The Murdered Grandfather Paradox is a proposed paradox about time travel, first described (under this title) by science fiction writer Rene Barzhavel in his 1943 book Le voyageur imprudent.
The paradox is this: suppose that a person with the help of a time machine went back to the past and killed his biological grandfather before the latter met the traveler's grandmother. As a result, one of the traveler's parents (and, as a consequence, the traveler himself) would never have been born. This means that he ultimately could not travel in time, which in turn means that his grandfather would have survived and the traveler would have been born, which allowed him to travel in time and kill his grandfather. Thus, every possibility implies a denial of itself, creating a logical paradox.
The option for his resolution is as follows: the fact that the time traveler is living in the present means that he simply does not seek to kill his progenitor. This means that you can act with complete freedom, because whatever you do in the past, you cannot change the present, because its consequences are already being felt.
Despite the name, the murdered grandfather paradox considers more than just the impossibility of being born. First of all, it concerns any actions that make it impossible to travel in time. The example of the name of the paradox is only the most often "coming to mind" if you choose from the whole range of such possible actions. Another example would be using scientific knowledge to invent a time machine, then going back in time and (be it murder or otherwise) hindering scientists from working on what would ultimately lead to the information you used to invent a time machine. The equivalent paradox is known in philosophy as "autoinfanticide": going back in time and killing oneself in childhood.
The murdered grandfather paradox is often used to assert that time travel to the past is impossible. However, a number of hypotheses have been proposed to avoid the paradox: for example, the assumption that the past cannot be changed, therefore, the grandfather must have already experienced an attempted murder (as mentioned earlier), or that a time traveler creates an alternative timeline. in which he will never be born.