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... time. Gödel's First Incompleteness Theorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true ... ...mpleteness Theorem is even more earth- shattering. It says that no consistent formal logical system can prove its own consistency. The system may be ... ...dox in the "Principia Mathematica", ostensibly a comprehensive and self consistent logical system. It was enough to discredit the whole magnificent... ...cal logician, Kurt Gödel (1906-1978) dealt with the completeness and consistency of logical systems. A passing acquaintance with his two theorems w... ... time. Gödel's First Incompleteness Theorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true ... ... exception: when something bad happens to the robot, its owner is shielded from the consequences by some kind of "firewall", or in-built defense. I... ...bly, bacteria and insects exert on Nature far more influence with farther reaching consequences than Man has ever done. Still, the "Law of the Mini... ...ranscendentalist spiritual connection with the inanimate (whatever that may be). In consequence, they refuse to intervene to counter or contain natu... ...he process. Like any psychopath, the USA believes that it should be immune to the consequences of its misconduct abroad. Hence its shock when al-Q...

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...ype of destruction that society has inflicted on women’s bodies. 9 The consequence has been that intrauterine life, for both women and men, is no... ...hate deadlock, and they were overcome by desperation, with its most direct consequence: suicide. In this situation, we see this problem acted out in... ...t in this life, on this earth. The important thing is that joy is a direct consequence of love and love implies a transformation. Isn’t it true that... ... ambivalent position towards their mothers, from birth onward. The possible consequences are either desperation, caused by a lack of faith that this ... ...at else are neurosis, psychosis, psychosomatic illness etc. except for the consequences we pay for having had to submit to the demands of the Psycho... ...e as a therapeutic process becomes like a regression, it breaks with every logical process. While you were talking, I was thinking about R. Laing’s ...

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...m the surname Empiricus would have been more appropriate, if it was given in consequence of prominence in the Empirical School. Sextus is known to th... ...ity to consist in subjective experience, but he does not follow this to its logical conclusion, and doubt the existence of anything outside of mind.... ...er of argument, by which the Sceptics arrived at the condition of doubt, in consequence of the equality of probabilities, and he calls the Tropes, th... ...stly be found in other authors of antiquity given in a similar way. [5] The logical result of the reasoning used to explain the first Trope, is that... ...not with equal understanding of the results to be deduced from it. [3] The consequence of the incompatibility of the mental representations produce... ...ted to Agrippa is a marked one, and shows the entrance into the school of a logical power before unknown in it. The latter are not a reduction of th... ...heories of Pyrrhonism, while the five are rather rules of thought leading to logical proof, and are dialectic in their character. We find this distin... ...points to an objective relativity, but with Agrippa to a general subjective logical principle. The originality of the Tropes of Agrippa does not lie... ...al assertion, Σεκεῖνλ νὐθ εἶλαη, [4] and proceeds to introduce the logical consequence of the denial of aetiology. The summing up of the Tropes of ...

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... Propositions Section 2 The Law of the Excluded Middle Section 3 Logical Equivalence Section 4 Well-Formed Formulas or WFFs Sectio... ...sophic Logic Section 1 Definition of Neutrosphic Logic Section 2 Logical Connectives in Neutrosophic Logic Section 3 Algebraic Propertie... ... 1 Classical Logic Section 1 Propositions In classical logic, a logical variable is restricted to the values of true(T) and false(F). The ... ...ry in the result column, there are 2 n different Boolean functions for n logical variables. Given the truth values in the column above the 5, ... ...on 1.1.4: In the expression p → q, p is known as the antecedent and q the consequence. The implication is often described as the if-then connective. ... ...on ( p /\ q ) \/ ( ¬ p /\ ¬q ). The ↔ connective can also be considered logical equality. Exclusive or (^) can be considered logical inequality ... ...is no middle between the two “extreme” values of true and false. One consequence of this law is the concept of a vacuous proof. What this means ... ...It is interpreted as a statement that if the antecedent is true, then the consequence is also true. The statement is then false if the antecedent is... ...also true. The statement is then false if the antecedent is true, but the consequence is false. With this notion, if it is not possible to prove the...

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...ical principles, any existential model presupposes its building through a logical construction* based on a non-contradictory assertional system*, as ... ...is hypothesis enables us, for example, to explain the phenomenon whereby a logical entity memorizes, paradoxically, more accurately the events from a... ...r than the length of the perpendicular from P to the primary limit. It is logical to designate the XY 9 segment of a maximum length (when P attai... ...ly explain the exceptional performances of some rational entities. It is logical to admit that famous rational entities such as Galileo Galilei, Leo... ...d reincarnation, can be the particular expression of a natural, inherent, logical and necessary process for the evolution of rationality within the ... ...itual reality, and that of permanet stochastic movement would be devoid of consequences, so that the MESER concept would have provided them randomly ... ...ity. The principles governing spiritual reality, far from being devoid of consequences, have the role of determining within the material reality, a ... ...ty is not increased. Nevertheless, the above mentioned scenario bears the consequence that the OX section of the XY area corresponding to the intell... ...the intellectual-affective activity is greater than the OY section – this consequence provides the possibility, for the entity in question, upon a ne...

