That Mathy Aura

We've all been victims of the stereotypes around "math people" being totally different than "language people". Fortunately, this is quite easily debunked: the existence of syntacticians.

Throughout my experience with syntax, I've always subconciously compared it to category theory. Sure, the theories make sense, but they're nearly always very abstract and focus almost entirely on logic based off what seems like a few specific observations. Furthermore, syntacticians often like to really assert themselves; often, they bring up about fifty extra sentences as counterclaims to possible objections to their theory. (Or maybe I've just encountered too much Chomsky.) Not that this is bad; it just gives a certain aura to the field of syntax that differs from that of phonology or morphology, for example. While reading the Carnie chapters, I've started to suspect that maybe this is because the reasoning in syntax is so similar to the reasoning in many parts of math and computer science theory.

For example, on page 68, Carnie gives a general rule for deriving a noun phrase: a possible determiner phrase, with any number of adjectives, followed by the noun itself (which has to be there), and finally, any number of prepositional phrases.

This looks exactly like a regex to me.

Of course, phrase-structure grammar is very similar to a context-free formal grammar, so this is, in a way, to be expected. And guess where else context-free grammars are used? Compilers. In fact, the notation that Carnie gives is strikingly similar to the BNF used with yacc - just with different symbols.

As syntacticians would probably bring up, these could just be superficial similarities or coincidences. So let me try something else. One point that really brought out the aura was Carnie's description of what classifies a noun. Part of this was, yes, the way he explained it, showing that the usual conception was wrong, and developing the "correct" idea piece by piece. But the definition also does what many other syntactical theories do - totally ignore semantics. He does mention them, but the final definition is completely based off of position in a sentence - zero word meanings included. Of course, all subjects in linguistics are interconnected, but syntax seems to be a little more introverted than the rest. When Carnie introduces trees, for example, very little in the semantics of the sentences from which trees are constructed is really considered, despite much of the theory being derived from what people intuit as grammatical or ungrammatical.

I'd like to bring up more points, such as recursion inherent in phrase structure, which, as so many CS teachers will testify, usually can't just be absorbed; specifically calling verb arguments "arguments" and classifying them as functions; defining multiple verbs for different transitivities, similarly to overloading functions with differently-typed arguments in C-like languages; and the similarity of assigning features to categories, and defining subcategories, to the object-oriented paradigm. Unfortunately, I'm reaching my 500-word limit.

Overall, the reading was fun to read and eye-opening. 4/5, would read again.