„Only someone who (like the Intuitionist) denies that the concepts and axioms of classical set theory have any meaning could be satisfied with such a solution, not someone who believes them to describe some well-determined reality. For in reality Cantor's conjecture must be either true or false, and its undecidability from the axioms as known today can only mean that these axioms do not contain a complete description of reality.“

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Kurt Gödel4
1906 - 1978
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„It is impossible by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. [Footnote: ] If this axiom be denied for all temperatures, it would have to be admitted that a self-acting machine might be set to work and produce mechanical effect by cooling the sea or earth, with no limit but the total loss of heat from the earth and sea, or in reality, from the whole material world.“

—  William Thomson British physicist and engineer 1824 - 1907
Mathematical and Physical Papers, Vol.1 http://books.google.com/books?id=nWMSAAAAIAAJ p. 179 (1882) "On the Dynamical Theory of Heat with Numerical Results Deduced from Mr Joule's Equivalent of a Thermal Unit and M. Regnault's Observations on Steam" originally from Transactions of the Royal Society of Edinburgh, March, 1851 and Philosophical Magazine iv, 1852

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„Nothing is more false than the axiom that governments are belligerent and peoples are pacific.“

—  Jacques Bainville French historian and journalist 1879 - 1936
Action Française (3 July 1913), quoted in William R. Keylor, Jacques Bainville and the Renaissance of Royalist History in Twentieth-Century France (Baton Rouge: Louisiana State University Press, 1979), p. 65.

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„War is wretched beyond description, and only a fool or a fraud could sentimentalize its cruel reality.“

—  John McCain politician from the United States 1936
Speech to the American Red Cross "Promise of Humanity" conference http://mccain.senate.gov/index.cfm?fuseaction=Newscenter.ViewPressRelease&Content_id=820 (6 May 1999).

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„Classical modern science described only the surface of things, a single dimension of reality. And the more dogmatically science treated it as the only dimension, as the very essence of reality, the more misleading it became.“

—  Václav Havel playwright, essayist, poet, dissident and 1st President of the Czech Republic 1936 - 2011
Context: Classical modern science described only the surface of things, a single dimension of reality. And the more dogmatically science treated it as the only dimension, as the very essence of reality, the more misleading it became. Today, for instance, we may know immeasurably more about the universe than our ancestors did, and yet, it increasingly seems they knew something more essential about it than we do, something that escapes us.

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„A: "Your objection to the self-evident has no validity. There is no such thing as disagreement. People agree about everything."
B: "That’s absurd; people disagree constantly, and about all kinds of things."
A: "How can they? There’s nothing to disagree about; no subject matter. After all, nothing exists."
B: "Nonsense. All kinds of things exist, you know that as well as I do."
A: "That’s one. You must accept the existence axiom, even to utter the term “disagreement.” But to continue, I still maintain that disagreement is unreal. How can people disagree when they are unconscious beings who are unable to hold any ideas at all?"
B: "Of course people hold ideas. They are conscious beings. You know that."
A: "There’s another axiom, but even so, why is disagreement about axioms a problem? Why should it suggest that one or more of the parties is mistaken? Perhaps all of the people who disagree about the very same point are equally, objectively right."
B: "That’s impossible. If two ideas contradict each other, they can’t both be right. Contradictions can’t exist in reality. After all, A is A."
Existence, consciousness, identity are presupposed by every statement and by every concept, including that of "disagreement." … In the act of voicing his objection, therefore, the objector has conceded the case. In any act of challenging or denying the three axioms, a man reaffirms them, no matter what the particular content of this challenge. The axioms are invulnerable.
The opponents of these axioms pose as defenders of truth, but it is only a pose. Their attack on the self-evident amounts to the charge. "Your belief in an idea doesn't necessarily make it true; you must prove it, because facts are what they are independent of your beliefs." Every element of this charge relies on the very axioms that these people are questioning and supposedly setting aside.“

—  Leonard Peikoff Canadian-American philosopher 1933
Objectivism: The Philosophy of Ayn Rand (1991) ; Dialogue used to show that existence, conciousness, identity, and non-contradiction are axioms, using A as a defender of the axioms, and B as an opponent of the axioms,

