At first reading this, it may not appear that this post really belongs in a mathematics forum, but on closer attention it may be found that its a very appropriate place for this seeming paradoxial word problem. Its nothing new, just (as far as I know) still mathematically/logically unanswered. I would prefer it to be spoken for or against on strictly mathematical terms, but verbal logic may also help.
First assumption: Paradoxes cannot exist. Human misunderstanding on logic/truth can.
Second assumption: Time travel is possible.
Third assumption: There will be at least more than one moderator considering deleting or moving this post.
No doubt most are familiar with this paradox that ancient greeks used to stay up all night debaiting and exausting that time period's supply of coffee:
Its an established fact that Cretens always lie.
A certain man who is of a set of people who are considered Cretens makes the statement "Cretens always lie" thus making a statement that is truthfull. But then, still being a Creten, he is still among the set of those considered Cretens, and having told the truth, the fact exists that there is at least one Creten who tells the truth, and in effect, his statement becomes a lie.
Now, if the paradoxial nature of this situation has at some point been solved, and there is no logical contradiction anymore due to modified understanding, then I would invite this post to be deleted as its irrelevent. If not, then here is a suggested answer to this paradox, making it logically sound, and then no longer a paradox.
So this man, who is a Creten (a peaple who only speak lies) makes a truthful statement. If it were left to the above we will see him either simultaniously speaking a falsehood and a truth, or we would see him perpetually being changed from the status of a liar to a truthteller to a liar to a truthteller...and so on.
Let us make another assumption, as a means to kill the paradox, and with it a few others that revolve around similar logic.
Assumption: Regardless of his geneology and cultural status, his statement of truth causes him no longer to be a Creten. Hense, at the moment he said "Cretens always lie" he stopped being a Creten.
Now, being that he himself is reading this, he finds it utterly rediculous that his ability to tell the truth altered his inherent status as a Creten by this new assumption, as it would be the logical equivilent of being changed from a boy to a girl based on the influence of nothing more than mere thought and words.
So to prove that such reasoning is foolish (he believes his geneology can't be altered based on his actions) and wishes to prove the paradox can exist he decides to travel back in time before he was concieved to kill his great grandfather. He expects that doing so will rule out his existence, as this would be the assumed case:
He exists. He goes back to kill his great grandfather, causing his existence to be annulled before it was concieved. If he did not exist, he couldn't kill his grandfather. Likewise, as his argument goes, its meant to be a paradox mentally and likely he will not be able to kill his grandfather as the governing dynamics of reality will probobly show his grandfather will always succesfully evade his murderer.
But we are saying that if he kills his grandfather, then the truth is the man was not his grandfather, and when the Creten discoveres who is real grandfather is, he will kill him, only to discover his real grandfather still exists and has yet to be killed, and he murdered two strangers in cold blood. So we have a repetition somewhat similar to the above. (e.i. the man who is responsible for his existence keeps rerouting itself everytime the Creten interpheres with his own existence.)
This may seem foolish, but it can be illustrated by a real phenomenon: As long as an electrical positive and negitive potential exists and a number of closed routes exist between the two, the electricity will always take the path of least resistence from its origin to its goal. If that path is blocked, it will find a new path of least resistence untill every concievable path is blocked. Let us assume that there is an infinite number of paths the electricity will always take in an infinitely large system, and its path can never be truly blocked.
In a system where time is a mental illusion and cause and effect (governed by the speed of light) are the only true dynamics, the Creten will never truly be able to block the path to his own existence, as an infinite number of possibilites exist and they will always reroute to give the final outcome, regardless of interpherence. (Or more simply said, he merely traveled backward in cause and effect and changed the dynamics that led to his own existence.)
So you might then realize that when he killed his great-grandfather, his geneology even preceding his great grandfather was changed, and traveling back in time did not merely change time from that point onward, but time previous to it and after it.
I'm certain this translates to a very simple argument in mathematics. I'm also certain many will not agree and this post will be deleted or reassigned to a different catagory.