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Destiny was, according to Vengorr, "the belief that the life's path is preordained". (AUDIO: Living Legend) Peri Brown thought that destiny was "just a fancy name for blind chance", while Yrcanos said that, if that were true, life would be meaningless. (TV: Mindwarp) As a time-traveller, the Doctor had a very different perspective on destiny. (AUDIO: Davros)
The Second Doctor told his companions Polly Wright and Ben Jackson that the TARDIS' seemingly random journeys were controlled by destiny, and that "if we just obey destiny blindly, all will be well", (PROSE: Only a Matter of Time) though he would later find out the truth. (TV: The Doctor's Wife) The Eleventh Doctor didn't believe in it, specifically that "there's no such thing as fortelling, trust a time traveler." (TV: The Doctor, the Widow and the Wardrobe)
Destiny was something that was not to be messed with. Amy Pond asked her younger self, "You're asking me to defy destiny, causality, the nexus of time itself, for a boy?" The Eleventh Doctor thought it impossible to "defeat pre-destiny", which he did manage to do. (TV: The Girl Who Waited) While something may have been erased from destiny, its possibility was still imprinted on the structure of the universe. (PROSE: Falls the Shadow)
When Donna Noble parked her car right next to where the Tenth Doctor would park his TARDIS, she said, "This is like destiny!" (TV: Partners in Crime) The Meta-Crisis Tenth Doctor later confirmed this:
It's like we were always heading for this. You came to the TARDIS. And you found me again. Your granddad. Your car. Donna, your car. You parked your car right where the TARDIS was going to land. That's not coincidence at all! We've been blind. Something's been drawing us together for such a long time.
"Destiny", or rather Dalek Caan's manipulation of time, led the Doctor to meet Donna twice, and her grandfather, so that Donna could become the Doctor-Donna and the Meta-Crisis Doctor could be created. This became instrumental in the defeat of Davros' plan to destroy all universes through the reality bomb. (TV: Journey's End)
After the Eleventh Doctor lost Clara Oswald again in Victorian London on Christmas 1892, he began searching for another version of her, hoping that, if he just wandered around enough, he'd find her eventually, "like destiny, sort of". A young Clara Oswald, who the Doctor did not recognise, called destiny "rubbish". (WC: The Bells of Saint John: A Prequel)
The Sixth Doctor said that "an advanced culture manipulating the destinies of a less developed civilisation" must be stopped; the Valeyard called these words arrogant in a Zenobia court. (TV: Mindwarp) Earlier in his time, Davros asked the Fourth Doctor if he thought he could change the course of destiny, to which the Doctor replied "let's just say I might tamper with it." (TV: Destiny of the Daleks)
When one began to reach their goals, such as De Flores coming close to forming the Fourth Reich, they felt that their destiny was approaching. In travelling to 1988 Lady Peinforte said that "destiny beckons." (TV: Silver Nemesis)