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Attempts to prove, in this second chapter of the author’s monograph, that with a new research programme, it is possible to build a methodological bridge between economics and all other natural sciences and the scientists should address this challenge. Reviews basic principles that govern nature, including Einstein’s findings along with such luminaries as Copernicus, Newton, Galileo and Jeans. Concludes that the future is safe, as a new generation of scientists is now emerging in the East and the West, and that the new methodology should provide enough space for new roads, ideas and interpretations, which may occur in the future. Closes by saying a new spirit should be initiated in economics and transplanted into natural sciences.

There is a double crisis in modern science and in particular in physics and mechanics. Among others Einstein and Stephane Lupasco, in the 1930s, warned about this crisis. The Quantum Theory cannot be reconciled with the Relativity Theory. Specifically there is a gap (cleavage) between micro – and macro‐physics and mechanics. Parallel or beneath there is also a second crisis derived from a discontinuity (again a cleavage) between classical and modern science, that is between two previous revolutions. A new research programme of a simultaneous equilibrium versus disequilibrium approach, initially applied in economics has now been extended to include natural sciences. It is the question of a new, more comprehensive methodology which is actually a sui generis synthesis between classical and modern heritage. The rigorous application of the new research programme leads to the organisation of an Orientation Table, that is, a methodological map of all possible combinations (systems). The Table shows, without any exaggeration, a few revolutionary results. For instance, with the help of the Table, modern science or the second revolution (Einstein, Bohr, Heisenberg) does not appear contradictory but rather complementary to classical science or the first revolution (Newton, Lavoisier). The Kuhnian thesis to the contrary is disproved and the second crisis is solved. With the help of the Universal Hypothesis of Duality (the basis of the Orientation Table), matter and energy, at the micro – and macro‐level, appear in a double form (the Principle of Duality): stable (equilibrium) particles and unstable (disequilibrium) waves. The strong interactions from modern physics are associated with the law of gravitation (attraction) or stable equilibrium which governs stable matter and energy. The weak interactions are associated with the law of disgravitation (dispersion or repulsion) including entropy or unstable equilibrium which governs unstable matter and energy. In this way the first crisis is also solved.

The purpose of this paper is to state new formulation of the programme‐styled framework of pansystems research and related expansions.

Pansystems‐generalized extremum principle (0**: (dy/dx=0)**) is presented with recognitions to various logoi of philosophy, mathematics, technology, systems, cybernetics, informatics, relativity, biology, society, resource, communications and related topics: logic, history, humanities, aesthetics, journalism, IT, AI, TGBZ* <truth*goodness*beauty*Zen*>, etc. including recent rediscoveries of 50 or so pansystems logoi.

A keynote of the paper is to develop the deep logoi of the analytic mathematics, analytic mechanics, variational principles, Hilbert's sixth/23rd problems, pan‐axiomatization to encyclopedic principles and various applications. The 0**‐universal connections embody the transfield internet‐styled academic tendency of pansystems exploration.

The paper includes topics: history megawave, pansystems sublation‐modes, pan‐metaphysics, pansystems dialogs with logoi of 100 thinkers or so, and pansystems‐sublation for a series of logoi concerning the substructure of encyclopedic dialogs such as systems, derivative, extremum, quantification, variational principle, equation, symmetry, OR, optimization, approximation, yinyang, combination, normality‐abnormality, framework, modeling, simulation, relativity, recognition, practice, methodology, mathematics, operations and transformations, quotientization, product, clustering, Banach completeness theorem, Weierstrass approximation theorem, Jackson approximation theorem, Taylor theorem, approximation transformation theorems due to Walsh‐Sewell mathematical school, Hilbert problems, Cauchy theorem, theorems of equation stability, function theory, logic, paradox, axiomatization, cybernetics, dialectics, multistep decision, computer, synergy, vitality and the basic logoi for history, ethics, economics, society OR, aesthetics, journalism, institution, resource and traffics, AI, IT, etc.

The economic science is again in a crisis and a new solution prolegomena to any future study in economics, finance and other social sciences has just been published by the International Institute of Social Economics in care of the MCB University Press in England. The roots of the major financial and economic problems of our time lie in an open conflict between theory and practice. In the 1930s and before the conflict was between classical theory and given realities. In the 1990s the conflict appears between the now prevailing modern, Keynesian theory and the actual realities. In addition during the twentieth century a great argument developed between the two schools of thought, argument which is not yet settled. In one sentence, the prolegomena tried and was successful to solve the conflict between theory and practice and the big doctrinal dispute of the twentieth century. It was a struggle of research and observation over half a century between 1947 and 1997.

Presents the scientific methodology from the enlarged cybernetical perspective that recognizes the anisotropy of time, the probabilistic character of natural laws, and the entry that the incomplete determinism in Nature opens to the occurrence of innovation, growth, organization, teleology communication, control, contest and freedom. The new tier to the methodological edifice that cybernetics provides stands on the earlier tiers, which go back to the Ionians (c. 500 BC). However, the new insights reveal flaws in the earlier tiers, and their removal strengthens the entire edifice. The new concepts of teleological activity and contest allow the clear demarcation of the military sciences as those whose subject matter is teleological activity involving contest. The paramount question “what ought to be done”, outside the empirical realm, is embraced by the scientific methodology. It also embraces the cognitive sciences that ask how the human mind is able to discover, and how the sequence of discoveries might converge to a true description of reality.

The framework, panorama, related applications and development of pansystems thinking are introduced and some problems concerning generalized systems, derivatives, symmetry and quantification are investigated, a sort of difference‐identity theory within the framework of pansystems thinking is cultivated, and a new type of clustering method with many intertransformations among some important pansystems concepts is presented. Related contents include: pansystems combination of mathematics, systems, dialectics and poetry thinking, methodology to comprehend laws by pansymmetries or by moving networks, the pansystems views of generalized order, quotientization and series‐parallel relations, control‐reachability, duality transformation, discoupling principle, communication theorems, general parental relations, etc.

The paper's purpose is to analyze the concepts of potential and actual infinities.

The exploration and research on potential and actual infinities generally touch on many disciplines, such as philosophy, logic, computer science, mathematics, etc. From the angle of a brief history, recall and development, the authors analyze the concepts of potential and actual infinities on one starting point and two locations to cut in.

Clarify the difference and connection of these two infinities on the level of mathematics and introduce the symbolized, descriptive definitions for potential and actual infinities.

It is the first time that the difference between the concepts of potential and actual infinities are clarified, which leads to the discovery of the fourth crisis in the foundations of mathematics.

Although fuzzy logic is being extensively used in electronics and mathematical sciences, it has found little or no application in the social sciences, especially criminology. As a mathematical system, fuzzy logic generalizes the Boolean logic and can be a very useful tool for the social sciences where concepts and terms involve shades of meanings. Outlines the essential mathematics behind this approach and develops a technique that could be useful in building offender profiles from fuzzy descriptions provided by witnesses. Also suggests several other possible areas of applications of this mathematical system.

Cybernetics and artificial intelligence are viewed primarily as being a major part of information science which is considered as we would any other scientific discipline. It is suggested that such a science must be capable of formalization. Language is considered as a major feature of science, where mathematics is a specialized part of language. The analysis of language in the form of semantics and pragmatics is regarded as essential to the understanding of any linguistic usage, particularly when some degree of precision is entailed. Discusses information science and its foundations in philosophy, logic and especially in semantics and pragmatics.