Editing Turtles all the way down

{{About|the saying|other uses|Turtles All the Way Down (disambiguation){{!}}Turtles All the Way Down}} 
{{Short description|Statement of infinite regress}} 

[[File:River terrapin.jpg|thumb|upright|alt=Three turtles of varying sizes stacked on top of each other with the largest at the bottom|The saying holds that the world is supported by an infinite stack of increasingly larger turtles.]]

"'''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.<ref name="Rocks" /> 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.<ref name="Locke 1689" /><ref name="Hume 1779" />

The expression has been used to illustrate problems such as the [[Regress argument (epistemology)|regress argument]] in [[epistemology]].

==History==
===Background in Hindu mythology===
{{further|World Turtle|World Elephant}}
[[File:PSM V10 D562 The hindoo earth.jpg|thumb|Four World Elephants resting on a World Turtle]]
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:
{{Verse translation|lang=la|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.<ref>J. Charpentier, 'A Treatise on Hindu Cosmography from the Seventeenth Century (Brit. Mus. MS. Sloane 2748 A).' Bulletin of the School of Oriental Studies, University of London 3(2) (1924), pp. 317-342, citing John Hay, ''De rebus Japonicis, Indicis, and Peruanis epistulæ recentiores'' (Antwerp, 1605, p. 803f.)</ref>}}

Veiga's account seems to have been received by [[Samuel Purchas]], who has a close paraphrase in his ''Purchas His Pilgrims'' (1613/1626), <!-- but note "tortoises" vs. the singular tortoise in Veiga-->
"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."<ref>Will Sweetman, [http://listserv.liv.ac.uk/cgi-bin/wa?A2=ind1004&L=indology&D=1&O=D&F=PP&P=1005 Indology mailing list], citing Dieter Henrich, 'Die "wahrhafte Schildkröte"' ''Hegel-Studien'' 2 (1963), pp.  281-91, and J.  Charpentier,   'A Treatise on Hindu Cosmography from the Seventeenth Century (Brit. Mus. MS. Sloane 2748 A).' Bulletin of the School of Oriental Studies, University of London 3(2) (1924), pp. 317-342.</ref> 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".<ref name="Locke 1689">John Locke (1689). ''[[An Essay Concerning Human Understanding]]'', Book II, Chapter XXIII, section 2</ref> 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 <!--sic; a common 19th-century spelling-->  made the world rest on an elephant, and the elephant on a tortoise, and had nothing to put under the tortoise."<ref>{{cite web|url=http://www.sniggle.net/Experiment/index.php?entry=excerpts04#04May52|title=TPL • Excerpts from H.D. Thoreau's journals (1852)|author=David M. Gross|work=The Picket Line|date=1852 }}</ref>

===Modern form===
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:

{{quote|"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!"<ref name="Rocks">{{cite news |newspaper=New-York Mirror |date=September 15, 1838 |volume=16 |number=12 |page=91 |title=Unwritten Philosophy |url=https://books.google.com/books?id=4n1NAAAAYAAJ&pg=PA91}}</ref>}}

Another version of the saying appeared in an 1854 transcript of remarks by preacher Joseph Frederick Berg addressed to [[Joseph Barker (minister)|Joseph Barker]]:

{{quote|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"<ref>{{cite book |last=Barker |first=Joseph |title=Great Discussion on the Origin, Authority, and Tendency of the Bible, between Rev. J. F. Berg, D.D., of Philadelphia, and Joseph Barker, of Ohio |publisher=J. B. Yerrinton & Son, Printers |date=1854 |location=Boston |page=48 |url=https://books.google.com/books?id=SGtYAAAAMAAJ&pg=PA48}}</ref>}}

[[File:William James b1842c.jpg|thumb|upright|[[William James]]]]

Many 20th-century attributions claim that philosopher and psychologist [[William James]] is the source of the phrase.<ref>[[Robert Anton Wilson]] (1983). [[Prometheus Rising]]. Phoenix, AZ: New Falcon Publishers. p. 25. {{ISBN|1-56184-056-4}}</ref> 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":

{{quote|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."<ref>{{cite journal |last=James |first=William |title=Rationality, Activity and Faith |journal=The Princeton Review |page=82 |date=July 1882 |url=http://quod.lib.umich.edu/m/moajrnl/acf4325.3-01.010/86:6?page=root;size=100;view=image}}</ref>}}

