„Gödel demonstrated that every logical scheme, including mathematics, is dependent upon axioms that it cannot prove and that cannot be reduced to the scheme itself.“

—  George Gilder, Context: Academic scientists of any sort expect to be struck by lightning if they celebrate real creation de novo in the world. One does not expect modern scientists to address creation by God. They have a right to their professional figments such as infinite multiple parallel universes. But it is a strange testimony to our academic life that they also feel it necessary of entrepreneurship to chemistry and cuisine, Romer finally succumbs to the materialist supersition: the idea that human beings and their ideas are ultimately material. Out of the scientistic fog there emerged in the middle of the last century the countervailling ideas if information theory and computer science. The progenitor of information theory, and perhaps the pivotal figure in the recent history of human thought, was Kurt Gödel, the eccentric Austrian genius and intimate of Einstein who drove determinism from its strongest and most indispensable redoubt; the coherence, consistency, and self-sufficiency of mathematics. Gödel demonstrated that every logical scheme, including mathematics, is dependent upon axioms that it cannot prove and that cannot be reduced to the scheme itself. In an elegant mathematical proof, introduced to the world by the great mathematician and computer scientist John von Neumann in September 1930, Gödel demonstrated that mathematics was intrinsically incomplete. Gödel was reportedly concerned that he might have inadvertently proved the existence of God, a faux pas in his Viennese and Princeton circle. It was one of the famously paranoid Gödel's more reasonable fears. As the economist Steven Landsberg, an academic atheist, put it, "Mathematics is the only faith-based science that can prove it." Knowledge and Power : The Information Theory of Capitalism and How it is Revolutionizing our World (2013), Ch. 10: Romer's Recipes and Their Limits <!-- Regnery Publishing -->
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„If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.“

—  John D. Barrow British scientist 1952
Context: If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.<!-- Ch. 5, p. 211

Bertrand Russell photo

„If a "religion" is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970
John D. Barrow, Between Inner and Outer Space: Essays on Science, Art and Philosophy (Oxford University Press, 2000, , ch. 5, Player Piano: Hearing by Numbers, p. 250

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Douglas Hofstadter photo
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John Angell James photo
Freeman Dyson photo

„Fifty years ago Kurt Gödel… proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics.“

—  Freeman Dyson theoretical physicist and mathematician 1923
Context: Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination. Ch. 3 : Manchester and Athens

John Locke photo

„The greatest part of mankind want leisure or capacity for demonstration, nor can carry a train of proofs, which in that way they must always depend upon for conviction, and cannot be required to assent to till they see the demonstration.“

—  John Locke English philosopher and physician 1632 - 1704
Context: The greatest part of mankind want leisure or capacity for demonstration, nor can carry a train of proofs, which in that way they must always depend upon for conviction, and cannot be required to assent to till they see the demonstration. Wherever they stick, the teachers are always put upon proof, and must clear the doubt by a thread of coherent deductions from the first principle, how long or how intricate soever that be. And you may as soon hope to leave all the day labourers and tradesmen, the spinsters and dairy-maids, perfect mathematicians, as to have them perfect in ethics this way: having plain commands is the sure and only course to bring them to obedience and practice: the greatest part cannot know, and therefore they must believe. And I ask, whether one coming from heaven in the power of God, in full and clear evidence and demonstration of miracles, giving plain and direct rules of morality and obedience, be not likelier to enlighten the bulk of mankind, and set them right in their duties, and bring them to do them, than by reasoning with them from general notions and principles of human reason? § 243

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„God exists since mathematics is consistent, and the Devil exists since we cannot prove it.“

—  André Weil French mathematician 1906 - 1998
As quoted in Mathematical Circles Adieu (Boston 1977) by H Eves

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Abraham Joshua Heschel photo

„All scientific conclusions are based on axioms, all reasoning depends ultimately upon faith.“

—  Abraham Joshua Heschel Polish-American Conservative Judaism Rabbi 1907 - 1972
Context: Reality is not exhausted by knowledge. Inaccessible to research are the ultimate facts. All scientific conclusions are based on axioms, all reasoning depends ultimately upon faith. Faith is virgin thinking, preceding all transcendent knowledge. To believe is to abide at the extremities of spirit. "The Holy Dimension", p. 338

Jiddu Krishnamurti photo

„You cannot depend upon anybody. There is no guide, no teacher, no authority. There is only you — your relationship with others and with the world — there is nothing else.“

—  Jiddu Krishnamurti Indian spiritual philosopher 1895 - 1986
Context: You cannot depend upon anybody. There is no guide, no teacher, no authority. There is only you — your relationship with others and with the world — there is nothing else. When you realize this, it either brings great despair, from which comes cynicism and bitterness, or, in facing the fact that you and nobody else is responsible for the world and for yourself, for what you think, what you feel, how you act, all self-pity goes. Normally we thrive on blaming others, which is a form of self-pity.

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