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[25] viXra:1008.0091 [pdf] submitted on 31 Aug 2010
Authors: Florentin Smarandache
Comments: 157 pages
It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) "neutrosophy" - study of neutralities as an extension of dialectics; b) and its derivative "neutrosophic", such as "neutrosophic logic", "neutrosophic set", "neutrosophic probability", and "neutrosophic statistics" and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics.
[24] viXra:1005.0059 [pdf] submitted on 14 May 2010
Authors: Dm. Vatolin
Comments: 15 pages, Russian.
This article formulates three geometrical axioms from which it follows that the continuum power is greater then any well-ordered set power.
[23] viXra:1005.0006 [pdf] submitted on 10 Mar 2010
Authors: Andrew Schumann, Florentin Smarandache
Comments: 121 pages
This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes' axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero, but smaller than each positive real number. Robinson applied this idea into modern mathematics in [117] and developed so-called non-standard analysis. In the framework of non-standard analysis there were obtained many interesting results examined in [37], [38], [74], [117].
[22] viXra:1004.0112 [pdf] submitted on 21 Apr 2010
Authors: V. Veeramani, Roque Batulan
Comments: 7 pages
This paper contains the Basic Definitions of an Intuitionstic Fuzzy Set theory and operations on it. Mainly we discussed the basic concepts of α - cut with examples and Characterisations.
[21] viXra:1004.0096 [pdf] submitted on 19 Apr 2010
Authors: Huang, Cheng-Gui
Comments: 1 pages.
I claim that Neutrosophy, by Professor Florentin Smarandache, is a deep thought in human culture. That gives advantage to break the mechanical understanding of human culture. For example, according to the mechanical theory: existence and non-existence could not be simultaneously. Actually existence and non-existence are simultaneously. Everyone knows that human life is like a way in the empty space of a bird flying. Everyone can not see himself a second ago, everyone can not see himself for the time being and everyone can not see himself a second future. Everyone could not know what is the existence of self. Everyone is also difficult to say the non-existence of self. So the existence and non-existence of self are simultaneously. And the existence and nonexistence of everything are simultaneously, where, the law of excluded middle does not apply. These basic facts express the depth of Smarandache's Neutrosophy. He has a lot of friends in ancient and in nowadays, in the West and in the East.
[20] viXra:1004.0092 [pdf] submitted on 19 Apr 2010
Authors: Feng Liu
Comments: 8 pages.
Logic should have been defined as the unity of contradiction between logic director and logic implementation. Chinese Daoism asserts that everything is defined in the unity of opposites, namely yin and yang, accordingly yang conducts change and yin brings it up (I-Ching, also known as Book of Changes). In this way logic is redefined in an indeterminate style to facilitate "both A and Anti-A" etc. in neutrosophics of logic. The unity of opposites is also described as neutrality in neutrosophy. An intermediate multi-referential model of excitation and inhibition is developed to derive a multiagent architecture of logic, based on Chinese yin-yang philosophy. This methodology of excitation/inhibition suggests a rhymed way of logic, leading to a dynamic methodology of weight strategy that links logic with neural network approach. It also confirms the crucial role of indeterminacy in logic as a fatal criticism to classical mathematics and current basis of science.
[19] viXra:1004.0091 [pdf] submitted on 19 Apr 2010
Authors: Feng Liu
Comments: 12 pages.
As a philosophical analysis of some fatal paradoxes, the paper distinguishes the conceptual difference between representation of truth and source of truth, and leads to the conclusion that in order to acquire the genuine source of truth, independently of specific representations possibly belonging to different worlds, one is necessary to ignore all the ideas, logics, conceptions, philosophies and representable knowledge even himself belonging to those misleading worlds, returning to his infant nature, as a preliminary step for his cultivation of unconstrained wisdom. It also carries out some coordinative crucial issues as natural-doctrine, minded-unwitting, logic-infancy, conception-deconception, determinacy-indeterminacy. The paper tries to verify the role of neutrosophy and neutrosophic logic in religious issues and open a gateway toward the oriental classics, excavating the lost treasure.
[18] viXra:1004.0065 [pdf] submitted on 10 Apr 2010
Authors: Florentin Smarandache
Comments: 8 pages
In this paper we introduce the operators of validation and invalidation of a proposition, and we extend the operator of S-denying a proposition, or an axiomatic system, from the geometric space to respectively any theory in any domain of knowledge, and show six examples in geometry, in mathematical analysis, and in topology.
