"Turtles all the way down" is an expression of the problem of infinite regress. The saying alludes to the mythological idea of a World Turtle that supports a flat Earth on its back. It suggests that this turtle rests on the back of an even larger turtle, which itself is part of a column of increasingly larger turtles that continues indefinitely.
The exact origin of the phrase is uncertain. In the form "rocks all the way down", the saying appears as early as 1838. [1] References to the saying's mythological antecedents, the World Turtle and its counterpart the World Elephant, were made by a number of authors in the 17th and 18th centuries. [2] [3]
The expression has been used to illustrate problems such as the regress argument in epistemology.
Early variants of the saying do not always have explicit references to infinite regression (i.e., the phrase "all the way down"). They often reference stories featuring a World Elephant, World Turtle, or other similar creatures that are claimed to come from Hindu mythology. The first known reference to a Hindu source is found in a letter by Jesuit Emanuel da Veiga (1549–1605), written at Chandagiri on 18 September 1599, in which the relevant passage reads:
Alii dicebant terram novem constare angulis, quibus cœlo innititur. Alius ab his dissentiens volebat terram septem elephantis fulciri, elephantes uero ne subsiderent, super testudine pedes fixos habere. Quærenti quis testudinis corpus firmaret, ne dilaberetur, respondere nesciuit. | Others hold that the earth has nine corners by which the heavens are supported. Another disagreeing from these would have the earth supported by seven elephants, and the elephants do not sink down because their feet are fixed on a tortoise. When asked who would fix the body of the tortoise, so that it would not collapse, he said that he did not know. [4] |
Veiga's account seems to have been received by Samuel Purchas, who has a close paraphrase in his Purchas His Pilgrims (1613/1626), "that the Earth had nine corners, whereby it was borne up by the Heaven. Others dissented, and said, that the Earth was borne up by seven Elephants; the Elephants' feet stood on Tortoises, and they were borne by they know not what." [5] Purchas' account is again reflected by John Locke in his 1689 tract An Essay Concerning Human Understanding , where Locke introduces the story as a trope referring to the problem of induction in philosophical debate. 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-back'd Tortoise, replied, something, he knew not what". [2] The story is also referenced by Henry David Thoreau, who writes in his journal entry of 4 May 1852: "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." [6]
In the form of "rocks all the way down", the saying dates to at least 1838, when it was printed in an unsigned anecdote in the New-York Mirror about a schoolboy and an old woman living in the woods:
"The world, marm," said I, anxious to display my acquired knowledge, "is not exactly round, but resembles in shape a flattened orange; and it turns on its axis once in twenty-four hours."
"Well, I don't know anything about its axes," replied she, "but I know it don't turn round, for if it did we'd be all tumbled off; and as to its being round, any one can see it's a square piece of ground, standing on a rock!"
"Standing on a rock! but upon what does that stand?"
"Why, on another, to be sure!"
"But what supports the last?"
"Lud! child, how stupid you are! There's rocks all the way down!" [1]
Another version of the saying appeared in an 1854 transcript of remarks by preacher Joseph Frederick Berg addressed to Joseph Barker:
My opponent's reasoning reminds me of the heathen, who, being asked on what the world stood, replied, "On a tortoise." But on what does the tortoise stand? "On another tortoise." With Mr. Barker, too, there are tortoises all the way down. (Vehement and vociferous applause.)
— "Second Evening: Remarks of Rev. Dr. Berg" [7]
Many 20th-century attributions claim that philosopher and psychologist William James is the source of the phrase. [8] James referred to the fable of the elephant and tortoise several times, but told the infinite regress story with "rocks all the way down" in his 1882 essay, "Rationality, Activity and Faith":
Like the old woman in the story who described the world as resting on a rock, and then explained that rock to be supported by another rock, and finally when pushed with questions said it was "rocks all the way down," he who believes this to be a radically moral universe must hold the moral order to rest either on an absolute and ultimate should or on a series of shoulds "all the way down." [9]
The linguist John R. Ross also associates James with the phrase:
The following anecdote is told of William James. [...] After a lecture on cosmology and the structure of the solar system, James was accosted by a little old lady.
"Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it's wrong. I've got a better theory," said the little old lady.
"And what is that, madam?" inquired James politely.
"That we live on a crust of earth which is on the back of a giant turtle."
Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position.
"If your theory is correct, madam," he asked, "what does this turtle stand on?"
"You're a very clever man, Mr. James, and that's a very good question," replied the little old lady, "but I have an answer to it. And it's this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under him."
"But what does this second turtle stand on?" persisted James patiently.
To this, the little old lady crowed triumphantly,
"It's no use, Mr. James—it's turtles all the way down."
