Grandfather Paradox

Grandfather Paradox was as more or less a theory (though could be considered an individual). The speaker's chair in The Eleven-Day Empire was left vacant to be taken by the Grandfather upon his appearance to the Faction Paradox. (EDA: Interference: Book One).

The Faction Paradox hold the Grandfather Paradox up as one of the ultimate forms of paradoxes.

The Grandfather Paradox (Theory)
The theory behind the term 'Grandfather Paradox' runs thus:
 * If I went back in time and killed my grandfather, I would therefore not exist. Therefore I would not be able to travel back in time and kill my grandfather.
 * However as this is undone I continue to go forth and travel back in time and kill my grandfather...and so on.

This is a temporal paradox.

Grandfather Paradox (Individual)
According to Faction Paradox legend the Grandfather Paradox will have one arm, he removed one of his arms to remove the Time Lord branding/tattoo of a prisoner, and that he would have committed the ultimate paradox (most likely the aforementioned Grandfather Paradox (Theory).

From a corrupted timeline
Resulting from a corrupted timeline, from Faction Paradox corrupted biodata a future version of the Eighth Doctor modelled himself as the Grandfather Paradox. (EDA: The Ancestor Cell)