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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.

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.

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

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.

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.

Survey of period infinite element developments The first infinite elements for periodic wave problems, as stated in Part 1, were developed by Bettess and Zienkiewicz, the earliest publication being in 1975. These applications were of ‘decay function’ type elements and were used in surface waves on water problems. This was soon followed by an application by Saini et al., to dam‐reservoir interaction, where the waves are pressure waves in the water in the reservoir. In this case both the solid displacements and the fluid pressures are complex valued. In 1980 to 1983 Medina and co‐workers and Chow and Smith successfully used quite different methods to develop infinite elements for elastic waves. Zienkiewicz et al. published the details of the first mapped wave infinite element formulation, which they went on to program, and to use to generate results for surface wave problems. In 1982 Aggarwal et al. used infinite elements in fluid‐structure interaction problems, in this case plates vibrating in an unbounded fluid. In 1983 Corzani used infinite elements for electric wave problems. This period also saw the first infinite element applications in acoustics, by Astley and Eversman, and their development of the ‘wave envelope’ concept. Kagawa applied periodic infinite wave elements to Helmholtz equation in electromagnetic applications. Pos used infinite elements to model wave diffraction by breakwaters and gave comparisons with laboratory photogrammetric measurements of waves. Good agreement was obtained. Huang also used infinite elements for surface wave diffraction problems. Davies and Rahman used infinite elements to model wave guide behaviour. Moriya developed a new type of infinite element for Helmholtz problem. In 1986 Yamabuchi et al. developed another infinite element for unbounded Helmholtz problems. Rajapalakse et al. produced an infinite element for elastodynamics, in which some of the integrations are carried out analytically, and which is said to model correctly both body and Rayleigh waves. Imai et al. gave further applications of infinite elements to wave diffraction, fluid‐structure interaction and wave force calculations for breakwaters, offshore platforms and a floating rectangular caisson. Pantic et al. used infinite elements in wave guide computations. In 1986 Cao et al. applied infinite elements to dynamic interaction of soil and pile. The infinite element is said to be ‘semi‐analytical’. Goransson and Davidsson used a mapped wave infinite element in some three dimensional acoustic problems, in 1987. They incorporated the infinite elements into the ASKA code. A novel application of wave infinite elements to photolithography simulation for semiconductor device fabrication was given by Matsuzawa et al. They obtained ‘reasonably good’ agreement with observed photoresist profiles. Häggblad and Nordgren used infinite elements in a dynamic analysis of non‐linear soil‐structure interaction, with plastic soil elements. In 1989 Lau and Ji published a new type of 3‐D infinite element for wave diffraction problems. They gave good results for problems of waves diffracted by a cylinder and various three dimensional structures.

In the drama of the evidentiary process, it would hardly be thought exceptional that the judge’s intuition of the formal order of things – which is to say, their sufficient standing-to-reason – should falter when confronted with the sprawling and confused immediacy of stubborn matter-of-fact. The circumstantial given is a bewildering Gordian Knot of data; the analytic legerdemain of localising our attention and following one of its threads cannot reduce the tangle into which it soon recedes. And in comparison to the knot’s multiplicity, our scope for unifying abstraction, or “large-scale” comprehension, is limited and flickering. We possess fragments of intuition, and fragments of formal connection between these fragments. But the panorama is merely agglutinative – the fragments do not congeal into one perfect, self-evident totality. And an offhand remark amongst the lectures of Alfred North Whitehead suggests that this defect is of more than methodological significance – even when one takes one’s example from arithmetic: “the snippet of knowledge that the addition of 1 and 4 produces the same multiplicity as the addition of 2 and 3, seems to me self-evident” (Whitehead, 1968, p. 47). And yet we would disclaim any such self-evidence were larger numbers involved – only skeptically could we hazard a guess. So, he continues, we have recourse to “the indignity of proof,” securing our opinion through the rationality of calculation. Nor is it so much that proof and method are chastening of themselves – the nemesis, the sting of the creatural condition is rather having to prove, the imperfection of finite judgment and the infinite possibility of perfecting it. This predicament was already known to Sophocles; if humanity “holds out” against the overwhelming by its inventiveness, by finding a means in to mêchanoen technas, the machinations of technique, it is because our ultimate condition with regard to the overwhelming is amêchanôs, aporos, resourceless and without means.

The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and misspecification-robust alternative to the quasi-maximum likelihood estimator (QMLE). In this paper we investigate the asymptotic behavior of the VTE when the stationary distribution of the GARCH process has infinite fourth moment. Existing studies of historical asset returns indicate that this may be a case of empirical relevance. Under suitable technical conditions, we establish a stable limit theory for the VTE, with the rate of convergence determined by the tails of the stationary distribution. This rate is slower than that achieved by the QMLE. The limit distribution of the VTE is nondegenerate but singular. We investigate the use of subsampling techniques for inference, but find that finite sample performance is poor in empirically relevant scenarios.

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.

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

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.

The structure of the mathematical concepts is elaborated.

This paper aims to explore the root cause of growing gap in Islamic moral ideals and practices by examining paradigmatic foundation and moral axioms of Islamic business ethics. It compares and contrasts Tawhidi and secular paradigms in terms of their moral axioms and ethical mandates.

The paper first presents the paradigmatic foundation of Islamic ethics, namely, ihsan ethics. Second, it compares Tawhidi paradigm of Islam with secular paradigm in respect to their ontological, axiological, anthropological and teleological differences. Third, it links to Islamic moral axioms to the relevant paradigmatic pillars. Fourth, it defines “ihsan ethics” based on Tawhidi paradigm and moral axioms. Finally, it sheds some light on the gap between moral ideals and realities through the theory of ihsan ethics.

The paper attempts to provide strong conceptual and theoretical tools to understand ethical problems in the Muslim societies. The paper makes a strong case that Muslim minds shall be de-secularized to perceive the reality, truth and telos within Tawhidi worldview. As Muslims reach the level of ihsan by perceiving transcendental reality, they are likely to practice what they preach.

The paper proposes “ihsan ethics” based on Tawhidi worldview and Islamic moral axioms.

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.

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.”

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.

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.

This Chapter applies the philosophy of Emmanuel Levinas to business’ role in the ‘War on Terror’. Specifically, it uses Levinasian ethics to explain how organisations, often with an abundance of ethical resources, become associated with military drones strikes against civilians, and offers ideas that challenge this practice. The chapter comprises several sections beginning with a brief introduction to the ‘War on Terror’ and the use of military drones. A concise discussion about business ethics and just war theory follows after which, the chapter explains Levinas’ ethics and his views on war. These ideas are applied to transform business ethical practice in this controversial area. The Chapter concludes with a summary of its main points.