Temporal paradox

Temporal Paradoxes are one elements of time travel, not just for the Time Lords but all time active civilizations.

The Faction Paradox (as the name suggests) practically worshipped the act of a Paradox, not just for the idea, but the power that a Paradox evokes. (EDA: Alien Bodies, Unnatural History, Interference)

Grandfather Paradox
The most commonly known form of a paradox is the Grandfather Paradox. In some organizations it is a symbol of almost god-like power. The Grandfather Paradox is as follows (in many variations):


 * If I went back in time and killed my grandfather before my father was born, my father would not be born, and thus I would not be able to travel back in time... so my grandfather lives, and my father is born, and thus I am alive and able to travel back in time...

Other
Another example is when Rose Tyler saved her father, Pete Tyler. There was also the problem that an earlier Doctor and Rose Tyler were watching this change in the timeline.

When the paradox occurred, the earlier versions of the Doctor and Rose disappeared and the inside of the Doctor's TARDIS disappeared, rendering it an empty police box-shaped shell. There also seemed to be unusual occurrences such as a song being played before it was made or the first phone call being repeated. As well, the car which should have killed Pete Tyler, kept on following him in order to repeat the accident. Eventually, the Reapers were able to break into normal reality, where they tried to eat all the people they could find.

Pete Tyler was able to fix the paradox by getting killed by the car. This caused all the damage that was done by the Reapers and the paradox to repair itself. Though there were still changes to the timeline, Peter's death was apparently enough. (DW: Father's Day)


 * The Doctor mentioned that when the Time Lords still existed, creation of paradoxes was impossible and that any paradoxes that did manifest could be fixed. This might mean that paradoxes weren't possible or common before the Last Great Time War or they had different effects.