Unfortunately I gave up on Doctor Who after Tom Baker left. He is for me the quintessential doctor. But yes there are endless paradoxes in the show and they are never addressed properly - probably because they can't be.
And yes there are paradoxes in going to the future as well. So let's say your character does as you say and goes to the future to pick up a time machine from his grandson? Let's say he goes a hundred years into the future. Then he goes back and lives out his normal life in the present. At every stage of his life in the present he is changed because of his trip to the future. And that change must affect his behaviour and so in turn affects the world around him. So how does he live a life in the present that is exactly as it should have been had he not gone to the future?
The answers are of a course a philosophical grab bag. The first one is that he doesn't. He lives a different life, and that life is in fact the one that leads to the future where he can find a future in which his past self will arrive (have arrived? Tenses are problematic here.) But that leads us straight into destiny (not the predictions of greatness type.) It means that everything he does from the point at which he left until the point in the future at which he arrived is completely predestined. Not just him but everyone else as well. In short there is no such thing as either free will or chance.
The next choice is the parallel worlds options where, the world split at the point when he travelled to the future. Thus he went to "A" future but not necessarily "THE" future. So that future will not have to exist later. This runs into a different problem, one of energy. If every time I walk down a street and turn right instead of left a new possible universe is created, where did the energy forthat come from? It certainly didn't come from me turning in one direction. And we are talking about the creation of an entire universe here.
And the third option is the one touched on by Devor. The so-called B series of time. In the B series time does not change, but rather we move through it. It's rather like reading a book, where the present is the page your reading, but most importantly every other page in the book - those you've read (the past) and those still to read (the future) exist in exactly the same way that the present does. Now in this scenario time travel is paradox free. The reason is simply that if I take out my little red pen and start rewriting some of the pages from the past or the future, it makes no difference to the page I'm on. They are all already written.
However there are consequences too, and the biggest one is that cause and effect no longer applies to anything. For example if on one page I throw a ball and on the next it is flying, there is no actual reason for it to be flying save that someone wrote that it was. Because every page - every present - is completely indipendant of every other one. So if I change the previous page such that I no longer threw the ball, in the next page it still flies. Which simply means that the reason the ball flies has nothing to do with anything done on a previous page.
Hi psychotic, I gave up on Doctor Who when the Daleks learnt how to fly and climb stairs! I have a copy of the first Doctor Who book, ah, those were the days!
The book I'm writing (or not, more like procrastinating ) mixes magic, time travel and science. The time traveller is a magician who turns up in the wrong year to bring the MC back to the future, but she is still living in her own time and hasn't time travelled yet. She hasn't met him before and thinks he's deranged. So while he's trying to fix the machine, he hooks up with his Great Grandfather, who's worked with him in the future. He also finds another prototype of the time machine there that someone else has stolen. So, how many paradoxes have I got so far? And the MC hasn't even time travelled yet! This is only part of the main plot.
Btw this is just the prequel to my other WIP where the MC is stuck in the future. It's also complicated by having to write everyone's ancestors and descendants and work out the maths of how old everyone is. Plus the historical research necessary for writing about the past. But the time travel paradoxes are the most complicated aspects of this plot.
So far I have about 100 characters for the two books, including a couple of rabbits and a poodle used in magic acts.
I don't know whether to abandon this and write some chick lit with maybe three characters and an unrequited love story.
Having said that, I do like what I've written so far, it's just needing to know what rules will work. I'm reading a couple of time travel stories now as research.
Thanks for your help!
((Btw Sorry I haven't thanked anyone for their interesting post today, but I seem to have run out of those at the moment! ))