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

The Substitution of Similars, The True Principles of Reasoning (1869)
Context: Aristotle's dictim... may then be formulated somewhat as follows:—Whatever is known of a term may be stated of its equal or equivalent. Or, in other words, Whatever is true of a thing is true of its like.... the value of the formula must be judged by its results;... it not only brings into harmony all the branches of logical doctrine, but... unites them in close analogy to the corresponding parts of mathematical method. All acts of mathematical reasoning may... be considered but as applications of a corresponding axiom of quantity...

Source: Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry (1871), Ch. XXXII : Sublime Prince of the Royal Secret, p. 841
Context: All hypotheses scientifically probable are the last gleams of the twilight of knowledge, or its last shadows. Faith begins where Reason sinks exhausted. Beyond the human Reason is the Divine Reason, to our feebleness the great Absurdity, the Infinite Absurd, which confounds us and which we believe. For the Master, the Compass of Faith is above the Square of Reason; but both rest upon the Holy Scriptures and combine to form the Blazing Star of Truth.
All eyes do not see alike. Even the visible creation is not, for all who look upon it, of one form and one color. Our brain is a book printed within and without, and the two writings are, with all men, more or less confused.

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 -->
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."

Source: Information service in libraries (1958), p. 13

The History of Rome

Twitter, November 25, 2013 ( archive http://archive.is/khKVm)
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Progress, Coexistence and Intellectual Freedom (1968)
Context: We regard as "scientific" a method based on deep analysis of facts, theories, and views, presupposing unprejudiced, unfearing open discussion and conclusions. The complexity and diversity of all the phenomena of modern life, the great possibilities and dangers linked with the scientific-technical revolution and with a number of social tendencies demand precisely such an approach, as has been acknowledged in a number of official statements.

The Tragic Sense of Life (1913), XI : The Practical Problem
Context: My conduct must be the best proof, the moral proof, of my supreme desire; and if I do not end by convincing myself, within the bounds of the ultimate and irremediable uncertainty of the truth of what I hope for, it is because my conduct is not sufficiently pure. Virtue, therefore, is not based upon dogma, but dogma upon virtue, and it is not faith that creates martyrs but martyrs who create faith. There is no security or repose — so far as security and repose are obtainable in this life, so essentially insecure and unreposeful — save in conduct that is passionately good.

The Tragic Sense of Life (1913), IX : Faith, Hope, and Charity
Context: Faith makes us live by showing us that life, although it is dependent upon reason, has its well spring and source of power elsewhere, in something supernatural and miraculous. Cournot the mathematician, a man of singularly well-balanced and scientifically equipped mind has said that it is this tendency towards the supernatural and miraculous that gives life, and that when it is lacking, all the speculations of reason lead to nothing but affliction of the spirit.... And in truth we wish to live.