  Nevertheless, when one restricts to theories that “arise in nature” (that is, the kind of formal systems that one encounters in a mathematical text as opposed to examples of the type above, which are metamathematically manufactured by logicians to have the deviant properties in question) the interpretability ordering is quite simple: There are no descending chains and there are no incomparable elements. In other words, it is a well-ordering. This is quite remarkable: If one takes any two “natural theories”—even from completely different domains, say one from analysis and another from combinatorics—then generally it turns out that one is interpretable in the other and that the two line up along a well-founded path through the interpretability hierarchy. 