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...any various volumes, is bound, above all things, to make that condensation logical and striking. For the only justification of his writing at all is t... ...fault, as all of us do, and openly overtaken, as not all of us are, by its consequences, to gloss the matter over, with too polite biographers, is to ... ...lainly, what every one well knows, of Burns’s profligacy, and of the fatal consequences of his marriage. And for this there are perhaps two subsidiary... ...r represent an act that was vir- tuous in itself, as attended by any other consequences than a large family and fortune. To hint that Burns’s marriage... ...timidly made elsewhere, have in them been carried boldly out to their last consequences; much that was indefinite in literary tenden- cies has attaine... ...from another point of view – to reproduce a colour, a sound, an outline, a logical argument, a physical action. He can show his readers, behind and ar... ...e nature of tragedy. The gospel according to Whitman, even if it be not so logical, has this advantage over the gospel according to Pangloss, that it ... ... the price we have to pay for cochineal. And with that murder- ous parody, logical optimism and the praises of the best of possible words went irrevoc... ... afternoon, or at morning as he lay awake in bed. With our deeper and more logical sense of life, we can have no idea how large a space in the attenti...

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...an also see how one way of thinking overwhelms the other and creates dire consequences. I do think, however, that when Ulysses is meditating on wh... ...help a woman free herself from her ties with her mother and not suffer the consequences. One must risk one’s life a thousand times and one must also... ...into consideration. A narcissistic wound of traumatic origin is often the consequence of a trauma to the fetal I, or the infant I being deprived of... ...into a second of the present, when that second is embraced with all of its consequences, good or bad that they might be. The present is always alte... ...If we extinguish desire, pain will disappear. For the Bible, pain is the consequence of the wrong committed in Eden and , even when the Messiah wi... ...e that what the other is thinking and feeling can be just as true. Is this logical? And so it is impossible to arrive at a solution to the conflict, ...

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...ts with those to physical property. (I outline that process and its negative consequences in the next chapter.) They will argue, and again I agree, th... ...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... ...might, during sixty years, to Boswell’s eldest son. What would have been the consequence? An unadulterated copy of the finest biographical work in the ... ...om the same evidence” or from extending those arguments and developing their consequences. In a line that Hesse rightly highlights, he declares that a... ... of authors’ rights it turned out, in Hesse’s words, to reflect “an epistemo- logically impure and unstable legal synthesis that combined an instrument... ...century.” Poor Jefferson. How lucky we are to have Mr. Helprin to remedy the consequences of his lack of vision. Or perhaps not. Think of the way that... ...imply because they may be used to infringe copyrights. That, however, is the logical implication of their claim. The re- quest for an injunction below... ...ss to the property. The rules that forbid circumvention of these systems are logically, if not elegantly, referred to as the anticircumvention provisi... ... ing the operation of computers, a metaphor that enables us to imitate their logical processes. In the words of Wikipedia, “despite their simplicity—[...

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...trongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Prof. Ba... ... this stimulus input vector with FCM matrix, K.C. Lee et al [65] obtain a consequence vector as follows: (0, 0, 0, 0, 0.3, 0, – 0.3, 0.5) × FCM ma... ...3, 0, – 0.3, 0.5) × FCM matrix = (– 0.5, 0, 0.24, 0, – 0.08, 0, 0). The consequence vector may be interpreted such that changes in those three fact... ... vector can be organized into (0, 0, 0, – 0.1, 0.3, 0, – 0.3, .2). Then a consequence vector may be obtained as (– 0.15, .02, 0, – 0.24, 0, –0.12, 0... ...∩ M j ) ⊂ ( ~ Q j ∩ M j ). Here “⊂” stands for fuzzy set inclusion (logical implication). For brevity, fuzzy causal relationship is abbreviate... ...ity, fuzzy causal relationship is abbreviated as FCR in the following. Logical implication has an antecedent (or premise) and a consequent (or con... ...t (or premise) and a consequent (or conclusion). A typical example of the logical implication is “If A, then B”. In the logical implication, there a... ...quence: negation of A (or ¬ A). The FCR is more complicated than the logical implication. 1. Modus tollens does not hold in the FCR. “When mi... ...ble for relations between several concepts are indeterminate). 2. In a logical implication “If A, Then B”, we cannot draw inference in case when ...

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...- plish a change in their attitude and habits is too urgent to leave these consequences wholly out of account. Since our chief business with them is t... ...thing to which he is naturally inclined by arous- ing fear of disagreeable consequences if he persists. But 31 John Dewey he may be left in the posit... ...m has no means of foreseeing their outcome. If a person cannot foresee the consequences of his act, and is not capable of under- standing what he is t... ... some cases, it is well to permit him to experi- ment, and to discover the consequences for himself in order that he may act intelligently next time u... ...d with its first systematic exposition. 2 This conception is, of course, a logical correlate of the conceptions of the external relation of stimulus a... ...y stage short of attainment of this goal is merely an unfolding toward it. Logically the 61 John Dewey doctrine is only a variant of the preparation ... ...with rigid ad- herence to their past customs. On such a basis it is wholly logical to fear intercourse with others, for such contact might dissolve cu... ...upposed) except the acknowledgment of duty or the value of discipline. The logical result is expressed with literal truth in the words of an American ... ...nt is developed below in a discussion of what are termed psychological and logical methods respectively. See p. 219. 188 Democracy & Education Chapte...