The linguist [[John R. Ross]] also associates James with the phrase:

{{quote|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<ref>{{cite thesis |first=John R. |last=Ross |author-link=John R. Ross |year=1967 |title=Constraints on variables in syntax |type=Doctoral dissertation |publisher=Massachusetts Institute of Technology |hdl=1721.1/15166 }} See page iv of the ms., page 4 of the electronic file.</ref>}}

== Turtle world, infinite regress and explanatory failure ==
The mythological idea of a ''turtle world'' is often used as an illustration of [[infinite regress]]es. 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.<ref name="Cameron">{{cite web |last1=Cameron |first1=Ross |title=Infinite Regress Arguments |url=https://plato.stanford.edu/entries/infinite-regress/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |date=2018}}</ref> 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.<ref name="Cameron"/><ref name="Maurin">{{cite book |last1=Maurin |first1=Anna-Sofia |title=Hommage À Wlodek |date=2007 |publisher=Department of Philosophy, Lund University |url=https://philpapers.org/rec/MAUIR |chapter=Infinite Regress - Virtue or Vice?}}</ref> 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 [[Infinite regress#Viciousness|vicious]].<ref name="Cameron"/><ref name="Huemer">{{cite book |last1=Huemer |first1=Michael |title=Approaching Infinity |date=2016 |publisher=New York: Palgrave Macmillan |url=https://philpapers.org/rec/HUEAI-2 |chapter=13. Assessing Infinite Regress Arguments}}</ref> There are different ways in which a regress can be vicious.<ref name="Huemer"/><ref name="Wieland">{{cite journal |last1=Wieland |first1=Jan Willem |title=Infinite Regress Arguments |journal=Acta Analytica |date=2013 |volume=28 |issue=1 |pages=95–109 |doi=10.1007/s12136-012-0165-1 |s2cid=170181468 |url=https://philpapers.org/rec/WIEIRA}}</ref> 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.<ref name="Huemer"/><ref name="Wieland"/> This is akin to the [[informal fallacy]] of [[begging the question]].<ref name="Clark">{{cite journal |last1=Clark |first1=Romane |title=Vicious Infinite Regress Arguments |journal=Philosophical Perspectives |date=1988 |volume=2 |pages=369–380 |doi=10.2307/2214081 |jstor=2214081 |url=https://philpapers.org/rec/CLAVIR|url-access=subscription }}</ref> 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''.<ref name="Huemer"/><ref name="Cameron"/> 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.<ref name="Cameron"/><ref name="Huemer"/>

==In epistemology and other disciplines==
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:<ref name="Fichte 1794">Fichte, J. G. (1794). Ueber den Begriff der Wissenschaftslehre oder der sogenannten Philosophie (Concerning the Conception of the Science of Knowledge Generally) (A. E. Kroeger, Trans.).</ref>{{page needed|date=November 2017}}

{{quote|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{{mdash}}who knows on what?{{mdash}}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:<ref name="Hume 1779">David Hume (1779). ''[[Dialogues Concerning Natural Religion]]'', part 4.</ref>

{{quote| 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:

{{quote|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.'}}

==Modern allusions or variations==
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 (song)|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]]''.<ref>{{cite web|last=Hendrickson|first=Matt|title=Sturgill Simpson: Country Philosopher|url=http://gardenandgun.com/articles/sturgill-simpson-country-philosopher/|website=Garden & Gun|date=2014|access-date=30 October 2017}}</ref> "Gamma Goblins ('Its Turtles All The Way Down' Mix)" is a remix by [[Ott (record producer)|Ott]] for the 2002 [[Hallucinogen (musician)|Hallucinogen]] album ''[[In Dub (Hallucinogen album)|In Dub]]''.<ref>{{Cite book|url=https://books.google.com/books?id=xxfGBQAAQBAJ&pg=PT154|title = The Local Scenes and Global Culture of Psytrance|isbn = 9781136944338|last1 = John|first1 = Graham St|date = 10 June 2010| publisher=Routledge }}</ref> ''[[Turtles All the Way Down (novel)|Turtles All the Way Down]]'' is also the title of a 2017 novel by [[John Green]] about a teenage girl with [[obsessive–compulsive disorder]].<ref>Senior, Jennifer (October 10, 2017).  [https://www.nytimes.com/2017/10/10/books/review-john-green-turtles-all-the-way-down.html "In John Green’s 'Turtles All the Way Down,' a Teenager’s Mind Is at War With Itself."]  ''The New York Times''.  Retrieved October 29, 2017.</ref>

