Monday, March 8, 2010

Kornai's Chapter 4

Chapter 4 of Mathematical Linguistics deals with morphology. At this point, the book really shows its value not just as a mathematical compendium, but as a survey of linguistics. The treatment of word structure is founded in the notion of the morpheme, which I have spent some energy crusading against. I was swayed by the theory known as Whole Word Morphology, due apparently to Alain Ford and Rajendra Singh. I learned it from a graduate student at the University of Chicago, and we published one short paper stemming from his work in the ACL Workshop on Morphological and Phonological Learning (2002). Oddly enough, according to databases like Google Scholar, this is my most highly cited piece of work.

In any event there a few other things to quarrel with in Kornai's survey of morphology. For one thing, he restates the old yarn that derivational affixes appear closer to the stem than inflectional ones, and this appears to be not the case in the Athabaskan languages such as Navajo. He also considers the parts of speech to have a morphological foundation, but since they need to be used in syntactic derivations of sentences, it seems to me that parts of speech should have a more sound syntactic and semantic foundation as some kind of word-usage classes.

The section discussing Zipf's law is very useful. In sum I know of no survey of morphology that is anything like this chapter, it is a very important piece of literature. I wish Kornai would consider a mathematical treatment of word-based approaches like Whole Word Morphology; this is something I have been planning to work on for a long time now.


  1. Hi Sean, the Navajo system is a pain to understand for sure. Please take a look at the intro to Ch 4 where I talk about near-truths. The idea that derivational affixes are closer to the stem than inflectional ones is not an "old yarn", it is one of these tantalizing near-truths that the filed is blessed (or cursed) with. It's true enough to make the possible exceptions like Navajo really interesting. Having been primarily socialized in a different, more cumulative area (see 1.2 of the Intro), I am always struck by the willingness of linguists to discard overwhelmingly good observations just because there are some tricky corner cases. To me, a good statistical generalization is worth having, just as Newtonian physics is worth having even though it is empirically false at speeds approaching that of light.

  2. I've also found it rather odd of many linguists, the dislike of accepting exceptions to a rule or framework. But statistical generalizations, one can't even discuss them in a class.

  3. Well sure, if the generalization buys you something as great as being able to compute motion under forces, then I like it too. I don't see what's so great about knowing that "inflectional" morphology is usually outside "derivational," or even what is the point of this dichotomy in morphological theory.