Imagine you are a judge in a small town. A terrible crime has been committed, and the townspeople are furious. You know that if you do not convict someone quickly, there will be riots, and several people will be killed. You have a suspect in custody. The evidence against him is thin — he is probably innocent. But if you convict him, the riots will not happen, and those lives will be saved. What do you do? This is exactly the kind of nightmare that a particular school of moral philosophy was built to handle. It is called Utilitarianism, and its answer is both bracingly clear and deeply unsettling. Do whatever produces the greatest amount of happiness for the greatest number of people. If convicting an innocent man saves five lives, the maths says convict him. Welcome to one of the most influential — and most controversial — ethical theories ever devised.

Utilitarianism was born in late eighteenth-century England, a time of radical change. The Industrial Revolution was reshaping society. The American and French Revolutions had shown that political orders could be overturned. And a group of reformers believed that morality itself needed to be rebuilt on rational foundations, stripped of superstition, tradition, and the arbitrary authority of kings and priests. The man who gave this movement its clearest philosophical voice was Jeremy Bentham. Bentham was, by any measure, an extraordinary eccentric. He spent decades writing obsessively detailed plans for a prison he called the Panopticon, designed so that a single guard could watch all prisoners at once. He requested that his body be preserved after death and displayed in a wooden cabinet, which he called his Auto-Icon. You can still visit it today at University College London, where it sits in a corridor, his actual skeleton inside his clothes, topped with a wax head. Bentham wanted to be useful even in death. Usefulness, after all, was his entire philosophy.

Bentham's central claim was simple and radical. He believed that nature had placed human beings under the governance of two sovereign masters: pleasure and pain. Everything we do, we do either to seek pleasure or to avoid pain. And if that is true, Bentham argued, then the only rational basis for morality is to maximise pleasure and minimise pain — not just for yourself, but for everyone affected by your actions. He called this the Principle of Utility, or the Greatest Happiness Principle. The right action is the one that produces the greatest happiness for the greatest number. Bentham was not talking about vague, spiritual happiness. He meant actual, measurable pleasure and pain. And he believed you could calculate it.

Bentham proposed what he called the hedonic calculus — a method for measuring pleasure and pain as if they were quantities you could weigh on a scale. When deciding what to do, you should consider several factors about the pleasures and pains involved. How intense is the pleasure? How long will it last? How certain is it that the pleasure will actually occur? How soon will it arrive? Will it lead to further pleasures or pains down the line? How pure is it — meaning, is it likely to be followed by opposite sensations? And finally, how many people will be affected? Add up the pleasures, subtract the pains, and you have your answer. The action with the highest score is the morally correct one. Bentham was entirely serious about this. He genuinely believed that moral questions could be resolved the way mathematical problems are resolved — by calculation.