There is a guest post over at NYU morphlab on Phases and Phrases: Some thoughts on Weak Equivalence, Strong Equivalence, and Empirical Coverage by Hagen Blix and Adina Williams that I highly recommend everyone to read.
They start out with a discussion of theories of the movement of celestial bodies (they comment: “an arena where nobody never quarreled ever, so safe travels!”), pointing out that at least for some time, both geo- and heliocentric approaches could explain the same data, so in a sense they were “weakly equivalent” (ignoring the phases of Venus for now).
They then turn to linguistics (and for some reason avoid any pun centered around linguistic invisible ‘movement’) to explore the analogy between the weak equivalence of physics theories and what that concept usually means in linguistics.
To sum up, before we finally return to linguistics: Both models made assumptions about the way bodies move in the heavens (unobservable at the time). Both models could derive the movements of bodies in the sky (observable) as a projection from one onto the other. Both models also made predictions about the phases of celestial bodies, again based on the same assumptions about orbits. But only for one model were these predictions actually in line with the newly observable data, the phases of Venus. This was the new kind of data that made the heliocentric models win out […]
Now, we may say that two models for the movement of celestial bodies are weakly equivalent if they generate the same movement of bright spots across the sky (2D). But only if they were to also assign them the same movement in the heavens (3D) would we call them strongly equivalent. Astronomers, it turns out, did not care whether geocentric models are weakly equivalent to heliocentric ones. They cared about which one covered the larger range of relevant phenomena.
This means that equivalency (weak or strong) can only be understood as relative to a particular collection of phenomena (i.e., relative to the data that the theory is here to explain). In short, it is scientifically ridiculous to focus on the fact that geocentric theories are weakly equivalent to heliocentric ones relative to predicting the paths of bright spots across the sky. Clearly, that’s not the only desideratum, and it is rather blinkered to get stuck worrying about only one particular type of data. The astronomers of the day knew this, even though nobody could directly observe any movement in the heavens – at that point a purely theoretical, abstract postulate.
They then drive home the point that in theoretical linguistics, too, one has to postulate “unobservables”, and see how far they can take you
Syntacticians are, unfortunately, in a position reminiscent of the one that 16th century astronomers found themselves in (possibly worse, but probably with less persecution): Just as astronomers postulated unobservable movement in the heavens to explain observable movement in the sky, syntacticians postulate unobservable phrasal nodes (say, a verb phrase in English) to account for the things we directly observe: Strings such as “Jo kicked the prof” or “Mary had them eat a cake” and their associated meanings. To a syntactician, strings are a little like the bright spots moving across the sky: They are the most immediately observable phenomenon we have. We certainly want to explain them. Like the astronomers, though, we too keep uncovering new phenomena, and we definitely care about whether our previous unobservables (our abstract postulates, our structure of phrasal nodes) can account for all of them.
They visualize with some toy grammars that some grammars are better than others, by capturing more regularities with less abstract concepts, making the correct predictions for which syntactic constructions can refer to which phrasal nodes.
While I agree with 99% of what they say, here are some minor quibbles:
While they admirably make the point for abstract theoretical concepts, the post comes off as a tiny bit too dismissive of computational complexity results in linguistics for my taste. I do share the sentiment that if your local (hopefully straw person) computational linguist were to say something like “I don’t care what the correct analysis of passive in natural language is, they are all weakly equivalent anyway” or “Two grammatical formalisms are weakly equivalent so why bother showing which one is a more accurate account of language”: this doesn’t cut it.
However, weak generative capacity is more than a concept that we can safely ignore because we have our much stronger razor by Occam. And ignoring it like this makes the theoretical linguist as dismissive as the computational linguist above.
What weak generative capacity does is to provide interesting lower and upper bounds on our grammatical theories. It is absolutely true as said above that this doesn’t help us for our analysis of passive. But I find it an interesting result in its own right that early transformational grammar is too powerful a formalism and could generate anything, and it’s good that we have more clearly defined theories now.
It is also interesting that not all grammar formalisms are equally powerful, e.g. that TAG and CCG are less powerful than Minimalist Grammars (see e.g. Stabler 2009 “Computational models of language universals” for a short overview). If we were to find a construction that unambiguously crosses that boundary, I would view that as a very interesting find.
Again, wgc only provides upper and lower bounds, with saying hardly anything about what happens within those bounds – but that makes the edge cases all the more interesting especially since these bounds are independent from the grammatical framework we use to describe them.
It’s also quite intriguing that for phonology where much more complexity subclasses of the regular languages are known, the frequency of phenomena is inversely correlated with how high they are in the hierarchy (see e.g. this post over at outdex). It would be cool if we had the same for syntax, i.e. a more finegrained distinction of context-free/sensitive classes of phenomena in which we can arrange them, a sort of periodic table for syntactic phenomena, independent of the formalism that is used (however, in my amateur understanding, one of the difficulties in finding these subclasses is precisely the fact that in syntax phenomena can be much less disentangled from their analyses).
To conclude, apart from these minor issues it’s really an entertaining and illustrative blog post. Go over there and read it!