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Page "History of logic" ¶ 5
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However and logic
However, expressing these properties as axioms requires use of second-order logic.
However Prolog is not particularly user friendly and is an order of logic away from human logic.
However, if one finds one single black swan, deductive logic admits the conclusion that the statement that all swans are white is false.
However, inclinations towards deeming hair texture " adaptively trivial " may root in certain cultural value judgments more than objective logic.
However, the new geopolitical logic of the Cold War made possible that the former enemy Italy, a hinge-country between Western Europe and the Mediterranean, and now a new, fragile democracy threatened by the proximity of the Iron Curtain and the presence of a strong Communist party, was considered by the USA as an important ally for the Free World, and received under the Marshall Plan US $ 1, 204 million from 1947 to 1951.
However, more expressive languages are likely to require more complex logic and algorithms to construct equivalent inferences.
However, even simple systems based on this simple logic can be used to represent data that is well beyond the processing capability of current computer systems: see computability for reasons.
However, the first proposal to use the clausal form of logic for representing computer programs was made by Cordell Green ( 1969 ).
However, later in antiquity, the propositional logic developed by the Stoics was no longer understood.
However, advances in propositional logic were still made after Frege.
However, in the 1930s Gödel's incompleteness theorems convinced many mathematicians that mathematics cannot be reduced to logic alone, and Karl Popper concluded that " most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently.
However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he proves is in fact intuitionistically true.
However, Principia Mathematica required, in addition to the basic axioms of type theory, three further axioms that seemed to not be true as mere matters of logic, namely the axiom of infinity, the axiom of choice, and the axiom of reducibility.
However, the I / O devices needed more electronic logic to manage their own word count and transfer address registers.
However, the enthymeme based upon logic ( especially, based upon the syllogism ) was viewed as the basis of rhetoric.
However, since the time of Aristotle, logic has also changed, for example, Modal logic has undergone a major development which also modifies rhetoric.
However, in the 19th century, with the development of historical-comparative linguistics, linguists began to realize the sheer diversity of human language, and to question fundamental assumptions about the relationship between language and logic.
However, logic does not deal with truth in the absolute sense, as for instance a metaphysician does.
However, using this 9-valued logic (< tt > U </ tt >,< tt > X </ tt >,< tt > 0 </ tt >,< tt > 1 </ tt >,< tt > Z </ tt >,< tt > W </ tt >,< tt > H </ tt >,< tt > L </ tt >,< tt >-</ tt >) instead of simple bits ( 0, 1 ) offers a very powerful simulation and debugging tool to the designer which currently does not exist in any other HDL.
However, many statisticians are persuaded by the work of Bruno de Finetti that only one kind of mathematical uncertainty is needed and thus fuzzy logic is unnecessary.
However, vacuous truth also appears in, for example, intuitionistic logic in the same situations given above.
However, it is well known that sentences of this kind cannot be interpreted in first-order logic, where individual variables stand for individual things.
However, formal logic makes no such guarantee if any premise is false, the conclusion can be either true or false.

However and studies
However, the Greek tradition is referring to the existence of vapours and chewing of laurel-leaves, which seem to be confirmed by recent studies.
However, when applied to data from non-randomized experiments or observational studies, model-based analysis lacks the warrant of randomization.
However, studies of processes that
However, Paris ignored the powerful developments in quantitative studies underway in the U. S. and Britain, which reshaped economic, political and demographic research in those countries, while France fell behind.
However not all reception of Steinsaltz ' studies have been wholly positive.
However, studies have shown that blind cave fish embryos begin to grow eyes during development but then something actively stops this process and flesh grows over the partially grown eyes.
However, Dr. Andrew Newberg said that Hira stayed at the University of Pennsylvania only for brain scans on studies of meditation, not his ability to fast indefinitely.
However, the first modern studies of magnetism only started with the development of electrodynamics by Faraday, Maxwell and others in the nineteenth century, which included the classification of materials as ferromagnetic, paramagnetic and diamagnetic based on their response to magnetization.
However, in 1936, the geologists John D. Boon and Claude C. Albritton Jr. revisited Bucher's studies and concluded that the craters that he studied were probably formed by impacts.
However, it is important to note that the patients in these studies received some form of spiritual healing ( i. e. not Christian Science ' treatment ') in addition to, not instead of, conventional medical care.
However, several studies have demonstrated interference competition between coyotes and bobcats, and in all cases coyotes dominated the interaction.
However, studies of mitochondrial DNA show that the divergence between each of the three chipmunk groups is comparable to the genetic dissimilarity between Marmota and Spermophilus.
However, this meta-analysis included two large studies of smokers, so it is not clear that the results apply to the general population.
However, during 2006-8, several reviews of case reports and pilot studies have failed to confirm this effect, collectively indicating no statistically significant interaction between daily consumption of 250 mL cranberry juice and warfarin in the general population.
However the increasing use of cropmarks to identify sites in lowland areas has tended to diminish the relative value of these cairns in Neolithic studies.
However, more recent studies which use the records of civil magistrates suggest that China did in fact have a very well developed system of civil law, in which provisions of the criminal code were interpreted to allow civil causes of action.
However, according to recent studies, California chaparral is extraordinarily resilient to very long periods without fire and continues to maintain productive growth throughout pre-fire conditions.
However, molecular pharmacology studies have shown that alcohol has only a few primary targets.
Because reported AIDS cases in Africa and other parts of the developing world include a larger proportion of people who do not belong to Duesberg's preferred risk groups of drug addicts and male homosexuals, Duesberg writes on his website that " There are no risk groups in Africa, like drug addicts and homosexuals ," However, many studies have addressed the issue of risk groups in Africa and concluded that the risk of AIDS is not equally distributed.
However, Fahrenheit's interest in natural science led him to begin studies and experimentation in that field.
However, studies have shown that the removal of tuition fees at third level has increased the number of students overall and those from lower socio-economic backgrounds.
However, the individual studies still require careful critical appraisal.
However, these studies failed to account for the impact of ethnic and cultural diversity and third-world immigration in its impact on purported social well-being and income distribution.
However, new studies focus on adenoviruses that can be permitted to reproduce, and destroy cancerous cells in the process, since the adenoviruses ' ability to infect normal cells is substantially impaired, potentially resulting in a far more effective treatment.
However evidence for archaic admixture in modern humans had been suggested by some studies.

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