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Axioms Quotes

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Axioms Quotes

“As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies.”

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Author:Albert Einstein
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“Pointed axioms and acute replies fly loose about the world, and are assigned successively to those whom it may be the fashion to celebrate.”

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Book:The Beauties of Samuel Johnson, LL.D.: Consisting of Maxims and Observations, Moral, Critical, and Miscellaneous, to which are Now Added, Biographical Anecdotes of the Doctor, Selected from the Late Productions of Mrs. Piozzi, Mr. Boswell, ...
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“As a leader... I have always endeavored to listen to what each and every person in a discussion had to say before venturing my own opinion. Oftentimes, my own opinion will simply represent a consensus of what I heard in the discussion. I always remember the axiom; a leader is like a shepherd. He stays behind the flock, letting the most nimble go out ahead, whereupon the others follow, not realizing that all along they are being directed from behind.”

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Author:Nelson Mandela
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“A priori one should expect a chaotic world which cannot be grasped by the mind in any way... The kind of order created by Newton's theory of gravitation...is wholly different. Even if the axioms of the theory are proposed by man, the success of such a project presupposes a high degree of ordering of the objective world.... That is the "miracle" which is being constantly reinforced as our knowledge expands.”

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Author:Albert Einstein
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“Fanon calls his ideology a new humanism, not only in contrast to the elite humanism of the West, but also on the axiom that the wretched of the earth, understood socially, think and thus must be a basis of a new politics. This, of course, is not achieved immediately, but it must become an explicit element of the struggle for liberation.”

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Author:Nigel Gibson
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“The Iranian issue I don't think has much to do with nuclear weapons frankly. Nobody is saying Iran should have nuclear weapons ­nor should anybody else. But the point in the Middle East, as distinct from North Korea, is that this is center of the world's energy resources. Originally the British and secondarily the French had dominated it, but after the Second World War, it's been a U.S. preserve. That's been an axiom of U.S. foreign policy, that it must control Middle East energy resources.”

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Author:Noam Chomsky
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“A dozen more questions occurred to me. Not to mention twenty-two possible solutions to each one, sixteen resulting hypotheses and counter-theorems, eight abstract speculations, a quadrilateral equation, two axioms, and a limerick. That's raw intelligence for you.”

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Book:Bartimaeus Trilogy, Book Three: Ptolemy's Gate
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“In one day I had altered my life; my life, therefore, was alterable. This simple axiom did not call out for exegesis; no, it entered my bloodstream directly, as powerful as heroin. I could feel it pump and surge, the way it brightened my veins to a kind of glass. I had wakened that morning to narrowness and predestination and now I was falling asleep in the storm of my own free will.”

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Author:Carol Shields
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“If nature leads us to mathematical forms of great simplicity and beauty - by forms I am referring to coherent systems of hypothesis, axioms, etc. - to forms that no one has previously encountered, we cannot help thinking that they are "true," that they reveal a genuine feature of nature... You must have felt this too: The almost frightening simplicity and wholeness of relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.”

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Author:Werner Heisenberg
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“Having a moment of clarity was one thing; I'd had moments like that before. It had to be followed with a dedicated push of daily exercise. It's a trite axiom, but practice DOES make perfect. If you want to be a strong swimmer or an accomplished musician, you have to practice. It's the same with sobriety, though the stakes are higher. If you don't practice your program every day, you're putting yourself in a position where you could fly out of the orbit one more time.”

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Author:Anthony Kiedis
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“The writer who neglects punctuation, or mispunctuates, is liable to be misunderstood for the want of merely a comma, it often occurs that an axiom appears a paradox, or that a sarcasm is converted into a sermonoid.”

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Book:Complete Collection of Edgar Allan Poe - 170+ eBooks (Complete Tales, Poems, Novels, Essays, Miscellaneous, Play)
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“There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgment and to the discovery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried.”

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Book:The Great Instauration
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“If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.”

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Book:Mathematical discovery: on understanding, learning, and teaching problem solving
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“The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.”

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Author:Kurt Gödel
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“We may lay it down as an incontestible axiom, that, in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment; the quality and quantity of the elements remain precisely the same; and nothing takes place beyond changes and modifications in the combination of these elements. Upon this principle the whole art of performing chemical experiments depends: We must always suppose an exact equality between the elements of the body examined and those of the products of its analysis.”

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Book:Elements of chemistry, tr. by R. Kerr
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“Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]”

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Author:Augustus De Morgan
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“I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek.”

IfsWantMeanCoursesFoundGamesLostTermLinesKnownGroupsLosingConceptsAddDefinitionsConfusionPlanesExplanationCharacteristicsConfusedEnterpriseEtcVagueSectionsConfusingAxiomsStraight LinesDegeneratesParaphraseHide And Seek
Author:David Hilbert
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