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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... ...Manifesto of the PARADOXISM is especially a revolt of the emigrant to the United States who doesn't speak English, against the language - an anti- la... ...oems; - poems in Pirissanorench (language spoken in the South-West of the United States by a single person!); - super-poems; 6 - graphic poems; ... ...che/IonSoare2.pdf. 8 - - - - - - - Introduction: The Non-Standard Real Unit Interval - Abstract: In this paper one defines the non-standard real ... ...ization, a theory loses its transcendental, myth, beauty, and becomes too arithmeticsized, technical, mechanical. Or, if a system of axioms is defin... .... Logicism: Frege's axioms for set theory, to derive the whole arithmetic, were inconsistent (see Bertrand Russell's Paradox). Look at t... ...last or second one respectively. An intriguing idea would be to take the arithmetic average of the corresponding components of the truth-, indetermi...

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...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 mat...

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...Charles Ashbacher INTRODUCTION TO NEUTROSOPHIC LOGIC American Research Press Rehoboth 2002 1 Charles As... ... Rehoboth 2002 1 Charles Ashbacher Introduction to Neutrosophic Logic American Research Press ... ... ISBN: 1-931233-60-8 Standard Address Number: 297-5092 Printed in the United States of America 3 Foreword As someone who works heav... ... 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 ... ...ERRED. p I p 1 \/ p 2 \/ . . . \/ p r • Unit resolution If a disjunction is true and one of the elements is false,... ...ic are not numeric, the definitions of the connectives cannot involve any arithmetic operations such as max and min. This can be a limitation in th... ...n p, we can infer p \/ q having a value greater than or equal to p. The unit-resolution rule of inference does not apply in Lukasiewicz three-value...

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...As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical...

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...roceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics ... ...OCEEDINGS OF THE FIRST INTERNATIONAL CONFERENCE ON NEUTROSOPHY, NEUTROSOPHIC LOGIC, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS ... ... ISBN: 1-931233-67-5 Standard Address Number: 297-5092 Printed in the United States of America First International Conference o... ...erica First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and Statistics December 1-3, 2001 Univer... ...rt and “ &” its non-standard part. Then, we call ] - 0, 1 + [ a non-standard unit interval. Obviously, 0 and 1, and analogously non- standard numb... ...less than 0 or infinitely small but greater than 1, belong to the non-standard unit interval. Actually, by “ - a” one signifies a monad, i.e. a set ... ...s, the overall result would evaluate as NL(0.01, 0.9, 0.09), assuming standard arithmetic connectives (summing over a simple diagonal matrix of trip...

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.... The former is a self-contained Universe, replete with its "laws of physics" and "logic". It can bear resemblance to the real world or not. It can... ...rect and strong relationship to the world. It must obey the rules of physics and of logic. The absence of such a relationship renders it meaningless... ... unaware of the work of an important, though eccentric, Czech-Austrian mathematical logician, Kurt Gödel (1906-1978). A passing acquaintance with hi... ...eorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true but unprovable ("not decidable") sente... ...ther he is still the same person - he has been "replaced". Finally, we can try to unite all the strands of our discourse into this double definiti... ...he world (women) – or of living longer (children). Societal etiquette reflects the arithmetic of the species, in this (and in many another) case. ... ...eorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true but unprovable ("not decidable") sente... ...t, their surrogate. The robot and its operator, the human being, are an ontological unity: both share identical, objective experiences. There is one... ... thought experiments is that the brain and its flesh-and- blood container were once united, before science or technology had them sundered. But what...

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... midst of all change of time and space, and fluctuations of mortal things, preserve the unity, the continuity and perpetuity of the Church, in the m... ...tablishment in their own land, to be the head of nations, and the centre of the earth’s unity, and the going forth from them of that Spirit of righte... ...world, is but preparatory. We have had the variety of the wicked earth, we wait for the unity of the saved earth; we have had the humility of the suf... ... the Lord hath adopted this prophetic method in the revelation of his Word, and not the logical, or the dogmatical, or the predicative? I answer, t... ... closet, or some rhetorical performance proper to the platform or the stage, or some dry logical question proper to the schools. The effect of which ... ...he prophets were t aught the future by means of these emblems, as a blind man is taught arithmetic by means of counters. They never speak in the spi... ...ay confidently with St. Ambrose; away with arguments when faith is in question, now let logic be silent; not the reasoners, but the fishermen are to ...

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...In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative sy...

