user) in knowledge item correctness, e.g., knowledge item is certain for the knower (knowledge user) when this knower is supremely convinced of its truth However, there are kinds, or more exactly, interpretations of certainty Another kind is epistemic certainty, which is not a psychological but an epistemological characteristic estimating that an epistemic structure (knowledge item) has the highest possible epistemic status This status has to be validated in epistemology as the theory of knowledge Epistemic certainty often but not always correlates with psychological certainty For instance, it is possible that a knower (knowledge user) has epistemically certain knowledge, e.g., a belief that enjoys the highest possible epistemic status, but does not have psychological page 120 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 121 121 certainty either being unaware of epistemic certainty or having doubt about its validity An opposite situation is also possible when a knower (knowledge user) has psychological certainty about certain knowledge item strongly believing in its truthfulness, but in spite of this, the knowledge item does not have epistemic certainty For instance, Aristotle was (psychologically) certain that all swans were white but as it was discovered later, this belief was not epistemically certain A more general than epistemic certainty is source certainty, which is a knowledge characteristic reflecting the highest possible status of the knowledge item coming from some source For instance, epistemic certainty gets the status from epistemology Moral certainty discussed by some philosophers gets the status from God or from tradition External certainty, as a highest degree of external confidence, gets the status from an authoritative group or individual, e.g., a knowledge item can be certain because Aristotle or Kant said so Psychological confidence and certainty can be based on different reasons — on assurance, validation, groundedness, or even on persuasion For instance, groundedness by evidence reflects the extent of the of knowledge evaluation When confidence is ungrounded, it is called arrogance or hubris It is natural to consider degrees of confidence and certainty For instance, Carnap treated epistemic certainty as a having some degree, which could be objectively measured Definite techniques for measuring confidence and consequently, certainty have been developed in statistics where such concepts as confidence level, confidence interval, confidence coefficient and confidence bounds have been introduced for this purpose A confidence interval is an interval estimate of the confidence that a sample characteristic or parameter gives confident (reliable) knowledge of the same characteristic (parameter) for the whole population (Fisher, 1956) How frequently the calculated confidence interval contains the parameter is determined by the confidence level or confidence coefficient, which is a numerical estimate of the confidence For instance, a 90% confidence level means that it is possible to expect the corresponding confidence interval to include 90% September 27, 2016 122 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes of the sample characteristic or sample parameter estimated for different samples While two-sided confidence limits form a confidence interval, their one-sided counterparts are called lower or upper confidence bounds and are also numerical estimates of the confidence (Fisher, 1956) There are also methods of discriminating degrees of psychological confidence and certainty For instance, in the legal practice, the following degrees of certainty are used: no credible evidence, some credible evidence, a preponderance of evidence, clear and convincing evidence, beyond reasonable doubt, beyond any shadow of a doubt, what is usually recognized as an impossible standard to meet Degrees of certainty are related to degrees of confidence but they are not the same For instance, a reasonable degree of confidence can correspond to a low degree of certainty It also happens that the degree of psychological confidence is different from the degree of epistemological confidence When the degree of psychological confidence is essentially larger than the degree of epistemological confidence, people speak about overconfidence or presumptuousness For instance, overconfidence is an excessive belief in someone or something, e.g., a plan, succeeding, without any regard for possible failure 2.3.4 Complexity and clarity of knowledge Complexity has become a buzzword in contemporary science This term utilized in a variety of scientific fields and from them, it entered popular usage on a new level of credibility Trying to explain, why complexity is so important and why it is more important now than it was before, we come to three following issues First, people have to deal with more and more complex systems On one hand, the development of science is bringing cognition to page 122 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 123 123 more and more complex systems On the other hand, the development of engineering and social organization resulted in building more and more complex technical systems and developing more and more complex social systems All this is directly related to knowledge Studying complex systems in nature, society, and technology, scientists, as a rule, need adequately complex knowledge systems to represent and model systems they study To create and invent complex systems, engineers, including software and social engineers, need sufficiently complex operational knowledge Second, complexity serves as a measure of needed resources In turn, needed resources correlate with system efficiency Indeed, when two systems give the same results but the first one demands less resources than the second system, then the fist system is more efficient than the second Thus, complexity becomes a measure of efficiency For instance, knowledge that demands less time or less efforts for understanding is more efficient for learning At the same time, usually simple knowledge demands less time and efforts for understanding than complex knowledge For instance, it is easier to understand that + = than the statement that there are infinitely many prime numbers Pager (1970) defines efficiency of computation as the value that is inversely proportional to complexity of the same computation In the same way, it is possible to define efficiency of any process as the value that is inversely proportional to complexity of this process Efficiency is a clue problem and a pivotal characteristic of any activity Inefficient systems are ousted by more efficient systems Consequently, problems of efficiency are vital to any society and any individual Many great societies, Roman Empire, British Empire and others perished because they had become inefficient However, there are many different criteria of efficiency, and to understand this importance and, at the same time, complex phenomenon, it is necessary to use mathematical methods Such methods are provided by the mathematical theory of complexity Moreover, many other properties of systems are related to complexity For example, Carlson and Doyle (2002) investigate relations September 27, 2016 124 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes between complexity and robustness in biological, social, economical, and engineering systems They show a non-trivial interplay of these important properties Third, complexity helps to comprehend what is practically possible to achieve and what is not Many things that are possible to build or compute in theory are not constructible in reality because there are no means to this That is why, in particular, in the theory of algorithms, the field oriented at operational knowledge, difference is made between computable and tractable problems Manin (1991) suggests that the development of mathematical knowledge, and we would like to add, also of scientific knowledge is directed by complexity issues The reason is that simpler systems are more feasible for cognition Therefore, cognition goes from simple to more and more complex systems of knowledge In the past, mankind has learned to understand reality mostly through simplification and analysis, ignoring a huge number of factors and details That is why, for example, physics is more developed than biology: biological systems are much more complex than physical systems However, in spite of all its importance, there is no generally accepted, formalized, and unique definition of complexity in general and knowledge complexity, in particular Complexity has proved to be an elusive concept Different researchers in different fields are bringing new philosophical and theoretical tools to deal with complex phenomena in complex systems “What is complexity?” is a basic question of Gell-Mann (1995) However, after many elaborate considerations and creative insights, he comes to the conclusion that “a variety of different measures would be required to capture all our intuitive ideas about what is meant by complexity and by its opposite, simplicity.” Going back to the origin of the word complexity, we find the Latin word “complexus”, which means “entwined” or “twisted together” That is why, in mathematics (more exactly, in topology), topological complex is a structure built from simplexes (Spanier, 1966) This also reflects the situation when a system that consists of many parts is considered complex However, this is