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...15. Florentin Smarandache, Neutrosophy./ Neutrosophic Probability, Set, and Logic, American Research Press, Rehoboth, SUA, 1998 16. Florentin Smaran... ...viste nuîncape îndoial ă (formulele sunt în limbaj LaTeX): <Starting from mathematical logic and its class of paradoxes: “All is ${\cal C}$, then n... ...e îndoial ă (formulele sunt în limbaj LaTeX): <Starting from mathematical logic and its class of paradoxes: “All is ${\cal C}$, then non-${\cal C}$... ... as Infinite Sets”). Paralogismul se refer ă la gândirea contrar ă legilor logicii, iar paradoxismul - la crea ţia contrar ă legilor literare, cont... ...lor literare, contrar ă sensurilor cli şeelor. Apoi Newton, C. da Costa şi logica sa paraconsistent ă, ajungând pân ă la logica neutrosofic ă (gener... ...ophy, Neutrosophic Probability, Set, an Logic, în “Notices of the American Mathematical Society”, March 2001. [9 ] Smarandache, Florentin, Linguist... ...d now hear this Indian tale, more than 25 years old joke, that ends in a … mathematical formula! Once upon a time, somewhere in North America, an In... ...e la care am colaborat, unele – de circula ţie interna ţional ă (“American Mathematical Monthly!, “Nieuw Archief voor Wiskunde”, “Zentralblatt fur M... ...uiesc s ă se duc ă la bibliotec ă şi s ă cerceteze “Notices of the American Mathematical Society” (octombrie 1987, nr. 34, p. 924-925), unde este ins...

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...ne of the advantages of living in Charles Street that stables were near. The logic of her conduct was none of the clearest; for if she had been alone ... ... 48 The Bostonians of patches of remembered eloquence, of childish lapses of logic, of flights of fancy which might indeed have had success at Topeka; ... ...ion; and, on the other hand, how weak Verena would be on the statistical and logical side if she herself should not bring up the rear. Together, in sh... ... the hand of fate, of which the small, ignoble scenes unrolled themselves so logically. The denouement would of course be in keeping, and would consis... ...sn’t so majestic, I would have it pulled down.’ ‘That is delightful feminine logic!’ Ransom answered. ‘If, when women have the conduct of affairs, the... ...eded, in the same cool, mild, deliberate tone, as if he were demonstrating a mathematical solution, ‘you ought to know that your connection with all t...

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...FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC ... ...s Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC ... ...tion: 9 1. Neutrosophy - a new branch of philosophy: 13 2. Neutrosophic Logic - a unifying field in logics: 87 3. Neutrosophic Set - a unifying fi... ...ived from Neutrosophics: 120 2 Preface to Neutrosophy and Neutrosophic Logic by Charles T. Le 1 Introduction. It was a surprise for me when in ... ...ed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, which rigorously defines the infinitesimals. Informall... ...n's Paradox: Let M be a mathematician who may not be characterized by his mathematical work. a) To be a mathematician, M should have some mathematic... ...ork. 31 b) The reverse judgement: if M may not be characterized by his mathematical work, then M is not a mathematician. Divine Paradox (I): ... ...false", where S(n) is a sentence relating on parameter n. Can we prove by mathematical induction that P(n) is true? d) "<A> is true if and only if <... ...., "A Practical Guide to Cooperative Learning in Collegiate Mathematics", Mathematical Association of America, Washington, D.C., 1995. ] The m...

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...oven? A: Yes, it is. Start studying and you will see that there is nothing as logical or scientific that provides a fuller picture of our world, and ... ... can study them on our own, bit by bit, and open all the worlds, and even the logic of the Creator, that we say is missing. Naturally, the explanati... ...h itself, which uses drawings, formulas, and matrices. Kabbalah utilizes pure mathematical rules in order to express spiritual phenomena. There are ... ...actical science of all; it explains how we can all “live well.” Q: What is the mathematical structure of the wisdom of Kab- balah? A: The mathematical... ...n with religion. In most cases, this is a result of the difficulty in finding logic in the old Kmost cases, this is a result of the difficulty in fin... ...ng logic in the old Kmost cases, this is a result of the difficulty in finding logic in the old K customs and the various prohibitions in the Mitzvot ... ...that leave many questions open. We want to analyze the Torah scientifically, logically. What does the Torah really talk about? And most importantly:...

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...wrongly understood!), as well as - as much as I could understand- some of his mathematical, philosophical, enigmatical etc. creations. I recognize th... ...s to read “our daily paradoxes” Smarandache has not certainly referred to the logical, mathematical or linguistic meaning of the word/notion “parado... ... “our daily paradoxes” Smarandache has not certainly referred to the logical, mathematical or linguistic meaning of the word/notion “paradox”, but t... ...nsurgent from Balcesti-Gallup, his protest could not be expressed by means of mathematical formulae or notions and he had to appeal to literature. At... ...Popescu when he talks about the self(?)destruction of the traditional work: “A logic of cancellation, a dynamic of breaks, made from the gesture tha... ...egetes of paradox and paradoxism start their analysis from the affiliation to logic or aesthetics of this notion -”an old structure in philosophy and... ...tics of this notion -”an old structure in philosophy and a matter of study in logic”(Titu Popescu), Smarandache explains unequivocally in one of his ... ...a rectitude that we can find only at the strong natures and brave people The mathematical qualities appear for both at secondary school already, man... ...nifesting themselves through contributions with problems and solutions in The mathematical newspaper. The literary debut of Ion Barbu was at 22 year...

