Axioms Quotes - Page 2

• Life cannot be captured in a few axioms. And that is just what I keep trying to do. But it won't work, for life is full of endless nuances and cannot be captured in just a few formulae.

  Etty Hillesum

  Trying, Nuance, Life Is

  Etty Hillesum (1985). “An Interrupted Life: The Diaries of Etty Hillesum, 1941-1943”

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• Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

  David Hilbert

  Simple, Small Numbers, Principles

  David Hilbert (1910). “The Foundations of Geometry”

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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.

  Francis Bacon

  Fashion, Truth, Discovery

  Francis Bacon (2012). “The Great Instauration”, p.30, Simon and Schuster

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• At first it seems obvious, but the more you think about it the stranger the deductions from this axiom seem to become; in the end you cease to understand what is meant by it.

  Bertrand Russell

  Math, Thinking, Understanding

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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.

  Edgar Allan Poe

  Sarcasm, Misunderstood, Want

  Edgar Allan Poe (2014). “Complete Collection of Edgar Allan Poe - 170+ eBooks (Complete Tales, Poems, Novels, Essays, Miscellaneous, Play)”, p.1206, Ageless Reads

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• The two basic maxims of the so-called historical criticism are the postulate of the common and the axiom of the ordinary. Postulate of the common: everything really great, good, and beautiful, is improbable, since it is extraordinary and therefore at least suspect. Axiom of the ordinary: our conditions and environment must have existed everywhere, for they are really so natural.

  Karl Wilhelm Friedrich Schlegel

  Beautiful, Two, History

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• Whatever is referred to must exist. Let us call this the axiom of existence.

  John Searle

  Existence

  "Speech Acts: An Essay in the Philosophy of Language". Book by John Searle, 1969.

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• Words are really powerful. I don't believe that axiom at all - words can absolutely hurt you. Words can wound. They can do a lot of damage. I think they can do way more damage than sticks and stones. I'll take sticks and stones.

  Mary-Louise Parker

  Hurt, Powerful, Believe

  Interview with Kyle Ryan, www.avclub.com. June 17, 2009.

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• The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.

  John Maynard Keynes

  Work Out, World, Lines

  John Maynard Keynes (2006). “General Theory Of Employment , Interest And Money”, p.15, Atlantic Publishers & Dist

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• My fundamental axiom of speculative philosophy is that materialism and spiritualism are opposite poles of the same absurdity-the absurdity of imagining that we know anything about either spirit or matter.

  Thomas Huxley

  Philosophy, Opposites, Fundamentals

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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.

  Albert Einstein

  Men, Order, Miracle

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• Applying the axioms of physical science to human life has something reprehensible to it.

  Albert Einstein

  Human Life, Humans, Physical Science

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• We must start with scientific fundamentals, and that means with the data of experiments and not with assumed axioms predicated only upon the misleading nature of that which only superficially seems to be obvious. It is the consensus of great scientists that science is the attempt to set in order the facts of experience.

  R. Buckminster Fuller

  Mean, Order, Data

  "The Wellspring of Reality". "Synergetics: Explorations in the Geometry of Thinking" by Buckminster Fuller, 1975.

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• What exactly is mathematics? Many have tried but nobody has
  really succeeded in defining mathematics; it is always something
  else. Roughly speaking, people know that it deals with numbers,
  figures, with relations, operations, and that its formal procedures
  involving axioms, proofs, lemmas, theorems have not changed
  since the time of Archimedes.

  Stanislaw Ulam

  Numbers, Exactly Is, People

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• ...the mathematician uses an indirect definition of congruence, making use of the fact that the axiom of parallels together with an additional condition can replace the definition of congruence.

  Hans Reichenbach

  Together, Use, Definitions

  Hans Reichenbach (1958). “Philosophie Der Raum-Zeit-Lehre”, p.87, Courier Corporation

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• My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments: In order to which, I shall premise the following Definitions and Axioms.

  Isaac Newton

  Book, Science, Light

  Opticks Book One, Part I

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• One of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example.

  William Stanley Jevons

  Taken, Men, Important

  William Stanley Jevons (1973). “Papers and correspondence of William Stanley Jevons”

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• The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke.

  John Allen Paulos

  Science, Four, Firsts

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• We find sects and parties in most branches of science; and disputes which are carried on from age to age, without being brought to an issue. Sophistry has been more effectually excluded from mathematics and natural philosophy than from other sciences. In mathematics it had no place from the beginning; mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly, we find no parties among mathematicians, and hardly any disputes.

  Thomas Reid

  Philosophy, Party, Issues

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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]

  Augustus De Morgan

  Writing, Thinking, Years

  "Budget of Paradoxes". Book by Augustus De Morgan (p. 178), 1872.

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• An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.

  David Berlinski

  Steps, Assuming, Enough

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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.

  Carol Shields

  Morning, Powerful, Fall

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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.

  Noam Chomsky

  War, Thinking, Issues

  Source: www.counterpunch.org

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• It has long been an axiom of mine that the little things are infinitely the most important.

  Arthur Conan Doyle

  Life, Wisdom, Past

  Adventures of Sherlock Holmes (1892) "Case of Identity"

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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.

  Antoine Lavoisier

  Art, Science, Quality

  Antoine Laurent Lavoisier (1802). “Elements of chemistry, tr. by R. Kerr”, p.226

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