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...Fettercairn, one of the Bar ons of the Exchequer in Scotland, and was, in consequence, sent to the University of Edinburgh, at the expense of a fund ... ... expression on the other), and had re duced it to rules, grounded on the logical analysis of a sen tence. These rules he strongly impressed upon me... ...e as anyone that Christians do not, in general, undergo the de moralizing consequences which seem inherent in such a creed, in the manner or to the e... ...eory involving a contradiction in terms, prevents them from perceiving the logical conse quences of the theory. Such is the facility with which man ... ...other, and so few are those who draw from what they receive as truths, any consequences but those recom mended to them by their feelings, that multit... ... fact. This point in my early education had, however, incidentally one bad consequence deserving notice. In giving me an opinion contrary to that of t... ...er, my father put into my hands Condillac’s Traité des Sensations, and the logical and meta physical volumes of his Cours d’Etudes; the first (notwi... ...ervice to me, by compelling precision in conceiving and expressing psycho logical doctrines, whether accepted as truths or only regarded as the opini... ...a desire to promote the exercise of other mental faculties than the purely logical, he advised me to make my next exercise in composition one of the o...

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...itted that vengeance and punishment went together, they were at least more logical, for executions were in the open light of day so all might see and ... ...quirements that the young should visit prisons that they might realize the consequences of crime, and that all execu- tions should be public and shoul... ...never be cata- logued because new ways are constantly coming to light. The logical end of all these indefinite and uncertain laws is to pass one statu... ...g families and friends of sorely needed money, and the direct and indirect consequences are sometimes small and sometimes very great. These can be rea... ...men. Even the legal tests as to insanity and feeble-mindedness are neither logical nor humane. Often the definition is given by courts that if one is ... ... teaching and moral suasion; those methods are too slow, and the evils and consequences of dis- belief are too great. Laws of this drastic character a... ...ent him from trying to do his part to restore sanity to the world. Another consequence of war which America is passing through is the spirit of super-... ...o that the species may be controlled. At first glance this seems to be the logical thing to do, especially as the effects of heredity can no more be d... ...cated, more accus- tomed to weighing evidence and able to arrive at a more logical conclusion than most juries. Still none of these quali- 166 ties n...

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... because of this. They don’t care what they do, nor do they care about the consequences. I believe that because my mom was there, she taught me the th... ...as and statistics have come from is an act of plagiarism. Serious academic consequences can result from such behavior, and it is a federal crime to co... ...rents that the police cited me for underage drinking. I never knew all the consequences of drinking and I chose the wrong way to find them out. I’m no... ... I’m not sure I could have handled. The campus was notified, adding to the consequences I had to accept. Even though we were caught off campus, the ca... ...Segments, whether sec- tions or paragraphs, are fully developed and follow logically from what precedes them. Headings and subheadings are appropri- a... ... has an effective introduction and conclusion. The order of information is logical, and the reader can follow it because of well-chosen transitions. P... ... can follow it because of well-chosen transitions. Paragraph divisions are logical, and the paragraphs use enough specific detail to make their point ...

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...otal failure of En- gland to do that business of government, as at least a logical reason for the claim. England has confessedly failed; the world say... ...ng in the Commons with the gravity of platonic disputants. But they have a logical position, equivalent to the best of arguments. They are representat... ... occupied Goito, a position which he held till the evening of the 27th. In consequence of the concentrating movement of the Ital- ian army which I hav... ...uld be, until further notice, subjected to a quarantine of fifteen days in consequence of cholera having made its appearance at the latter place. A sa...

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...nd powerful, in fact all the qualities resulting from strength, and that, in consequence, all forces which tend to promote or elevate life have been s... ...spirit of gravity, and all that it created: con- straint, law, necessity and consequence and purpose and will and good and evil:— For must there not b... ...rom their flock, and his lectures at the University of Bale were deserted in consequence; but it was not until 1879, when he finally severed all conne... ...ising soci- ety to a higher level and preached the profoundest Opti- mism in consequence. Chapter XLII. Redemption ZARATHUSTRA HERE ADDRESSES cripples... ...crifice something to us—His only begotten Son. Such a process carried to its logical conclusions must ultimately end in His own destruction, and thus ...

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...ime went on, the old lady lost the use of her legs and took to her bed. In consequence of which event the house was left without a woman to look after... ...turn him into a servant for some Captain Kopeikin or midshipman Dirka! How logical!” “It’s not hard work, Pavel Ivanitch. Y ou get up in the morn- ing... ... world the truth to their faces; and he had a great deal to put up with in consequence.” Pavel Ivanitch was exhausted with talking and gasped for brea...