Contradiction on the people in the future's views regarding the grandfather paradox
In Tenet, the people of the future suffer because of the climate change of the people of the present. Therefore, the people of the future use things (weapons...) that travel back in time in order to kill the people of the present.
Here the question of the grandfather paradox arises: Do you die if you travel back in time and kill your grandfather or other ancestors? In Tenet, it is clearly stated that the people of the future think that the answer to this question is no - they think they can kill their ancestors without dying. Thus people of the future see no temporal paradox, instead, they simply believe changing their past (by killing the whole of humankind) does not change their present. At the same time, the people of the future believe that changing the climate of their past does make a change in their present. Isn`t this a clear contradiction?
My question is about this contradiction in the view of the people of the future, not about the logical inconsistencies of the grandfather paradox itself. Meaning: It does not matter what the grandfather paradox says about changes in the past but just what people of the future think that changes in their past mean. The assumptions of the people of the future are the ground of the whole story because they are the reason why the war starts.
Edit: My question is based on linear thinking where time goes forward, i.e. the cause precedes the effect. In linear time we can ask things like "do they think changing the past changes their present?". But the machine the people of the future breaks this linear time flow and with this the contradiction described in my question vanishes. (I suggested this edit to the answer but it was not approved for some reason.)
They simply believe changing their past (by killing the whole humankind) does not change their present. At the same time the people of the future believe that changing the climate of their past does make a change in their present. Isn`t this a clear contradiction?
The people in the future are not trying to "change the climate of their past." They're trying to trigger the algorithm in their present to invert the entropy of the world, and if successful, this will result in the complete destruction of everyone and everything in the present. There is no contradiction between their belief regarding the grandfather paradox and what they're trying to do.
The people in the future's motivations for triggering the algorithm are discussed by Sator and The Protagonist in this dialogue (emphasis mine):
Sator: Now time itself switches direction. The same sunshine we basked in will warm the faces of our descendants' generations to come.
Protagonist: How could they wanna kill us?
Sator: Because their oceans rose and their rivers ran dry. Don't you see? They have no choice but to turn back. We're responsible.
Sator: Knowing this, do you still want me to stop?
Protagonist: Yes. Each generation looks out for its own survival.
Sator: That's exactly what they're doing.
Protagonist: But not you. You're a traitor. Bringing death to all, because you have no life of your own left.
Sator: When I'm done, life continues.
The main goal of the people in the future is to save their own world. Their main goal is their survival. To survive, they're looking to trigger the algorithm in their present to invert the entropy of the world. The "grandchild" doesn't care if their "grandfather" gets killed in the process.
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What does the grandfather paradox show?The grandfather paradox is a potential logical problem that would arise if a person were to travel to a past time. The name comes from the idea that if a person travels to a time before their grandfather had children, and kills him, it would make their own birth impossible.
Does the grandfather paradox make sense?The first solution to this famous paradox is that when you go back in time to kill your grandfather, you're not going back to your own history, but a copy of your history, and everything you do in this version of your history will affect the alternate future of that universe, not your own.
What is the solution to the grandfather paradox?This scenario was first suggested in short stories published in the US science fiction magazine Amazing Stories as early as 1929/1930 in various levels of detail, and with various motivations for people wanting to kill their own grandfathers.
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