Linguistics and Category Theory

Over at the n-category café, John Baez and students have some ideas about using category theory for linguistics

(, see for some notes on John Baez’ blog)


I do not understand a word of what they’re saying, just wanted to put it out there for people that might be interested in it … –

although I’m pretty sure that “modules of noncommutative Hopf algebras, or something like that” could turn out to be useful. However, I know much more about the latter than the former 😉

Jokes aside, I think it’s cool when mathematicians try their hand at linguistics.

In the blogs, some linguist asked for a good introduction to understand that stuff, getting the following link:

I only had the time to skim the paper, so just a few thoughts:

Lambek’s types seem to be a funny mix of semantic types and the syntactic head parameter: for one, `works’ in his example specifies what kind of input it wants, and what it outputs, i.e. in modern semantic parlour type <e,t>. `poor’ modifying `John’ says that it takes a noun, and outputs a noun. While this is achieved by predicate modification in formal semantics and not by functional application (i.e. taking an argument and outputting something), this n/n notation remarks that after the composition the part of speech type is not changed which means that `poor John’ is still more a noun, comparable to just `John’ than it is an adjective.

This is the core idea what it means to be a head in a phrase.

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2 Responses to Linguistics and Category Theory

  1. may be related if its not known already (i agree with the math as i understand but not the interpretation—connectionists are not chomskyites)


    • Hey Mart, thanks for the link! And you’re the first comment on my blog, so thanks again 🙂
      As for the paper: I don’t think I’m able to follow the maths, however, some sentences in the introduction made me pretty skeptical.
      First: the numerous critiques of GG that have all been rebutted. At this point, I don’t think it is possible to decide which theory of grammar is the _cognitively_ adequate one. They’re probably all logically consistent, and there are possibly infinitely many of such consistent theories of grammar.
      The work that should be done is to find out what the neural code and the primitive operations of the brain grammar relies on, see e.g. the work by David Poeppel (, and not to build ever more beautiful mathematical theories that don’t describe nature.
      Second: what are the numerous critiques? I have the bad feeling that this is a kind of motte and bailey argument. GG is equated with POS arguments, which are rebutted, which then means that all the primitives assumed in GG have to be correct (phrase structure grammars, movement, etc…).
      Third: as beautiful Fibonacci numbers, symmetry breaking and the like are, I don’t see how this should help linguistics apart from making it sound more scientific and closer to physics – which it is not, unfortunately.


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