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... ISBN: 1-931233-76-4 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Dedication 4 Preface 5 Cha... ... OF DISSENT 5 PREFACE In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itsel... ...apability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that... ...orld. Out of this need arose the system of Neutrosophy, and its connected logic, Neutrosophic Logic. Neutrosophy is a new branch of philosophy that ... ... election. Now each party has its own opinion and when they join up as an united front we will see the result. So, let us take the opinion of 4 expe... ...of a variable and shows the cumulative strength of variables entering the unit ∑ = = N k kj j a v id 1 ) ( . The immediate domain of a variabl... ...he causal strength per one unit-time s * ij on an edge e ij , simply the arithmetic division might be considered (i.e. s * ij = s ij / t ij for a... ...I recently designed a system that, had I implemented it using an FCM, the arithmetic-multiply operator would have been a necessary operator. "Arm...

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...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...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... ...ys been the most fervent anti-Semites. Jews are not so much a race as a community, united in age-old traditions and beliefs, lore and myths, histor... ...y. This viral hijacking of the host country's agenda is particularly evident in the United States where the interest of Jewry and of the only super... ...are no exception. Jews are, indeed, over-represented in certain professions in the United States. But they are under-represented in other, equally ... ...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... ...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...he world (women) – or of living longer (children). Societal etiquette reflects the arithmetic of the species, in this (and in many another) case. B...

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...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...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... ...ys been the most fervent anti-Semites. Jews are not so much a race as a community, united in age-old traditions and beliefs, lore and myths, histor... ...y. This viral hijacking of the host country's agenda is particularly evident in the United States where the interest of Jewry and of the only super... ...are no exception. Jews are, indeed, over-represented in certain professions in the United States. But they are under-represented in other, equally ... ...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... ...sting dice). Alternatively, we could add and subtract rights in a somewhat macabre arithmetic. If a mother's life is endangered by the continued ex... ...he world (women) – or of living longer (children). Societal etiquette reflects the arithmetic of the species, in this (and in many another) case. B...

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... ISSN: 1555-5615 (online) Standard Address Number: 297-5092 Printed in the United States of America APRIL 2005 VOLUME 1 CONTENTS D. Rabounski A New Me... ...ache F. Invisible paradox. Neutrosophy, Neutrosophic Probability, Set, and Logic, American Research Press, Reho- both, 1998 (see the third e-print edi... ...atter, mss., 1980, Archives Vˆ alcea. 2. Smarandache F. A unifying feld in logics: neutrosophic logic. Neutrosophy, Neutrosophic Probability, Set, and... ...ogics: neutrosophic logic. Neutrosophy, Neutrosophic Probability, Set, and Logic. American Research Press, Rehoboth, 2002, 144 p. (see it in e-print: ... ...ormations that leave in- variant the phase-space interval are given by (in units of =c=1) (dω) 2 =(dT) 2 −(dX) 2 + (dE) 2 −(dP) 2 b 2 = =(dτ) 2 1+... ...ubling” version of the Lorentz groupSO(1,3). Low discussed the irreducible unitary representations of such U(1,3) group and the relevance for the stro... ...r to fnd an analogous result that had been previously obtained by a purely arithmetical way. We will use the second option because it is easier (alt- ... ..., 2000, v. 43(2), 205–209. 4. Shnoll S. E. Discrete distribution patterns: arithmetic and cosmophysical origins of their macroscopic fuctuations. Biop...

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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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...che/ ISBN: 1-931233-53-5 Standard Address Number 297-5092 Printed in the United States of America 4 Foreword In the history of thought and cre... ...literary movement of Paradoxism, conceived in Romania and affirmed in the United States, which is closely bound to the temperament, inclination, tas... ...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”. ... ...onism and put in the modern light of the antonymic vision of dynamism. The unity is the 9 equilibrium of dramatic oppositions. The unity is the co... ... Journal (Harwey Mudd College, Claremont, CA, USA, 12, 1995): POEM IN ARITHMETIC SPACE By Larry Seagull There exist sequences defined as “Sma... ...” amalgamate small but firm spaces and introduce the simple colored line; arithmetic, in palimpsest, is canceled, by color, with a ludic exposing dur... ...Larry Seagull publishes, in Humanistic Mathematics Network (USA), Poem in arithmetic space, on the base of Smarandache sequence of numbers, together ...

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...ww.ce-review.org/authorarchives/vaknin_archive/vaknin_main.html Visit Sam Vaknin's United Press International (UPI) Article Archive – Click HERE! ... ...angible, retarded wealth formation. In some respects, the West - and especially the United States - are poorer now than they were in 1988. This monu... ...guess. Return The Bursting Asset Bubbles I. Overview Also published by United Press International (UPI) The recent implosion of the glo... ...available equilibrium strategies. The altruists in our example are prisoners of the logic of the game. Only an "outside" power can release them from... ..., to cooperate and to cooperate in the formation of an outside agency. There is no logical or mathematical reason to exclude the latter possibility... ...troducing rational solutions to this highly charged EMOTIVE- PSYCHOLOGICAL problem. Logic cannot eliminate envy, ratio cannot cope with jealousy and... ... and BEAR markets 22. Consolidation pattern - if underlying trends continues 23. Arithmetic versus logarithmic graphs 24. Seasaw - non breakthro...

