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...ty of births attained under its influence. T o begin these speculations in logical order we must begin at the birth point, we must begin by asking how... ...service. It must be a good exercise to write precise definitions of words. Logic also is an integral portion of the study of the mother-tongue. But to... ... remember, was oratory. This aspect of school work was the traditional and logical development of the culture language-teaching. But as in Europe the ... ...ion to that pitch. There is no deliberate and professed training at all in logical thought—except for the use of Euclid’s Elements to that end—nor in ... ...mparison with the apparatus of modern math- ematical method. And while the mathematical subjects of the quadrivium were taught as science and for thei... ...and minima, as it is now to be able to read and write. This development of mathematical teaching is only another aspect of the neces- sity that is bri... ...eneral scheme that is the real obstacle to any material improvement in our mathematical teaching. Professor Perry, in his open- ing address to the Eng... ...irmly into the teachers’ hands. The problem is much simpler in the case of mathematical teaching than in the case of English, because the educational ... ...t and trial I have suggested for the organization of English teaching. The mathematical reformer may begin now at a point the En- glish language refor...

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...Migration acquires great significance in the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has enormous impact on livelihood, life-styles, employment, socioeconomic and political stability; or in other words, it influences the entire society. When u...

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...osophy 453 Further Reading 456 Index 468 Preface Neutrosophic logic grew as an alternative to the existing topics and it represents a ma... ...c logic grew as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, unde... ...tency, redundancy and contradiction. Despite various attempts to reorient logic, there has remained an essential need for an alternative system tha... ...world. Out of this need arose the system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept o... ...oor uneducated labourers from rural Tamil Nadu. This book is an extended mathematical analysis of the book Love.Life.Lust.Loss: 101 Real Life Stori... ...te vector using the dynamical system. Appendix 9 deals with Neutrosophic logic. We have included a list of further reading. We deeply acknowledge... ...the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has eno... ...f the literature on the said topic. We like to point out that most of the mathematical research into migration has dealt with it on purely statistic... ...tions simple and easy. 14 It is important to mention that the relevant mathematical notions used in each of these chapters are described in the ...

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...ear 1986. Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. FCM was a fuzzy extension of the cognitive map pioneered in 1976 by political scientist Robert Axelord, who used it to represent knowledge as an interconnected, directed, bileve...

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...Preface 5 Chapter One INTRODUCTION 7 Chapter Two BASIC CONCEPTS 21 Chapter Three CAUSES OF SCHOOL DROPOUTS – A MATHEMATICAL ANALYSIS 35 Chapter Four SCHOOL DROPOUTS AS CHILD LABOURERS 59 Chapter Five SCHOOL DROPOUTS AS RAG PICKERS USING FUZZY MODELS 79 Chapter Six PERFORMANCE ASPECTS OF SCHOOL STUDENTS USING RULE BASED CONTROL ...

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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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...lism, and also of dialectic, or , in modern phraseology , of metaphysics and logic (Theaet., Soph.). Like Plato, he is struggling after something wide... ...g’is a figure of speech, really corresponding to the processes which a later logic designates by the terms ‘abstraction’ and ‘gen eralization.’ When ... ...gs in fact to the Megarian age of philosophy , and is due to their illogical logic, and to the general ig norance of the ancients respecting the part... ... is the object of these para doxes, some have answered that they are a mere logical puzzle, while others have seen in them an Hegelian propaedeutic o... ...ber and figure may be made a calculus of thought. It exaggerates one side of logic and forgets the rest. It has the ap pearance of a mathematical pro... ...gerates one side of logic and forgets the rest. It has the ap pearance of a mathematical process; the inven 41 Parmenides tor of it delights, as ma... ...anger of error is the most serious; for , if they remain unexamined, as in a mathematical demonstration, all that flows from them is affected, and the...

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...f it disgusts you to be reconciled to it; by the way of the most inevitable, logical combinations to reach the most revolting conclusions on the everl... ...ests they may at once become good and noble—are, in my opinion, so far, mere logical exercises! Y es, logical exercises. Why, to maintain this theory ... ...omes softer, and consequently less bloodthirsty and less fitted for warfare. Logically it does seem to follow from his arguments. But man has such a p... ...tionally, he is ready to deny the evidence of his senses only to justify his logic. I take this example because it is the most glaring instance of it.... ...ll human actions will then, of course, be tabulated according to these laws, mathematically, like tables of logarithms up to 108,000, and entered in a... ...w economic relations will be established, all ready made and worked out with mathematical exactitude, so that every possible question will vanish in t... ...what they are aiming at in one case and in another and so on, that is a real mathematical formula—then, most likely, man will at once cease to feel de... ...sciously desire anything disadvantageous to himself, that that can be proved mathematically. I thoroughly agree, it can—by mathematics. But I repeat f... ...n, but is the beginning of death. Anyway, man has always been afraid of this mathematical certainty, and I am afraid of it now. Granted that man does ...

