Still more distributional arguments

We were all struggling to figure out exactly what is gained by referring to the spread of [back] and [round] in Turkish with a single Spread(Color) constraint. As McCarthy (2003:85) notes (in a different context), if we still acknowledge the independent existence of Spread(back) and Spread(round), then the additional existence of Spread(Color) does not alter the predicted factorial typology. More to the point, the fact that [back] and [round] both spread in Turkish but that [round] spreading is limited to [+high] vowels can be equally described with some combination of the following rankings:

  • Spread(back) >> Ident(back) — [back] spreading
  • *Nonhigh/round >> Spread(round) >> Ident(round) — [+high]-limited [round] spreading

You might be able to argue that Spread(back) and Spread(round) don’t exist, and that to describe cases where only one of the features spreads at all, you have (for example) Ident(round) >> Spread(Color) >> Ident(back), which would describe [back] spreading only. Without Spread(Color) you’d need the two independent rankings Ident(round) >> Spread(round) and Spread(back) >> Ident(back). (Possible interesting difference: the ranking with Spread(Color) has Ident(round) >> Ident(back) by transitivity, whereas the ranking without Spread(Color) does not.)

We felt that there had to be more to it, though, which is when we tried to mount an argument based on Padgett’s claim (p. 10) that “some researchers have taken it to be significant that [back] and [round] harmonize within a single language recurrently”. What seems (to me) to be assumed here is that having a feature class Color will somehow lead to an explanation for this recurrence, and I think the only plausible argument for this assumption must take something like the following form:

  1. Given Spread(Color), there are more total rankings of constraints compatible with [back] and [round] spreading together than there would be without Spread(Color).
  2. Given no Spread(Class)-type constraint for an arbitrary pair of features (say, [back] and [high]), there are fewer total rankings of constraints compatible with [back] and [high] spreading together.
  3. Assuming that total rankings are roughly evenly distributed throughout the world’s languages, [back] and [round] spreading together is more likely to be found than [back] and [high] spreading.

Let me clarify that Padgett did not make this argument; this is entirely a construct developed during our seminar discussion (and is something I’ve generally been thinking about for a while). But I’d honestly like to know whether there’s any other way to interpret the appeal to “recurrence” in an overall argument for a UG construct such as the one Padgett proposes. Even if we were able to unequivocally state that [back] and [round] spreading recur in a controlled/balanced sample of (attested!) languages in a way that [back] and [high] spreading do not, why should we assume that total rankings are evenly distributed throughout that sample? I suppose what I’m questioning here is (a) whether it’s the job of the formal theory of grammar to account for recurrence, and (b) if so, whether the assumption of even distribution at the heart of the argument above is the right way (or even a right way) to go about it.

I should add that Padgett’s paper concludes (p. 35) with the following remark about how research into the phonetic underpinnings of phonology may provide an answer to the “deeper questions” of why and which feature classes exist:

Why do features pattern into classes at all, and why the particular classes found? Though Feature Geometry and Feature Class Theory are noteworthy in capturing feature class patterning, their formal mechanisms do not provide any answer to these deeper questions. Instead, the answers have been attributed to phonetic underpinnings: feature classes have a basis in the phonetic parameters of place of articulation, laryngeal state, and so on. Yet this assumption deserves further scrutiny, not because it is likely to be wrong, but rather because more attention to the phonetic bases would probably bring a new depth of explanation to the research program.

Recurrence seems to me to be a subcase of these deeper questions, and it also seems to me that if we find the answers in the phonetic underpinnings, we should even more seriously question whether we even need feature classes as formal objects (whether in feature geometry or in Padgett’s feature class theory). That is, if [back] and [round] pattern together for good phonetic reasons, then those reasons might simply be held responsible for the fact that some rankings/grammars are more commonly attested than others, without the need for a separate Color class/node.

3 thoughts on “Still more distributional arguments

  1. Adam Albright

    I was interested to read this, because I had actually ended up telling my undergrad class something along these same lines on Thursday, and had then been pondering whether I really was telling them the right thing. The discussion was slightly different because it was in the context of rule-based grammar, but it had a similar flavor.

    Essentially, after rehearsing the argument that a good feature set should make it easier to express common processes, I had them ponder why common classes should be easier to express. Aside from convenience and economy, there seemed to be two possible arguments (one stupid and one maybe not so stupid):

    1) If rules were constructed by some random process in which it was increasingly unlikely to add additional feature specifications to them, then most of the rules in the world’s languages would be simple ones. (A purely formal generative process for generative phonologies…)

    2) If learners had a bias to assume simple rules, then no matter how the pattern actually arose, the scenario in (1) would be played out in the course of acquisition: whatever the phonetic basis, there would be a tendency to reanalyze processes as involving easier-to-state classes. This would be a strong argument if we observed that common classes were also phonetically unnatural, since it would point to distinct cognitive biases for how sounds should be classified.

    In OT, this would translate into an argument not about the distribution of grammars across the world’s languages, but rather, learning biases in choosing among competing characterizations of the context. (There is a connection here with the various proposals in the ranking literature for picking out the correct level of generality for faithfulness constraints; e.g., Prince & Tesar 1999, Hayes 1999.)

  2. Marc Ettlinger

    I’ve also been considering some of the same questions re: classes recently and I think one alternate way of thinking about it, actually analogous to Adam’s first point (which I assume was the stupid one), is in terms of category theory. If there is a rule, or a process, or a generalization that operates over some thing, that thing must be defined as a category. Classical category theory (which I think most closely corresponds to feature theory) has long fallen out of favor with cognitive psychologists that study category theory and there are a number of alternate proposals out there including exemplar-based models, prototype models, modified feature-based theories, and even Bayesain network models.
    I’m far from familiar with the subtleties of the debate, but considering whether /b, d, g/ or /b, d, k/ can be better acquired as a category based on these different models may go a long way towards answering the question. So, in that sense it parallels Adam’s first suggestion in that it does become increasingly diffucult to learn a category that has more tenuous, numerous or irregular associations between their members. Instead of a bias towards simpler rules, which to me has an element of circularity (what make a rule simple? being able to be learned easily?), the bias is towards learnable categories. Whether this could be translated into the recent exemplar-based models that have become popular in Lx recently is a question I’ve been trying to think about. And perhaps this is what Adam meant by simpler rules and I am rather just suggesting appealing to category theories as a way of defining simple.
    I don’t totally follow Adam’s point regarding how simple rules would translate into the language of OT – some clarification would be great!

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