Theory of KNowledge structures and process

The approach presented in this book provides a new explanation of important relations between knowl-edge and information demonstrating new kinds of possibilities for knowledge management

8893_9789814522670_TP.indd 1 12/10/16 8:22 AM

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 1 Theory of Information — Fundamentality, Diversity and Unification

by Mark Burgin

Vol 2 Information and Computation — Essays on Scientific and Philosophical

Understanding of Foundations of Information and Computation

edited by Gordana Dodig-Crnkovic & Mark Burgin

Vol 3 Emergent Information — A Unified Theory of Information Framework

by Wolfgang Hofkirchner

Vol 4 An Information Approach to Mitochondrial Dysfunction:

Extending Swerdlow’s Hypothesis

by Rodrick Wallace

Vol 5 Theory of Knowledge: Structures and Processes

by Mark Burgin

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 5 | 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,

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Desk Editors: Dr Sree Meenakshi Sajani/Tan Rok Ting

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Printed in Singapore

1.1 The role of knowledge in the contemporary

society 3

1.2 A brief history of knowledge studies 9

1.3 Structure of the book 39

2 Knowledge Characteristics and Typology 45 2.1 The differentiation and classification of knowledge 45

2.2 Existential characteristics of knowledge 77

2.3 Descriptive properties of knowledge and corresponding typology 91

2.3.1 Dimensions and other characteristics of knowledge 94

2.3.2 Correctness, relevance, and consistency of knowledge 96

2.3.3 Confidence in and certainty of knowledge 119

2.3.4 Complexity and clarity of knowledge 122

2.3.5 Significance of knowledge 131

2.3.6 Efficiency of knowledge 134

2.3.7 Reliability of knowledge 136

v

2.3.8 Abstractness and generality of knowledge 1372.3.9 Completeness of knowledge versus precision

of knowledge 1392.3.10 Meaning of knowledge 1402.3.11 Other descriptive properties of knowledge 1492.4 Metaknowledge and metadata 151

3 Knowledge Evaluation and Validation

3.1 Knowledge in the context of epistemic structures

and knowledge scales 1703.2 Knowledge evaluation, justification, and testing 215

3.2.1 Knowledge evaluation 2153.2.2 Knowledge validation, justification,

and testing 2403.3 Local consistency versus global consistency

in knowledge representation 263

4 Knowledge Structure and Functioning:

4.1 Basic structures of knowledge units on the quantum

level — knowledge quanta and semantic links 309

Semantic link theory of knowledge (SLTK) 3294.1.3 QTK–SLTK connection 340

4.3 Operations with and relations between quantum

knowledge units 3584.3.1 Properties of and relations between nodes

and links in SLN and knowledge quanta

in QTK 360

quanta 369

and complete semantic links 380

5 Knowledge Structure and Functioning:

5.1 Language as a universal tool for knowledge

representation 402

5.1.1 Natural languages 403

5.1.2 Languages of science and mathematics 411

5.1.3 Algorithmic and programming languages 423

5.2 Logic as a tool for knowledge representation and production 428

5.2.1 Concepts, names, terms, and objects 446

5.2.2 Statements, queries, and instructions 481

5.2.3 Logical systems of inference 491

5.3 Theory of abstract properties 500

5.4 Semantic networks and ontology 518

5.5 Scripts and productions 527

5.6 Frames and Schemas 536

6 Knowledge Structure and Functioning: Megalevel or Global Theory of Knowledge 593 6.1 A typology of structures and scientific knowledge 595

6.2 Nuclear and comprehensive knowledge systems 603

6.3 Logic-linguistic knowledge system and descriptive knowledge 612

6.4 Model-representation knowledge system and representational knowledge 617

6.5 Procedural, axiological and instrumental knowledge systems, and operational knowledge 622

6.6 Relations between and operations with global knowledge systems 631

6.7 Hierarchies of knowledge systems 636

7 Knowledge Production, Acquisition, Engineering, and Application 643 7.1 Knowledge production, learning, and acquisition as basic cognitive processes 644

7.1.1 Scientific cognition 658

7.1.2 Intuition as a cognitive instrument 669

7.1.3 Computers and networks as cognitive tools 688

7.1.4 Learning 696

7.1.5 Knowledge creation in organizations 705

7.2 Knowledge organization and engineering 711

7.3 Knowledge management and application 714

8 Knowledge, Data, and Information 721 8.1 Epistemic structures and cognitive information 722

8.2 Structural aspects of knowledge–information duality 727

8.3 Information as a source of knowledge 760

8.4 Dynamic aspects of knowledge, data, and information interaction 766

8.5 Knowledge as a measure of information 791

9 Conclusion 803 Appendix 809 A Set theoretical foundations 809

B Elements of the theory of algorithms 819

C Elements of algebra and category theory 825

D Numbers and numerical functions 831

E Topological, metric and normed spaces 833

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

knowl-edge 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

knowl-edge 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

organiza-tion intensified studies of knowledge There are three main direcorganiza-tions

ix

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

con-cepts 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

trans-disciplinary at the same time The approach presented in this book

provides a new explanation of important relations between

knowl-edge and information demonstrating new kinds of possibilities for

knowledge management, information technology, data mining,

infor-mation sciences, computer science, knowledge engineering,

psychol-ogy, 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?

