The concept of an operator is used in a variety of practical and theoretical areas. Operators, as both conceptual and physical entities, are found throughout the world as subsystems in nature, the human mind, and the manmade world. Operators, and what they operate, i.e., their substrates, targets, or operands, have a wide variety of forms, functions, and properties. Operators have explicit philosophical significance. On the one hand, they represent important ontological issues of reality. On the other hand, epistemological operators form (...) the basic mechanism of cognition. At the same time, there is no unified theory of the nature and functions of operators. In this work, we elaborate a detailed analysis of operators, which range from the most abstract formal structures and symbols in mathematics and logic to real entities, human and machine, and are responsible for effecting changes at both the individual and collective human levels. Our goal is to find what is common in physical objects called operators and abstract mathematical structures, with the name operator providing foundations for building a unified but flexible theory of operators. The paper concludes with some reflections on functionalism and other philosophical aspects of the ‘operation’ of operators. (shrink)

The problem of infinities in quantum field theory (QFT) is a longstanding problem in particle physics. To solve this problem, different renormalization techniques have been suggested but the problem persists. Here we suggest another approach to the elimination of infinities in QFT, which is based on non-Diophantine arithmetics – a novel mathematical area that already found useful applications in physics, psychology, and other areas. To achieve this goal, new non-Diophantine arithmetics are constructed and their properties are studied. In addition, non-Diophantine (...) integration is developed in these arithmetics. These constructions allow using constructed non-Diophantine arithmetics for computing integrals associated with Feynman diagrams. Although in the conventional QFT such integrals diverge, their non-Diophantine counterparts are convergent and rigorously defined. As the result, QFT becomes consistent with quantum experiments. (shrink)

We live in an information society where the usage, creation, distribution, manipulation, and integration of information is a significant activity. Computations allow us to process information from various sources in various forms and use the derived knowledge in improving efficiency and resilience in our interactions with each other and with our environment. The general theory of information tells us that information to knowledge is as energy is to matter. Energy has the potential to create or modify material structures and information (...) has the potential to create or modify knowledge structures. In this paper, we analyze computations as a vital technological phenomenon of contemporary society which allows us to process and use information. This analysis allows building classifications of computations based on their characteristics and explication of new types of computations. As a result, we extend the existing typologies of computations by delineating novel forms of information representations. While the traditional approach deals only with two dimensions of computation—symbolic and sub-symbolic, here we describe additional dimensions, namely, super-symbolic computation, hybrid computation, fused computation, blended computation, and symbiotic computation. (shrink)

We live in an information society where the usage, creation, distribution, manipulation, and integration of information is a significant activity. Computations allow us to process information from various sources in various forms and use the derived knowledge in improving efficiency and resilience in our interactions with each other and with our environment. The general theory of information tells us that information to knowledge is as energy is to matter. Energy has the potential to create or modify material structures and information (...) has the potential to create or modify knowledge structures. In this paper, we analyze computations as a vital technological phenomenon of contemporary society which allows us to process and use information. This analysis allows building classifications of computations based on their characteristics and explication of new types of computations. As a result, we extend the existing typologies of computations by delineating novel forms of information representations. While the traditional approach deals only with two dimensions of computation—symbolic and sub-symbolic, here we describe additional dimensions, namely, super-symbolic computation, hybrid computation, fused computation, blended computation, and symbiotic computation. (shrink)

Scientific knowledge systems function as effective and specialized apparatus for formulating, analyzing and solving scientific problems. In science, problems become internal parts of the knowledge systems; thus they acquire new forms and properties in comparison with common-sense problems. Definite theoretical structures connected with problems and questions appear in the theory. Among them are erotetic expressions and languages, calculi and algebras of problems. On the basis of the structure-nominative reconstruction of a theory, the unified treatment of these structures is given. Methods (...) of the theory of named sets are used in the logical analysis of problems and their systems. As a consequence a new formalized model of the problem part of theory is constructed. (shrink)

Agents and agent-based systems are becoming essential in the development of various fields, such as artificial intelligence, ubiquitous computing, ambient intelligence, autonomous computing, and intelligent robotics. The concept of autonomous agents, inspired by the observed agency in living systems, is also central to current theories on the origin, development, and evolution of life. Therefore, it is crucial to develop an accurate understanding of agents and the concept of agency. This paper begins by discussing the role of agency in natural systems (...) as an inspiration and motivation for agential technologies and then introduces the idea of artificial agents. A systematic approach is presented for the classification of artificial agents. This classification aids in understanding the existing state of the artificial agents and projects their potential future roles in addressing specific types of problems with dedicated agent types. (shrink)

