Some more targeted thoughts:
- I really liked in section 1 where the quotes from Tomasello were presented - this gives a clear idea about what exactly is claimed by the item-based approach, and how they have previously used (apparently flawed) intuitions about expected productivity to support that approach. I thought a quote at the end of section 3.3 summed it up beautifully: "...the advocates of item-based learning not only rejected the alternative hypothesis without adequate statistical tests, but also accepted the favored hypothesis without adequate statistical tests."
- The remark in section 2.2 about how even adult usage isn't "productive" by the standard of the item-based crowd is a really nice point. If adult usage isn't "productive", but we believe adults have a generative system, then this should make us question our assumption that "unproductive" child usage indicates a lack of a generative system. Of course, I suppose one might argue that maybe we don't think adults have a fully generative system (this is the view of construction grammar, to some extent, I believe.)
- In section 3.2, I thought Table 1 was a beautiful demonstration of the match between expected overlap for the generative system and the empirically observed overlap in children's speech.
- A minor point about the S/N threshold discussed in 3.2 - I get that S/ln N is a reasonable approximation for rank, especially as N gets very large. However, I'm not quite sure I understand why S/N was chosen as the threshold. I get that it's an upper bound kind of thing, but if S/ln N grows more slowly than S/N, why not just use S/ln N to get a more accurate threshold? It's not as if ln N is hard to calculate.
- In section 3.3, I get that this is merely an attempt to make the item-based approach explicit (and maybe the item-based folk would think it's not the right characterization), but I think it's a pretty good attempt. It gets at the heart of what their theory predicts - you get lots of storage of individual lexical item combinations. Then, of course, Table 2 shows how this representation doesn't match the empirically observed overlap rates nearly as well, so we have a point against that representation.
- Section 4 is nice in that it suggests that this way of testing theoretical representations should be a general-purpose one - do it for determiner usage, but also for verbal morphology and verb argument structure. Though this analysis wasn't conducted for those other phenomena, I was very convinced that the data show a Zipfian distribution, and so we might expect a generative system to be compatible with them.
Bannard, C., Lieven, E. & Tomasello, M (2009). Modeling children's early grammatical knowledge. Proc Natl Acad Sci U S A, 106(41), 17284-9.