not always true For instance, the sequence 11 that consists of a thousand of symbols, is not page 124 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 125 125 complex At the same time, the sequence that consists of a thousand of symbols from the number “pi” taken from the left side is complex In general, as Heylighen (1996) writes, complexity can be characterized by lack of some symmetry or “symmetry breaking”, that is, by the fact that no part or aspect of a complex entity can provide sufficient information to actually or statistically predict the properties of the others parts In other words, complexity is connected to the difficulty of modeling associated with complex systems If we analyze what it means when we say that some system or process is complex, we come to a conclusion that it is complex to something with this system or process: to study it, to describe it, to build it, to control it, and so on Here are two examples of types of complexity taken from the world of business and industry (Paul, 2002) The first one is complexity of functioning that reflects a high number of operations to be performed The second one is complexity of integration that reflects a high number of problems encountered in integration processes The same is true for complexity of knowledge, which is estimated from the perspective of related processes For instance, complexity of knowledge depends on such processes as knowledge acquisition, knowledge transmission, knowledge integration, teaching, and learning Thus, complexity is always complexity of doing something Being related to activity and functioning, complexity allows one to represent efficiency in a natural way: when a process has high efficiency, it is simple from the point of view of demanded resources, and when a process has low efficiency, it is complex from the point of view of demanded resources For example, we can take time as a measure of efficiency: what is possible to in one hour is efficient, while what is impossible to even in 1,000 years is inefficient To estimate temporal efficiency of processes and procedures, such measure as computational complexity is utilized It estimates time of computation or any other algorithmic process At the same time, as there are many resources, there are many corresponding measures of complexity There are various relations September 27, 2016 126 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes between different measures of complexity In particular, an important and interesting relation is trade-off between different kinds of complexity For example, in computation, it is possible in some cases to use more memory for program execution, decreasing the time of execution, or to use less memory, paying for with more time Highly optimized tolerance (HOT) is one recent attempt, in long history of efforts, to develop a general framework for studying complexity in such fields as biology and engineering (Carlson and Doyle, 2002) The main idea of HOT is that higher structural complexity of a system (more complex for construction, modeling or understanding) is aimed at decreasing behavioral/functioning complexity of a system (simpler maintenance, less changes under external influence, etc.) This shows how a trade-off between structural and behavioral complexity can inspire the development of systems Here we use the informal definition of complexity from the book (Burgin, 2005) Definition 2.3.23 Complexity of a system R with respect to a process (or a group of processes) P is the quantitative or qualitative characteristic (measure) of resources necessary for (used by) the process P involving R There are different kinds of involvement P may be a process in the system R For instance, R is a scientific domain, e.g., physics, as a dynamic knowledge system, P is a process of the development of a scientific theory in R, and the resource is researchers who work in this area P may be a process that is realized by the system R For instance, R is a computer, P is a computational process in R, and the resource is memory P may be a process controlled by the system R For instance, R is operational knowledge in the form of a program, P is a computational process controlled by R, and the resource is time P may be a process that builds the system R For instance, R is operational knowledge in the form of a software system, P is the process of its design, and the resource is programmers page 126 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 127 127 P may be a process that operates with R, e.g., transforms, utilizes, models, and/or predicts behavior of the system R For instance, R is operational knowledge in the form of a program, P is the process of writing the program R, and the resource is programmers who are writing this program Definition 2.3.24 Complexity of a system R with respect to a process (or a group of processes) P is the quantitative or qualitative characteristic (measure) of resources necessary for (used by) the process P involving R Definition 2.3.25 A complexity measure on a set of systems U is a (partial) numerical function that assigns higher numbers to systems with higher complexity In cognitive processes, complexity is closely related to information and knowledge, representing specific kind of information and knowledge measures In turn, processes use different kinds of resources: Natural resources consumed by a process P : time, space, information, energy, power, minerals, and so on Social resources consumed by a process P : people involved, their time, efforts, expertise, knowledge, and so on Artificial resources consumed by a process P : system time, system space, data, knowledge, memory, system units, system actions, computers, experimental devices, e.g., telescopes or microscopes, and so on The general definition of system complexity gives us definition of knowledge complexity Definition 2.3.26 Complexity of a knowledge system K with respect to a process (or a group of processes) P is the quantitative or qualitative characteristic (measure) of resources necessary for (used by) the process (the processes from) P involving K September 27, 2016 128 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Different kinds of processes determine different kinds of complexity: — If processes from P are processes of utilization of K, then we have utilization complexity of K — If processes from P are processes of transformation of K, then we have transformation complexity of K — If processes from P are using K for solving some problems, then we have problem complexity of K — If processes from P are processes for obtaining, e.g., acquisition of, K, then we have cognitive complexity of K Note that in the first three cases, knowledge K plays the role of the used resource and its complexity is a significant characteristic of this resource Problem complexity is very important because problems represent a pivotal form of erotetic knowledge People solve problems all the time and solution of some of these problems is vital for individuals, organizations, and communities Thus, complexity of some problems is essentially important for people If it is impossible to solve a problem with given resources, we assume that it has infinite complexity The halting problem for Turing machines is an example of a problem with infinite complexity for operational knowledge in the form of Turing machines since we know that it has no solution in the class of all Turing machines However, for operational knowledge in the form of inductive Turing machines, this problem has finite complexity This shows that, in general, problem complexity is a relative property, which essentially depends on knowledge used for solving the problem Definitions 2.3.25 and 2.3.27 imply that complexity is always complexity of doing something and although complexity is attributed to a system, it is a principal characteristic of a process and of the operational knowledge in the form of an algorithm if the process is determined by an algorithm However, it is possible to extend the constructions of such measures to complexity of arbitrary processes and through processes to arbitrary systems For instance, if we take some non-algorithmic process, such as cognition, then it is possible page 128 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 129 129 to measure its complexity by the amount of resources this process needs To make Definitions 2.3.25 and 2.3.27 constructive, it is necessary to build mathematical models of efficiency One of such models is complexity of algorithms Complexity is a mirror reflection of efficiency: the more efficient is an algorithm (system of algorithms) A for a problem P (problems from some class K ), the less complex is P (problems from K ) for the algorithm (system of algorithms) A Mathematical models of complexity allow researchers to measure efficiency of various algorithms It is necessary to have different complexity measures to estimate complexity of knowledge from different perspectives For instance, complexity of working with such a representational knowledge as a model depends on the coarse graining (level of detail) of the description of the entity, on the previous knowledge and understanding of the world that is assumed, on the language employed, on the coding method used for conversion from that language into a string of bits, and on the particular ideal computer chosen as a standard (Gell-Mann, 1995) It is possible to consider these characteristics separately