I know I said I wasn’t going to go there, but now I feel the need to talk about Lexicon Optimization. Bob’s alternative suggestion, Lexicon Underoptimization, is an interesting idea, given the apparent facts that Bob thought it up to account for. But actually making it fly involves a whole lot more than Bob lets on.

One of the most controversial hypotheses made within Optimality Theory is that the constraints that grammars are made of are universal, and that grammars may differ from each other only in terms of constraint ranking. A corrolary of this hypothesis is that inputs are not language-specific; any input fed to the grammar should result in a grammatical output. This is the so-called Richness of the Base (RotB) hypothesis. (Note: RotB is often confused with the claim that all grammars have the same underlying representations. I’m not going to bother trying to address this confusion here.)

There is a general consequence of RotB, a specific instance of which is that morphemes like latter or ladder, homophonous for most (American) English speakers with a nonalternating medial tap, can arise optimally from any of three different inputs: one with a /t/, one with a /d/ and one with a /ɾ/. For those who might feel uncomfortable with this ambiguity — and I’m not one of them — Lexicon Optimization gets rid of it by asking: which of these three input-output mappings is optimal? The answer is /ɾ/ → [ɾ] in both cases, because this mapping is faithful; both /t/ → [ɾ] and /d/ → [ɾ] incur faithfulness violations that the identity map avoids.

Note that the Lexicon Optimization procedure depends on the (reasonable) assumption that markedness constraints apply to outputs only; thus, none of the three input-output mappings differs in terms of markedness, because they all have the same output [ɾ]. They differ in terms of faithfulness only, but (in this kind of case, at least), the ranking of faithfulness constraints is completely irrelevant: the /ɾ/ → [ɾ] mapping violates no faithfulness constraints, and so is the best regardless of ranking, and so Lexicon Optimization operates identically regardless of the grammar (again, in this kind of case, at least).

A formal implementation of Bob’s Lexicon Underoptimization alternative, on the other hand, would (also) have to allow markedness constraints to evaluate inputs in order for /t/ to be considered less marked than /d/ as an input. But note that this procedure would still select /ɾ/ as better than both /t/ and /d/: in English, [ɾ] is less marked than both [t] and [d] in the context of flapping, which is why we have flapping in the first place!

One way around this problem is for /ɾ/ to be disregarded as a possible input, but note that this is just giving up on RotB. (Which I’m not passing judgment on — I’m just pointing out the consequence.)

Another way around the problem is to stipulate that the context-specific markedness constraint(s) that disallow [t] and [d] in the context of flapping don’t participate in the evaluation of possible inputs for nonalternating [ɾ]. In other words, only general, context-free markedness constraints like *[-son, +voi] are allowed to play a role in the evalution of possible inputs. There are a number of reasons why I think this is just wrong, but suffice it to say that it’s a stipulation, following from no general principle that I can think of. Sure, it accords with what “markedness” means in some intuitive sense, but not to what markedness means in the formal sense defined in OT. (See note below.)

In the end, I still have to ask: “Does this even matter for phonological theory?” Bob’s answer was: “I think it does.” I remain unconvinced. If the grammar functions the same way regardless of the underlying representation you choose for a given nonalternating morpheme, who cares what you choose? Sure, we may one day discover how learners actually specify their lexical entries in the absence of evidence such as alternations, orthography, etc., but I don’t think it’ll be the job of phonological theory to account for that.

OK, but what about the apparent facts that led Bob to suggest Lexicon Underoptimization in the first place? Quibbles about experimental method aside, Sally Thomason found that English-speaking preschool kids always pronounced a [t] when asked to slowly repeat words with taps. This is undoubtedly interesting, but I am extremely skeptical of the idea that this reveals anything about those kids’ lexical representations of those words — other than that they are probably the same, given the lack of evidence for any differences among them. Asking someone to pronounce something slowly doesn’t completely turn off their phonological apparatus; if anything, it probably just affects the contextual applicability of some rules/constraints, which in this case may very well result in taps being disfavored even in flapping contexts and thus realized as (unmarked) [t]. This would be consistent with the Lexicon Optimization conclusion that /ɾ/ underlies nonalternating [ɾ].


It’s this intuitive sense of “markedness” that leads to the widely-accepted idea — echoed in Bob’s post — that degree of underspecification is a good way to represent relative markedness. A [t] lacks a feature that a [d] has, and presumably both lack a feature (or features) that [ɾ] has. But consider the fact that a [t] in a flapping context must violate some markedness constraint that motivates flapping, and a [ɾ] in that same context does not violate that constraint. Do we want to say that a (suboptimal) [t] in this context is differently specified than a [t] in another context? Of course not — the ranking of markedness constraints handles the compelementary distribution with no need for underspecification. There may be other reasons to adopt underspecification, but this is just not one of them.

But speaking of underspecification: In this 1994 ROA paper (presented at NELS at UPenn that year), Sharon Inkelas has an interesting argument that is highly relevant to what we’re discussing here. Suppose that inputs can be featurally underspecified, and that mapping an underspecified feature in the input to either of its specified values in the output violates no faithfulness constraints. A morpheme with an alternating segment (say, between [t] and [d]) will have an underspecified underlying representation [T] by Lexicon Optimization, because /t/ incurs faithfulness violations when it maps to [d] and /d/ incurs faithfulness violations when it maps to [t]. Inkelas argues that the three-way distinction afforded by underspecification is useful to account for exceptionally nonalternating forms (e.g., exceptions to final devoicing), though it’s never been clear to me how this accounts for the exceptionality part of it.