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Page "Unifying theories in mathematics" ¶ 34
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fact and Langlands
In fact, Murty showed that Artin L-functions corresponding to irreducible representations of the Galois group of a solvable extension of the rationals are automorphic as predicted by the Langlands conjectures.

fact and program
Sir -- Permit me to commend your editorial in which you stress the fact that a program of county colleges will substantially increase local tax burdens and that taxpayers have a right to a clear idea of what such a program would commit them to.
The fact that companies on the AIA lists were already participating in the defense program because of the manner of their selection.
West of Rock Creek Park is still monolithically white and is in fact increasingly white as a result of Georgetown's conversion-by-renovation housing program.
The RAND Corporation's Memorandum 5446-ISA / ARPA states: " the fact that the VC obtain most of their food from the neutral rural population dictates the destruction of civilian crops ... if they ( the VC ) are to be hampered by the crop destruction program, it will be necessary to destroy large portions of the rural economy – probably 50 % or more ".
: Nils Nilsson writes " If a program behaves as if it were multiplying, most of us would say that it is, in fact, multiplying.
Although the initial certificate is available to anyone with a high school education, the diploma is meant to be a post-graduate qualification and in fact can be incorporated into a Master's degree program.
A distinction is sometimes drawn between syntactic garbage, those objects the program cannot possibly reach, and semantic garbage, those objects the program will in fact never again use.
In fact, if the voucher program alone were considered a school district, it would mark the sixth-largest district in Wisconsin.
But this solution has a defect: expert system runs slower than a traditional program because he consistently " thinks " when in fact a classic software just follows paths traced by the programmer.
* The fact that never returns also means that a GLUT program cannot exit the event loop.
Every access to the translated file, or files below a hierarchy in the second case, is in fact handled by the program.
Many others also include negatives, such as denials that the thing defined is or resembles something else ( which the thing defined does in fact resemble or is even derived from ), to indicate that, despite the similarities, it was distinct from the program it was based on.
The song initially had a reference to the legendary movie program host Simon van Collem till it transpired that he was in fact René's father.
Celebrity supporter Tom Cruise asserts that Narconon is " the only successful drug rehabilitation program in the world ", adding " It's a statistically proven fact that there is only one successful drug rehabilitation program in the world.
This process is known as base-bound relocation ; each user program sees core memory as a contiguous block words with length FL, starting with address 0 ; in fact the program may be anywhere in the physical memory.
This fact is sometimes thought to have severe consequences for the program of logicism proposed by Gottlob Frege and Bertrand Russell, which aimed to define the natural numbers in terms of logic ( Hellman 1981, p. 451 – 468 ).
This amendment provides that when the Secretary of Commerce determines that the nationals of a foreign country are diminishing the effectiveness of an international fishery conservation program ( including the IWC's program ), the Secretary shall certify this fact to the President.
She was the inaugural Olympic champion in the event, since athletics for women had not been on the program before, and its inclusion was in fact still heavily disputed among officials.
Hilbert's program was strongly impacted by incompleteness theorems, which showed that sufficiently strong proof theories cannot prove their own consistency ( provided that they are in fact consistent ).
Until the 2. x and especially the 2. 3x versions, this was in fact the only way to give commands, and this was largely responsible for creating Blender's reputation as a difficult-to-learn program.

fact and philosophy
Kant is not generally considered to be a modern anthropologist, however, as he never left his region of Germany nor did he study any cultures besides his own, and in fact, describes the need for anthropology as a corollary field to his own primary field of philosophy.
Swift also recognizes the implications of such a fact in making mercantilist philosophy a paradox: the wealth of a country is based on the poverty of the majority of its citizens.
In fact, Dummett's writings on anti-realism can be seen as an attempt to integrate central ideas from the Philosophical Investigations into analytical philosophy.
In fact, Shestov used the story of Job as a central signifier for his core philosophy ( the vast critique of the history of Western philosophy, which he saw broadly as a monumental battle between Reason and Faith, Athens and Jerusalem, secular and religious outlook ):
In around 500 BCE, after the Zhou state weakened and China moved into the Spring and Autumn Period, the classic period of Chinese philosophy began ( it is an interesting fact that this date nearly coincides with the emergence of the first Greek philosophers ).
Lynn Montross, writing on that topic in War Through the Ages ( 1960 ), said ; " This outcome ... may be explained by the fact that Jomini produced a system of war, Clausewitz a philosophy.
There is some question as to whether advanced mathematical skills or talent are in fact necessary for fields such as history, English, philosophy, or art.
Anatoli, in fact, was the first man to translate the commentaries of Averroes into Hebrew, thus opening a new era in the history of Aristotelian philosophy.
But at the same time he adopted the Stoic doctrine of the " seminal word ," and so philosophy was to him an operation of the Word — in fact, through his identification of the Word with Christ, it was brought into immediate connection with him.
In other words, we are urged to believe that Plato's theory of ideas is an abstraction, divorced from the so-called external world, of modern European philosophy, despite the fact Plato taught that ideas are ultimately real, and different from non-ideal things -- indeed, he argued for a distinction between the ideal and non-ideal realm.
Although he nowhere defines truth in terms of a thought's likeness to a thing or fact, it is clear that such a definition would fit well into his overall philosophy of mind.
This suggests that many of the traditional domains of philosophy, e. g. ethics and metaphysics, cannot in fact be discussed meaningfully.
In fact, philosophy was only a second option for him at that time, to be able to emigrate to escape the imminent Anschluss.
In fact, the Spartans were also rigorously trained in logic and philosophy.
Finally, Kripke gave an argument against identity materialism in the philosophy of mind, the view that every mental fact is identical with some physical fact.
Some older scholarship speculated that the Bibliotheca was in fact compiled in Baghdad at the time of Photius's embassy to the Abbasid court, since many of the mentioned works were rarely cited during the so-called Byzantine Dark Ages c. 630-c. 800, and it was known that the Abbasids were interested in works of Greek science and philosophy.
This may be explained by the fact that the ages-old ideological struggle between the monarchically oriented Orangist party and its successive opponents of a more " republican " bent ( going back to at least the conflict between Johan van Oldenbarnevelt and Prince Maurice ), of which the Patriots were only the latest incarnation, was being refought in the standard works of 19th-century Dutch historians like Guillaume Groen van Prinsterer, who saw plenty to despise in the " popular-sovereignty " philosophy of the Patriot radicals.
Some analytic philosophers have in fact claimed, since at least the 1980s, that Derrida's work is " not philosophy.
The history of the Fatimids, from this point of view, is in fact the history of knowledge, literature and philosophy.
In philosophy, the concept fact is considered in epistemology and ontology.
Just as in philosophy, the scientific concept of fact is central to fundamental questions regarding the nature, methods, scope and validity of scientific reasoning.
In the various neo-Hegelian schools-proposing a history of our species some consider to be at variance with Darwin, as well as with the dialectical materialism of Karl Marx and Friedrich Engels, and with what is now called analytic philosophythe point of departure is not so much formal logic and scientific fact but ' identity '.
For example, the sponsoring organisation adopts a philosophy of self-regulation and offers the user connection to the local network and also connection to the Internet providing that the user accepts the fact she / he is going to be personally responsible for actions taken when connected to the network or Internet.

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