Thought Experiments. Philosophers often engage in 'thought experiments'. They describe hypothetical situations, sometimes realistic and sometimes fantastical, and then ask about our 'intuitions' regarding the case. 'Intuition' is a key term in modern philosophical methods though philosophers disagree about what they are and what their significance is. I will here just take them to be your thoughtful judgments about various things.
Why would philosophers do this? Oddly, though this procedure is very common, there is no general agreement on what these thought experiments show or why they are valuable. But there is general agreement that we can use these thought experiments to help test what we really believe about various things. Here is one sort of use of the thought experiment. Suppose you say 'I believe such and such', where 'such and such' refers to a general principle of some kind. I wonder whether you really do believe that general principle. So I devise a thought experiment, a hypothetical situation, about which I ask you to make a judgment.
It is interesting that people often make judgments in these thought experiments that differ from the general principles they think they believe. In such cases, we can suggest that you might not really believe he general principle that you thought you believed! Here is a second use of thought experiments. Suppose you simply do not have an opinion about a general principle regarding a particular subject matter. I can devise thought experiments and ask your intuitions about those cases. Even though you were unable to state a general principle, you might be able to make many particular judgments that, bit by bit, suggest a general principle that might underlie those judgments.
Philippa Foot devised the Trolley Problem in her article "The Problem of Abortion and the Doctrine of the Double Effect" (1967). Soon after, variants were developed by Judith Thomson and other philosophers. More recently, moral psychologists have taken over the Trolley Problem, developed numerous variants on it, and have collected judgments about these cases from many people in a number of countries.
What is the Purpose of this Thought Experiment? The Trolley Problem can be seen as a way to test whether our judgments are utilitarian. Basic utilitarianism is the view that acts are right when and only when they produce the best possible consequences. How those consequences are brought about, the means used, does not matter. So if two acts have the same consequences, they should be right or wrong together, even when different means are employed to get those consequences.
For the utilitarian, the only morally significant factor in the trolley cases is the number of lives saved. How those lives are saved does not matter. So a utilitarian would judge that in the first case, we should pull the switch, directing the trolley away from the larger group and toward the single man. One life is lost and four are saved. The utilitarian would also say that in the second case, we should push the fat man off the bridge and into the path of the trolley. Again, one life is lost and four are saved. Since the consequences are the same, the acts are equally right.
Foot's suggestion was that we do not judge this way. We do not judge in accordance with utilitarianism. Rather, she thinks, we judge it is right to pull the switch directing the trolley toward the one man and away from the five, but wrong to push the fat man on to the track killing him and saving five. Modern experimental psychologists have gone beyond Foot's armchair speculations, and that of the many other philosophers who have thought about this problem, and put it to the experimental test. They found that substantial numbers of people, though not all, judge as Foot does. They think it is right to pull the switch but wrong to push the fat man, even though the results are exactly the same.
But if we do not judge in accordance with utilitarianism, is there some principle that describes how we do judge? A standard answer is that we judge in accordance with the Doctrine of Double Effect.