The last two lessons assumed we know what should be equal. We do not, and the question turns out to be the deepest one in the field.

In 1979 Amartya Sen gave a lecture with a title that reframed the argument: "Equality of What?" His observation was disarming. Almost every serious political position is egalitarian about something — the libertarian about rights, the utilitarian about the weight given to each person's welfare, the socialist about resources. They are not arguing about whether to be equal. They are arguing about what to equalise, and choosing one space means accepting inequality in the others.

And the answer determines what a society would actually have to do, which is why this apparently philosophical lesson has more practical consequence than either of the two before it.

The four spaces