[17] viXra:1004.0051 [pdf] submitted on 8 Mar 2010
Authors: Haibin Wang, Florentin Smarandache, Yanqing Zhang, Rajshekhar Sunderraman
Comments: 4 pages
Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the settheoretic operators on an instance of neutrosophic set, we call it single valued neutrosophic set (SVNS). We provide various properties of SVNS, which are connected to the operations and relations over SVNS.
[16] viXra:1004.0026 [pdf] submitted on 3 Apr 2010
Authors: Florentin Smarandache
Comments: 14 pages
These paradoxes are called "neutrosophic" since they are based on indeterminacy (or neutrality, i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the Venn Diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, illdefined ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth table and introduce two neutrosophic operators (neuterization and antonymization operators) give many classes of neutrosophic paradoxes.
[15] viXra:1004.0016 [pdf] submitted on 8 Mar 2010
Authors: Florentin Smarandache
Comments: 11 pages
In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies.
[14] viXra:1004.0013 [pdf] submitted on 8 Mar 2010
Authors: Florentin Smarandache, V. Christianto
Comments: 15 pages
We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.
[13] viXra:1004.0010 [pdf] submitted on 8 Mar 2010
Authors: Florentin Smarandache
Comments: 6 pages
The paper presents an initial explorations on T, I, F operations based on genetic concept hierarchy and genetic referential hierarchy, as a novel proposal to the indeterminacy issue in neutrosophic logic, in contrast to the T, I, F values inherited from conventional logics in which those values would fail to demonstrate the genetic aspect of a concept and accordingly loose the connection between generality and practicality. Based on the novel definition of logic and on the relativity of T, F concept, it illustrates that T, F are hierarchical operations which inter-consist and inter-complement each other, that "I" relates to a learning behavior profiled by an inspiration from I-ching, and that the neutralization operation, as the means to solve contradictions, will eventually come to the unification of opposites, leading to the fundamental issues in Buddhism and such alike. It also implies that Buddhism and Daoism are not religions.
[12] viXra:1004.0006 [pdf] submitted on 8 Mar 2010
Authors: Florentin Smarandache
Comments: 10 pages
Based on the authors intensive investigation on the oriental dialectics, the paper presents a novel theoretical frame of matter element in the world leading science, extenics dealing with inconsistency or incompatibility, covering the widest range of application area from informatics, system engineering to management and finance. The dialectic matter-element is defined as the integral of all existing and prospecting ones based on all the infinite possible cognitive models. The novel model serves as the origin of constraint matter elements, the unity of both state description and cognitive action (cognition force with respect to neural science), a latent part of extenics, and possibly as essence of matter element. It explains, in a novel perspective, the origin of a name, and uncovers the source of contradiction and even the impetus of cognition.
[11] viXra:1003.0269 [pdf] submitted on 8 Mar 2010
Authors: C. Le
Comments: 4 pages, edited by C. Le, and translated into German by Bernd Hutschenreuther
The Smarandache's Class of Paradoxes are semantic paradoxes of the form "All is <A>, the <nonA> too!", where <nonA> is what is not <A>. As a particular case, replacing <A> but an attribute (or, in general, by an idea) it is well know the Smarandache semantic paradox: "All is possible, the impossible too!" which is the motto of the Paradoxism movement in arts, letters, and sciences.
[10] viXra:1003.0224 [pdf] submitted on 7 Mar 2010
Authors: Charles Ashbacher
Comments: 145 pages
As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by where I do not use some topic from those courses.
[9] viXra:1003.0171 [pdf] submitted on 6 Mar 2010
Authors: Florentin Smarandache
Comments: 4 pages
In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.
[8] viXra:1003.0167 [pdf] submitted on 6 Mar 2010
Authors: Florentin Smarandache
Comments: 7 pages
In this article one builds a class of recursive sets, one establishes properties of these sets and one proposes applications. This article widens some results of [1].
[7] viXra:1003.0119 [pdf] submitted on 6 Mar 2010
Authors: Florentin Smarandache
Comments: 6 pages
Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and afterwards. They have a more educational interest because make the students think different!
[6] viXra:1003.0117 [pdf] submitted on 6 Mar 2010
Authors: Florentin Smarandache
Comments: 12 pages
Classes of linguistic paradoxes are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such paradoxes one grammatically adjusts the sentences.
