Here’s a question I first heard from Hans-Martin Gärtner many years ago. I don’t remember the exact date, but I believe it was in 2009 or 2010. We both happened to be in Berlin, chowing down on some uniquely awful sandwiches. Culinary cruelties notwithstanding the conversation was very enjoyable, and we quickly got to talk about linguistics as a science, at which point Hans-Martin offered the following observation (not verbatim):

It’s strange how linguistic theories completely lack modularity. In other sciences, each phenomenon gets its own theory, and the challenge lies in unifying them.

Back then I didn’t share his sentiment. After all, phonology, morphology, and syntax each have their own theory, and eventually we might try to unify them (an issue that’s very dear to me). But the remark stuck with me, and the more I’ve thought about it in the last few years the more I have to side with Hans-Martin.

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In an earlier post I looked at privativity in the domain of feature sets: given a collection of features, what conditions must be met by their extensions in order for these features to qualify as privative. But that post concluded with the observation that looking at the features in isolation might be a case of the dog barking up the wrong tree. Features are rarely of interest on their own, what matters is how they interact with the rest of the grammatical machinery. This is the step from a feature set to a feature system. Naively, one might expect that a privative feature set gives rise to a privative feature system. But that’s not at all the case. The reason for that is easy to explain yet difficult to fix.

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One topic that came up at the feature workshop is whether features are privative or binary (aka equipollent). Among mathematical linguists it’s part of the general folklore that there is no meaningful distinction between the two. Translating from a privative feature specification to a binary one is trivial. If we have three features \(f\), \(g\), and \(h\), then the privative bundle \(\{f, g\}\) is equivalent to \([+f, +g, -h]\). In the other direction, we can make binary features privative by simply interpreting the \(+\)/\(-\) as part of the feature name. That is to say, \(-f\) isn’t a feature \(f\) with value \(-\), it’s simply the privative feature \(\text{minus} f\). Some arguments add a bit of sophistication to this, e.g. the Boolean algebra perspective in Keenan & Moss’s textbook Mathematical Structures in Language. So far so good unsatisfactory.

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There’s many conceptual pillars of linguistics that are, for one reason or another, considered contentious outside the field. This includes the competence/performance split, the grammar/parser dichotomy, underlying representations, or the inverted T-model. These topics have been discussed to death, but they keep coming up. Since it’s tiring to hear the same arguments over and over again, I figure it’d be interesting to discuss some little known ones that are rooted in computational linguistics. This will be an ongoing series, and its inaugural entry is on the connection between the T-model and bimorphisms.

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