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Infinite regress is a series of an infinitely cascading propositions, where the validity of one depends on the validity of the one which follows and/or proceeds it. Viciously circular infinite regressions, are propositions which reintroduce their own proposition in the solution. One example of a viciously infinite regression arises in intelligent design creationism; which states that there are problems in the theory of Darwinian evolution by natural selection which can only be resolved by invoking a designer or first cause without proposing a solution to the immediate question "who designed the designer?" Despite that, the response to this is an example of special pleading, creationists assert that God is an eternal presence which did not need to create Himself. No evidence for this has ever been presented for peer review, or critical analysis of any kind.
The "Turtles all the way down" anecdote illustrates a popular example of infinite regress:
“”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!
|—Stephen Hawking, A Brief History of Time|