— J. R. Ross, Constraints on Variables in Syntax, 1967 [10]
The mythological idea of a turtle world is often used as an illustration of infinite regresses. An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. [11] The main interest in infinite regresses is due to their role in infinite regress arguments. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. [11] [12] For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. [11] [13] There are different ways in which a regress can be vicious. [13] [14] The idea of a turtle world exemplifies viciousness due to explanatory failure: it does not solve the problem it was formulated to solve. Instead, it assumes already in disguised form what it was supposed to explain. [13] [14] This is akin to the informal fallacy of begging the question. [15] In one interpretation, the goal of positing the existence of a world turtle is to explain why the earth seems to be at rest instead of falling down: because it rests on the back of a giant turtle. In order to explain why the turtle itself is not in free fall, another, even bigger turtle is posited, and so on, resulting in a world that is turtles all the way down. [13] [11] Despite its shortcomings in clashing with modern physics, and due to its ontological extravagance, this theory seems to be metaphysically possible, assuming that space is infinite, thereby avoiding an outright contradiction. But it fails because it has to assume rather than explain at each step that there is another thing that is not falling. It does not explain why nothing at all is falling. [11] [13]
The metaphor is used as an example of the problem of infinite regress in epistemology to show that there is a necessary foundation to knowledge, as written by Johann Gottlieb Fichte in 1794: [16] [ page needed ]
If there is not to be any (system of human knowledge dependent upon an absolute first principle) two cases are only possible. Either there is no immediate certainty at all, and then our knowledge forms many series or one infinite series, wherein each theorem is derived from a higher one, and this again from a higher one, etc., etc. We build our houses on the earth, the earth rests on an elephant, the elephant on a tortoise, the tortoise again—who knows on what?—and so on ad infinitum. True, if our knowledge is thus constituted, we can not alter it; but neither have we, then, any firm knowledge. We may have gone back to a certain link of our series, and have found every thing firm up to this link; but who can guarantee us that, if we go further back, we may not find it ungrounded, and shall thus have to abandon it? Our certainty is only assumed, and we can never be sure of it for a single following day.
David Hume references the story in his 1779 work Dialogues Concerning Natural Religion when arguing against God as an unmoved mover: [3]
How, therefore, shall we satisfy ourselves concerning the cause of that Being whom you suppose the Author of Nature, or, according to your system of Anthropomorphism, the ideal world, into which you trace the material? Have we not the same reason to trace that ideal world into another ideal world, or new intelligent principle? But if we stop, and go no further; why go so far? why not stop at the material world? 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. By supposing it to contain the principle of its order within itself, we really assert it to be God; and the sooner we arrive at that Divine Being, so much the better. When you go one step beyond the mundane system, you only excite an inquisitive humour which it is impossible ever to satisfy.
Bertrand Russell also mentions the story in his 1927 lecture Why I Am Not a Christian while discounting the First Cause argument intended to be a proof of God's existence:
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.'
References to "turtles all the way down" have been made in a variety of modern contexts. For example, American hardcore band Every Time I Die titled a song “Turtles All the Way Down” on their 2009 album “New Junk Aesthetic”. The lyrics mention the turtle world theory.
"Turtles All the Way Down" is the name of a song by country artist Sturgill Simpson that appears on his 2014 album Metamodern Sounds in Country Music . [17] "Gamma Goblins ('Its Turtles All The Way Down' Mix)" is a remix by Ott for the 2002 Hallucinogen album In Dub . [18] Turtles All the Way Down is also the title of a 2017 novel by John Green about a teenage girl with obsessive–compulsive disorder. [19]
Stephen Hawking incorporates the saying into the beginning of his 1988 book A Brief History of Time : [20]
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 centre 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!"
Former U.S. Supreme Court Justice Antonin Scalia discussed his "favored version" of the saying in a footnote to his 2006 plurality opinion in Rapanos v. United States : [21]
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."
Microsoft Visual Studio had a gamification plug-in that awarded badges for certain programming behaviors and patterns. One of the badges was "Turtles All the Way Down", which was awarded for writing a class with 10 or more levels of inheritance. [22]
In a TED-Ed video discussing Gödel's incompleteness theorems, the phrase "Gödels all the way down" is used to describe the way in which one can never get rid of unprovable true statements in an axiomatic system. [23]
A cosmological argument, in natural theology, is an argument which claims that the existence of God can be inferred from facts concerning causation, explanation, change, motion, contingency, dependency, or finitude with respect to the universe or some totality of objects. A cosmological argument can also sometimes be referred to as an argument from universal causation, an argument from first cause, the causal argument, or the prime mover argument. Whichever term is employed, there are two basic variants of the argument, each with subtle yet important distinctions: in esse (essentiality), and in fieri (becoming).
Epistemology is the branch of philosophy concerned with knowledge. Epistemologists study the nature, origin, and scope of knowledge, epistemic justification, the rationality of belief, and various related issues. Debates in contemporary epistemology are generally clustered around four core areas:
In epistemology, the regress argument is the argument that any proposition requires a justification. However, any justification itself requires support. This means that any proposition whatsoever can be endlessly (infinitely) questioned, resulting in infinite regress. It is a problem in epistemology and in any general situation where a statement has to be justified.
The teleological argument is an argument for the existence of God or, more generally, that complex functionality in the natural world which looks designed is evidence of an intelligent creator.