Information is a basic structure of the world, while computation is a process of the dynamic change of information. This book provides a cutting-edge view of world's leading authorities in fields where information and computation play a central role. It sketches the contours of the future landscape for the development of our understanding of information and computation, their mutual relationship and the role in cognition, informatics, biology, artificial intelligence, and information technology. -/- This book is an utterly enjoyable and engaging (...) read which gives readers an opportunity to understand and relate phenomena seemingly unrelated in a completely new light — especially the connections between information, computation, cognition and life. -/- Contents: Cybersemiotics and the Question of Knowledge (Søren Brier) Information Dynamics in a Categorical Setting (Mark Burgin) Mathematics as a Biological Process (G J Chaitin) Information, Causation and Computation (John Collier) From Descartes to Turing: The Computational Content of Supervenience (S Barry Cooper) A Dialogue Concerning Two World Systems: Info-Computational vs Mechanistic (Gordana Dodig-Crnkovic & Vincent C Müller) Does Computing Embrace Self-Organization? (Wolfgang Hofkirchner) Analysis of Information and Computation in Physics Explains Cognitive Paradigms: From Full Cognition to Laplace Determinism to Statistical Determinism to Modern Approach (Vladik Kreinovich, Roberto Araiza & Juan Ferret) Bodies — Both Informed and Transformed Embodied Computation and Information Processing (Bruce J MacLennan) Computation on Information, Meaning and Representations: An Evolutionary Approach (Christophe Menant) Interior Grounding, Reflection, and Self-Consciousness (Marvin Minsky) A Molecular Dynamic Network: Minimal Properties and Evolutionary Implications (Walter Riofrio) Super-recursive Features of Evolutionary Processes and the Models for Computational Evolution (Darko Roglic) Towards a Modeling View of Computing (Oron Shagrir) What's Information, for an Organism or Intelligent Machine? How can a Machine or Organism Mean? (Aaron Sloman) Inconsistent Knowledge as a Natural Phenomenon: The Ranking of Reasonable Inferences as a Computational Approach to Naturally Inconsistent (Legal) Theories (Kees (CNJ) de Vey Mestdagh & Jaap Henk (JH) Hoepman) On the Algorithmic Nature of the World (Hector Zenil & Jean-Paul Delahaye) . (shrink)

In this paper we propose an informal exposition of the structure approach in the philosophy of science. Scientific knowledge is here considered as a collection of scientific theories. Each scientific theory has logico-linguistic, model-representing, pragmatic-procedural, and problem-heuristical subsystems and a subsystem of ties. The pivotal methodological concept for the exact description of these subsystems is the named set. We also outline the possibility of applying the structure-nominative approach to certain problems in the philosophy of science.

In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the conventional approach to computation. Then we explain how new models of algorithms turned the classical closed algorithmic universe into the open world of algorithmic constellations, allowing higher flexibility and expressive power, supporting constructivism and creativity in mathematical modeling. As Goedels undecidability theorems demonstrate, the closed algorithmic universe restricts (...) essential forms of mathematical cognition. In contrast, the open algorithmic universe, and even more the open world of algorithmic constellations, remove such restrictions and enable new, richer understanding of computation. (shrink)

ZusammenfassungVor dem Hintergrund der medialen Debatte um die beiden Therwiler Schüler, die sich mit Verweis auf religiöse Gründe weigerten, ihrer Lehrerin die Hand zu reichen, strebten Politikerinnen und Politiker im Kanton Basel-Landschaft an, die dortige Verfassung zu ändern. Dabei wurde auf rechtliche und erinnerungskulturelle Diskurse aus dem Kulturkampf des 19. Jahrhunderts – und auf solche, die dazu Bezug nehmen – verwiesen. Diese Verweise werden in einem (partiellen) Close Reading des Kommentars zur geplanten (letztlich aber nicht realisierten) Änderung der basellandschaftlichen Kantonalverfassung (...) erörtert und in den konfligierenden Narrativen des liberalen und des konservativen Lagers verortet. Dabei wird der Kommentar als Dokument gelesen, in welchem spezifische Geschichtsbilder, politische Identitäten und das Recht als sozial konstruierte Entitäten verwoben werden – und in welchem spezifische Konstruktionen und Reifikationen von Identität und Alterität angelegt sind. (shrink)

For millennia, the enigma of the world of Ideas or Forms, which Plato suggested and advocated, has been challenging the most prominent thinkers of the humankind. This paper presents a solution to this problem, namely, that an Idea in the Platoʼs sense can be interpreted as a scientific object called a structure. To validate this statement, this paper provides rigorous definition of a structure and demonstrates that structures have the basic properties of Platoʼs Ideas. In addition, we describe the world (...) of structures and prove its existence. This allows us to resolve the controversy between Plato and Aristotle concerning Ideas or Forms and to build a scientific interpretation of the metaphor of the Divided Line, which Plato uses in his theory of Ideas. (shrink)

Representative models are considered parts of real scientific theories.

Introduction -- Algorithms, programs, procedures, and abstract automata -- Functioning of algorithms and automata, computation, and operations with algorithms and automata -- Basic postulates and axioms for algorithms -- Power of algorithms and classes of algorithms: comparison and evaluation -- Computing, accepting, and deciding modes of algorithms and programs -- Problems that people solve and related properties of algorithms -- Boundaries for algorithms and computation -- Software and hardware verification and testing -- Conclusion.

This book aims to synthesize different directions in knowledge studies into a unified theory of knowledge and knowledge processes. It explicates important relations between knowledge and information. It provides the readers with understanding of the essence and structure of knowledge, explicating operations and process that are based on knowledge and vital for society. The book also highlights how the theory of knowledge paves the way for more advanced design and utilization of computers and networks.