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Philosophies 2017, 2(3), 21; doi:10.3390/philosophies2030021

Operators in Nature, Science, Technology, and Society: Mathematical, Logical, and Philosophical Issues

1
Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095, USA
2
International Center for Transdisciplinary Research, Chemindu Collège 1, P.O. Box 235, Paris, France
*
Author to whom correspondence should be addressed.
Received: 10 May 2017 / Revised: 15 August 2017 / Accepted: 16 August 2017 / Published: 7 September 2017
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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. View Full-Text
Keywords: function; information; logic; mathematics; ontology; epistemology; nature; operator; science; society; system; theory function; information; logic; mathematics; ontology; epistemology; nature; operator; science; society; system; theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Burgin, M.; Brenner, J. Operators in Nature, Science, Technology, and Society: Mathematical, Logical, and Philosophical Issues. Philosophies 2017, 2, 21.

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