Back in the Spring of 1999, Harvard and MIT hosted a symposium called Phonology 2000. (I’m forced to link here to the program as announced on LINGUIST List because the original website for the symposium appears to be MIA.) A significant group of established phonologists were invited to give talks and to participate in discussions and debates about the current and future direction(s) of the field. The main theme, as you may have guessed, was whether (or to what extent) Optimality Theory is A Bad Thing. Though there was a healthy group of OT-defenders in the audience, not many gave talks — several were invited, mind you, but declined for reasons you can ponder in your own copious spare time.
One of the talks struck a particular chord with me, for reasons I discuss in this post. (If you’re not in the mood for a rant, you may want to skip this.)
It was the second talk on the program: David Odden‘s simply titled “Ordering”. (Here is the paper based on the talk, and just in case it’s ever removed, here’s a copy.) The main reason this talk stood out for me is that I thought at the time that I had found a major problem with Odden’s reasoning, but he proved me wrong during the question period. Or so I thought — I e-mailed him just a few days later (May 3, 1999) with my revised commentary, but he never wrote back. And I’ve always wondered why — did he not understand my point? Am I wrong? Or is he embarrassed to admit that I’m right?
None of this will make any sense without hearing the relevant portion of the talk. Since that’s not possible — at least, I don’t think anyone recorded it — here’s the relevant portion of the paper (beginning at the top of page 6).
Even without the power of Sympathy theory, it is easy to show that OT predicts hypothetical process interactions which could not arise under standard derivational theory, and, importantly, which do not arise in natural languages. A number of Bantu languages have a dissimilative tone deletion called Meeussen’s Rule which deletes a H after a H […]. Deletion of H after H is a consequence of the OCP, where deletion is an active repair for OCP violations. Another common tonal process in Bantu is rightward Tone Doubling, where H spreads once to the right, eliminating singly linked H tones. In a number of languages with tone Doubling, a following H tone blocks the rule which is an effect of the OCP as well. (12) illustrates an interaction between these precesses with hypothetical data from the imaginary language Kintupú. We will further assume that tone Doubling does not spread H to a pre-pausal syllable, a very common restriction on this process; this restriction allows us to determine that the second of two H’s does indeed delete, as in the first example. The second example illustrates spread of H rightward by one syllable. The third example illustrates the interaction between these processes.
What should be noticed in the mapping from input to output is that in the third example, a sequence of H’s, two out of every three H tones ends up being deleted. This pattern can be described easily in OT. The crucial constraints are the constraint against HH, and a constraint against monosyllabic H domains. In the imaginary langauge Kintupú, these two constraints are undominated, and the tableau in (13) shows how the correct form is selected, by satisfying both of these constraints at the expense of Max-H. To guarantee that tones delete rather than fusing, Uniformity must also dominate Max-H.
A derivational analysis of such processes would be founded on two rules, Meeussen’s Rule which deletes H after H, and a rightward Tone Doubling rule, which is blocked from spreading H to a syllable before a H.
The possible outputs from these rules are specified in (15), given either right-to-left or left-to-right iteration in each rule, and either of the possible rule orderings.
The pattern of retaining one tone and deleting two following tones, as was easily described under OT, ends up not being describable with ordered rules.
(What follows addresses the question I asked Odden during the question period. My thought then was: What stops you from writing a single rule with the precise effect of the bottom half of what’s shown in (12)?)
Nor could one construct some new rule to perform this operation in one step, along the lines of (16).
This ‘rule’ has numerous properties which are prohibited by the general theory of rule construction. First, the rules have to refer to structurally nonadjacent elements. Second, the rule must simultaneously affect multiple foci (in principle, an unbounded sequence). Third, this rule is not even a well-formed rule, insofar as the expression ‘…’ has no formal status in the theory. The theory of rule ordering and rule formulation makes specific restrictive predictions about the interaction of processes, predictions not shared by OT. Lacking any indication that such processes are actually found in human language, this constitutes excessive power on the part of OT.
Let’s ignore for the moment the vacuous appeal to the unspecified and unreferenced “general theory of rule construction”. It’s true that the rule in (16) has to “refer to structurally nonadjacent segments”, a point I return to shortly. However, the other two objections are artifacts of the simplistic way I asked my question at the time and the way that Odden has chosen to represent it in this paper. Consider the alternative that I e-mailed to Odden a few days later (and presumably before he finished writing the paper):
H Dissimilation (left-to-right iterative):
σ → σ / σ σ | | | H H H H __
Note that this rule still crucially refers to structurally nonadjacent segments, but the other two objections that Odden raises with respect to (16) are no longer applicable because this rule is left-to-right iterative — no simultaneous application and no ‘…’ expression are necessary. The direct result of this rule is not exactly the representation in (12), but applying the independently necessary Meeussen’s Rule and Tone Doubling after this rule will take care of that (though the result would be superficially vacuous).
So let’s address the reference-to-structurally-nonadjacent-segments issue. I think we can all agree that rules that refer to structurally nonadjacent segments are not preferable to rules that do not do so, but such references are not at all uncommon in rule ordering analyses. In fact, Odden’s Tone Doubling rule itself has such a reference: note the “blocked by H on following syllable” condition on this rule as stated in (14). This is a crucial reference to a structurally nonadjacent segment: the syllable that the H would spread from is separated from the H that would block it by the syllable that the H would spread to. (Note that one cannot argue that the blocking H is rendered adjacent to the spreading H by the fact that the latter spreads, because the fact is that the latter does not spread because it’s blocked from doing so. Whatever principle one might come up with to license this blocking condition by the “general theory of rule construction” would surely also license the H Dissimilation rule that I suggested above.)
(Side note: Just for fun, I’m going to start collecting examples of rules proposed in the literature that make crucial reference to structurally nonadjacent segments. If you find any yourself, please e-mail me with the rule and citation. I’ll eventually summarize the collection in a separate post.)
In sum, I think that Odden’s hypothetical Kintupú example — and probably my rant about it here, at least to a certain extent — demonstrates one of the major pitfalls of cross-framework comparison: with a little ingenuity and lot of disregard for the wider implications of the straw-man analysis within the “other” framework, there seems to be no limit to what one can (or cannot, as the case may be) describe in either framework.