assigning to each a specific complexity measure or to build an integral complexity measure for estimation of the overall complexity Complexity of a system, e.g., of a knowledge system, or a process, e.g., of cognition depends on the system making estimation It may have an external observer, a user, or a designer Relativity of complexity in general and of knowledge complexity, in particular, is perfectly demonstrated by the following joke A Mathematician (M) and an Engineer (E) attend a lecture by a Physicist The topic concerns Kaluza–Klein theories involving knowledge about spaces with dimensions of 11, 12 and even higher M is sitting, clearly enjoying the lecture, while E is frowning and looking generally confused and puzzled By the end, E has a terrible headache After the lecture ends, M comments about the wonderful lecture E says, “How you understand this stuff?” M: “I just visualize the process.” September 27, 2016 130 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes E: “How can you POSSIBLY visualize something that occurs in 11dimensional space?” M: “Easy, you first visualize it in an n-dimensional space, then let n go to 11.” Mathematics makes subjective complexity objective introducing various criteria for complexity For instance, a problem A is complex because its solution demands a huge amount of memory, while a problem B is complex because its solution involves performance of a huge amount of operations Consequently, the problem A is complex for a computer with small memory, but it is simple for a computer with big memory At the same time, the problem B is simple for a high performance computer, but is complex for an ordinary computer Clarity and comprehensibility show easiness of understanding and often vary with the individual user of knowledge, e.g., the reader of a book It is a very important property because if a knowledge item is unclear, it is hard to determine other properties of this item, e.g., whether it is accurate or relevant In fact, it is impossible to tell anything about it without understanding what information it conveys There are several practical criteria of clarity: — — — — It It It It is is is is possible possible possible possible to to to to elaborate further on that issue express that issue in another way give an illustration for that issue give an example for that issue Accessibility of knowledge is a kind of knowledge complexity There are different measures of knowledge accessibility Here we reflect on two of them In developed knowledge systems, there are different levels of knowledge storage, which have different complexity, e.g., time, of knowledge access This situation is modeled by the measure of actuality — the easier is the access the higher is the measure of actuality On the other hand, complexity, e.g., time, of extraction and/or production of potential knowledge from actual knowledge can be page 130 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 131 131 rather different for different knowledge items This situation is modeled by the measure of potentiality — the easier is the extraction/ production the less is the measure of potentiality The size of knowledge representation is a kind of complexity For instance, an algorithm or a program is an operational knowledge item, while the length of an algorithm or a program is a popular measure of complexity in the theory of algorithms and in algorithmic information theory (Burgin, 2005) Other examples of operational knowledge complexity measures are: — — — — — — — — — Kolmogorov or algorithmic complexity; Time complexity; Space complexity; Average time complexity; Average space complexity; Static complexity measures; Dynamic complexity measures; Direct complexity measures; Dual complexity measures These and other complexity measures are used in various areas Axiomatic approach to complexity of operational knowledge in the form of algorithms and abstract automata is developed in (Blum, 1967; Burgin, 2005; 2010d; Cˆ ampeanu, 2012) Axiomatic approach to complexity of operational knowledge in the form of computer software is developed in (Prather, 1984; Bollmann and Zuse, 1987; Burgin and Debnath, 2003) 2.3.5 Significance of knowledge Significance of knowledge is a relative characteristic, which depends on the person or system that evaluates this knowledge What is significant for one person can be insignificant for another For instance, a scientist makes observation, which is not important or even significant for him but is very important for his colleague In a similar way, social knowledge is, as a rule, not important for a physicist but rather essential for a sociologist September 27, 2016 132 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes It is possible to find an interesting example of knowledge significance in the areas of real number representations and computer arithmetic In the standard decimal or binary representation, a real number is represented by a signed sequence of digits These digits give knowledge about numbers For instance, if the last digit of a number in the standard decimal representation is 4, then it is an even number In a similar way, if a number has three digits in the standard decimal representation, then this number is larger than 99 Note that by tradition, the positive sign + is not usually displayed For instance, 246.159 is the standard decimal representation of a real number It is also possible to represent the same number by the sequence 00246.159000 However, zeroes in this sequence are insignificant because they not change the number and they are omitted, as a rule, in the standard representation Besides, what is significant in one type of representations can become insignificant in another type of representations For instance, there is the scientific notation or scientific representation of real numbers, which consists of three parts: the sign of the number, the mantissa of the number, and the exponent of the number The mantissa of the number is a real number, which is less than 10 and larger or equal to one, and the exponent is an arbitrary integer number For instance, 3.159 × 1011 is the scientific notation In science, very large and very small numbers frequently occur in many fields So, to represent these numbers in a much shorter form, scientists invented scientific notation For instance, the mass of a proton is approximately 0.00000000000000000000000165 gram This is the standard representation of a decimal number In scientific notation, this number has a much shorter representation Namely, it is equal to 1.65 × 10−24 gram Here is one more example France’s national debt at the end of 2012 was $5,200,000,000,000 In scientific notation, we have $5.2 × 1012 We see that only digits in the mantissa are significant with respect to scientific notation, while in the standard notation are significant Later scientific notation was used as the floating point representation of real numbers in computers This technique allows computers to operate in a much larger range of numbers than the fixed point, page 132 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 133 133 i.e., standard representation However, the floating point representation has its pitfalls One of the significant problem that arises in different situations is the loss of significant digits For instance, numbers 246.1593 and 246.1592 have seven significant digits and thus, seven-digit accuracy, while their difference 246.1593 − 246.1592 = 0.0001 = × 10−4 has only one significant digit and thus, only onedigit accuracy Being relative, significance, nevertheless, is an important characteristic of knowledge because for an individual to successfully function, this individual needs knowledge that is significant with respect to her or his functioning Sometimes absence of the necessary knowledge can cause very bad consequences and even bring to disaster At the same time, the whole amount of knowledge accumulated by society and its members is so huge that one individual cannot acquire all of it and it is necessary to make the right selection Significance is one of the most important criteria for this selection It is possible to treat significance as a binary property with two values — significant and insignificant However, a more accurate approach regards significance as a gradual property of knowledge It is possible to represent graduality in different scales The most exact are numerical scales, in which it is possible to have significance of order or of order There are also ordered scales For instance, for a student it is more significant what she will get as a final grade than what will be her grade at an intermediate test There are also nominal scales For instance, it is possible to use such a scale {extremely significant, very significant, moderately significant, sufficiently significant, slightly significant, almost insignificant, insignificant, completely insignificant} High orders or levels of significance are called importance It is possible to use the threshold for importance in the scale of significance — knowledge significance of which is larger than the threshold for importance is important Otherwise, it is unimportant In this case, importance of knowledge can be a binary property as significance can be However, it is more natural to consider different grades of importance treating it as a gradual property Importance September 27, 2016 134 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes of knowledge as a