Musician [[Captain Beefheart]] used the phrase in 1975 to describe playing with [[Frank Zappa]] and [[The Mothers of Invention]] (captured on the album ''[[Bongo Fury]]'') when he told Steve Weitzman of ''[[Rolling Stone]]'' that he "had an extreme amount of fun on this tour. They move awfully fast. I've never travelled this fast with the Magic Band—turtles all the way down."<ref>{{Cite magazine |last=Weitzman |first=Steve |date=July 3, 1975 |title=Zappa and the Captain Cook |url=http://www.beefheart.com/zappa-and-the-captain-cook-by-steve-weitzman/ |magazine=Rolling Stone}}</ref>

[[Stephen Hawking]] incorporates the saying into the beginning of his 1988 book ''[[A Brief History of Time]]'':<ref>{{cite book | author=Hawking, Stephen | title= A Brief History of Time | url=https://archive.org/details/briefhistoryofti00step_1 | url-access=registration | publisher=[[Bantam Books]] | date=1988 | isbn=978-0-553-05340-1}}</ref>

{{quote|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]]'':<ref>{{cite web |title=Rapanos v. United States |date=June 19, 2006 |at=Section VII, footnote 14 |url=https://www.law.cornell.edu/supct/html/04-1034.ZO.html#14 |via=Cornell Law School Legal Information Institute's Supreme Court collection}}</ref>

{{quote|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 (computer programming)|class]] with 10 or more levels of [[Inheritance (object-oriented programming)|inheritance]].<ref>{{cite web |title=The coding game: Microsoft's Visual Studio gets badges, achievements and leaderboard |date=January 18, 2012 |url=https://www.geekwire.com/2012/coding-fun-microsofts-visual-studio-badges-leaderboard/}}</ref>

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.<ref>{{cite web |last1=du Sautoy |first1=Marcus |title=The paradox at the heart of mathematics: Gödel's Incompleteness Theorem |url=https://www.ted.com/talks/marcus_du_sautoy_the_paradox_at_the_heart_of_mathematics_godel_s_incompleteness_theorem |website=TED Talks |access-date=19 October 2023 |language=en |date=20 July 2021}}</ref>

==See also==<!-- PLEASE RESPECT ALPHABETICAL ORDER -->
{{div col|colwidth=22em}}
* {{annotated link|Axiom of foundation}}
* {{annotated link|Cartesian theater}}
* {{annotated link|Chicken or the egg}}
* {{annotated link|Cosmological argument}}
* {{annotated link|Discworld}}
* {{annotated link|God of the gaps}}
* {{annotated link|Homunculus argument}}
* {{annotated link|Kurma}}
* {{annotated link|Matryoshka doll}}
* {{annotated link|Münchhausen trilemma}}
* {{annotated link|Primum Mobile}}
* {{annotated link|Unmoved mover|Primum movens}}
* {{annotated link|Problem of the creator of God}}
* {{annotated link|Pyrrhonism}}
* {{annotated link|Siphonaptera (poem)|''The Siphonaptera''}}
* {{annotated link|Teleological argument}}
* {{annotated link|Transfinite induction}}
* {{annotated link|Turtle Island (Native American folklore)}}
* {{annotated link|World Turtle}}
* {{annotated link|Yertle the Turtle and Other Stories|''Yertle the Turtle and Other Stories''}}
{{div col end}}

==References==
===Notes===
{{Reflist|group=upper-alpha}}

===Citations===
{{reflist|30em}}

==Further reading==
*{{cite journal |url=https://muse.jhu.edu/article/708768/summary |title=Turtles All the Way Down: Foundation, Edifice, and Ruin in Faulkner and McCarthy |first1=Robert |last1=Rudnicki
|journal=[[The Faulkner Journal]] |publisher=[[Johns Hopkins University Press]] |volume=25 |number=2 |date=Spring 2010 |pages=23–52 |doi=10.1353/fau.2010.0002|s2cid=171782610 |url-access=subscription }}

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