"Turtles all the way down" is a jocular expression of the infinite regress problem in cosmology posed by the "unmoved mover" paradox. The phrase was popularized by Stephen Hawking in 1988. The "turtle" metaphor in the anecdote represents a popular notion of a "primitive cosmological myth", viz. the flat earth supported on the back of a World Turtle.
A comparable metaphor describing the circular cause and consequence for the same problem is the "chicken and egg problem". Another metaphor addressing the problem of infinite regression, albeit not in a cosmological context, is Quis custodiet ipsos custodes? The same problem in epistemology is known as the Münchhausen Trilemma.
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The origins of the turtle story are uncertain.
The most widely known version appears in Stephen Hawking's 1988 book A Brief History of Time, which starts:
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!"—[1]
There is an allusion to the story in David Hume's Dialogues Concerning Natural Religion (published in 1779):
How can we satisfy ourselves without going on in infinitum? And, after all, what satisfaction is there in that infinite progression? Let us remember the story of the Indian philosopher and his elephant. It was never more applicable than to the present subject. If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world.—[2]
In 1905, Oliver Corwin Sabin, Bishop of the Evangelical Christian Science Church, wrote:
The old original idea which was enunciated first in India, that the world was flat and stood on the back of an elephant, and the elephant did not have anything to stand on was the world's thought for centuries. That story is not as good as the Richmond negro preacher's who said the world was flat and stood on a turtle. They asked him what the turtle stood on and he said another turtle, and they asked what that turtle stood on and he said another turtle, and finally they got him in a hole and he said. "I tell you there are turtles all the way down."—[3]
In J. R. (Haj) Ross's 1967 linguistics dissertation, Constraints on Variables in Syntax, the scientist is identified as the Harvard psychologist and philosopher William James. Of the story's provenance, Ross writes:
This quote also appears in Robert Anton Wilson's Prometheus Rising (1983); he attributes the story to William James:
William James, father of American psychology, tells of meeting an old lady who told him the Earth rested on the back of a huge turtle. "But, my dear lady", Professor James asked, as politely as possible, "what holds up the turtle?" "Ah", she said, "that's easy. He is standing on the back of another turtle." "Oh, I see", said Professor James, still being polite. "But would you be so good as to tell me what holds up the second turtle?" "It's no use, Professor", said the old lady, realizing he was trying to lead her into a logical trap. "It's turtles-turtles-turtles, all the way!"—[6]
Additionally, Stephen Fry, in an episode of the BBC's comedy-quiz show QI (Series 1, episode 2), attributes the turtles anecdote to an exchange between an elderly lady and William James. Also, David Sloan Wilson does the same in his book Evolution for Everyone (Delacorte, 2007): 133.
Hawking's suggested connection to Russell may be due to Russell's 1927 lecture Why I Am Not a Christian. In it, while discounting the First Cause argument intended to be a proof of God's existence, Russell comments (with an argument not relevant to modern Hindu beliefs):
If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu's view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, "How about the tortoise?" the Indian said, "Suppose we change the subject."
Philosophical allusion to the story goes back at least as far as John Locke. In his 1690 tract An Essay Concerning Human Understanding, Locke compares one who would say that properties inhere in "substance" to the Indian who said the world was on an elephant which was on a tortoise "but being again pressed to know what gave support to the broad-backed tortoise, replied — something, he knew not what."[7]
Henry David Thoreau, in his journal entry of 4 May 1852,[8] writes:
Men are making speeches… all over the country, but each expresses only the thought, or the want of thought, of the multitude. No man stands on truth. They are merely banded together as usual, one leaning on another and all together on nothing; as the Hindoos made the world rest on an elephant, and the elephant on a tortoise, and had nothing to put under the tortoise.
Despite these accounts, Hindu myths do not actually contain the myth in the form described. Locke appears to have taken the idea from Samuel Purchas.[9] Some accounts involve the earth supported by a single unsupported tortoise, as Jñanaraja argued: "A vulture, which has only little strength, rests in the sky holding a snake in its beak for a prahara [three hours]. Why can [the deity] in the form of a tortoise, who possesses an inconceivable potency, not hold the Earth in the sky for a kalpa [billions of years]?"[10]
Note also that Lewis Carroll, the author of Alice in Wonderland, used the story of the tortoise for a philosophical regressus-argument in the philosophical Journal Mind (1895), "What the Tortoise Said to Achilles". The article was reprinted in the same Journal in 1995 with a subsequent article by Simon Blackburn titled: Practical Tortoise Reasoning.[11] It was also reprinted in Gödel, Escher, Bach by Douglas Hofstadter. Moreover, the tortoise-argument was used by Wilfrid Sellars in his Empiricism and the Philosophy of Mind (1956, secs. 34 and 38).
The story can also be found in Bernard Nietschmann's "When the Turtle Collapses, the World Ends", Natural History, 83(6):34 (June–July 1974). A version of the story also appears in Clifford Geertz's, "Thick Description: Towards an Interpretive Theory of Culture", in his 1973 book The Interpretation of Culture, with the scientist and old woman replaced by an Englishman and an Indian respectively.[12]
Carl Sagan recited a version of the story as an apocryphal anecdote in his 1979 book Broca's Brain: Reflections on the Romance of Science, as an exchange between a "Western traveler" and an "Oriental philosopher".
Justice Antonin Scalia of the U.S. Supreme Court discussed his "favored version" of the tale in a footnote to his plurality opinion in Rapanos v. United States (decided June 19, 2006):
In our favored version, an Eastern guru affirms that the earth is supported on the back of a tiger. When asked what supports the tiger, he says it stands upon an elephant; and when asked what supports the elephant he says it is a giant turtle. When asked, finally, what supports the giant turtle, he is briefly taken aback, but quickly replies "Ah, after that it is turtles all the way down."—[13]
The anecdote has achieved the status of an urban legend on the Internet, as there are numerous versions in which the name of the scientist varies (e.g., Arthur Stanley Eddington, Thomas Huxley, Linus Pauling, or Carl Sagan) although the rest is the same.