Computational linguists overall agree that morphology, with the exception of reduplication, is regular. Here regular is meant in the sense of formal language theory. For any given natural language, the set of well-formed surface forms is a regular string set, which means that it is recognized by a finite-state automaton, definable in monadic second-order logic, a projection of a strictly 2-local string set, has a right congruence relation of finite index, yada yada yada. There’s a million ways to characterize regularity, but the bottom line is that morphology defines string sets of fairly limited complexity. The mapping from underlying representations to surface forms is also very limited as everything (again modulo reduplication) can be handled by non-deterministic finite-state transducers. It’s a pretty nifty picture, though somewhat loose in my subregular eyes that immediately pick up on all the regular things you don’t find in morphology. Still, it’s a valuable result that provides a rough approximation of what morphology is capable of; a decent starting point for further inquiry. However, there is one empirical argument that is inevitably brought up whenever I talk about the regularity of morphology. It’s like an undead abomination that keeps rising from the grave, and today I’m here to hose it down with holy water.