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Kurt Gödel Quotes

Kurt Friedrich Gödel was an Austro-Hungarian-born Austrian logician, mathematician, and analytic philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor.

Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers , there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

He also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted axioms of set theory, assuming these axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic. Wikipedia  

✵ 28. April 1906 – 14. January 1978
Kurt Gödel photo
Kurt Gödel: 12   quotes 21   likes

Famous Kurt Gödel Quotes

“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.”

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.”

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

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

Kurt Gödel

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

Kurt Gödel Quotes

“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.”

Kurt Gödel
Reality , Falseness

“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.”

Kurt Gödel

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

Men , World , Religion

“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”

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

Law , Nature , Time

“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).”

Kurt Gödel

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

“I like Islam, it is a consistent idea of religion and open-minded.”

Kurt Gödel

As quoted in A Logical Journey: From Gödel to Philosophy (1996) by Hao Wang

Religion , Idea

“But every error is due to extraneous factors (such as emotion and education); reason itself does not err.”

Kurt Gödel

Attributed as a remark of 29th November 1972, in Incompleteness (2005) by Rebecca Goldstein

Education , Error

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