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...tical economy, by its destruction of property and human labor; of rational logic, by the frequent absurdity of its pretexts. The wrong, which is put f... ... the authority of individual conscience in matters of religion.’ Errors of logic show themselves more often in a man’s termi- nology, and his antithes... ...ere not, in relation to its own absolute merits; and this treatment is the logical treatment, applying itself to what is permanent in the nature of th... ... hold myself a doctor seraphicus, and also inexpugnabilis upon quillets of logic, justify Phil., whilst also I blame him. He defends himself rightly f... ... conforming to the truth of abstractions, compel us to seeming breaches of logic. It would be right practically to distinguish the Radical 49 Thomas ... ...n: and the miracle has the same advantage over facts of experience, that a mathematical truth has over the truths which rest on in- duction. It is the...

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...rinciple of philosophy; and the law of contradiction, which is affirmed by logicians to be an ultimate principle of the human mind, is displaced by an... ... hended by the purest mind and reason. The lower sci- ences, including the mathematical, are akin to opinion rather than to reason, and are placed tog... ...est of actions, and sometimes varying in successive sentences. And as in a mathematical demonstration an error in the origi- 48 Philebus nal number d... ...to him in the Philebus than in the earlier Platonic writings. The germs of logic are beginning to appear, but they are not col- lected into a whole, o... ...out entering on this wide field, even a superficial consider- ation of the logical and metaphysical works which pass under the name of Aristotle, whet... ...ngular acknowl- edgment which may be regarded as the anticipation of a new logic, that ‘In going to war for mind I must have weapons of a different ma...

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... de- ficient in “exactness,” in precision of statement, and close- ness of logical concatenation. We must not look for a math- ematics of conduct. The... .... The whole treatment is confused by the unhappy attempt to give a precise mathematical form to the principles 14 The Ethics of Aristotle of justice ... ...l and impossible as on those which are in our own power: again, Opinion is logically divided into true and false, not into good and bad as Moral Choic... ...I do not mean one of the five senses, but the same by which we take in the mathematical fact, that no rectilineal figure can be contained by less than... ...asis of previous knowledge, as will appear on an examina- tion of all. The Mathematical Sciences, and every other sys- tem, draw their conclusions in ... ...heir lack. But this is not the case with all Pleasures: those attendant on mathematical studies, for instance, are unconnected with any Pain; and of s... ...ason for its own impulses. The other phrase means the actual possession of mathematical truths as part of the mental furniture, i.e. knowing them. P 2... ...s belonging to the body,” etc. P . 32, l. 32. Being about to give a strict logical definition of Virtue, Aristotle ascertains first what is its genus ... ... opening statement of the Post Analytics. P . 133, l. 27. Aristotle in his logical analysis of Induction, Prior. Analytics II. 25, defines it to be “t...

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...ing a verdict. If they do extort a hearing, they are subjected to a set of logical requirements totally different from those ex acted from other peop... ...ist. Therefore there must be the power of forcing them. How often has this logic been used!and, but for one flaw in it, without doubt it would have be... ...fficulty than others have in obtaining their services. To this there is no logical answer except”I will not”: and as people are now not only ashamed, ... ...knows as much of mathematics as is now needful for making any considerable mathematical discovery: is it any proof of inferiority in women, that she h...

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...strong, Alyosha. I have a longing for life, and I go on living in spite of logic. Though I may not believe in the order of the universe, yet I love th... ... spring, the blue sky— that’s all it is. It’s not a matter of intellect or logic, it’s loving with one’s inside, with one’s stomach. One loves the fir... ... life more than the meaning of it?” “Certainly, love it, regardless of logic as you say, it must be regardless of logic, and it’s only then one wi... ...elt a shiver of fear run down his spine. At that moment he saw fully, as a mathematical certainty, that this was his last hope, that if this broke dow... ...at has passed with Katerina Ivanovna; you couldn’t, you couldn’t, that’s a mathematical certainty.” “The realism of actual life, madam, that’s wha... ...then not he, Ivan. This letter at once assumed in his eyes the aspect of a logical proof. There could be no longer the slight- est doubt of Mitya’s gu... ...nd. Does all that exist of itself, or is it only an emanation of myself, a logical development of my ego which alone has existed for ever: but I make ... ...Mitya had written at the Metropolis tavern, which Ivan had spoken of as a “mathematical proof.” Alas! its mathematical conclusiveness was recognised, ...