category of knowledge significance can be represented in numerical scales, ordered scales, and nominal scales Value of knowledge also reflects its significance Starting with Plato, philosophers have discussed what is it about knowledge (if anything) that makes especially valuable for people With the development of human civilization, the value of knowledge has continuously grown However, different thinkers expressed diverse opinions on this issue For instance, in 1775, Samuel Johnson (1709–1784) wrote, “All knowledge is, of itself of some value,” while Samuel Taylor Coleridge (1772–1834) stated, “The worth and value of knowledge is in proportion to the worth and value of its object” connecting value to the knowledge object or domain Pragmatic approach, which is already present in Plato dialogues, asserts that the value of knowledge depends how this knowledge helps people in their activity aimed at achieving definite goals, e.g., Francis Bacon (1561–1626) declared “Knowledge Itself Is Power” (ipsa scientia potestas est), while Alvin Toffler (1990) proposed that knowledge is a wealth and force multiplier, in that it augments what is available or reduces the amount needed to achieve a given purpose 2.3.6 Efficiency of knowledge The efficiency dimension reflects the role of a knowledge item in achieving certain goals or solving particular problems It means that efficiency of knowledge is a relative property — the same knowledge item can be highly efficient for one goal and have low efficiency for another goal For instance, knowledge in a textbook in mathematics is efficient for learning mathematics and is not efficient for learning music In addition, efficiency also depends on the knowledge user One individual can use the same knowledge more efficiently than another one For instance, knowledge in a monograph on category theory will be useless, and thus, inefficient, for a non-professional but it may be very efficient for a mathematician who works in this area Let us consider efficiency of operational knowledge One kind of efficiency is related to the number of problems that can be solved using this operational knowledge page 134 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 135 135 Definition 2.3.27 The more problems can be solved using an operational knowledge item K, the more potentially efficient K is However, it is important not only to know that it is possible to solve some problem P in principle, but also to be able to find a relevant solution in practice Such problems for which the latter is possible are called tractable Tractability of a problem is a relative property, being dependent on the operational knowledge that is used for solution This gives us a definition for pragmatic efficiency of operational knowledge Definition 2.3.28 The more problems are tractable with respect to an operational knowledge item K, the more pragmatically or functionally efficient K is Thus, pragmatic efficiency of operational knowledge depends on two parameters: power of the provided by operational knowledge means for solving problems and resources that are used in the process of solution If it is impossible to get the necessary resources, it is unattainable to solve the problem under consideration Thus, we come to the concept of resource efficiency of algorithms Definition 2.3.29 The fewer resources are used for solution of a problem (of problems from some class) by means provided by operational knowledge, the more resource efficient this operational knowledge is with respect to this problem (class of problems) One more kind of efficiency is related to the quality of solution Definition 2.3.30 The better solution for problems is provided by operational knowledge, the more mission efficient this operational knowledge is Reliability, exactness, and relevance are examples of mission efficiency demonstrating that different dimensions of knowledge may have common components as, for example, relevance is a component of both correctness and efficiency This analysis shows that knowledge efficiency is a function E(K, G, U ) where K is a knowledge item, G is a goal and U is a knowledge September 27, 2016 136 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes user Note that not only an individual but also a software system or a robot can be a knowledge user 2.3.7 Reliability of knowledge What Ketelaar wrote about information (Ketelaar, 1997) can be even more applied to knowledge, especially, because information is the source of knowledge: Why we demand more of the quality of food or a car than we demand of that other essential resource — knowledge? Reliability and authenticity determine the credibility and the usefulness of knowledge These concepts, developed in different cultures and at different times, are essential for our information society in its dependence on trust in knowledge and information When new knowledge is created and distributed, conditions should be met to ensure the reliability and authenticity of this knowledge Reliability of knowledge shows to what extent it is possible to rely on some knowledge item For instance, if a person remembers the telephone number of her friend, but when she dials this number, she finds that the number is incorrect This shows that her knowledge of the telephone number is not very reliable There are different reasons for this unreliability — she may simply forget the right number, her friend can change her number or she can dial a wrong number by mistake Reliability of knowledge has three dimensions: Reliability of knowledge content depends on several attributes such as accuracy, veracity, credibility, correctness, and validity Reliability of knowledge source is obtained when the attributes of content reliability are applied to the origin of knowledge, e.g., the author or corporate source of knowledge in the same way as to its content This may be, for example, a rating of the previous content reliability of knowledge from this source, or of the circumstances under which a particular message originated Reliability of knowledge transmission or/and production is obtained when the way (technique or process) of knowledge transmission or/and production is estimated page 136 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 137 137 All these three dimensions are important for knowledge First, people often judge reliability of knowledge they receive from some source by the reliability of this source For instance, people are more inclined to believe authoritative individuals Second, reliability of knowledge transmission may be crucial because invalid transmission can convert true knowledge into false knowledge This sometimes happen in newspapers when truth is intentionally or unintentionally distorted For instance, all newspapers in the Soviet Union provided false knowledge about Western countries to their readers Third, humankind strived to develop reliable methods of knowledge production One of the most (if not the most) reliable in this field is science Unfortunately, even in science, some researchers faked their results demonstration that it is possible to corrupt even reliable knowledge production by an unreliable source 2.3.8 Abstractness and generality of knowledge Abstractness and generality as properties of knowledge stem from two cognitive operations — abstraction and generalization In the abstractness/generality dimension, abstractness reflects the level of abstraction of a knowledge item It is possible to compare knowledge items with respect to their generality It is possible to measure the level of abstraction of a knowledge item by the quantity of features in describing/representing the knowledge object or knowledge domain When fewer features are taken into account, then the level of abstraction increases Analyzing abstraction, it is possible to introduce levels of abstractness or levels of abstraction for epistemological structures in general and knowledge, in particular Definition 2.3.31 (a) Knowledge (an epistemological structure) the domain of which consists of material objects has the first level of abstractness (b) Knowledge (an epistemological structure) the domain of which consists of knowledge (epistemological) structures of the level n of abstractness has the (n + 1)th level of abstractness September 27, 2016 138 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Note that the level of abstractness is not an absolute characteristic of a knowledge item but reflects the angle of contemplation In mathematics, levels of abstraction are formalized, for example, in type theory developed by Whitehead and Russell (1910–1913) In this theory, a set may contain only sets that have types lower than this set as its elements Therefore, each type determines the corresponding level of abstraction Another attempt to describe levels of abstraction was done by Hayakawa (1949), who introduced the concept Abstraction Ladder based on the approach from (Korzybski, 1933) In the Abstraction Ladder, individual (proper) names of material things form the first (verbal) level of abstraction, while common names, such as a dog or a plane, form the second level of abstraction Higher level are constructed by taking concept with less and less defining properties As a characteristic related to abstractness, generality reflects degree of generalization achieved by a knowledge item The degree of generalization of a knowledge item reflects the scope of the described/ represented knowledge domain The degree