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„Ich glaube nicht an Naturwissenschaft.“

Kurt Gödel

zu John Bahcall, der der Fakultät in Princeton seit 1970 angehörte, als er sich Gödel beim Fakultätsdinner als Physiker vorstellte. Zitiert bei Ed Regis: Einstein, Gödel & Co. / Genialität und Exzentrik - die Princeton-Geschichte. Aus dem Amerikanischen von Anita Ehlers. Berlin 1989.
Original englisch: "I don't believe in natural science" - zitiert bei Ed Regis: Who got Einstein's office? Eccentricity and Genius at the Institute for Advanced Study. Simon & Schuster 1988. p. 58

„Satz XI: Sei κ eine beliebige rekursive widerspruchsfreie Klasse von FORMELN, dann gilt: Die SATZFORMEL, welche besagt, daß κ widerspruchsfrei ist, ist nicht κ-BEWEISBAR; insbesondere ist die Widerspruchsfreiheit von P in P unbeweisbar, vorausgesetzt, daß P widerspruchsfrei ist (im entgegengesetzten Fall ist natürlich jede Aussage beweisbar).“

Kurt Gödel

p. 192 books.google https://books.google.de/books?id=5ya4A0w62skC&pg=PA192&lpg=PA192&dq=xi
Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.

„Satz VI: Zu jeder ω-widerspruchsfreien rekursiven Klasse κ von FORMELN gibt es rekursive KLASSENZEICHEN r, so daß weder v Gen r noch Neg (v Gen r) zu Flg (κ) gehört (wobei v die FREIE VARIABLE aus r ist).“

Kurt Gödel

p. 172 books.google https://books.google.de/books?id=5ya4A0w62skC&pg=PA172&dq=vi
Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.

Kurt Gödel: Zitate auf Englisch

“The more I think about language, the more it amazes me that people ever understand each other at all.”

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Kurt Gödel

“There is a difference between a thing and talking about a thing.”

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Kurt Gödel

“Our total reality and total existence are beautiful and meaningful…. We should judge reality by the little which we truly know of it. Since that part which conceptually we know fully turns out to be so beautiful, the real world of which we know so little should also be beautiful. Life may be miserable for seventy years and happy for a million years: the short period of misery may even be necessary for the whole.”

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Kurt Gödel

“The meaning of the world is the separation of wish and fact. Wish is a force as applied to thinking beings, to realize something. A fulfilled wish is a union of wish and fact. The meaning of the whole world is the separation and the union of fact and wish.”

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Kurt Gödel

As quoted in The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us (MIT Press) 2013 by Yanofsky, Noson S

“I don't believe in empirical science. I only believe in a priori truth.”

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Kurt Gödel

“Either mathematics is too big for the human mind, or the human mind is more than a machine.”

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Kurt Gödel

As quoted in Topoi : The Categorial Analysis of Logic (1979) by Robert Goldblatt, p. 13

“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 Gödel

“Ninety percent of [contemporary philosophers] see their principal task as that of beating religion out of men's heads. … We are far from being able to provide scientific basis for the theological world view.”

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Kurt Gödel

As quoted in Logical Dilemmas : The Life and Work of Kurt Gödel (1997) by John W. Dawson Jr.

“The formation in geological time of the human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field is as unlikely as the separation of the atmosphere into its components. The complexity of the living things has to be present within the material [from which they are derived] or in the laws”

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Kurt Gödel

governing their formation
As quoted in "On 'computabilism’ and physicalism: Some Problems" by Hao Wang, in Nature’s Imagination (1995), edited by J. Cornwall, p.161-189

“To every ω-consistent recursive class κ of formulae there correspond recursive class signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg (κ) (where v is the free variable of r).”

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Kurt Gödel

Proposition VI, On Formally Undecidable Propositions in Principia Mathematica and Related Systems I (1931); Informally, recursive systems of axioms cannot be complete.