— How these models are used to better understand and utilize

com-puters and Internet, cognition and education, communication and

computation?

Knowledge is inseparable from information People acquire

knowl-edge receiving cognitive information At the same time, knowlknowl-edge,

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

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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,

Alexan-der 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

discus-sions with those who have communicated with me on these

prob-lems 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

phys-ical 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

knowl-edge 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

math-ematical modeling of semantic networks Collaboration with Dmitri

Gorsky from the Moscow Institute of Philosophy contributed to the

xiii

further development of mathematical theory of concepts

Collabora-tion 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

Interdis-ciplinary 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

infor-mation 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,

Semi-nar of Theoretical Computer Science of the Department of Computer

Science at UCLA, various conferences where I presented these

mate-rials and the Internet discussion group on Foundations of Information

Science (FIS) were useful in the development of my views on

knowl-edge 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

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

philos-ophy 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

Sci-ence at the National Academy of SciSci-ences 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

Advi-sory Committee at Science of Information Institute, Washington

He was the Editor-in-Chief of the international journals

Integra-tion and InformaIntegra-tion, as well as an Editor and Member of Editorial

Boards of various journals Dr Burgin is doing research, has

publica-tions, 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

informa-tion, 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

mathe-matics) and made essential contributions to fields such as

founda-tions of mathematics, theory of algorithms and computation, theory

of knowledge, theory of intellectual activity, and complexity studies

xv

He was the first to discover Non-Diophantine arithmetics, the first to

axiomatize and build mathematical foundations for negative

proba-bility used in physics, finance and economics, and the first to

explic-itly 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

Com-ponents of Creativity” (1998), “Fundamental Structures of

Knowl-edge 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 8 books

Chapter 1Introduction

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

sug-gested in this area The whole area of knowledge related activities

consists of three parts:

1 Knowledge studies (theoretical and experimental ).

2 Knowledge engineering.

3 Knowledge utilization and management.

The two latter parts belong to knowledge technology — knowledge

engineering deals with technology of knowledge production,

orga-nization, transformation, management, preservation, capture and

acquisition, while knowledge utilization studies how people and

orga-nizations use knowledge, developing new techniques and approaches

for this purpose

1

There are three types of knowledge theories:

1 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

knowl-edge acquisition, i.e., what it is possible to know; and (3) ways

of knowledge creation and acquisition, i.e., how knowledge

is obtained

2 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

3 Empirical theories are oriented at the practice of knowledge

func-tioning, including theories of many disciplines, such as artificial

intelligence, knowledge management, knowledge bases,

cognitol-ogy, knowledge acquisition, cognitive psycholcognitol-ogy, cognitive

neu-roscience, 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

experi-ments 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

knowl-edge is built and what properties it has

• Axiological analysis of knowledge aims at explanation of those

fea-tures that are primary for knowledge as a social and technological

phenomenon

• Functional analysis of knowledge tries to find how knowledge

func-tions, 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

epistemol-ogy, 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

manage-ment just to keep up More and more people and organizations are

coming to the understanding that the optimal generation,

acquisi-tion, 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

quantitatively and qualitatively, due to the development and

uti-lization 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

process-ing In contemporary knowledge-driven economy, organizations

ulti-mately 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

Knowl-edge processing and management make problem solving much more

efficient and are crucial (if not vital) for big companies and

insti-tutions (Ueno, 1987; Osuga, 1989; Dalkir, 2005) To achieve this

goal, it is necessary to make a distinction between knowledge and

knowledge representation to know regularities of knowledge

struc-ture, 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

embed-ded in a diversity of systems across most industry sectors,

rang-ing 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

Tech-nology (NIST) reported that low quality software costs the U.S

econ-omy 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

cur-rent 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 20thcentury, 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,

data-and knowledge bases, global networks (e.g., the Internet),

informa-tion 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

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

knowl-edge (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

dif-ficult 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,

dissem-ination, 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

piv-otal characteristic Some researchers suggest that knowledge society

is the next stage of the information society In essence, every

soci-ety has its own knowledge assets However, in our times, knowledge

together with information is becoming the key tool not only for

fur-ther 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

knowl-edge, 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

sub-stance and money substitutable, meaning that knowledge can replace,

to some extent, capital, labor, or physical materials Namely,

knowl-edge allows one to use less money, labor, or physical materials than

it is possible to do without this knowledge As a result, the

cre-ated wealth is measured less by the output of work itself but more

and more by the general level of scientific and technological

develop-ment (Jaffe and Trajtenberg, 2002) Amidon explained that

knowl-edge 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

commod-ity, developing techniques for measuring the magnitude of its

pro-duction and distribution within a modern economy He correctly

assumed that all devices involved in knowledge production,

dissem-ination, and utilization have to be taken into account in these

mea-surements

A diversity of activities linked to research, education, and

ser-vices, tend to assume increasing importance in the knowledge

econ-omy Besides, the importance of knowledge in economic activity is

not confined to the high-tech sectors but also pervades modes of

orga-nization 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

given purpose (Toffler, 1990) Stewart calls knowledge the intellectual

capital (Stewart, 2002)

