TITLE:
The Maximum Ordinality Principle (MOP) and Its Formal Language, Namely the “Incipient” Differential Calculus (IDC), Open, and at the Same Time Offer, A Radically New Perspective to Modern Science
AUTHORS:
Corrado Giannantoni
KEYWORDS:
IDC, TDC, Theoretical Com-Possibility, Operative In-Equivalence, Harmonious Over-Ordinal Com-Possibility
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.9,
September
14,
2022
ABSTRACT: The aim of the paper, as explicitly indicated by its title, is to show that The Maximum Ordinality Principle (MOP) and its Formal Language, namely The “Incipient” Differential Calculus (IDC), open, and at the same time offer, a Radically New Perspective to Modern Science. The methodology adopted, in this respect, is articulated in two parts: 1) firstly, by recalling the general characteristics of the Self-Organizing Systems, whose behavior is described by the Maximum Ordinality Principle and, at the same time, the reasons for the introduction of a different Formal Language termed as IDC (“Incipient” Differential Calculus); 2) afterwards, by comparing the specific properties of the MOP and IDC, and the Fundamental Differences they introduce in describing the surrounding world, with respect to any Scientific Discipline based on TDC. Self-Organizing Systems, in fact, always show an unexpected “excess” with respect to their phenomenological premises. An “excess” can be termed as Quality (with a capital Q) because it is not a simple “property” of a given phenomenon. In fact, it is never reducible to the usual categories of the Traditional Science: efficient causality, logical necessity, functional relationships. Consequently, the description of such an “Emerging Quality” requires new mental categories (Generative Causality, Adherent Logic, Ordinal Relationships) and, correspondingly, a new Formal Language, termed IDC. The result of such a comparison is that the New Scientific Perspective, in spite of the different ways of describing Physical, Biological and Human System, always remains, by itself, a “com-possible” option with respect to the Traditional one. The two Perspectives, in fact, are not in contrast between them. They simply “co-exist”, because of the absence of Perfect Induction in their corresponding Logics. However, in spite of the fact that the two Perspectives are “com-possible” in principle, their differences become significantly “marked” at the operative level, as shown by the several study cases, analyzed in the second part of the Paper, in the light of a General Methodology for Strategic Decisions based on both MOP and IDC. The conclusions thus would (apparently) be that TDC and IDC can be operatively adopted only separately (or, at the most, both “in parallel”) in order to research for the optimal solutions, according to their respective operative validity. Without forgetting, however, that in all cases: 1) TDC “reflects” the presuppositions of the Traditional Scientific Approach, so that, by itself, it is “self-referential”; 2) IDC, vice versa, “reflects” the presuppositions of the New Scientific Approach, so that, by itself, it is “hetero-referential”. In reality, the paper also shows that there exists an ulterior possibility, which represents an Over-Conclusion. In fact, in adherence to the General Methodology for Strategic Decisions presented in the paper, TDC and IDC can be “seen” as generating a Unique Feed-Back Logical Process. Like “Two Brothers”, that cooperate between them. Consequently, and surprisingly, TDC and IDC “reveal” that, in the context of the abovementioned Logical Structure, they are “nothing but” a unique “casket” of “precious pearls”.