All of the sciences ask: how is the world? Or, what comes to the same: what should we believe? Thus, at the basis of the sciences is a conception of our beliefs or, more generally, of our epistemic states. This is why probability theory is so important and ubiquitous in the sciences. Ranking theory provides a similarly general and powerful alternative representation of epistemic states, which is moreover able to capture the notion of belief simpliciter. The talk gives a brief introduction into that theory, which is bound to remain fairly abstract, but tries to make the big claims at least plausible.