Editing Paradox (section)

=== Other elements ===
Other paradoxes involve false statements and [[half-truth]]s or rely on hasty assumptions (A father and his son are in a car crash; the father is killed and the boy is rushed to the hospital. The doctor says, "I can't operate on this boy. He's my son." There is no contradiction, the doctor is the boy's mother.).

Paradoxes that are not based on a hidden error generally occur at the fringes of context or [[language]], and require extending the context or language in order to lose their paradoxical quality. Paradoxes that arise from apparently intelligible uses of language are often of interest to [[logic]]ians and [[philosopher]]s. "This sentence is false" is an example of the well-known [[liar paradox]]: it is a sentence that cannot be consistently interpreted as either true or false, because if it is known to be false, then it can be inferred that it must be true, and if it is known to be true, then it can be inferred that it must be false. [[Russell's paradox]], which shows that the notion of ''the [[set (mathematics)|set]] of all those sets that do not contain themselves'' leads to a contradiction, was instrumental in the development of modern logic and set theory.<ref name=":1" />

[[Thought experiment]]s can also yield interesting paradoxes. The [[grandfather paradox]], for example, would arise if a [[time travel]]er were to kill his own grandfather before his mother or father had been conceived, thereby preventing his own birth. This is a specific instance of the [[butterfly effect]]{{snd}}in that any interaction a time traveler has with the past would alter conditions such that divergent events "propagate" through the world over time, ultimately altering the circumstances in which the time travel initially takes place.

Often a seemingly paradoxical conclusion arises from an inconsistent or inherently contradictory definition of the initial premise. In the case of that apparent paradox of a time traveler killing his own grandfather, it is the inconsistency of defining the past to which he returns as being somehow different from the one that leads up to the future from which he begins his trip, but also insisting that he must have come to that past from the same future as the one that it leads up to.