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...atements cannot be derived with certainty from any negative statement. This formal-logical trait reflects a deep psychological reality with unsettl... ...nd self-aggrandizement, and the reification and embodiment of said subversion. The logical outcome is to call for the overthrow of all political sy... ...eing which, in principle, can never be tackled with the instruments and the formal logic of science. A compromise was proposed long ago: the soul i... ...: a series of potentialities with attached probabilities, the potentials being the logically and physically possible products. What can we learn a... ...xample of which is the spreadsheet). Data items were related to each other through mathematical formulas. This is the equivalent of the increasing ... ... or end and what, precisely, does it include? A fractal curve (boundary) is an apt mathematical treatment of this question. Indeterminacy can be de... ...ts). His space-time is a four dimensional continuum. What commenced as a matter of mathematical convenience was transformed into a hallowed doctrin... ...al systems (better known as "Chaos Theory") has also violated long held notions of mathematical continuity. The sets of solutions of many mathemati... ...gers. This set has a boundary and will react in the same way, simultaneously, to a mathematical action (say, to a multiplication by a constant). Bu...

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...the second one, that comes immediately, is the perception of something concealed and absurd. Something, that is dissimulated under the level of the logical acceptance, jumps out abruptly in the main point to consider and constrains to acknowledgment. It looks as if it were an error, but not so big as to take alarm and not even to be clearly inhibited. It is a mechanism...

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...cealed and absurd. Something, that is dissimulated under the level of the logical acceptance, jumps out abruptly in the main point to consider and c... ...lthough it is an old construction of philosophy and an object of study for logic, the paradox has remained an insoluble sophism, an insoluble approac... ...erature: “all these texts that have flourished about the great enigmas of logic and that, through the subtlety of speculation, fascinate our mind”. ... ...gs the language”, more generally all that has something of that illogical logic” that Al. Macedonsky defined. The literary historian justifies the... ...hen the absence of any word or literary sign whatever), any abstract sign (mathematical, chemical, physical) put on a page... The nonliterature, cr... ...e avant- gardes since it surprises the paradox in action. Here is the mathematical and lyrical essentiality of the sequence of the semantic para... ...e of the semantic paradoxes anthologized by Florentin Smarandache in the “mathematical poem” entitled “The paradox of our life”: Let us put “@” an... ...e is created in the scriptural simultaneity of former experiments, as the mathematical ones (ordering, lacks, cycles, rhythms, lines, points, progre... ...verses” or a “non-intelligible intelligible language”, not properly of ...mathematical problems. Paradoxism, as we could see, is sensible to the cla...

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.... During the second half of the 20 th century, several new and interesting mathematical theories have emerged in parallel with the development of ... ...se non poems an imaginative use of the unimaginative geometrical figures and mathematical symbols has been made. - It is a composite art form rangin... ...talat în fotoliul paradoxismului, matematicianul şi-a adus de acolo nu numai logica, subtilitatea titrat ă şi simbolurile translucide, dar şi gândir... ...te prin conven ţie (care î şi reduc laten ţele la conven ţionalul necesar). Logica şi/ şi pe care o imprim ă aceast ă literatur ă/nonliteratur ă ad... ... to read “our daily paradoxes” Smarandache has not certainly referred to the logical, mathematical or linguistic meaning of the word/notion “paradox... ...“our daily paradoxes” Smarandache has not certainly referred to the logical, mathematical or linguistic meaning of the word/notion “paradox”, but to... ...orile umane sunt anihilate şi înlocuite cu stereotipuri. Via ţa nu mai curge logic dup ă voin ţa oamenilor, cu bogăţie de sentimente şi de cuget, ci... ...us, personajele evolueaz ă după legile fire şti ale unei ac ţiuni închegate, logica întâmpl ărilor r ămâne limpede pe tot parcursul ac ţiunii, impre... ...mbued not anthroimpositions but preexisting eons ago logical inconsistancies mathematically absurd, but yet not absurd, conditions mutually exclusiv...

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...as in nearly all the other dialogues of Plato, we are made aware that formal logic has as yet no existence. The old difficulty of framing a definition... ...would be as useless to examine his arguments by the re- quirements of modern logic, as to criticise this ideal from a merely utilitarian point of view... ...e able to illustrate best by parallel notions, which, whether justifiable by logic or not, have always existed among mankind. We must remind the reade... ...from them as if they were not figures but realities, is due to the defective logical analysis of his age. Nor does he distinguish between the sufferin... ...refore he some- times appears to be careless of the ordinary requirements of logic. Yet in the highest sense he is always logical and consistent with ... ...y of Socrates, is perhaps the only exception. To make the list complete, the mathematical figure of the number of the state (Republic), or the numeric...

