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The so-called "Grandfather paradox" refers to a situation in which a person could turn back in time and perform the murder of his or her grandfather because he or she hates him. It is known that grandfather's death occurred in the year of 1957 from natural causes. The time travelling machine though takes the grandson to 1921.The question which arises regards the very possibility for such a crime to take place. The matter has been formulated by a division in two possible arguments.
According to the first argument the grandson has what it takes and if he has what it takes he can kill the grandfather. The conclusion is that he can kill the grandfather. According to the second argument, he did not kill the grandfather and if he did no kill him then it mean he can not kill him. The conclusion thus deriving is that he can not kill the grandfather.
Analyzing the first argument it is obvious that a contradiction appears. If one kills his grandfather before he conceives an offspring who will be the very father of the assumed assassin, then the assassin, let's call him Tim can not be born in the first place. Assuming that Tim goes back in time after his parent what already born and has all the required conditions in order to kill his grandfather, it could be safe to assert that he kills him indeed. But there is a factual information according to which the grandfather died from natural causes. The contradiction is so big that it makes us consider the entire affirmation false.
The analysis of the second argument proves to be more complex. Just as Paul Horwich puts it, the fragility of the argument derives from the logical connection between the premises, which is directly causal. If Tim did not kill his grandfather then it results that he can not kill him. It is only common seems to acknowledge that there are many things which we do not do even if we can do them and the fact that we have not performed them does not determine our capacity of performing them.
Lewis on the other hand focused on the importance of the context. According to him the capacity of a person to do something depends on the circumstances he or she finds himself in. In other words somebody many be able to do something in a certain context and unable to do it if the context differs.
Therefore, from his perspective, both arguments can be proved to be unsound. Under the circumstances in which grandfather died in 1957, then it is obvious that Tim can not kill the grandfather and so the premise "Tim can kill grandfather" will result to be false. If we assume that there is no information regarding neither grandfather nor Tim after the date of 1920, then "Tim can kill grandfather" becomes a true premise and "Tim can't kill grandfather" is false. The overall argument is thus unsound.
It must be underlined that the arguments are proven to be unsound but for this different contexts are needed. According to Lewis' claim, in order to obtain a contradiction, the same context would be needed in order to prove both arguments to be false. Since this condition is not fulfilled then the "Grandfather paradox" can not be considered a challenge for the philosophical issue of time travelling.
The perdurantists believe that objects persist throughout time by having temporal parts. This means that a person is made up by herself today, herself yesterday and herself tomorrow. The sum of all these moments or better said, existing-in-time parts is what makes sure that a person benefits from an identity. This theory explains how a person is always the same but differs in many times as time goes by.
Endurantism on the other hand is a conception according to which things persist by being entirely present at different temporal stages. In other words it is against the view according to which one's identity can be divided into fragments. The focus is on the unity of the being. This means that today I am the person that I was yesterday and the person I will be tomorrow even if my characteristics change as I move on the time axis.
The main difference resides in the very approach to the matter, for one depends on Time while the other judges things from an atemporal point-of-view.
If we are to accept the perdurantist conception, one could probably better understand how it is possible for one to be divided on the time axis. From this point Lewis would be an endurantist as opposed to Horwich who would be a perdurantist. However, since both of them seem to have a common goal under these circumstances, and through this I refer to the fact they both prove the grandfather paradox arguments to be false, it might be argued that their difference of conceiving the entire situation is irrelevant.
The argument that Lewis brings when he discusses the importance of context is supported by the very conception that people are entities which basically remain the same in time. The power and the potential of their actions changes as the circumstances which they find themselves in change.
Therefore, the changes occur outside the being and not inside it. This would explain why the adepts of this particular philosophical view put so much emphasis on the "constancy" (and unity) of a person's identity throughout time.
It might be argued that under these circumstances the potential of the human being's actions is always fulfilled (or not) due to the circumstances the being finds herself in. this means that if Tim goes back in time with a will to kill his grandfather and he is not only has the means and the occasion to perform the murder, it is necessary for him to do it. However, it is absurd to say that our deeds do not have consequences. Therefore, if Tim kills his grandfather before the birth of one of his own parents, then the direct consequence is that Tim also ceases to exist. But it must be mentioned that he ceases to exist even before he can take into consideration the desire to kill his grandfather. It seems that the argument is cyclical and self contradictory.
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