[5] viXra:1003.0065 [pdf] submitted on 6 Mar 2010
Authors: Feng Liu, Florentin Smarandache
Comments: 10 pages
The paper presents a fresh new comprehensive ideology on Neutrosophic Logic based on contradiction study in a broad sense: general critics on conventional logic by examining the essence of logic, fresh insights on logic definition based on Chinese philosophical survey, and a novel and genetic logic model as the elementary cell against Von Neumann oriented ones based on this novel definition. As for the logic definition, the paper illustrates that logic is rather a tradeoff between different factors than truth and false abstraction. It is stressed that the kernel of any intelligent system is exactly a contradiction model. The paper aims to solve the chaos of logic and exhibit the potential power of neutrosophy: a new branch of scientific philosophy.
[4] viXra:1003.0062 [pdf] submitted on 6 Mar 2010
Authors: Feng Liu, Florentin Smarandache
Comments: 7 pages
The paper presents a fresh new start on the neutrality of neutrosophy in that "both A and Non-A" as an alternative to describe Neuter-A in that we conceptualize things in both intentional and unintentional background. This unity of opposites constitutes both objective world and subjective world. The whole induction of such argument is based on the intensive study on Buddhism and Daoism including I-ching. In addition, a framework of contradiction oriented learning philosophy inspired from the Later Trigrams of King Wen in I-ching is meanwhile presented. It is shown that although A and Non-A are logically inconsistent, but they are philosophically consistent in the sense that Non-A can be the unintentionally instead of negation that leads to confusion. It is also shown that Buddhism and Daoism play an important role in neutrosophy, and should be extended in the way of neutrosophy to all sciences according to the original intention of neutrosophy.
[3] viXra:0912.0017 [pdf] submitted on 8 Dec 2009
Authors: Feng Xu
Comments: 6 pages, first published in 2006 in Hadronic Journal, volume 29, page 227
The set of all the subsets of a set is its power set, and the cardinality of the power set is always larger than the set and its subsets. Based on the definition and the inequality in cardinality, a set cannot include its power set as element, and a power set cannot include itself as element. "Russell's set" is a putative set of all the sets that don't include themselves as element. It can be shown, however, that "Russell's set" can never take in all such sets. This is because its own power set, which (like any power set) is a set that doesn't include itself (thus qualifies as an element for "Russell's set"), cannot (although should) be taken in due to the cardinality inequality. Thus "Russell's set" can never be formed. Without it, Russell's paradox, which forced the modification of Cantor's intuitive set theory into a more restricted axiomatic theory, can never be formulated. The reported approach to resolve Russell's paradox is fundamentally different from the conventional approaches. It may restore the self-consistency of Cantor's original set theory, make the Axiom of Regularity unnecessary, and expand the coverage of set to assemblies that include themselves as element.
[2] viXra:0910.0041 [pdf] submitted on 21 Oct 2009
Authors: Amrit S. Sorli
Comments: 2 pages
In 1949, Gödel postulated a theorem that stated: "In any universe described by the theory of relativity, time cannot exist". Gödel idea was that forth coordinate of space-time is not time. Fourth coordinate is spatial too. In this article will be shown that on the base of elementary perception and experimental data Gödel theorem is right. With eyes one observes universe is in a continuous change. A change n gets transformed into a change n+1, the change n+1 into a change n+2 and so on. Clocks measure a frequency, velocity and numerical order of change. Experimental date confirms that changes and clocks do not run time; they run in space only. Time is not a part of space. Fourth coordinate of space-time is spatial too. Space itself is timeless. Physical time that is clocks run is man created physical reality. Fundamental arena of the universe is timeless space. In the timeless space into which massive bodies and elementary particles move there is no past and no future. Past and future belong to the inner neuronal space-time that is a result of neuronal activity of the brain.
[1] viXra:0909.0039 [pdf] submitted on 16 Sep 2009
Authors: Victor Porton
Comments: 2 Pages.
In the framework of ZF formally considered generalizations, such as whole numbers generalizing natural number, rational numbers generalizing whole numbers, real numbers generalizing rational numbers, complex numbers generalizing real numbers, etc. The formal consideration of this may be especially useful for computer proof assistants.
[2] viXra:1004.0026 [pdf] replaced on 22 Apr 2010
Authors: Florentin Smarandache
Comments: 14 pages
These paradoxes are called "neutrosophic" since they are based on indeterminacy (or neutrality, i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the Venn Diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, illdefined ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth table and introduce two neutrosophic operators (neuterization and antonymization operators) give many classes of neutrosophic paradoxes.
[1] viXra:1002.0003 [pdf] replaced on 15 Mar 2010
Authors: Willi Penker
Comments: 3 pages
To shift assignments between infinite sets is to create a disturbance within the assignment itself that cannot be removed. An assignment carrying such a disturbance cannot be regarded as static.