of generalization increases when a broader domain is described/represented or more aspects of the domain are mirrored These two options are revealed in two components of generality — depth and breadth Depth of a knowledge item reflects how many and to what extent aspects of an issue related to the knowledge item domain are taken into account This shows that depth is the aspect of generality Breadth of a knowledge item reflects the scope of the knowledge item domain, i.e., whether the knowledge content is applicable to a broad domain or to highly specific one Note that a line of reasoning may be clear accurate, precise, relevant, and deep, but lack breadth as in an argument from either the conservative or liberal standpoint, which gets deeply into an issue, but only recognizes the insights of one side of the question (Elder and Paul, 2009) It is possible to compare knowledge items with respect to their generality The more abstract knowledge is usually more general page 138 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Knowledge Characteristics and Typology page 139 139 Definition 2.3.32 A knowledge item (an epistemological structure) K the domain of which contains the domain of a knowledge item (an epistemological structure) H is more general than H Analyzing generality, it is useful to introduce degrees of generality for epistemological structures in general and knowledge, in particular Let us consider two knowledge items (epistemological structures) K and H Definition 2.3.33 (a) If the domain of the knowledge item (the epistemological structure) K contains the domain of the knowledge item (the epistemological structure) H and there is no knowledge item (the epistemological structure) G such that the domain of K contains the domain of G, which, in turn, contains the domain of H, then K has the first degree of generality over H (b) If the knowledge item (the epistemological structure) K has the first degree of generality over a knowledge item (the epistemological structure) G and G has the degree n of generality over the knowledge item (the epistemological structure) H, then K has the degree n + of generality over H As we can see, the level of generality is not an absolute characteristic of a knowledge item but reflects the angle of contemplation Mathematical formalization of knowledge generality and abstraction are elaborated in Section 4.3.1 2.3.9 Completeness of knowledge versus precision of knowledge Completeness of a knowledge item (system) K with respect to a domain D characterizes to what extent all essential aspects of the domain D are represented by K For instance, knowledge that most birds fly but there are birds, e.g., penguins, that not fly is more complete with respect to birds than knowledge that all birds fly Knowledge that there are white and black swans is more complete with respect to birds than knowledge that all swans are white There is a direction in epistemology that focuses on partial knowledge In most cases, it is impossible to have complete knowledge and September 27, 2016 140 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes what we have is, as rule, incomplete or partial knowledge It is possible to find complete knowledge about the state of affairs only in mathematical problems from a textbook In real life, knowledge is only more or less complete Thus, people use partial knowledge to solve real-life problems and epistemology studies partial knowledge One of the consequences of this situation is that only bounded rationality is possible as complete knowledge and comprehensive information are inaccessible when people make decisions in real life situations Precision of a knowledge item (system) K with respect to an issue (aspect) A characterizes the difference (or ratio) between (of) the issue (aspect) A and (to) its representation by K For instance, correct knowledge of time in minutes is more precise than correct knowledge of time in hours Knowledge that number π is equal to 3.14 is more precise than knowledge that number π is equal to There is an ongoing conflict between completeness of knowledge versus precision of knowledge in information retrieval in databases and in search engines on the Internet In information retrieval, precision (also called positive predictive value) is the ratio of the number of retrieved relevant instances, e.g., documents, to the number of all retrieved instances (documents) Precision ratios are often used in evaluation of the search engine quality Completeness (also called recall) is the ratio of the number of retrieved relevant instances, e.g., documents, to the number of all relevant instances in the system While it is possible to estimate this characteristic in database information retrieval, it is unrealistic even to try to calculate this value in the Internet search because search engines are unable to index or retrieve all the potentially available information However, it is possible to make estimates of the precision of a given search engine for some area of knowledge 2.3.10 Meaning of knowledge Knowledge exists in different forms and shapes The most popular form is symbolic expressions, which are carriers of this knowledge page 140 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 141 141 However, as we discussed in Section 2.1, practical knowledge or “know-how” often is embodied in customized dispositions, affective states such as emotions and sentiments, and phenomenological acquaintances conferred, for example, by sensory experience or artistic representation Various images can be carriers of knowledge Therefore, speaking about meaning of knowledge, it is necessary to take into account, knowledge carriers, and representations We start with the meaning of symbolic expressions for three reasons First, it is the most popular representation of knowledge Second, the theory of meaning is mostly developed for expressions in natural languages, logical languages, and programming languages Third, it is much easier to assign meaning to expressions than to other forms of knowledge representations, e.g., for emotions or feelings When knowledge exists in the form of an expression, it is possible to derive its meaning by finding meaning of this expression To this, it is possible to use a special discipline called semantics, which has been developed in semiotics, linguistics, computer science and logic and studies meaning of expressions (in linguistics and logic) and signs (in semiotics) Often researchers not discern semantics and theory of meaning However, a more exact approach separates semantics as an operational theory of meaning that assigns semantic contents to signs and expressions of a language and the foundational theory of meaning, which explores the reason in virtue of which signs and expressions have the semantic contents that they have (Speaks, 2014) Here we consider only the operational theory of meaning but in a much broader sense, namely, as a theory the goal of which is to assign meaning to arbitrary objects We begin with semantics in the classical sense Semanticists generally recognize two sorts of meaning that an expression (such as the sentence “Knowledge is power”) or a sign (such as the sign ∫ ) may have: extensional meaning and intentional meaning Extensional meaning is the relation that the expression (the sign) has to things and situations in the real world, as well as in possible worlds September 27, 2016 142 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Intentional meaning is the relation the expression (the sign) has to other expressions (signs) In semiotics, extensional meaning is presented by the relation between a sign and its object, which is traditionally called denotat or denotation Intentional meaning presented by the relation between a given sign and the signs that serve in practical interpretations of the given sign is traditionally called sign connotation However, many theorists prefer to restrict the application of semantics to the denotative aspect, using other terms or completely ignoring the connotative aspect As a result, semiotic semantics related to symbols (signs), e.g., letters, words and texts, consists of two components One of them, relational semantics, expresses intentional meaning and represents relations between symbols (signs) The other one, denotational semantics, expresses extensional meaning and represents relations between symbols and objects these symbols (signs) represent In knowledge theory, extensional meaning of a knowledge item is presented by the relation between the knowledge item and its domain, which we call denotation of the knowledge item Intentional meaning of a knowledge item is presented by the relations between of the knowledge item and other knowledge items, which we call connotation or content of the knowledge item As a result, we get the Epistemological Triad presented in Figure 2.4 For instance, the domain of procedural knowledge consists of procedures and experiences in a field of work or behavior At the same time, the corresponding content of procedural knowledge contains relations between descriptions of such procedures and experiences, as well as the way they can be applied, e.g., protocols in the medical sector, acceptation rules in the insurance branch, and methods of portfolio analysis in the business world Knowledge Item Denotation/Domain Connotation/Content Figure 2.4 The Epistemological Triad page 142 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 