Dialectical logic for mythical and mystical superstructural systems (ii)

José Luis Usó Doménech (Departament of Applied Mathematics, Universitat d’Alacant, Alacant, Alicante, Spain)
Josué Antonio Nescolarde-Selva (Departament of Applied Mathematics, University of Alicante, Alicante, Spain)
Hugh Gash (Institute of Education, Dublin City University, Dublin, Ireland)
Lorena Segura-Abad (Departament of Applied Mathematics, Universitat d’Alacant, Alacant, Alicante, Spain)


ISSN: 0368-492X

Publication date: 27 April 2019



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.


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


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.


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.



Usó Doménech, J., Nescolarde-Selva, J., Gash, H. and Segura-Abad, L. (2019), "Dialectical logic for mythical and mystical superstructural systems (ii)", Kybernetes, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/K-08-2018-0433

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