A paradox or temporal paradox is divided into two broad categories.The first is the grandfather paradox which is a suggested irony in time travel which brings about a contradiction through altering occurrences in the past. It is explained as follows like this: a time traveller travels back in time and kills his/her grandfather, destroying the possibility of one of his/her parents ever being born. As a result of this, the time traveller also cannot be born. Now, if the time traveller was never born, then he/she can not go through time to kill his/her grandfather, meaning that since the time traveller is already born, how then could he have killed his grandfather? This negation of the entire series of events is referred to as inconsistent causal loop.
The grandfather paradox is one of the strongest arguments against the belief in the possibility of time travel and was first mentioned in 1931, and although the story only addresses the act of killing one’s grandfather, it doesn't only address that particular story by addresses any action that involves altering the past.
The second category of paradoxes is called the consistent causal loop, let us look at it this way: A songwriter travels into the future and steals a record-shattering song. The songwriter now gives the song to one of his most talented clients to sing. Then, that talented client eventually grows up to be that same person the songwriter stole the song from to begin with.
According to the Novikov self-consistency principle, there is a way time travel can occur without the danger of a paradox. According to this principle, physics or time machines can only work in obedience to the universal laws of physics, and therefore only self-consistent occurrences can happen. Whatever a time traveller does in his/her journey to the past must have already been part of history in one way or the other all along.
Critical thinking suggests that paradoxes are logical arguments against and for time travel. The grandfather paradox is extremely reasonable in the sense that it doesn't not only apply to someone going back in time to kill a parent. Take, for instance, I travel five days back in time wearing a red jacket I bought days back and in my travel back in time, I returned the jacket immediately I bought it, what then happens to the same jacket I wore back in time?
But at the same time, the argument of the consistent causal loop also makes some sense. Since nature has a way of balancing itself, it is plausible to believe that the past can only be altered, the eventual outcome in the future cannot be changed, one way or another, nature looks for a way to balance it out and ensure that the same outcomes are gotten.
There is also another time travel model called the post-selected model; this model explains things this way: imagine you are the time traveller sent to kill your grandfather. The post-selected time travel model basically makes your grandfather impossible to kill. No matter what you try or do, you will never succeed in killing him. This is also a plausible argument in support of time travel.
The truth is that until we actually succeed in travelling through time, we will never know which of these theories is true.