143 143 The domain of descriptive knowledge consists of different objects, their properties and relations between these objects At the same time, the corresponding content of descriptive knowledge contains properties of and relations between knowledge items that describe such properties and relations of objects The domain of representational knowledge consists of different objects with their properties and relations, while the corresponding content of representational knowledge contains relations between knowledge items that describe such objects with their properties and relations Practical experience of people in the knowledge domain shows that there are gradations of meaning of knowledge items, e.g., concepts In particular, Langacker (1991a) considers two levels of meaning — profile and base The profile of a knowledge item K is the direct, e.g., literal, interpretation of K For instance, a definition of a concept is its profile, while the base is the encyclopedic knowledge that the concept presupposes In a general case, it is possible to understand the meaning of a knowledge item K as a knowledge system associated with K, e.g., a semantic network of a concept is treated as the concept meaning Then the larger is the associated knowledge system the deeper meaning it reveals Types of knowledge induce forms of meaning in semantics as a whole It gives us three basic form of meaning: ∗ Descriptive meaning of knowledge reflects how this knowledge describes its domain For instance, the statement “Aristotle was a philosopher” means that Aristotle had high intelligence ∗ Operational meaning of knowledge reflects processes, actions, rules, procedures, and algorithms related to this knowledge For instance, the statement “Aristotle was a philosopher” means that Aristotle developed philosophical theories and ideas ∗ Representational meaning of knowledge reflects what this knowledge represents For instance, the statement “Aristotle was a philosopher” means that there was a philosopher with the name Aristotle September 27, 2016 144 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes In addition, there are various kinds of semantics with their specific conception of meaning Logical semantics is related to propositions and involves truth values of these propositions There is much philosophical discussion about the nature of “truthbearers” — the kinds of things that can be true or false Various writers have suggested such things as propositions, statements, assertions, utterances, sentence-types, sentence-tokens, beliefs, opinions, theories, doctrines, facts, etc Linguistic semantics is related to words and texts and is expressed by relations between them There are different directions in linguistic semantics Let us consider some of them Formal semantics studies the logical aspects of meaning, such as sense, reference, implication, and logical form Lexical semantics is a subfield of linguistic semantics and studies word meanings and word relations According to this methodology, words either denote things in the world or concepts, depending on the particular approach to lexical semantics Conceptual semantics studies the cognitive structure of meaning Cognitive semantics is part of the cognitive linguistics movement and is based on the following assumptions First, grammar is a conceptualization of meaning Second, conceptual structure is embodied in and motivated by the usage of words in a language Third, the ability to use language draws upon general cognitive resources and not on a special language module However, there are psychologists and neurophysiologists who claim that linguistic abilities are based on very specific structures in the brain Structural semantics, as logical positivists maintain, is the study of relationships between the meanings of terms within a sentence, the meanings of sentences within a text, and how meaning of larger systems can be composed from meanings of smaller systems Frame semantics developed by Charles J Fillmore (1929–2014) attempts to explain meaning in terms of their relation to general understanding, asserting that it is impossible to understand the meaning of a word or a text without access to all the essential page 144 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 145 145 knowledge that relates to that word or text This essential knowledge is called the semantic frame of the corresponding word or text In other words, a semantic frame of a word or text can be defined as a coherent structure of concepts that are related to this word or text such that without knowledge of all of them, one does not have complete knowledge of this word or text Frames are based on recurring experiences (Fillmore, 1976; 1982) For instance, the writing frame is based on recurring experiences of writing Semantics for computer applications falls into three categories (Nielson and Nielson, 1995): — Operational semantics is the field where the meaning of a construct is specified by the computation it induces when it is executed on a machine In particular, it is of interest how the effect of a computation is produced — Denotational semantics is the field where meanings are modeled by mathematical objects that represent the effect of executing the constructs Thus, only the result is of interest but not how it is obtained — Axiomatic semantics is the field where specific properties of the effect of executing the constructs represent meaning and are expressed as assertions Thus, there are always aspects of the executions that are ignored Another dimension of meaning is studied by pragmatics, which is the study of the ability of natural language users (e.g., speakers or writers) to communicate not only the general meaning but also their intentions, goals, and feelings, what the users mean and not the text To distinguish the semantic meaning from the pragmatic meaning of a message (or sentence), communication researchers use the term the informative intent, also called the sentence meaning, and the term the communicative intent, also called the sender meaning or speaker meaning when it is an oral communication (Sperber and Wilson, 1986) In semiotics, pragmatics represents relations of signs to their impacts on those who use them, e.g., relations of signs to interpreters This impact exists when a sign makes sense to the interpreter Sense of a message (information) is defined by Vygotskii (1956) as a system September 27, 2016 146 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes of psychological facts emerging in the brain caused by the received message (information) The ability to understand another sender intended meaning is called pragmatic competence A statement about pragmatic functions belongs to metapragmatic While pragmatics deals with the ways people reach their goals in communication, metapragmatics explains how it is possible to reach the same goal with different syntax and semantics Suppose, a person wants to ask someone else to stop smoking This can be achieved by using several utterances It is possible to say directly, “Stop smoking, please!” This utterance has straightforward and clear semantic and pragmatic meaning Alternatively, one could say, “Oh, this room needs more air conditioners”, or “We need more fresh air here.” In the given context, these utterances imply a similar meaning but are indirect requiring pragmatic inference to derive the intended meaning A popular assumption in the philosophy of mind and cognitive science is that the propositional attitudes of subjects are underwritten by an internal language of thought and comprised of mental representations In other words, linguistic meaning is explained directly in terms of the contents of mental representations Here are two theories of meaning based on these conjectures The picture theory of meaning is a theory of linguistic reference and meaning verbalized by Ludwig Wittgenstein (1889–1951) In his Notebooks 1914–16 Wittgenstein wrote that language is first and foremost a representational system, with which people make (logical or mental) pictures of facts and these pictures are models of reality Elements of the picture are combined with one another in a definite way by relations and connections According to Wittgenstein, sentence is meaningful if and only if it is a fact, which corresponds to a possible fact in the world To be a picture, a fact must have something in common with what it pictures Thus, a meaningful proposition pictures a state of affairs or atomic fact in the world In other words, the picture theory of meaning asserts that statements are meaningful if they can be defined or pictured in the real world Wittgenstein compared the concept of logical/mental pictures (German Bild) with spatial pictures page 146 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 147 147 A similar approach is the image theory of meaning, which is a theory in which meaning of linguistic expressions derived from mental images associated with these expressions There are different kinds and types of mental images Conceptual networks and diagrammatic schemas are mental images of structural knowledge These images increase efficiency of knowledge processing and utilization Specific mental images form the foundation of image theory, which is a descriptive theory of decision-making based on the assumption that decision makers represent meaning of knowledge as images (Beach and Mitchell, 1987) One image consists of principles that recommend pursuit of