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Article
Publication date: 25 January 2019

José Luis Usó Doménech, Josué Antonio Nescolarde-Selva, Lorena Segura-Abad and Mario Sabán

The doctrine of coincidentia oppositorum (the coincidence of opposites), the interpenetration, interdependence and unification of opposites has long been one of the defining…

Abstract

Purpose

The doctrine of coincidentia oppositorum (the coincidence of opposites), the interpenetration, interdependence and unification of opposites has long been one of the defining characteristics of mystical (as opposed to philosophical) thought. Mystics of various persuasions have generally held that such paradoxes are the best means of expressing within language, truths about a whole that is sundered by the very operation of language itself. Any effort, it is said, to analyze these paradoxes and provide them with logical sense is doomed from the start because logic itself rests upon assumptions, such as the principles of non-contradiction and excluded middle, that are violated by the mystical ideas.

Design/methodology/approach

Mathematical development of a dialectical logic with truth-values in a complex field.

Findings

The coincidentia oppositorum is a common trope in many religious traditions, particularly those with a mystical or initiatory aspect, and fields of knowledge such as Psychology and Quantum Physics, with wave-particle duality. The aim of this paper is to present a mathematical theory of the coincidence of opposites, and where truth-values are expressed in a complex field. A propositional coincidentia oppositorum algebra is developed.

Originality/value

Although the literature of paraconsistent logics is abundant, the authors think that this is the first time that a dialectical logic has been developed with truth-values belonging to a complex field. The impossibility of reaching an absolute truth from opposite propositions is discovered, both being true, because of the existence of irrational numbers in the truth-values.

Article
Publication date: 20 May 2019

José Luis Usó Doménech, Josué Antonio Nescolarde-Selva, Hugh Gash and Lorena Segura-Abad

The distinction between essence and existence cannot be a distinction in God: in the actual infinite, essence and existence coincide and are one. In it, maximum and minimum…

Abstract

Purpose

The distinction between essence and existence cannot be a distinction in God: in the actual infinite, essence and existence coincide and are one. In it, maximum and minimum coincide. Coincidentia oppositorum is a Latin phrase meaning coincidence of opposites. It is a neo-Platonic term, attributed to the fifteenth-century German scholar Nicholas of Cusa in his essay, Docta Ignorantia. God (coincidentia oppositorum) is the synthesis of opposites in a unique and absolutely infinite being. God transcends all distinctions and oppositions that are found in creatures. The purpose of this paper is to study Cusanus’s thought in respect to infinity (actual and potential), Spinoza’s relationship with Cusanus, and present a mathematical theory of coincidentia oppositorum based on complex numbers.

Design/methodology/approach

Mathematical development of a dialectical logic is carried out with truth values in a complex field.

Findings

The conclusion is the same as has been made by thinkers and mystics throughout time: the inability to know and understand the idea of God.

Originality/value

The history of the Infinite thus reveals in both mathematics and philosophy a development of increasingly subtle thought in the form of a dialectical dance around the ineffable and incomprehensible Infinite. First, the authors step toward it, reaching with their intuition beyond the limits of rationality and thought into the realm of the paradoxical. Then, they step back, struggling to express their insight within the limited scope of reason. But the Absolute Infinite remains, at the border of comprehensibility, inviting them with its paradoxes, to once again step forward and transcend the apparent division between finite and Infinite.

Details

Kybernetes, vol. 48 no. 8
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 16 May 2023

José Luis Usó Doménech, Hugh Gash, Josué Antonio Nescolarde-Selva and Lorena Segura-Abad

The process of elaboration of the symbolic universe leads to important insights into the role of symbols in understanding human reasoning. Symbols become explanatory axes of…

Abstract

Purpose

The process of elaboration of the symbolic universe leads to important insights into the role of symbols in understanding human reasoning. Symbols become explanatory axes of universal global realities. Myths were constructed on these explanatory paths forming a superstructure of all belief systems with paraconsistent logic for the symbolism and a symbolic syntax. Myths and symbols are to be found in all cultures. Some of the most powerful and influential ones occur in popular culture since these often have the greatest immediate social impact.

Design/methodology/approach

Semiotic and logical development of the symbols is in mythical systems. The dissolution of the myth and the degradation of the myth's symbols constitute a long-drawn-out process in modern Western society and wherever s influence reaches. Myth is a story that may contain symbolic elements, but compared to the symbols or images of the exceptional, myth is characterized by a “story.”

Findings

Starting from a minimal definition to define myths and propose the following definition: Myth is a traditional tale that relates memorable and exemplary actions of extraordinary personages in prestigious and distant times, and myths have various forms and functions, perhaps some more clearly defined with a signifier than others, and different approaches can be combined for a better understanding of the myths. Dispensing with such simplistic assertions, and starting from a minimal definition to define myth, myth is a traditional tale that relates memorable and exemplary actions of extraordinary personages in prestigious and distant times.

Originality/value

Any symbol F originates in a unit that has two aspects and functions when the unit is restored. Thus, the symbol is rather “for something” than “of something” and the symbolic objects express the objects' correspondence in one unit or hendiadys. One semantic characteristic of symbols is “recognition”. The symbol F reveals a reality by means of the homogenous association of the signifier and significance in the symbol's constitution; although reality is separate, there is a homogeneous relation between the symbolizing and symbolized in symbolization.

Details

Kybernetes, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 18 May 2021

José Luis Usó Doménech, Josué Antonio Nescolarde-Selva and Hugh Gash

Categories (particular (P) and general (V)) constitute a bipole with epistemological implications. The mutual categorical implication of this bipole is embodied in ordinary…

Abstract

Purpose

Categories (particular (P) and general (V)) constitute a bipole with epistemological implications. The mutual categorical implication of this bipole is embodied in ordinary notions. It follows that a concept because it forms an element of concrete, sensible-rational, practical-theoretical activity has to unite the two inseparable poles, the general and the particular. If the concept of a physical quantity is abstract in relation to the physical object, it is concrete in comparison with mathematical quantity. This product of a secondary abstraction covers the background of physical qualities to extract the pure number, legitimately named abstract number. Both kinds of numbers are mutually exclusive: either the numbers are attached to a unit name and the number is concrete or nothing is attached and the number is abstract. However, in addition to their coordination in extension, they involve each other in comprehension: in fact, the pure number is the general pole V and concrete numbers form the particular pole of the dialectical concept of number K. The purpose of this paper is to provide a model for epistemological issues that arise in the context of meaning, concepts and use of words.

Design/methodology/approach

A dialectical theory of the binomial comprehension-extension of mathematical magnitudes.

Findings

The findings provide an objection to the traditional deductive order being also true in mathematics, and also that the reverse order cannot be considered as characteristic of mathematics, but show dialectic as universal. This opens the way to the special scientific deduction (mathematical, physical, biological, etc). going from the general to individual.

Originality/value

The structure of the mathematical concepts is elaborated.

Details

Kybernetes, vol. 51 no. 1
Type: Research Article
ISSN: 0368-492X

Keywords

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