"Traditionally, another reason physicists dismissed the idea of time travel was because of time paradoxes ... This is important, because science is based on logically consistent ideas; a genuine time paradox would be enough to completely rule out time travel. These time paradoxes can be grouped into several categories:
Grandfather paradox. In this paradox, you alter the past in a way that makes the present impossible. For example, by going back into the distant past to meet the dinosaurs, you accidentally step on a small, furry mammal that is the original ancestor of humanity. By destroying your ancestor, you cannot logically exist.
Information paradox. In this paradox, information comes from the future, which means that it may have no origin. For example, let’s say a scientist creates a time machine and then goes back in time to give the secret of time travel to himself as a youth. The secret of time travel would have no origin, since the time machine the youthful scientist possesses was not created by him but was handed to him by his older self.
Bilker’s paradox. In this kind of paradox, a person knows what the future will be and does something that makes the future impossible. For example, you make a time machine to take you to the future, and you see that you are destined to marry a woman named Jane. However, on a lark, you decide to marry Helen instead, thereby making your own future impossible.
The sexual paradox. In this kind of paradox, you father yourself, which is a biological impossibility. In a tale written by the British philosopher Jonathan Harrison, the hero of the story not only fathers himself, but he also cannibalizes himself. In Robert Heinlein’s classic tale “All You Zombies,” the hero is simultaneously his mother, father, daughter, and son—that is, a family tree unto himself. (See the notes for details. Unraveling the sexual paradox is actually rather delicate, requiring knowledge of both time travel and the mechanics of DNA.)"
–Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos by Michio Kaku