Right, this thread does just seem like it's been created to mock the other Philosophy threads but I'll bite.
Basically you are talking about is a paradox (as opposed to the "time space continum"). A more commonly known paradox of this variety is the Grandfather Paradox, which involves going back in time and killing your grandfather before your fathers (or mothers) conception, thus preventing your own existance.
One scientist (it might have been Hawking, but not sure) theorised that if time travel ever advanced to such a high level that these kind of paradoxes became possible (ie. if human beings were able to choose an exact place and time which they wanted to travel too), then the Universe would simply cancel the paradox out.
For example, if you went back to before the conception of one of your parents in an attempt to kill your grandfather then the attempt may either fail (gun jamming, only being wounded etc.) or it will turn out that the man you thought was your biological grandfather, actually wasn't, and therefore your existance wasn't prevented by his death.
This does seem like the only logically solution to that particular type of paradox, as by nature they are ment to be unsolvable.
Another famous type of paradox is a self-fullfilling paradox, which is where information or an object appears from nowhere.
For example, a older man (or woman) comes up to you and tells you they are from the future and gives you the secret to time travel. You then create a time machine and begin travelling through time. On your travels you find yourself back in your own past and realise that it was you who gave yourself the information regarding time travel and pass on the information once more.
This becomes a paradox as the information never actually originated anywhere, meaning that noone actually invented time travel. The most popular explanation for these type of paradoxes seems to be that after you got the information from yourself, but before you passed it back on, someone else developed time travel in the same way without ever having met you and you observed this information too. Therefore, even though you received the information from yourself first it did orginate from somewhere.
The paradox becomes more complex when it becomes objects rather than information, as going back in time and giving yourself an object would cause the age of the object to rise by an infinite amount (as it is constantly going around the cycle between your past and future selves).
An explanation for this type of paradox is that before you go back in time to give the object to yourself, you replace it with an exact replica, therefore each object only ages one extra cycle rather than an infinite amount. This explanation was given in the short story By His Bootstraps by Robert A. Heinlein (a fantastic read for either paradox fans, time-travel fans or just sci-fi fans in general) in which a character is given a notebook full of information from the future, but before it travels back into the past, he copies up all the notes exactly into a replica notebook, so the books doesn't age infinitly.
There are many other different types of paradox, but I'll don't have time to list them all now, so I'll add more later (probably after work).