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...structed and expected to do one, and only one, thing. It has a single purpose and a unitary function. We, humans, are more like computers than like ... ...fy and explain one's conduct or, more often, misconduct by resorting to ":rational, logical, socially- acceptable" explications and excuses. Rational... ...h fluid shifts in meanings permit the narcissistic personality to maintain apparent logical consistency while minimising evil or weakness and exagge... ...nuous, fragmenting, undercathected self of the child not seen or responded to as a unit of its own, not recognised as an independent self who wants... ...reoccupied to stay attuned at all times to the child's emotional needs. The family unit itself may be disintegrating with looming divorce or separa... ...aise and nurture their younger relatives more that straights do. Moreover, the arithmetic of genetics would rule out such a stratagem. If the a... ...ll" people operate within a (usually coherent) worldview, with consistent internal logic, and rules of right and wrong (ethics). Yet, these rarely ...

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...essed through the author’s website at http://james-boyle.com. Printed in the United States of America. ISBN: 978-0-300-13740-8 Library of Congress Con... ... 1 Each person has a different breaking point. For one of my students it was United States Patent number 6,004,596 for a “Sealed Crustless Sandwich.” ... ...ract from our totals the works that are clearly in the public domain. In the United States, that is generally work produced before 1923. That material... ...1.qxd 8/28/08 11:04 AM Page 19 milk, you cannot. Excludable property is, logically enough, property from which others can easily be excluded or ke... ... of authors’ rights it turned out, in Hesse’s words, to reflect “an epistemo- logically impure and unstable legal synthesis that combined an instrument... ...gh they are harder to classify. They bemoaned the relentless power of market logic to migrate to new areas, disrupting traditional social relation- sh... ...net, working out the daily prices of a bundle of mutual funds through simple arithmetic, or buying something online with one click. 45 I would have as...

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...ords and sentences, the monk from York makes writing forever easier to read. -- 9. Largest Land Empire Ever-Illiterate tribes of nomad herder-hunters unite under Genghis Khan and then take less than a century to create the largest contiguous empire in world history. -- 10. Mongols Open the Way They open the gate blocking direct human contact between Europe and China just i...

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... 9. Largest Land Empire Ever Illiterate tribes of nomad herder-hunters unite under Genghis Khan and then take less than a century to create the l... ... 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... ...ook twelve years of schooling just to learn to read, write, and do simple arithmetic. Pictographic culture‘s rigorous nature, moreover, left prie... ...d practices?) It‘s quite ironic, however, that:  The alphabet‘s rigid logic helped hide the dangerous but vital missing number, which Chapter 11... ...icles to the beginning of the decline of the Roman Empire. In 2011 the United States is less than half that age. CHAPTER 6 ―Chinese ships... ...ge of literature and learning in an England that was gradually becoming a united kingdom. It was to England‘s scholars that Charlemagne—the illit... ...the quadrivium’s Real Art—―the four ways‖— moved on to the studies of:  arithmetic—math applied to basic numbers  geometry—math applied to space ...

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... 9. Largest Land Empire Ever Illiterate tribes of nomad herder-hunters unite under Genghis Khan and then take less than a century to create the l... ... 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... ...ook twelve years of schooling just to learn to read, write, and do simple arithmetic. Pictographic culture‘s rigorous nature, moreover, left priest... ...hed practices?) It‘s quite ironic, however, that:  The alphabet‘s rigid logic helped hide the dangerous but vital missing number, which Chapter 11... ...ericles to the beginning of the decline of the Roman Empire. In 2011 the United States is less than half that age. CHAPTER 6 ―Chinese ships... ...ge of literature and learning in an England that was gradually becoming a united kingdom. It was to England‘s scholars that Charlemagne—the illiter... ... the quadrivium’s Real Art—―the four ways‖— moved on to the studies of:  arithmetic—math applied to basic numbers  geometry—math applied to space ...

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...ay. I love both you and Minna, believe me. To me you two are as one being. United thus you can be my brother or, if you will, my sister. Marry her; le... ...y be seen in chemistry, when two antagonistic substances which science has united separate. For the last few days whenever Wilfrid entered Seraphita’s... ...f their details. A man whose scientific eminence is incontestable, and who united in his own per- son powers of conception, will, and imagination, wou... ...space puts all human science out of sight beneath the grandeur of a divine logic. According to the Seer, the inhabitants of Jupiter will not cultivate... ...ngs compose—in order to fit the problem of Creation to the measure of your logic—a block of finite Matter; but were it infinite, God would still not b... ... inexplicable, incomprehensible, to the existence of which I may apply the logical dilemma which, as we have seen, prevents you from believing in God.... ...e fitted it to your own proportions by creating (if indeed you did create) arithmetic, the basis on which all things rest, even your societies. Just a... ... self-styled atheists believe— 91 Balzac organized physical creations, so arithmetic, in the employ of Number, organized the moral world. This numera...

