A crucial point in Well’s argumentation against static approaches to alternation comes from Latin. Interestingly, his point seems to argue at the same time against rule ordering, although neither Wells nor Goldsmith mention this point.
In Latin, pat-tus becomes passus and met-tus becomes messus. This is very difficult to understand in a ‘static’ way (Wells even calls this ‘fatal’, as Goldsmith points out), for instance by only using output constraints. We cannot invoke a constraint *ts and/or a constraint *st, because words such as etsi and este stay unaffected. Only /t/’s which are adjacent to underlying /t/’s turn into [s]. As far as I can see, the only OT mechanism ever proposed which could do this kind of analysis are two-level constraints (which I don’t think anybody is seriously working with).
On the other hand, we can deal with this phenomenon in a ‘dynamic’ way, by positing rules of the following type:
- t->s / _ + t
- t->s / t + _
But we can only do this if we do not order these rules, but let them apply simultaneously. As soon as we order the rules they do not work, or the etsi/este problem arises again. That is the reason why the two-level constraint approach to this is the only one which works as far as I can see: Sympathy, Stratal OT, Comparative Markedness, OT-CC, etc. are all too ‘derivational’.
There also is no clear representational solution (changing a geminate /t/ to a geminate [s], leaving singletons unaffected), since it seems to be a crucial condition that there is a morpheme boundary between the /t/’s.
These thus are very important data, if they are real. Does anybody know about this? Has anybody ever tried to analyze this alternation?
What’s wrong with treating the geminate as a unit and saying
tt → ss / V_V
or something like that, but better thought out? Are there specific examples where tt doesn’t go to ss that we can compare?
James — Marc already addressed this idea in his second-to-last paragraph:
But of course, one might think that the solution to this problem is simply this:
t+t → s+s / V__V
But we’re clearly headed in the direction of observational adequacy at the expense of explanatory adequacy here.
I haven’t looked at the Goldsmith paper, but from glancing at Wells, I got the impression that he used ‘static’ to mean interacting rules, and ‘dynamic’ to mean simultaneously-applying rules, not the other way around. I admit I haven’t read it carefully enough, but if that’s right, then I see no reason not to follow Wells’s conclusion that, under the ‘static’ conception (the derivational approach, on my reading), “[the rules] are definitely non-automatic” – that is, morphologically conditioned. Thus we don’t see the alternation in the forms of ‘to be’ cited. (My guess would be that this occurs exactly in the past participle, but the Latin in my head withers more every day.) That would also suggest that we should be able to formulate a purely phonological solution *more* easily under a monostratal approach – but, as you point out, the constraints still need to be able to make reference to the morpheme boundary, though no longer the identity of the morphemes. If that isn’t pure enough for your taste, I’m not sure there’s a solution.
Well, the rules in (i) and (ii) would no longer fall under the definition of context-sensitive grammars, because two symbols need to be crucially rewritten at the same time.
(i) tt → ss / V_V
(ii) t+t → s+s / V_V
In the case of (i), this could be solved by using a feature [+long] or [geminate] or something similar, but that is not possible for (ii). We would thus end up with an unrestricted rewrite system, more powerful than that of SPE. It’s no surprise that it is possible to formulate the change under such a ‘dynamic’ view, because we could formulate any imaginable change in this formalism.
By the way, using diacritics, we can of course still do it even in context-sensitive grammar:
(iii) t → t[+long] / V_tV
(iv) t → 0 / Vt[+long]_V
(v) t[+long] → s[+long] / V_V
But here we have lost all hope for ‘explanatory adequacy’ (in particular because the [+long] feature shouldn’t be present in underlying, monomorphemic geminates).
Actually, I believe the rule wouldn’t take a phonological grammar outside the class of finite-state transducers (FSTs) — a far less powerful kind of formal system than even a context free grammar, let alone an unrestricted rewrite system, the most powerful kind.
I don’t think I can do justice to an example of an FST here, but the paper at http://www.utexas.edu/depts/linguistics/TLF-Harm.pdf contains a good phonological example.
What’s important is the limitation of this class of automata: no FST could ever take as input a string of the form VVVVV…CCCCC…, and turn it into, say, a #, if and only if there were an equal number of V’s and C’s, otherwise (say) a +.
On the other hand, you could easily get a context-free grammar (CFG), or a more powerful formal system, to do a task like this. CFG’s are made up of rules like normal phonological rules, but they can do more exactly because we assume, in a CFG, that the rules can apply arbitrarily many times to their own output. In other words, if you start formulating recursive rules that feed themselves, you’re out of the FST park; otherwise, you’re fine. And we’re not trying to do that here.
I’m told Johnson 1972 has a classic formal proof to this effect, but it’s easy enough to construct an FST from any phonological rule. If you apply a finite number of them in sequence you still get an FST out. If you start applying them recursively, bad things happen.
By the way (and I tried to post on this earlier, but somehow it didn’t show up before), I’m don’t personally find this data terribly intriguing. My skim of Wells suggests he was investigating which alternations were purely phonological (‘automatic’) and which morphologically conditioned (‘non-automatic’). (In the class of automatic alternations he clearly includes things that only apply across a morpheme boundary.) About this alternation he concludes that, under all but a particular conception of phonology, we would need to say it was non-automatic – that is, morphologically conditioned. Surely it would be madness to deny that morphologically conditioned alternations exist, so I would bet that that’s exactly what this is.
Diachrony strike again!
According to Andrew Garrett, in PIE there was a change *tt > *tst (which is still a synchronic rule in Hittite). In Latin *tst->ss, but only in the morphologized context.
It’s still not clear to me how a two-level constraint (in the McCarthy 1996 sense) solves this. A constraint like *Tt/*tT (with caps indicating input form) would still run into problems with with /VttV/->[VttV] sequences in Latin, and so first, a morpheme boundary is still necessary in the statement of the constraint.
In regular OT, a *t+t paired with a *t+s/*s+t constraint would work just as well unless [t+s] sequences are valid (etsi is monomorphememic, yes?). But if you’re referring to morpheme boundaries, you might as well have the constraint(s) refer to a particular morpheme, like English k->s/ity (*anar[s]ism).
No. It’s et + si.
Marc,
I’m unclear of the details of this issue. Why are you considering constraints like *ts and *st? The alternation shows that pas+sus is preferred to pat+tus. But, neiither proposed constraint rules out pattus. What am I missing?