The Trolley Problem was firstly introduced by Philippa Foot in 1967. A trolley is facing a track with one man tied to the track and the only action he can take to avoid killing the man is to divert the trolley to another track which has five men tied to the track. This is a classical dilemma in ethics which serves the purpose to inspire your thinking and debate.
The dilemma is you would choose one dead or five dead. We are forced to use an utilitarian view in this case because whatever our choice is there will be death happens. I believe most people would choose to remain on the track with one man on it, if I am correct.
The arguments here are:
1. the act of moving to another track constitutes a participation in the moral wrong, making one partially responsible for the death when otherwise no one would be responsible;
2. the incommensurability of human lives.
The counterargument here is the moral obligation. The truth of simply being present in this situation and being able to influence its outcome constitutes an obligation to participate. Then, deciding to do nothing would be considered an immoral act if one values five lives more than one.
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