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... satire changed now into coarse pike-points (hammered out of railing); all logic reduced to this one primitive thesis, An eye for an eye, a tooth for ... ...and odd hundreds,—not more than that. (See Hist. Parl. xvii. 421, 422.) In Arithmetical ci- phers, and Lists drawn up by accurate Advocate Maton, the ... ...n, is it not, as we often say, a reunion of incalculable Influences; every unit of it a microcosm of Influences;—of which how shall Science cal- culat... ...gued. Thou beholdest here the small beginning of a Controversy, which mere logic will not settle. Two small well-springs, September, Departmental Guar... ...riot: who shall say that Robespierre is not a thorough- going man; bold in Logic at least? To the like effect, or still more plainly, spake young Sain... ... At home this Killing of a King has divided all friends; and abroad it has united all enemies. Fraternity of Peoples, Revo- lutionary Propagandism; At... ... the number of Parties ought to be Seven Hundred and Forty-Nine; for every unit entertains his opinion. But now as every unit has at once an indi- vid... ...low-mortals; with noyadings, conflagratings by infernal column, which defy arithmetic. This is the La Vendee War. (Histoire de la Guerre de la Vendee,...

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...ive entirely apart, and have nothing in common but their name. The show of unity is only for the world. The cream of the Court and diplomatic circles ... ...le, “for I am every inch your child!” “In short,” he went on, “one must be logical. Y ou can’t have 53 Balzac the end without the means, and it is ou... ...olace. His faith, therefore, should have the simplicity of a child, though united to the firm conviction of an intelligent man, who has examined the f... ...ish to be yours. Friend- ship is the bond between a pair of kindred souls, united in their strength, and yet independent. Let us be friends and comrad... ...ce of the heart’s storms than live in the arid atmosphere of your cautious arithmetic! As girls, we were both unusually enlightened, because of the la... ... divine likeness. Like all other first prin- ciples, it is not a matter of arithmetic; it is the Infinite in us. I cannot but think you have been tryi... ...rea- soning or calculations. Passion is an element in life bound to have a logic not less pitiless than yours. Monday. Yesterday night I placed myself... ...urnt nothing. Here, then, is the first love-letter I have received, madame logician: each to her kind:— “Louise, it is not for your peerless beauty I ...

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...was necessarily majestic, accord- ing to the principle which matrimonially unites contrasts. She was much given to tying up her head in a pocket-handk... ...e him, R. Wilfer generally seemed to say to himself, after a little mental arithmetic, ‘Oh! here’s another of ‘em!’ before adding aloud, ‘How de do, J... ...es’s Church, the Reverend Blank Blank, assisted by the Reverend Dash Dash, united in the bonds of matrimony, Alfred Lammle Esquire, of Sackville Stree... ...he elaborately chased ice- 122 Our Mutual Friend pails. They even seem to unite in some vague utterance of the sentiment that the landlord and landla... ...right dark eye and a resolute face, yet quite a tender creature too; not a logically- reasoning woman, but God is good, and hearts may count in Heaven... ... stretch of legislative wisdom to set these perverse people right in their logic? ‘Johnny , my pretty ,’ continued old Betty , caressing the child, an... ...ired mechanically a great store of teacher’s knowledge. He could do mental arithmetic mechanically, sing at sight mechanically, blow various wind inst... ...n were half a year ahead of every other letter in the alphabet. And Mental Arithmetic, administered by Miss Peecher, often devoted itself to provid- i... ...f giving myself a sight of your reviving face. Besides,’ said Betty , with logical good faith, ‘I shall have a debt to pay off, by littles, and natura...

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...e of God, the catechism, the Old and the New Testaments, and a very little arithmetic. That was all; the worthy sister thought it enough; it was in fa... ...ntly at Veronique as she returned to her seat from the altar where she had united herself with God,—a moment when she appeared to all the parish in he... ...f all chance of the episcopate. 38 The Village Rector This eminent priest united in himself great Christian mod- esty and a noble character. Without ... ..., ended at a little wall, from which small columns rose at equal distances united by a railing, more, however, for ornament than protection, for the b... ...ca with the money of old Pingret. The theft led to the murder by the fatal logic which the punishment of death inspires. And so,” she added with an ap... ...ance. Those who have proceeded to de- molish the ancient edifice have been logical in dividing equally the family property, in diminishing the authori... ... the world for the long deception to which I have been led by the terrible logic of society. Jean-Francois T ascheron was not as guilty as he seemed. ...