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A predestination paradox (also called causal loop, causality loop, and, less frequently, closed loop or closed time loop) is a paradox of time travel that is often used as a convention in science fiction. It exists when a time traveler is caught in a loop of events that "predestines" or "predates" them to travel back in time. Because of the possibility of influencing the past while time traveling, one way of explaining why history does not change is by saying that whatever has happened must happen. A time traveler attempting to alter the past in this model, intentionally or not, would only be fulfilling their role in creating history as we know it, not changing it. Or that the time-traveler's personal knowledge of history already includes their future travels to their own experience of the past (for the Novikov self-consistency principle).
In layman's terms, it means this: the time traveller is in the past, which means they were in the past before. Therefore, their presence is vital to the future, and they do something that causes the future to occur in the same way that their knowledge of the future has already happened. It is very closely related to the ontological paradox and usually occurs at the same time.
Temporal causality loop 
A temporal causality loop or predestination paradox is a theoretical phenomenon, which is said to occur when a chain of cause-effect events is circular. For instance, if event A causes event B, and event B causes event C, and event C causes event A, then these events are said to be in a causality loop.
The concept of a causality loop is functionally comparable to positive feedback, coproduction, and co-evolution, each of which describes how two or more variables of a system affect each other and therefore create each other, albeit with respect to different variables operating at different scales. Co-production is concerned with the variables of science/technology and society operating at the scale of society. Co-evolution is concerned with the variables of species operating at the scale of the evolutionary process. Causality loops and positive feedback are more abstract, and theoretically applicable to any set of variables operating at any scale.
Co-production, causality loops, and positive feedback are also related to the concept of virtuous circle and vicious circle – when the co-production, causality loop, or positive feedback produces a desirable effect, systems change is described as a virtuous circle; when they produce an undesirable effect, systems change is described as a vicious circle. Because these concepts refer to variables interacting in a complex system, they all produce unintended consequences – virtuous cycles produce unintended benefits and vicious cycles produce unintended harms. Although such consequences are unintended in the sense that no actor deliberately intends for them to occur, unintended consequences are an expected emergent property of systems change (in accordance with the ways Langdon Winner proposes that artifacts can ‘have politics’), and can be used as an indicator of systems change. Taking examples from the field of environmental justice, although community empowerment was an unintended benefit of bucket brigades (which were originally intended as a practical air sampling device), they are an indicator of systems change. On the flipside, although environmental injustices may be unintentional, they are an expected consequence of inequality in our socio-economic system.
Although these various concepts have significant differences, a result of the disciplines from which they emerged and the topics to which they’re applied, they are functionally comparable in that they satisfy a similar conceptual function of describing dynamic and generative interaction between two or more variables in a system.
A dual example of a predestination paradox is depicted in the classic Ancient Greek play 'Oedipus'. Laius hears a prophecy that his son will kill him and marry his wife. Fearing the prophecy, Laius pierces newborn Oedipus' feet and leaves him out to die, but a herdsman finds him and takes him away from Thebes. Oedipus, not knowing he was adopted, leaves home in fear of the same prophecy that he would kill his father and marry his mother. Laius, meanwhile, ventures out to find a solution to the Sphinx's riddle. As prophesied, Oedipus crossed paths with a wealthy man leading to a fight in which Oedipus slays him. Unbeknownst to Oedipus the man is Laius. Oedipus then defeats the Sphinx by solving a mysterious riddle to become king. He marries the widow queen Jocasta not knowing she is his mother.
A variation on the predestination paradoxes which involves information, rather than objects, traveling through time is similar to the self-fulfilling prophecy. For example, a man receives information about his own future, telling him that he will die from a heart attack. He resolves to get fit so as to avoid that fate, but in doing so overexerts himself, causing him to suffer the heart attack that kills him.
In these examples, causality is turned on its head, as the flanking events are both causes and effects of each other, and this is where the paradox lies.
One example of a predestination paradox that is not simultaneously an ontological paradox is the following. In 1850, Bob's horse was spooked by something, and almost took Bob over a cliff, had it not been for a strange man stopping the horse. This strange man was later honored by having a statue of him erected. Two hundred years later, Bob goes back in time to sight-see, and sees someone's horse about to go over a cliff. He rushes to his aid and saves his life.
In most examples of the predestination paradox, the person travels back in time and ends up fulfilling their role in an event that has already occurred. In a self-fulfilling prophecy, the person is fulfilling their role in an event that has yet to occur, and it is usually information that travels in time (for example, in the form of a prophecy) rather than a person. In either situation, the attempts to avert the course of past or future history both fail.
Examples from fiction 
Many fictional works have dealt with various circumstances that can logically arise from time travel, usually dealing with paradoxes. The predestination paradox is a common literary device in such fiction. Examples include Robert Heinlein's "—All You Zombies—", in which a young man is taken back in time and tricked into impregnating his younger, female self before he underwent a sex change, or The Man Who Folded Himself, a 1973 science fiction novel by David Gerrold that includes a series of similar paradoxes.
Prior to the use of time travel as a plot device, the self-fulfilling prophecy variant was more common. Shakespeare's Macbeth is a classic example of this. Others include the movie Minority Report, in which a police chief sets out to discover why psychics foretell him killing a man he has yet to meet, and a prophecy by Sybill Trelawney in the Harry Potter Universe about the birth of a wizard "with the power to vanquish" Voldemort.
See also