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...ient thinker, the germs of future knowledge are contained. The sciences of logic and psychology, which have supplied so many instru ments of thought ... ...epublic, and were probably first invented by Plato. The 3 greatest of all logical truths, and the one of which writers on philosophy are most apt to ... ... confu sion of them in his own writings. But he does not bind up truth in logical formulae,—logic is still veiled in metaphys ics; and the science w... ...y, at least a great part of it, and ought not to be judged by the rules of logic or the probabilities of history. The writer is not fashioning his ide... ... for the preservation of such productions and constructions; and as to the mathematical sciences which, as we were saying, have some apprehension of ...

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...nd appliances of thought, but the thoughts themselves. This commenced with Logic, in which I began at once with the Organon, and read it to the Analy... ...ead the whole or parts of several of the Latin treatises on the scholastic logic; giving each day to him, in our walks, a minute account of what I had... ...tions. After this, I went in a similar manner through the Computatio sive Logica of Hobbes, a work of a much higher order of thought than the books o... ...bes, a work of a much higher order of thought than the books of the school logicians, and which he esti mated very highly; in my own opinion beyond i... ...them: and this he deemed peculiarly fitting in the case of the syllogistic logic, the use fulness of which had been impugned by so many writers of au... ...im posed on by vague, loose, or ambiguous terms. The boasted influence of mathematical studies is nothing to it; for in mathematical processes, none ... ...nt effect. But is this a legiti mate process? In dynamics, and in all the mathematical branches of physics, it is; but in some other cases, as in che... ...the argument. In attempting to clear up the real nature of the evidence of mathematical and physical truths, the System of Logic met the intuitive p...

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...e internally renounced, cannot send forth the open, fearless characters, and logical, consistent in tellects who once adorned the thinking world. The... ...e said on the wrong side of the question. The peculiarity of the evidence of mathematical truths is, that all the argument is on one side. There are n... ...antago nists. It is the fashion of the present time to dispar age negative logic—that which points out weak nesses in theory or errors in practice,... ...e few great thinkers, and a low general average of intellect, in any but the mathematical and physical departments of speculation. On any other subjec... ...tion to slavery. What is called Christian, but should rather be termed theo logical, morality , was not the work of Christ or the Apostles, but is of... ...f those who regard them as impieties; and unless we are willing to adopt the logic of per secutors, and to say that we may persecute others because w...

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...hat the definition of a science would occupy the same place in the chrono- logical which it commonly does in the didactic order. As a treatise on any ... ... definition of the science itself as should not be liable to well-grounded logical objections. From this remark, we cannot except the authors of eleme... ...itical Economy has remained des- titute of a definition framed on strictly logical principles, or even of, what is more easily to be had, a definition... ... the art of gunnery and the theory of projectiles, or between the rules of mathematical land-surveying and the science of trigonometry. The definition... ... one cause, a knowledge of the law of that cause would, unless there was a logical error in our reasoning, en- able us confidently to predict all the ... ...nd 1830 before his reputation had been established by the publica- tion of Logic in 1843. Their successful reception no doubt hastened the composition...

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...chains, And Wit dreads exile, penalties and pains. There foam’d rebellious Logic, gagg’d and bound, There, stripp’d, fair Rhetoric languish’d on the g... ... kept prudishly away. Each stanch polemic, stubborn as a rock, Each fierce logician, still expelling Locke, 396 Came whip and spur, and dash’d through... ... a Gentleman of C. C. C. Oxon. Printed for J. Roberts, octavo. The Arts of Logic and Rhetoric, partly taken from Bouhours, with New Reflections, &c. B... ...ome mathematicians in calculating the gradual de- cay of moral evidence by mathematical proportions; accord- ing to which calculation, in about fifty ...

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...of the States will be a majority of confederated America. But this kind of logical legerdemain will never counteract the plain suggestions of justice ... ...le of no limits, even in imagination. In this view of the subject, by what logic can it be maintained that the local gov- ernments ought to command, i... ...gnty in the Union, with com- plete sovereignty in the States; to subvert a mathematical axiom, by taking away a part, and letting the whole remain. Al... ...a council, the omission of a formal bill of rights, the I know not by what logic it could be maintained, that the declarations in the State constituti... ... rare instances in which a political truth can be brought to the test of a mathematical demonstration. Those who see the matter in the same light with...

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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...