specific goals A second image represents the future state of events that would result from attainment of those goals A third image consists of the plans that are being implemented in the attempt to attain the goals A fourth image represents the anticipated results of the plans Decisions consist of (1) adopting or rejecting potential candidates to be new principles, goals, or plans, and (2) determining whether progress toward goals is being made, i.e., whether the aspired-to future and the anticipated results of plan implementation correspond Decisions are made using either (1) the compatibility between candidates and existing principles, goals and plans, as well as the compatibility between the images of the aspiredto and the anticipated states of events; or (2) the potential gains and losses offered by a goal or plan The denotation meaning of a knowledge item is the domain described or represented by this item The relation meaning of a knowledge item is the structure (network of relations) with this item in the knowledge space The estimate/significance meaning of a knowledge item is the significance of this item to the knower or to the knowledge observer The relation meaning of a knowledge item includes the implicational meaning of this knowledge item, which consists of the knowledge implied by this item The relation meaning of a knowledge item also includes the contextual meaning of this knowledge item, which consists of all contexts in which this item appears September 27, 2016 148 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Usually, the concept of a context is applied only to languages Namely, a context of a word w (a text t) is a text T that includes w (respectively, t) Then the contextual meaning of a word w (a text t) is the set of all contexts in which this word (text) appears However, it is possible to define context for knowledge Definition 2.3.34 A context of a knowledge item k (a knowledge system K) is a knowledge system N that includes k (respectively, K) For instance, if a knowledge item is a mathematical theorem th from a textbook, then one context of th is the theory to which this theorem belongs, e.g., if th states that the derivative of the sum of two functions is the sum of the derivatives of these two functions, then the context is the Calculus Another context to this knowledge item is the content of the textbook that contains th Many mentalist theories of meaning have in common that they analyze one sort of representation — linguistic representation — in terms of another sort of representation — mental representation It means a reduction of structural entities to mental entities Grice developed an analysis of meaning based on two assumptions (Grice, 1989): (1) facts about what expressions mean are to be explained, or analyzed, in terms of facts about what speakers mean by utterances of them; and (2) facts about what speakers mean by their utterances can be explained in terms of their intentions These two theses allow one reducing meaning of expressions (utterances) to the contents of the intentions of speakers Another approach to analysis of meaning is based on the concept of belief, i.e., beliefs are taken into account rather than intentions of speakers An interesting approach to meaning was elaborated by Osgood et al (1978), introduced a measure of meaning and constructed a technology for measurement of meaning page 148 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 149 149 2.3.11 Other descriptive properties of knowledge External characteristics of knowledge are molded by systems that are related to knowledge Different authors explicated and discussed various external characteristics of knowledge Such characteristics (properties) as availability, accessibility, being personal, being implicit, being explicit, being operational, being representational, being descriptive, and some others are considered in Section 2.1 Let us depict additional characteristics The location of a knowledge item describes the place where the knowledge carriers of this item are situated For instance, within the company or organization, carriers of a knowledge item can be situated in the front or the back-office, but also on the other side of the world There are different types of knowledge carriers: people, documents on paper in the form of books, newspapers or reports, documents in computer files, web sites, pictures, paintings, etc The form of a knowledge item describes the form of the representation of this knowledge item For instance, it is possible to represent one knowledge item by a text and another knowledge item by speech The material form of a knowledge item describes the carrier of this knowledge item For instance, the material form of one knowledge item is a book and the material form of another knowledge is a computer The content of a knowledge item describes what aspects of the domain (object) of this knowledge item it reflects There are several temporal characteristics (properties) used in databases and knowledge bases The generation time of a knowledge item describes the date when the knowledge item was generated The acquisition time of a knowledge item describes the date when the knowledge item was obtained Acquisition time is very important for temporal databases (Snodgrass and Jensen, 1999; Burgin, 2008a) The transformation time of a knowledge item describes the last date when the knowledge item was transformed September 27, 2016 150 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes The accessibility time of a knowledge item describes what time it takes to access this knowledge item The availability time of a knowledge item notifies at what periods of time this knowledge item is available For instance, people can call 24 hours a day to get information from one organization or can obtain information from another organization only during its working hours Such a property as novelty of knowledge has three gradations: • New knowledge is knowledge that the knower (knowledge system) did not have before • Old knowledge has two meanings — it is either knowledge that the knower (knowledge system) obtained long ago or knowledge that is not new • Contemporary knowledge is knowledge the knower (knowledge system) has at the considered period All novelty gradations are relative For instance, knowledge can be new for one individual but not new for another one or for a group Knowledge about non-Euclidean geometries was new in the middle of the 19th century but it is old at the beginning of the 21st century The contemporary knowledge at the end of the 20th century is very different from the contemporary knowledge at the end of the 10th century Let us consider some more of knowledge properties A knowledge item (knowledge) is outdated if a more recent knowledge item gives a better representation of the knowledge domain (object) Knowledge is safe when it cannot be distorted by some process Knowledge is shareable because it does not decrease when it is given to others This shows that knowledge differs from material resources to a great extent Knowledge is private when only the person to whom it belongs has access to this knowledge Confidentiality of a knowledge item means that access to it is restricted only to authorized people or systems Note that privacy implies confidentiality page 150 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 151 151 Integrity of knowledge involves maintaining the consistency, accuracy, and trustworthiness of this of a knowledge item over its entire life cycle It means that integrity is a compositional property, which includes such components as the consistency, accuracy, and trustworthiness of a knowledge item Depth of knowledge characterizes to what degree of details knowledge describes or represents its domain Knowledge scope is the property, the value of which is the knowledge domain Such property as knowledge generality considered above reduces to the relation between the scope of different knowledge items Knowledge can be interesting or not For instance, Alfred North Whitehead (1861–1974) wrote, “It is more important that a proposition (i.e., propositional knowledge) be interesting than that it be true.” Thus, we see that an extremely active research in the knowledge studies domain has allowed researchers to find many properties of knowledge and knowledge processes and to use these properties in artificial intelligence, education, and psychology 2.4 Metaknowledge and metadata A library may be very large; but if it is in disorder, it is not so useful as one that is small but well arranged In the same way, a man may have a great mass of knowledge, but if he has not worked it up by thinking it over for himself, it has much less value than a far smaller amount which he has thoroughly pondered Arthur Schopenhauer The Greek word meta means “beside”, “after”, “later than” or “in succession to” Often people understand that something with the name “metaX” occurs later on the timeline than X However, a more popular meaning in contemporary languages is “beside” or “after.” For instance, carpus is the wrist, while metacarpus is the part of the human hand between the wrist and the fingers or we may say, after the wrist and before the fingers In a similar way, metatarsus is the part of the human foot after the tarsus and before the toes September 27, 2016 152 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes An important part of philosophy is metaphysics It came to philosophy