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„the reality beyond language is not completely reality, a reality that does not speak or say is not reality;
and the moment I say that, the moment I write, letter by letter, that a reality stripped of names is not reality, the names evaporate, they are air, they are a sound encased in another sound and in another and another, a murmur, a faint cascade of meanings that fade away to nothingness:
the tree that I say is not the tree that I see, tree does not say tree, the tree is beyond its name, a leafy, woody reality: impenetrable, untouchable, a reality beyond signs, immersed in itself, firmly planted in its own reality: I can touch it but I cannot name it, I can set fire to it but if I name it I dissolve it:
the tree that is there among the trees is not the tree that I name but a reality that is beyond names, beyond the word reality, it is simply reality just as it is, the abolition of differences and also the abolition of similarities;
the tree that I name is not the tree, and the other one, the one that I do not name and that is there, on the other side of my window, its trunk now black and its foliage still inflamed by the setting sun, is not the tree either, but, rather, the inaccessible reality in which it is planted:
between the one and the other there appears the single tree of sensation which is the perception of the sensation of tree that is vanishing, but
who perceives, who senses, who vanishes as sensations and perceptions vanish?“

—  Octavio Paz Mexican writer laureated with the 1990 Nobel Prize for Literature 1914 - 1998
Ch. 9

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„What he was, he became through having liberated himself from certain false axioms of the common and vulgar philosophy — I will not say blindness.“

—  Giordano Bruno Italian philosopher, mathematician and astronomer 1548 - 1600
Context: He was a man of grave and cultivated mind, of rapid and mature intelligence; inferior to no preceding astronomer, unless in order of succession and time; a man, who in natural ability was far superior to Ptolemy, Hipparchus, Eudoxus, and all those others who followed in their footsteps. What he was, he became through having liberated himself from certain false axioms of the common and vulgar philosophy — I will not say blindness. Nevertheless, he did not depart far from them; because, studying mathematics rather than Nature, he failed to penetrate and dig deep enough altogether to cut away the roots of incongruous and vain principles, and thus, removing perfectly all opposing difficulties, free himself and others from so many empty investigations into things obvious and unchangeable. In spite of all this, who can sufficiently praise the magnanimity of this German, who, having little regard to the foolish multitude, stood firm against the torrent of contrary opinion, and, although well-nigh unarmed with living arguments, resuming those rusty and neglected fragments which antiquity had transmitted to him, polished, repaired, and put them together with reasonings more mathematical than philosophical; and so rendered that cause formerly contemned and contemptible, honourable, estimable, more probable than its rival, and certainly convenient and expeditious for purposes of theory and calculation? Thus this Teuton, although with means insufficient to vanquish, overthrow, and suppress falsehood, as well as resist it, nevertheless resolutely determined in his own mind, and openly confessed this final and necessary conclusion : that it is more possible that this globe should move with regard to the universe, than that the innumerable multitude of bodies, many of which are known to be greater and more magnificent than our earth, should be compelled, in spite of Nature and reason, which, by means of motions evident to the senses, proclaim the contrary, to acknowledge this globe as the centre and base of their revolutions and influences. Who then will be so churlish and discourteous towards the efforts of this man, as to cover with oblivion all he has done, by being ordained of the Gods as an Aurora — which was to precede the rising of this Sun of the true, ancient philosophy, buried during so many centuries in the tenebrous caverns of blind, malignant, froward, envious ignorance; and, taking note only of what he failed to accomplish, rank him amongst the number of the herded multitude, which discourses, guides itself, precipitates to destruction, according to the oral sense of a brutal and ignoble belief, rather than amongst those who, by the use of right reason, have been able to rise up, and resume the true course under the faithful guidance of the eye of divine intelligence. Thoughts on Nicolaus Copernicus, as translated in Agnes Mary Clerke: Copernicus in Italy http://www.archive.org/stream/edinburghreview146londuoft#page/116/mode/2up

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