Axiom Quotes - page 3
In Poetry I have a few axioms, and you will see how far I am from their centre. I think Poetry should surprise by a fine excess and not by singularity - it should strike the reader as a wording of his own highest thoughts, and appear almost a remembrance - Its touches of Beauty should never be halfway thereby making the reader breathless instead of content: the rise, the progress, the setting of imagery should like the Sun come natural to him - shine over him and set soberly although in magnificence leaving him in the luxury of twilight - but it is easier to think what Poetry should be than to write it - and this leads me on to another axiom. That if Poetry comes not as naturally as the leaves to a tree it had better not come at all.
John Keats
It may be safely assumed as an axiom in the government of states that the greatest wrongs inflicted upon a people are caused by unjust and arbitrary legislation, or by the unrelenting decrees of despotic rulers, and that the timely revocation of injurious and oppressive measures is the greatest good that can be conferred upon a nation. The legislator or ruler who has the wisdom and magnanimity to retrace his steps when convinced of error will sooner or later be rewarded with the respect and gratitude of an intelligent and patriotic people.
Our own history, although embracing a period less than a century, affords abundant proof that most, if not all, of our domestic troubles are directly traceable to violations of the organic law and excessive legislation.
Andrew Johnson
Whenever we write an axiom, a critic can say that the axiom is true only in a certain context. With a little ingenuity the critic can usually devise a more general context in which the precise form of the axiom doesn't hold. [...] There simply isn't a most general context.
John McCarthy (computer scientist)
It has become an axiom that, to accomplish results organization is requisite. Nevertheless, there is "organization" and "organization."That this is so appears clearly from the fact that the pure and simmplers have been going about saying to the workers: "Organize! Organize!"and after they have been saying that, and have been organizing"and "organizing" for the past thirty or forty years, we find that they are virtually where they started, if not worse off; that their "organization" parttakes of the nature of the lizard, whose tail destroys what his foreparts build up.
Daniel De Leon
The noble lord who moved the address had, in the course of his speech, warned the House not to let an anxiety for liberty lead to a compromise of the safety of the state. He, for his part, could not separate those things. The safety of the state could only be found in the protection of the liberties of the people. Whatever was destructive of the latter also destroyed the former...The discontent existing in the country had been insisted on as a ground for the adoption of some measures...But there was another axiom no less true-that there never was an extensive discontent without great misgovernment...When no attention was paid to the calls of the people for relief, when their petitions were rejected and their sufferings aggravated, was it wonderful that at last public discontents should assume a formidable aspect?
Charles Grey, 2nd Earl Grey
Then I realised that it really is a philosophy that we're talking about, you know-the nonaggression axiom, that the government should be bound by the same moral laws that the rest of us are. Once you realise that, you're like, "Oh!" Your entire world opens up, and then your entire paradigm changes.
Glenn Jacobs
The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. ...Simplicius.
Morris Kline
In the field of non-Euclidean geometry, Riemann... began by calling attention to a distinction that seems obvious once it is pointed out: the distinction between an unbounded straight line and an infinite line. The distinction between unboundedness and infiniteness is readily illustrated. A circle is an unbounded figure in that it never comes to an end, and yet it is of finite length. On the other hand, the usual Euclidean concept of a straight line is also unbounded in that it never reaches an end but is of infinite length.
...he proposed to replace the infiniteness of the Euclidean straight line by the condition that it is merely unbounded. He also proposed to adopt a new parallel axiom... In brief, there are no parallel lines. This ... had been tried... in conjunction with the infiniteness of the straight line and had led to contradictions. However... Riemann found that he could construct another consistent non-Euclidean geometry.
Morris Kline
At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering. This principle quickly led mathematicians to break from physics and to separate from all other sciences. In the eyes of all normal people, they were transformed into a sinister priestly caste... Bizarre questions like Fermat's problem or problems on sums of prime numbers were elevated to supposedly central problems of mathematics.
Vladimir Arnold
At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering.
Vladimir Arnold
To every reversal of people's soveregnity, to every disappearance of the Republic corresponds a frank or disguised restitution in force of the regal justice. ‘'Tell me, according to what you judge and I'll tell you who you are.” [...] No axiom in politics is more certain than this.
François Mitterrand
Man is naturally self-centered and he is inclined to regard expediency as the supreme standard for what is right and wrong. However, we must not convert an inclination into an axiom that just as man's perceptions cannot operate outside time and space, so his motivations cannot operate outside expediency; that man can never transcend his own self. The most fatal trap into which thinking may fall is the equation of existence and expediency.
Abraham Joshua Heschel
Matthew's response: To me the conception of this law of Nature came intuitively as a self-evident fact, almost without an effort of concentrated thought. Mr Darwin here seems to have more merit in the discovery than I have had; to me it did not appear a discovery. He seems to have worked it out by inductive reason, slowly and with due caution to have made his way synthetically from fact to fact onwards; while with me it was by a general glance at the scheme of Nature that I estimated this select production of species as an a priori recognisable fact – an axiom requiring only to be pointed out to be admitted by unprejudiced minds of sufficient grasp.
Patrick Matthew