through the common name for several of Aristotle’s works However, Aristotle himself did not call the subject of these works by the name metaphysics but referred to it as “first philosophy” The name metaphysics comes from the editor of Aristotle’s works, Andronicus of Rhodes He placed the books on first philosophy right after the work called Physics, and called them Metaphysics meaning “the book that come after the [books on] physics” Due to this, later generations of philosophers called the subject metaphysics thinking it meant “the science of what is beyond the physical” However, now metaphysics is one of the pivotal branches of philosophy concerned with explaining the fundamental nature of being and the world as the manifestation of being and clarifying the fundamental notions by which people understand the world Due to fewer restrictions in philosophical exploration in comparison with research in physics, metaphysics often goes beyond physics in many aspects In contemporary understanding, the word “metaX” means above X However, the word above means after in a hierarchy when you go in the direction bottom-up This exactly relates to metaknowledge and metadata Metaknowledge or meta-knowledge is knowledge about knowledge For instance, it may be a cluster of definitions and methods aiming to guide you in gathering the pertinent knowledge with regard to your activity The metaknowledge is often used to guide functioning of a system including goal formation and future planning Metaknowledge is intrinsically connected to metadata Metadata (also called metacontent) are data that provide information about one or more aspects of the data For instance, data with the standard file information such as file size, type, location, and date of creation are metadata for data in the file If data are organized as a text, then their metadata usually contain information about: — the language of the text, — the number of words in the text, page 152 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology — — — — — b2334-ch02 page 153 153 the number of pages in the text, the number of symbols in the text, the number of lines in the text, who the author is, when the text was written, and in some cases, — a short summary of the text However, a summary of a text actually is metaknowledge as it contains knowledge about the text Another example of metaknowledge is an annotation of a book An important form of metadata is represented by named sets (Burgin, 1990; 1995; 2011) Indeed, it is demonstrated that all main data structures and models are efficiently represented in a form of named sets or chains of named sets (Burgin, 1992a) In addition, named sets and their chains also give a unifying data model for data structures used in programming languages, operating systems, and computer hardware: vectors, lists, arrays, trees, strings, tables, records, streams and the like The same is true for such forms of data on the Web as digital imagery (in the form of frames or pictures) and audio data In such a way, we come to a unified data meta-model that is suitable data models on all levels: from high-level or conceptual to representational or implementation to low-level or physical models In turn, named sets and their chains form efficient high-level metadata (cf., (Siegel and Madnick, 1991; Tannenbaum, 2002)) for different purposes, in particular, for XML documents and schemas (Nocedal et al., 2011) Such general representation allows us to introduce various operations with named sets and their chains oriented to data preparation, processing, search, and acquisition Some operations are similar to those found in relational algebras (Codd, 1990) Other operations, such as sequential composition of named sets and their chains, are different from operations in relational databases All these operations provide means for working with data models that are different from September 27, 2016 154 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes the relational ones For instance, sequential composition of named set chains represents extensions of hierarchies Although metadata have been used from the beginning of computer era, the term metadata was introduced in (Bagley, 1968) Since then it became popular in many areas such as information management, information science, information technology, librarianship, and databases For instance, library catalogs are metadata in libraries, which are created in the process of cataloging resources, such as books, journals, newspapers, magazines, manuscripts, DVDs, web pages, or digital images Here are more examples of information contained in metadata for some data: • • • • • • • • Means of creation of the data; Purpose of data creation and utilization; Time and date of creation; Source, creator or author of data; Location where the data was created; Location where the data are stored; Standards used; Data model for representing data structure Metadata research emerged as a discipline crosscutting many areas and domains It has been directed at the provision of structural descriptions (often called annotations) to Web resources or applications Descriptions in the form of metadata function as a basis for advanced services in many application areas, including search and location, personalization, federation of repositories, and automated delivery of information For instance, the HTML format for defining web pages has means for inclusion of various metadata, from basic annotations, dates and keywords to further advanced metadata schemas (Nocedal et al., 2011) In addition, metadata are used in database servers, data virtualization servers, and application servers Metadata in these servers are used for describing business objects in various enterprise systems and applications Structural metadata commonality is also important to support data virtualization page 154 September 27, 2016 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in Knowledge Characteristics and Typology b2334-ch02 page 155 155 In information systems, metadata are often attached to data in the form of labels and tags For instance, a digital tag is a simple system of keywords or terms assigned to a compound data (knowledge) item such as a computer file, digital image, or Internet bookmark The main goal of tagging is identification of a data (knowledge) item in a system for finding this item by browsing or searching Usually creators or users of data (knowledge) items informally choose tags for these items Tagging and labeling on the Internet has achieved wide popularity due to the growth of social networks, blogging, photography sharing and bookmarking sites These sites allow users to create and manage labels or tags in the form of keywords Often labels and tags provide semantic information about data (knowledge) items to which they are attached For instance, triple tags have three parts — a namespace, a predicate, and a value — for purpose of their meaningful interpretation by computer programs Metadata has become even more important for the Semantic Web with its technological framework for ontology-based metadata The central idea of the Semantic Web is to extend the existing Web by adding semantic means to the web management resources allowing better search, processing, integration, and presentation of the Web information in a meaningful, intelligent manner Different new means have been developed for the Semantic Web An example is the distributed intelligent managed element (DIME) network architecture described in (Burgin and Mikkilineni, 2014) Although it is possible to write books about metadata (cf., for example, (Siegel and Madnick, 1991; Tannenbaum, 2002)), our main concern here is metaknowledge Thus, the first step in this direction is understanding that the main feature of metadata is that they contain knowledge about data Some of this knowledge is related only to the corresponding data, while other describes knowledge contained in the corresponding data, For instance, taking data in the form of a text, we see that metadata that inform us about the size of the text, e.g., the number of pages, give knowledge about data, while metadata in the form of annotation give knowledge about knowledge in the text and this knowledge is metaknowledge September 27, 2016 156 19:40 Theory of Knowledge: Structures and Processes - 9in x 6in b2334-ch02 Theory of Knowledge: Structures and Processes Let us consider other kinds of metaknowledge that have existed from the times long before the first computers were created A kind of operational metaknowledge is represented by metarules There are many metarules in logic, i.e., rules about how to use other rules Metarules instruct how to manipulate expressions or formulas that are well formed or explain how to use deduction rules or how to perform deductions For instance, “the pair A → B, A implies B”is a deduction rule because it represents a variety of deduction rules such as “If it is a rain, the trees are wet” and “It is a rain” imply “The trees are wet” Models of systems and processes contain representational knowledge about these systems and processes In the same way as models contain knowledge about their domains, metamodels contain knowledge about models It means that metamodels contain metaknowledge Mathematics gives an abundance of examples of metamodels Let us consider some of these examples Differential equations in a general form, e.g., ∂ m ui (t, x) = ∂tm Pα (aαji (t, x), u(t, x), Dxα Dtk ui (t, x)) |α|+k≤m,k