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Dmytry comments on On accepting an argument if you have limited computational power. - Less Wrong
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The purpose of thought experiment is to analyse our theories in extreme situations. The understanding this gives can then be useful in non-extreme situations. An analogy to mathematics: When graphing y=x/(x^2+1) it is useful to consider the value of y as x goes to infinity, even if we only need a sketch for -2<x<2. Trolley Problems allow us to focus on the conflict between intuition and utilitarianism. The understanding thought experiments bring is important, even if their circumstances do not occur naturally. Indeed, the very fact that their circumstances do not occur naturally is what necessitates a thought experiment.
Well, we don't blame special relativity for seeming to fail with all the thought experiments involving objects moving faster than speed of light. edit: that is to say, it is important that thought experiments remain within certain bounds. In the case of the trolley problems, the small difference between the assumptions and real world (neglecting the small false positive rate while focussing on the extremely low probability scenario) turn out to lead to massively incorrect result which is then counter intuitive. edit: and indeed, there are things which are correct but counter intuitive. However most of the things which are counter intuitive are also wrong; Earth being a torus is very counter intuitive and wrong, ditto for the saddle shape, etc.
That's hardly a critique of the trolley problem. Special relativity itself stipulates that it doesn't apply to faster-than-light movement, but a moral theory can't say "certain unlikely or confusing situations don't count". The whole point of a moral theory is to answer those cases where intuition is insufficient, the extremes you talk about. Imagine where we'd be if people just accepted Newtonian physics, saying "It works in all practical cases, so ignore the extremes at very small sizes and very high speeds, they are faulty models". Of course we don't allow that in the sciences, so why should we in ethics?
In the practical reasoning, "A" is a shorthand for "I think A is true", et cetera - no absolute knowledge, nonzero false positive rate, and sufficiently refined moral theory has to take this into account.
Just as thought experiment relying on e.g. absolute simultaneity would render itself irrelevant to special or general relativity, so does trolley problem's implicit assumption of absolute, reliable knowledge render it irrelevant to the extreme cases where the probability of event is much smaller than false positive rate.
The analogy between moral theories and physics seems to suggest that just as we expect modern physics to act like Newtonian physics when dealing with big slow objects, we should expect some modern moral theory to act like folk morality when dealing with ordinary human life situations. Does that hold?