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea, primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno devised these paradoxes to support his teacher Parmenides's philosophy of monism, which posits that despite our sensory experiences, reality is singular and unchanging. The paradoxes famously challenge the notions of plurality, motion, space, and time by suggesting they lead to logical contradictions.
"What the Tortoise Said to Achilles", written by Lewis Carroll in 1895 for the philosophical journal Mind, is a brief allegorical dialogue on the foundations of logic. The title alludes to one of Zeno's paradoxes of motion, in which Achilles could never overtake the tortoise in a race. In Carroll's dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument. Ultimately, Achilles fails, because the clever tortoise leads him into an infinite regression.
Philosophical skepticism is a family of philosophical views that question the possibility of knowledge. It differs from other forms of skepticism in that it even rejects very plausible knowledge claims that belong to basic common sense. Philosophical skeptics are often classified into two general categories: Those who deny all possibility of knowledge, and those who advocate for the suspension of judgment due to the inadequacy of evidence. This distinction is modeled after the differences between the Academic skeptics and the Pyrrhonian skeptics in ancient Greek philosophy. In the latter sense, skepticism is understood as a way of life that helps the practitioner achieve inner peace. Some types of philosophical skepticism reject all forms of knowledge while others limit this rejection to certain fields, for example, knowledge about moral doctrines or about the external world. Some theorists criticize philosophical skepticism based on the claim that it is a self-refuting idea since its proponents seem to claim to know that there is no knowledge. Other objections focus on its implausibility and distance from regular life.
Pascal's wager is a philosophical argument advanced by Blaise Pascal (1623–1662), seventeenth-century French mathematician, philosopher, physicist, and theologian. This argument posits that individuals essentially engage in a life-defining gamble regarding the belief in the existence of God.
In philosophical epistemology, there are two types of coherentism: the coherence theory of truth, and the coherence theory of justification.
Meditations on First Philosophy, in which the existence of God and the immortality of the soul are demonstrated is a philosophical treatise by René Descartes first published in Latin in 1641. The French translation was published in 1647 as Méditations Métaphysiques. The title may contain a misreading by the printer, mistaking animae immortalitas for animae immaterialitas, as suspected by A. Baillet.
The Kalam cosmological argument is a modern formulation of the cosmological argument for the existence of God. It is named after the Kalam, from which its key ideas originated. William Lane Craig was principally responsible for giving new life to the argument in the 20th century, due to his book The Kalām Cosmological Argument (1979), among other writings.
An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor.
Originally, fallibilism is the philosophical principle that propositions can be accepted even though they cannot be conclusively proven or justified, or that neither knowledge nor belief is certain. The term was coined in the late nineteenth century by the American philosopher Charles Sanders Peirce, as a response to foundationalism. Theorists, following Austrian-British philosopher Karl Popper, may also refer to fallibilism as the notion that knowledge might turn out to be false. Furthermore, fallibilism is said to imply corrigibilism, the principle that propositions are open to revision. Fallibilism is often juxtaposed with infallibilism.
In epistemology, the Münchhausen trilemma is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without appealing to accepted assumptions. If it is asked how any given proposition is known to be true, proof in support of that proposition may be provided. Yet that same question can be asked of that supporting proof, and any subsequent supporting proof. The Münchhausen trilemma is that there are only three ways of completing a proof:
Epistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope (limitations) of knowledge. It addresses the questions "What is knowledge?", "How is knowledge acquired?", "What do people know?", "How do we know what we know?", and "Why do we know what we know?". Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims.
The World Turtle, also called the Cosmic Turtle or the World-bearing Turtle, is a mytheme of a giant turtle supporting or containing the world. It occurs in Hindu mythology, Chinese mythology, and the mythologies of some of the indigenous peoples of the Americas. The comparative mythology of the World-Tortoise discussed by Edward Burnett Tylor (1878:341) includes the counterpart World Elephant.
Bradley's regress is a philosophical problem concerning the nature of relations. It is named after F. H. Bradley who discussed the problem in his 1893 book Appearance and Reality. It bears a close kinship to the issue of the unity of the proposition.
In philosophy, the problem of the creator of God is the controversy regarding the hypothetical cause responsible for the existence of God, on the assumption God exists. It contests the proposition that the universe cannot exist without a creator by asserting that the creator of the Universe must have the same restrictions. This, in turn, may lead to a problem of infinite regress wherein each new presumed creator of a creator is itself presumed to have its own creator. A common challenge to theistic propositions of a creator deity as a necessary first-cause explanation for the universe is the question: "Who created God?" Some faith traditions have such an element as part of their doctrine. Jainism posits that the universe is eternal and has always existed. Isma'ilism rejects the idea of God as the first cause, due to the doctrine of God's incomparability and source of any existence including abstract objects.
"Why is there anything at all?" or "why is there something rather than nothing?" is a question about the reason for basic existence which has been raised or commented on by a range of philosophers and physicists, including Gottfried Wilhelm Leibniz, Ludwig Wittgenstein, and Martin Heidegger, who called it "the fundamental question of metaphysics".