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...medium of books, and would say: “But I don’t want to!” in a tone to make a logician thoughtful. Nature was very strong in him. 29 George Meredith He ... ... vexed by disappointment: “I am what I am. It might be demonstrated to you mathematically that it is corrected by equivalents or substitutions in my c... ...n’s fetters of her limbs and deliver her from the yawning mouth-abyss. His logical coolness of expostulation with her when she cast aside the silly mi... ... its axis. Thus to detach an injury done to us, and plant it in space, for mathematical measurement of its weight and bulk, is an art; it may also be ... ...f chestnuts.” “Then it follows that I am a daughter of Spain.” “Clearly.” “Logically?” “By positive deduction.” “And do I behold Patrick?” “As one loo... ...y 192 The Egoist to be quite harmless. And besides (you are not to expect logical sequences) the showery refreshment in thinking of him lay in the so... ...w none but Clara, hated none, loved none, save the intolerable woman. What logic was in him deduced her to be individual and most distinctive from the...

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... 148 7.5 Conclusion . . . . . 151 7.6 References . . . . . 152 Appendix: Derivation of the GPT for the 3D free DSm model . . . 153 8 Probabilized logics related to DSmT and Bayes inference 155 8.1 Introduction . . . . . 155 8.2 Belief Theory Models . . . . . 157 8.2.1 Preliminary: about probability . . . 157 8.2.2 Dempster Shafer Theory . . . . 161 8.2.3 Transfer...

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... Aquatic Apes theory, but to me a number of her conclusions seem far more logical than most of those in the savannah theory. Human babies, unlike... ...es the skills of analysis and matching that are so critical to developing logical, mathematical, and scientific thinking. How phonetic writing came... ...ills of analysis and matching that are so critical to developing logical, mathematical, and scientific thinking. How phonetic writing came into bei... ...d practices?) It‘s quite ironic, however, that:  The alphabet‘s rigid logic helped hide the dangerous but vital missing number, which Chapter 11... ...solving knowledge needed to build and govern empires. To me, it‘s only logical that increased access to problem-solving knowledge must have playe... ...ost words in ancient China could be spoken with a single syllable, so it‘s logical that the written language is logographic (i.e., each character rep... ...rld trade soaring. Bankers were major beneficiaries, because this new mathematical tool let them dispense with their counting boards. The ne... ... Then, as a twenty-two-year-old working on his PhD, Kemeny served as a mathematical assistant to Dr. Albert Einstein. (Asked why the famed physici...

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...h’s, if cunningly planted down, were no despicable pile, or floodgate, in the logical wear. For the rest, be it nowise apprehended, that any personal c... ...in petto thy remarkable V olume on Clothes. Nay, was there not in that clear logically founded Transcendentalism of thine; still more, in thy meek, si... ...hrough the Narrative portions, a certain show of outward method; but of true logical method and sequence there is too little. Apart from its multifari... ...xhibiting. Our Professor’s method is not, in any case, that of common school Logic, where the truths all stand in a row, each holding by the skirts of... ...Air castles are cunningly built of Words, the Words well bedded also in good Logic mortar; wherein, however, no Knowledge will come to lodge. The whol... ...he whole world must smart for it: will not the price of beaver rise? It is a mathematical fact that the casting of this pebble from my hand alters the...

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..., Whence turbulent Italy should draw Delight in Art whose end is peace, In logic and in natural law By sucking at the dugs of Greece. Your open hand b... ...lk that way? 138 THE COLLECTED POEMS OF W.B. YEATS TOM O’ROUGHLEY ‘THOUGH logic choppers rule the town, And every man and maid and boy Has marked a d... ...; But who is there to argue that Now Pearse is deaf and dumb? And is their logic to outweigh MacDonagh’s bony thumb? How could you dream they’d listen... ...ble labyrinth of the birds, century after century, Cast but dead leaves to mathematical equality; And God appointed Berkeley that proved all things a ...

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................363 47. Discounting Method for Multi-Criteria Decision Making (_-D MCDM), by Florentin Smarandache....................369 NEUTROSOPHIC LOGIC AND SET....................395 48. Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic, by Florentin Smarandache, published as “Definition of Neutrosophic Logic – A Generalization of the Intuitionis...

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................363 47. Discounting Method for Multi-Criteria Decision Making (_-D MCDM), by Florentin Smarandache....................369 NEUTROSOPHIC LOGIC AND SET....................395 48. Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic, by Florentin Smarandache, published as “Definition of Neutrosophic Logic – A Generalization of the Intuitionis...

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...he end of which there were two little sketches of the arts of rheto ric and logic, the latter finishing with a specimen of a dis pute in the Socrati... ...dvantage of more time for reading and studying, and a won derful genius for mathematical learning, in which he far outstript me. While I liv’d in Bos...