Two More Things about Minimalist Grammars

My intro post on Minimalist grammars garnered a lot more attention than I expected. People asked some damn fine questions, some of which I could not fully address in a single comment. So let's take a closer look at two technical issues before we move on to derivation trees next week (I swear, Norbert, we'll get to them soon).

The Merge Conspiracy [Part 3]

Part 2 and a half showed us the consequences of the MSO-Merge correspondence, both good and bad. In an ideal world, there should be a way to curtail the bad without limiting the good. Alas, ever since J.J. Abrams got his hands on Star Trek I have been uncertain about the degree of idealness of the world we inhabit.

The Merge Conspiracy [Part 2.5]

Yesterday we learned that a constraint can be expressed by Merge iff it can be defined in monadic second-order logic. But is this a good thing or a bad thing? The answer is both.

The Merge Conspiracy [Part 2]

Last time in our riveting story of intrigue and cabal, the seemingly innocuous subcategorization requirements encoded via Merge turned out to have a kinky bent to them: by splitting categories into smaller subcategories, we can regulate dependencies such as case-marking and gender agreement using only Merge. But the rabbit hole goes a lot deeper... ... ... ... (in fact, it is so deep I decided to pull a Wachowski and save the second half of the post for tomorrow).

The Merge Conspiracy [Part 1]

A while ago, Norbert wrote several interesting posts regarding the Specifier Island Constraint (SPIC) that caused me to chime in with some technical observations. The basic upshot was that SPIC cannot reliably block extraction from a specifier because we can use Merge rather than Move to displace constituents, in which case SPIC does not apply. Since the comments section isn't the ideal place for discussing such technical matters in an accessible form, Norbert was so kind to endow me with the divine power of publishing my remarks directly on his blog. So here's the first entry of a three part epic, the story of the power of Merge and how it can be used for both good and evil (rated PG-13 for some technical details; but hey, we're all grown-ups here).

Why Formalize- II?

Ewan (here) provides me the necessary slap upside the head, thereby preventing a personality shift from stiff-necked defender of the faith to agreeable, reasonable interlocutor. Thanks, I needed that. My recognition that Alex C (and Thomas G) had reasonable points to make in the context of our discussion, had stopped me from thinking through what I take the responsibilities of formalizations to consist in. I will try to remedy this a bit now. 

Here’s the question: what makes for a good formalization. My answer: a good formalization renders perspicuous the intended interpretation of the theory that it is formalizing.  In other words, a good formalization (among other things) clarifies vagaries that, though not (necessarily) particularly relevant in theoretical practice, constitute areas where understanding is incomplete. A good formalization, therefore, consults the theoretical practice of interest and aims to rationalize it through formal exposition. Thus formalizing theoretical practice can have several kinds of consequences. Here are three (I’m sure there are others): it might reveal that a practice faces serious problems of one kind or another due to implicit features of its practice (see Berwick’s note here) (or even possible inconsistency (think Russell on Frege’s program)), or it might lay deeper foundations (and so set new questions) for a practice that is vibrant and healthy (think Hilbert on Geometry), or it may attempt to clarify the conceptual bases of a widespread practice (think Frege and Russell/Whitehead on the foundations of arithmetic). At any rate, on this conception, it is always legit to ask if the formalization has in fact captured the practice accurately. Formalizations are judged against the accuracy of their depictions of the theory of interest, not vice versa.

Now rendering the intended interpretation of a practice is not at all easy.  The reason is that most practices (at least in the sciences) consist of a pretty well articulated body of doctrine (a relatively explicit theoretical tradition) and an oral tradition. This is as true for the Minimalist Program (MP) as for any other empirical practice. The explicit tradition involves the rules (e.g. Merge) and restrictions on them (e.g. Shortest Attract/Move, Subjacency). The oral tradition includes (partially inchoate) assumptions about what the class of admissible features are, what a lexical item is, how to draw the functional/lexical distinction, how to understand thematic notions like ‘agent,’ ‘theme,’ etc.  The written tradition relies on the oral one to launch explanations: e.g. thematic roles are used by UTAH to project vP structure, which in turn feeds into a specification of the class of licit dependencies as described by the rules and the conditions on them. Now in general, the inchoate assumptions of the oral tradition are good enough to serve various explanatory ends, for there is wide agreement on how they are to be applied in practice. So for example, in the thread to A Cute Example (here) what I (and, I believe David A) found hard to understand in Alex C’s remarks revolved around how he was conceptualizing the class of possible features. Thomas G came to the rescue and explained what kinds of features Alex C likely had in mind:

"Is the idea that to get round 'No Complex Values', you add an extra feature each time you want to encode a non-local selectional relation? (so you'd encode a verb that selects an N which selects a P with [V, +F] and a verb that selects an N which selects a C with [V, +G], etc)?"



Yes, that's pretty much it. Usually one just splits V into two categories V_F and V_G, but that's just a notational variant of what you have in mind.

Now, this really does clarify things. How? Well, for people like me, these kinds of features fall outside the pale of our oral tradition, i.e. nobody would suggest using such contrived items/features to drive a derivation. They are deeply unlike the garden variety features we standardly invoke (e.g. +Wh, case, phi, etc.) and, so far as I can tell, restricted to these kinds of features, the problem Alex C notes does not seem to arise.

Does this mean that all is well in the MP world?  Yes and No.

Yes, in the sense that Alex C’s worries, though logically on point, are weak in a standard MP (or GB) context for nobody supposes the kinds of features he is using to generate the problem exist. This is why I still find the adverb fronting argument convincing and dispositive with regard to the learnability concerns it was deployed to address. Though I may not know how to completely identify the feature malefactors that Thomas G describes, I am pretty sure that nothing like them is part of a standard MPish account of anything. [1] For the problem Alex C identifies to be actually worrisome (rather than just be possibly so) would require showing that the run of the mill, every day, garden variety features that MPers use daily could generate trouble, not features that practitioners would reject as “nutty” could.[2]

No, because it would be nice to know how to define these possible “nutty” features out of existence and not merely rely on inchoate aspects of the oral tradition to block them. If we could provide an explicit definition for what counts as a legit feature (and what not) then we will have learned something of theoretical interest even if it fails to have much of an impact on the practice as a result the latter’s phobia for such kinds of features to begin with. Let me be clear here: this is definitely a worthwhile thing to do and I hope that someone figures out a way to do this. However, I doubt that it will (or should) significantly alter the conclusion concerning FL/UG like those animated by Chomsky’s “cute example.” [3]  

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[1] Alex D makes this same point (here), and I agree:

I completely agree with you that if we reject P&P, the evaluation measure ought to receive a lot more attention. However, in the case of trivial POS argument such as subject/aux inversion, I think the argument can be profitably run without having a precise theory of the evaluation measure.

[2] Bob Berwick’s comment (here) shows how to do this in the context of GPSG and HPSG style grammars. These systems rely on complex features to do what transformations do in GB style theories. What Bob notes is that in the context of features endowed with these capacities, serious problems arise. The take home message: don’t allow such features.

[3] This seconds David Adger’s conclusion in the comment section (here). Let me quote:

I am convinced by what I think is a slightly different argument, which is that you can use another technology to get the dependency to work (passing up features), but that just means our theory should be ruling out that technology in these cases. as the core explanandum (i.e. the generalization) still needs explained. I think that makes sense…