Kurt Godel Quotes
Kurt Friedrich Godel was an Austrian-American mathematician, logician, and philosopher and one of the most important logicians in the history of the discipline. His incompleteness theorems, published in 1931, demonstrated that any consistent formal system of elementary arithmetic is incomplete and that its consistency cannot be proved within the system itself, decisively reshaping the philosophy of mathematics. The quotes below are attributed to Kurt Godel, organized by topic.
Browse Kurt Godel by topic
Kurt Godel on Freedom
-
“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 ).”
Proposition VI, On Formally Undecidable Propositions in Principia Mathematica and Related Systems I (1931); Informally, recursive systems of axioms cannot be complete.
Kurt Godel on God
-
“I like Islam , it is a consistent idea of religion and open-minded.”
As quoted in A Logical Journey: From Gödel to Philosophy (1996) by Hao Wang , p. 148 -
“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 .”
As quoted in Logical Dilemmas : The Life and Work of Kurt Gödel (1997) by John W. Dawson Jr. -
“Religions are, for the most part, bad-but religion is not.”
As quoted in A Logical Journey: From Gödel to Philosophy (1996) by Hao Wang , p. 316
Kurt Godel on Knowledge
-
“Proposition VI, On Formally Undecidable Propositions in Principia Mathematica and Related Systems I (1931); Informally, recursive systems of axioms cannot be complete.”
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 ). -
“Attributed as a remark of 29th November 1972, in Incompleteness (2005) by Rebecca Goldstein”
But every error is due to extraneous factors (such as emotion and education ); reason itself does not err.
Kurt Godel on Life
-
“There are other worlds and rational beings of a different and higher kind. The world in which we live is not the only one in which we shall live or have lived.”
As quoted in A Logical Journey: From Gödel to Philosophy (1996) by Hao Wang , p. 316
Kurt Godel on Mind
-
“Either mathematics is too big for the human mind, or the human mind is more than a machine.”
As quoted in Topoi : The Categorial Analysis of Logic (1979) by Robert Goldblatt , p. 13 -
“But every error is due to extraneous factors (such as emotion and education ); reason itself does not err.”
Attributed as a remark of 29th November 1972, in Incompleteness (2005) by Rebecca Goldstein -
“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.”
As quoted in The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us (MIT Press) 2013 by Yanofsky, Noson S
Kurt Godel on Nature
-
“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 [governing their forma”
As quoted in "On 'computabilism’ and physicalism: Some Problems" by Hao Wang , in Nature’s Imagination (1995), edited by J. Cornwall, p. 161-189
Kurt Godel on Time
-
“The completeness theorem , mathematically, is indeed an almost trivial consequence of Skolem 1923a . However, the fact is that, at that time, nobody (including Skolem himself) drew this conclusion (neither from Skolem 1923a nor, as I did, from similar considerations of his own).”
as quoted, from a 1967 letter to Hao Wang, by Hao Wang in From Mathematics to Philosophy , 1974, p. 8 -
“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 [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
Kurt Godel on Truth
-
Attributed to Kurt Godel:
“Any consistent formal system that contains elementary arithmetic is incomplete.”
-
Attributed to Kurt Godel:
“Mathematical objects are real; they are not the inventions of the mind.”
-
Attributed to Kurt Godel:
“I have come to the conclusion that the world is rational.”
-
“The more I think about language, the more it amazes me that people ever understand each other at all.”
Reflections on Kurt Gödel , MIT Press, Hao Wang 1987, page 95, according to Karl Menger