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In this paper, Florentin Smarandache, reputed professor at University of New Mexico, presents a new branch of philosophy, called neutrosphy, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Florin Smarandache is not only a high level scientist, he is also a propensity and complete artist who wanted to express and to share his cognition, thoughts, ideas in a moment and in a place when and where, was not possible, it was necessary to find the way to communicate somehow: so, it was born “the paradoxism”.
N-Norm and N-conorm are extended in Neutrosophic Logic/Set.
The subsets T, I, F are not necessarily intervals, but may be any real subsets: discrete or continuous; single-element, finite, or (either countably or uncountably) infinite; union or intersection of various subsets; etc.
In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental physics the author reaches the revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense, as compared with Einstein's view of physics as space-time geometry. This opens new, exciting prospects for the study of fundamental interactions. A formulation of logic in terms of matrix operators and logic vector spaces allows the author to tackle for the first time the intractable problem of cognition in a scientific manner. In the same way as the findings of Heisenberg and Dirac in the 1930s provided a conceptual and mathematical foundation for quantum physics, matrix operator logic supports an important breakthrough in the study of the physics of the mind, which is interpreted as a fractal of quantum mechanics. Introducing a concept of logic quantum numbers, the author concludes that the problem of logic and the intelligence code in general can be effectively formulated as eigenvalue problems similar to those of theoretical physics. With this important leap forward in the study of the mechanism of mind, the author concludes that the latter cannot be fully understood either within classical or quantum notions. A higher-order covariant theory is required to accommodate the fundamental effect of high-level intelligence. The landmark results obtained by the author will have implications and repercussions for the very foundations of science as a whole. Moreover, Stern's Matrix Logic is suitable for a broad spectrum of practical applications in contemporary technologies.
In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics).
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter
There are people for whom are too few things they do not know how to do, to approach them, to understand them. There are people who is enough to look at them because they understood the significance in your eyes, are people for whom you have not finished the uttered sentence and they are given the solution, there are ...people!
Symbolic logic may be superior to classical Aristotelian logic for the sciences, but not for the humanities. This text is designed for do-it-yourselfers as well as classrooms.
In this concern, neutrosophic logics and neutrosophy in general, established by Prof. Smarandache, is one of the promising research instruments, which could be successfully applied by a theoretical physicist. Naturally, neutrosophic logics, being a part of modern logics, states that neutralities may be between any physical states, or states of space-time. In particular, this leads, sometimes, to paradoxist situations, when two opposite states are known in physics, while the neutral state between them seems absolutely impossible from a physical viewpoint! Meanwhile, when considering the theoretically possible neutralities in detail, we see that these neutral states indicate new phenomena which were just discovered by the experimentalists in the last decade, or shows a new field for further experimental studies, as for example unmatter which is a state between matter and antimatter. Research papers presented in this collection manifest only a few of many possible applications of neutrosophic logics to theoretical physics. [D. Rabounski] The ⿿multi-space⿿ with its multi-structure is a Theory of Everything. It can be used, for example, in the Unified Field Theory that tries to unite the gravitational, electromagnetic, weak, and strong interactions (in physics). [F. Smarandache]