A jocular expression of the infinite regress problem in cosmology posed by the unmoved mover paradox – a philosophical concept described by Aristotle as a primary cause or mover of all the motion in the universe. As is implicit in the name, the unmoved mover is not moved by any prior action. Aristotle argues, in Book 8 of the Physics Book 12 of the Metaphysics: “there must be an immortal, unchanging being, ultimately responsible for all wholeness and orderliness in the sensible world.”
“Turtles all the way down” is a phrase that was popularized by Stephen Hawking in 1988. The turtle metaphor in the anecdote represents a popular notion of a so-called primitive cosmological myth, the flat earth supported on the back of a World Turtle. A person who believes the Earth rests on a giant turtle can thereby also deny the existence of the universe.
A comparable metaphor describing the circular cause and consequence for the same problem is the chicken and egg problem – which came first? Another metaphor addressing the problem of this infinite regression (as the turtles would imply), albeit not in a cosmological context, is Quis custodiet ipsos custodes? – a phrase coined by the Roman poet Juvenus which is often translated as “Who watches the watchmen?” The same problem in epistemology is known as the Münchhausen Trilemma.
The Trilemma was named after Baron Münchhausen, who allegedly pulled himself (and the horse he was sitting on) out of a swamp by his own hair. This Trilemma is a philosophical term coined to stress the purported impossibility to prove any truth even in the fields of logic and mathematics. If we ask of any knowledge: “How do I know that it’s true?”, we may provide proof; yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen Trilemma is that we have only three options when providing proof in this situation:
- The circular argument, in which theory and proof support each other (i.e. we repeat ourselves at some point) “Only an untrustworthy person would run for office. The fact that politicians are untrustworthy is proof of this.”
- The regressive argument, in which each proof requires a further proof ad infinitum (i.e. we just keep giving proofs, presumably forever) “A is proven by B, which is proven C, which proven by D etcetera ad infinitum.”
- The axiomatic argument, which rests on accepted precepts (i.e. we reach some bedrock assumption or certainty) “A. Baron Münchhausen exists, B. Baron Münchhausen has got hairs on his head etcetera.”
The first two methods of reasoning are fundamentally weak, and because the Greek sceptics advocated deep questioning of all accepted values and refused to accept (unconditional axiomatic) proofs of the third sort. The trilemma, then, is the decision among these three equally unsatisfying options.
Back to turtles. The most widely known version of the Turtles All The Way Down story 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 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!”
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.”
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.
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.”
The fact is the world does not rest on elephants, turtles or any other animal for that matter. However, the reasoning and philosophical attempts to prove a possibility of there being a giant tortoise on which the earth can rest are fascinating. Just as fascinating as the cultures out of which these beliefs have emerged.
To quote comedian Rich Hall: “This is why America has a space program.”
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