[W]e have no reason to trust anyone’s intuitions about very large numbers, however excellent their philosophy. Even the best philosophers cannot get an intuitive grasp of, say, tens of billions of people. That is no criticism; these numbers are beyond intuition. But these philosophers ought not to think their intuition can tell them the truth about such large numbers of people.

For very large numbers, we have to rely on theory, not intuition. When people first built bridges, they managed without much theory. They could judge a log by eye, relying on their intuition. Their intuitions were reliable, being built on long experience with handling wood and stone. But when people started spinning broad rivers with steel and concrete, their intuition failed them, and they had to resort to engineering theory and careful calculations. The cables that support suspension bridges are unintuitively slender.

Our moral intuitions are formed and polished in our homely interactions with the few people we have to deal with in ordinary life. But nowadays the scale of our societies and the power of our technologies raise moral problems that involve huge numbers of people. […] No doubt our homely intuitive morality gives us a starting point, but we have to project our morality beyond the homely to the vast new arenas. To do this properly, we have to engage all the care and accuracy we can, and develop a moral theory.

Indeed, we are more dependent on theory than engineers are, because moral conclusions cannot be tested in the way engineers’ conclusions are tested. If an engineer gets her calculations wrong, her mistake will be revealed when the bridge falls down. But a mistake in moral theory is never revealed like that. If we do something wrong, we do not later see the error made manifest; we can only know it is an error by means of theory too. Moreover, our mistakes can be far more damaging and kill far more people than the collapse of a bridge. Mistakes in allocating healthcare resources may do great harm to millions. So we have to be exceptionally careful in developing our moral theory.

John Broome, Weighing Lives, Oxford, 2004, pp. 56-57