Linguistics Anonymous

24 January 2006

Of mathematical constructs and functional heads

With regards to the previous discussion of LISP, I think it would also be interesting to point out the similarities between modern functional head syntax and common infix mathematics. If you look at the structures (a + b) and [Spec Head Comp], one could draw a huge number of parallels between them. This could serve as an interesting case study of why (a + b) is the most common structure of math as well as a possible reanalysis of how linguistics is treating functional heads.

Math uses operators as a way to link terms, and in a sense, tell the 'user' how to combine the first term with the second (note that the first term may be on the right). Indeed, this is exactly how operators are used in some programming languages like Java, C, and Python. The compiler will first come across a single term, then the operand which tells the compiler what to do with the former and the later term.

Suppose we were to apply this same logic to syntax and functional heads. Then the purpose of the functional head would be to link parts of a clause and in a sense give meaning to the elements. Thus the AgtP [He Agt drive] could be interpreted as follows:

1) an element VP(drive) is found
2) we are going to add an Agt it
3) 'He' is found and is added as an Agt

This reanalysis, or restating, of the idea of functional heads will probably have some severe consequences all of which I have not yet worked out(obviously), but here are a few interesting ones:

a) everything must be added to a clause(tree) structure by way of a functional head, ie: there are no lexical heads.
b) the lexicon may not include part of speach features since any lexeme could be merged into the Spec and the cases which are not parsable could be worked out by semantics. Think of how easy it is to crate new verbs from nouns: "I will phone you later" This could be simply stated as a 'noun' merging with a V functional head. In most instances however, semantics doesn't 'allow' it to parse, but it seems very productive: "I usually ipod on the way to class"(just made this up) meaning: "I usually listen to my ipod on my way to class"
c) prepositions are phonetically realized functional heads - is this the same as lexical heads? not really sure yet...

I really don't know how much of what I just said is actually logical or anything since I have really only begun to thinking about this idea or to see if research has already been done.

/woo! first post


  • I think one of the major obstacles to unifying mathematics with linguistics is the fact that so many mathematical operations are symmetrical, whereas syntactic structures are (arguably) never symmetrical.

    (a+b) and (b+a) are not only truth conditionally equivalent, they are equivalent in every way except notation. I can't think of a structure like that in syntax.

    By Blogger Justin, at 12:24 AM  

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