Last time I gave you a piece of my mind when it comes to the Kuratowski definition of pairs and ordered sets, and why we should stay away from it in linguistics. The thing is, that was a conceptual argument, and those tend to fall flat with most researchers. Just like most mathematicians weren’t particularly fazed by Gödel’s incompleteness results because it didn’t impact their daily work, the average researcher doesn’t care about some impurities in their approach as long as it gets the job done. So this post will discuss a concrete case where a good linguistic insight got buried under mathematical rubble.

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As some of you might know, my dissertation starts with a quote from My Little Pony. By Applejack, to be precise, the only pony that I could see myself have a beer with (and I don’t even like beer). You can watch the full clip, but here’s the line that I quoted:

Don’t you use your fancy mathematics to muddy the issue.

Truer words have never been spoken. In light of my obvious mathematical inclinations this might come as a surprise for some of you, but I don’t like using math just for the sake of math. Mathematical formalization is only worth it if it provides novel insights.

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Alright, syntax. Things are gonna get a bit more… convoluted? Nah, interesting! In principle we’ll see a lot of the same things as in phonology, and that’s kind of the point: phonology and syntax are actually very similar. But syntax isn’t quite as exhibitionist as phonology, it doesn’t show off its subregular complexity in the open for the world to see. So the first thing we’ll need is a suitable representation. Once we have that, it’s pretty much phonology all over again, but now with trees.

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