Abstract
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.
Highlights
Operators and ChangeHuman cognition is based on creation of concepts that reflect studied phenomena
The major objective of this paper is, to provide a comprehensive classification and discussion of natural operators and operations in several practical and theoretical areas of current interest, including a new kind of logic called Logic in Reality [5]. This logic is an extension of logic from its standard linguistic domain to real, complex processes and natural operators are themselves considered as active processes involved in effecting change at biological and cognitive levels of reality
We have used two different but complementary strategies to arrive at a new coherent picture of operators in nature, mind and machines
Summary
Human cognition is based on creation of concepts that reflect studied phenomena. in this process, many important concepts in philosophy and science have proven extremely resistant to systematic explanation and exact definition. The major objective of this paper is, to provide a comprehensive classification and discussion of natural operators and operations in several practical and theoretical areas of current interest, including a new kind of logic called Logic in Reality [5] This logic is an extension of logic from its standard linguistic domain to real, complex processes and natural operators are themselves considered as active processes involved in effecting change at biological and cognitive levels of reality. Our grounding of their properties in physics, as well as our conceptualization of the self-operation of human beings and their organizations, further supports the utility and roles of natural operators in general and their usefulness for information technology in particular.
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