  It is a well-known empirical phenomenon that natural axiomatic theories are
pre-well-ordered by consistency strength. Without a precise mathematical
definition of "natural," it is unclear how to study this phenomenon
mathematically. We will discuss the significance of this problem and survey
some strategies that have recently been developed for addressing it. These
strategies emphasize the role of reflection principles and ordinal analysis and
draw on analogies with research in recursion theory. We will conclude with a
discussion of open problems and directions for future research.
