Syntax, Pt. 6: Recursion

The question addressed at the end of the last post is a specific example of a more general problem with our phrase structure rules, as currently stated. If we have finite phrase structure rules (which, if our grammar is to be psychologically realistic, we had better), and a finite lexicon, how is it possible that there are an infinite number of unique sentences which could be generated? As Stephen Fry put it, when he first said “hold the newsreader’s nose squarely, waiter, or friendly milk will countermand my trousers”, he could be quite certain that it had never been uttered before, and yet despite this, it was easily categorized as grammatical. I have opted away from the more traditional “Colorless green ideas sleep furiously”, because that sentence has been dragged into another point entirely, that of meaningless but grammatical sentences.

Take any sentence. Now add ‘with gusto’ to it. Now add ‘on Friday’. For the most part, it seems you can do this ad nauseam, and will run into parsing issues before you run into actual ungrammaticality. Of course, there are some restrictions. You cannot add ‘on Friday’ and ‘on Saturday’ to the end of most sentences and still get a sentence. I think this is a syntactic issue, and not a practical one, although I do not know what the general linguistic opinion is. However, it is irrelevant to the point at hand.

To allow for infinite sentences from finite rules, our rules must be recursive, but not all elements ought be recursive. A first solution to this problem is simply to stipulate that all elements can be repeated. This is clearly not the proper result. All of the phrase rules required a certain element. This element is the head element, the element the phrase is built around. VPs require a V, PPs require a P, et cetera. This element cannot be subjected to the same sort of repetition. An NP gets one and only one N, a VP gets one and only one V. As well, certain elements do not seem repeatable. While APs, AdvPs, and PPs seem recursive, NPs cannot be added consistently. This is not an arbitrary postulate, as NPs, as we have already shown, require theta saturation. It is thus no surprise that there are constraints on where they can show up. One more category that seems to be limited as such is Determiners, and while there is a reason for this, I will not give it until later..

So our modified rules would allow any number of phrases of any given type to be added again in their location, with exception of heads, NPs, and for an important reason, Determiners. However, this rule faces further problems.

(24a) Sven kicked a puppy on Friday
(24b) *Sven kicked on Friday a puppy
(24c) Sven kicked at a puppy on Friday
(24d) *Sven kicked on Friday at a puppy
(24e) Sven kicked a puppy today
(24f) *Sven kicked today a puppy
(24g) Sven kicked at a puppy today
(24h) *Sven kicked today at a puppy

While the ungrammaticality of (24b) is predicted by our system (NPs within a VP come before PPs within a VP), the same cannot be said of (24d/f/h). They follow our phrase structure order, and yet in reality, they are ungrammatical. As well, (24g) is ruled ungrammatical by our current system, but it is a perfectly grammatical sentence. What changes would allow our system to deal with this problem?

As a sidenote, while the changes to the system should be a reaction to problems in the system, they should not solve only those problems (to avoid the system becoming too post-hoc). The changes should generalize to other cases, be empirically supported, and perhaps even offer insight into other situations.


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