Pondering Paradoxes

So I'm in this Honors Colloquim that is all about Paradoxes. Most of the time I don't listen mainly because it causes my head to hurt and because I keep thinking about all the other things I could be doing with my time, but I actually listened to some of the subjects brought up. I thought I would share one of the items we talked about last night:

If time travel was possible, then you could go back to the time - say 1925 - when your maternal grandfather was an infant and kill him. Now if Grandpa died in 1925, your mother would never have been born, and consequently you would not exist. But then, who killed Grandpa?

(It has that whole Back to the Future theme going on!)