Many researchers, economists, authors, governments,

policy-makers, 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

knowledge-based economy reflecting a qualitative transition in economic

condi-tions (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

knowl-edge production function As a result, knowlknowl-edge production and

exchange becomes an economy in itself (Foray, 2004) and the

devel-opment 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,

network-ing, 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.,

Inter-net), information science, knowledge engineering, and knowledge

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 BrightKnowledge 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

philo-sophical 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

epistemo-logical 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,

anal-ogy, 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

(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

prominent and one of the oldest directions in Indian philosophy

It belongs to the six basic schools of the classical Indian

philoso-phy Bhagavad Gita identifies Samkhya with understanding of

knowl-edge The word Samkhya is based upon the Sanskrit word samkhya

which means ‘number’ or ‘perfect knowledge’ An eminent, great sage

Kapila (between 8thand 6thB.C.E.) was the founder of the Samkhya

philosophy

Samkhya may be characterized as a dualistic realism It is

dualis-tic 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

acqui-sition 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

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

pro-ducing 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:

inde-terminate (nirvikalpa) perceptions and deinde-terminate (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

the-oretical 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

Bala-subramanian (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

con-sidered as the final layer of the Vedic canon By the 8th century,

the meaning of Vedanta changed for standing for all philosophical

traditions concerned with interpreting the three basic texts of

Hin-duist 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

self-indulgent 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

knowl-edge 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

medi-ate knowledge (Paroksa) and the immedimedi-ate 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

state-ment “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

revela-tion According to the Upanisads, knowledge comes from Brahman as

“he who knows the Brahman attains the highest” This asserts unity

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

get-ting knowledge about reality staget-ting 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

pro-ducing 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;

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

epistemol-ogy 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

knowl-edge (Pramana): valid knowlknowl-edge itself (Kevala Pramana), and the

instrument of knowledge (Anupramana) In turn, Anupramana

con-sists 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

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

obli-gations and prerogatives

The Mimamsa school traces the source of the knowledge of

dharma neither to sense-experience nor inference, but to verbal

cogni-tion (knowledge of words and meanings) In order to understand the

correct dharma for specific situations, it is necessary to rely on

exam-ples 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

con-veying commands, and led to an extensive exegesis of the Vedas and

a detailed analysis of semantics

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

testi-mony, recognized by other schools of Hinduism They are arthapatti

(pre-conception or postulation) and abhava (absence, negation,

non-existence) Mimamsa advanced the unique epistemological theory

that all cognition is valid All knowledge is true, until it is

super-seded 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

Knowl-edge plays an important part in the conception of soul and its

emancipation As a result, Jain epistemology or Jain theory of

knowl-edge 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

predica-tion (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

per-fect 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

distin-guishing characteristic of the soul It is of two sets — Jnana and

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

indi-rect knowledge Diindi-rect 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

weak-ness 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

per-ish 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

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

ideas”

yellow is green and is not green” or “there is and is no world of

ideas”

4 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

mean-ingless, 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

(Anub-hava) and recollection (Smrti) In turn, experience gives (is)

two-fold — 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 senses (indriyas).

— the sensual objects (artha).

— the contact of the senses and the objects (sannikarsa).

— the 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

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).

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

proce-dural 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

Confu-cius 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

rectifica-tion, 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.

When affairs cannot be carried on to success, proprieties and music

do not flourish When proprieties and music do not flourish,

punish-ments will not be properly awarded When punishpunish-ments are not properly

awarded, the people do not know how to move hand or foot”.

One of the basic aims of name rectification was to create a

con-sistent 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 Hs¨un Tzu, (ca 312–230 B.C.E.)

contin-ued 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

accor-dance 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

epistemolog-ical 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

encounter-ing difficulties or beencounter-ing neglected” (cf., (Dencounter-ing, 2008)).

Besides, explaining that understanding right and wrong causes

morality to be more unbiased, Xun Zi argued that without

univer-sally 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.

Xun Zi assumed that utilization of senses through seeing, hearing,

smelling, tasting, and touching is the key source for getting

knowl-edge 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

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

valida-tion 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:

knowl-edge as nothing but perception, knowlknowl-edge as true judgment, and,

finally, knowledge as a true judgment with justification, are

unsatis-factory

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

knowl-edge as a justified true belief is not adequate

Let us consider an example demonstrating deficiencies of this

def-inition (Russell, 1912; 1948; Scheffler, 1965) A woman looks at a

clock at 3 p.m The clock shows 3 p.m So, the woman thinks that it

is 3 p.m Thus, she has a belief, which is true and justified by

obser-vation 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 3 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

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

consis-tently 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

exis-tence 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

knowl-edge 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

abso-lute 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

cer-tainty in everything Some domains, such as human behavior, do

not permit precise knowledge The corresponding vague knowledge

involves expectations, chances, and imprecise explanations

Knowl-edge 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