Response to Norbert
I read with interest Norbert’s recent post on formalization: “Formalization and Falsification in Generative Grammar”. Here I write some preliminary comments on his post. I have not read other relevant posts in this sprawling blog, which I am only now learning how to navigate. So some of what I say may be redundant.
For me the quote by Frege in the Begriffsschrift (pg. 6 of the book “Frege and Godel”) indicates what is important when he analogizes the “ideography” (basically first and second order predicate calculus) to a microscope: “But as soon as scientific goals demand great sharpness of resolution, the eye proves to be insufficient. The microscope, on the other hand, is perfectly suited to precisely such goals, but that is just why it is useless for all others.” Similarly, formalization in syntax is a tool that needs to be employed when needed. It not an absolute necessity and there are many ways of going about things (as I discuss below). By citing Frege, I am in no way claiming that we should aim at the same level of formalization that Frege did.
There is an important connection with the ideas of Rob Chametzky (posted by Norbert) in another place on this blog. As we have seen, Rob divides up theorizing into meta-theoretical, theoretical and analytical. Analytical work, according to Chametzky is: “concerned with investigating the (phenomena of the) domain in question. It deploys and tests concepts and architecture developed in theoretical work, allowing for both understanding of the domain and sharpening of the theoretical concepts.” It is clear that more than 90% of all linguistics work (maybe 99%) is analytical, and that there is a paucity of true theoretical work.
A good example of analytical work would be Chomsky’s “On Wh-Movement”, which is one of the most beautiful and important papers in the field. Chomsky proposes the wh-diagnostics and relentlessly subjects a series of constructions to those diagnostics uncovering many interesting patterns and facts. The consequence that all these various constructions can be reduced to the single rule of “wh-movement” is a huge advanced, allowing one insight into UG. Ultimately, this paper lead to the Move-Alpha framework, and indirectly to Merge (the simplest and most general operation yet).
However, “On Wh-Movement” is what I would call “semi-formal”. It has semi-formal statements of various conditions and principles, and also lots of assumptions are left implicit. As a consequence it has the hallmark property of semi-formal work: there are no theorems and no proofs. Formalization is stating a theory clearly and formally enough that one can establish conclusively (i.e., with a proof) the relations between various aspects of the theory and between claims of the theory and claims of alternative theories.
Certainly, it would have been a waste of time to fully formalize “On Wh-Movement”. It would have expanded the text 10-20 fold at least, and added nothing. This is something that I think Pullum completely missed in his 1989 paper on formalization. The semi-formal nature of syntactic theory, also found in such classics as “Infinite Syntax” by Ross and “On Raising” by Postal, has led to a huge explosion of knowledge that people outside of linguistics/syntax cannot really understand (hence all the lame discussion out there on the internet and Facebook about what the real accomplishments of generative grammar have been), in part because syntacticians are not very good popularizers.
Theoretical work, according to Rob is: “is concerned with developing and investigating primitives, derived concepts and architecture within a particular domain of inquiry.” There are many good examples of this kind of work in the minimalist literature. I would say Uriagereka’s original work on multi-spell-out qualifies and so does Epstein’s work on c-command, amongst others.
My feeling is that theoretical work (in Chametzky’s sense) is the natural place for formalization in linguistic theory. The reason is that it is possible, using formal assumptions to show clearly the relationship between various concepts, assumptions, operations and principles. For example, it should be possible to show, from formal work, that things like the NTC and Extension condition should really be thought of as theorems proved on the basis of assumptions about UG. Since NTC and Extension condition are theorems, they can actually be eliminated from UG. And from this, one can wonder if that program can be extended to the full range of what syntacticians normally think about as constraints.
In this, I agree with Norbert who states: “It can lay bare what the conceptual dependencies between our basic concepts are.” Furthermore, as my previous paragraph makes clear, this mode of reasoning is particularly important for pushing the SMT forward. How can we know, with certainty, how some concept/principle/mechanism fits into the SMT? We can formalize and see if we can prove relations between our assumptions about the SMT and the various concepts/principles/mechanisms. Using the ruthless tools of definition, proof and theorem, we can gradually whittle away at UG, until we have the bare essence. I am sure that there are many surprises in store for us. Given the fundamental, abstract and subtle nature of the elements involved, such formalization is probably a necessity, if we want to avoid falling into a muddle of unclear conclusions.
A related reason for formalization (in addition to clearly stating/proving relationships between concepts and assumptions) is that it allows one to clarify murky areas. One of the biggest such areas nowadays is whether syntactic dependencies make use of chains, multi-dominance structures or something else entirely (maybe nothing else). Chomsky’s papers, including his recent ones, make references to chains at many points. But other recent work invokes multi-dominance. What are the differences and relations between these theories and are either of them really necessary? What assumptions about UG does multi-dominance or chains entail? I am afraid that without formalization it will be impossible to answer these questions. I am investigating these questions in my seminar this semester.
These questions about syntactic dependencies interact closely with TransferPF (Spell-Out) and TransferLF, which to my knowledge, have not only not been formalized but not even stated in an explicit manner. Investigating the question of whether multi-dominance, chains or some something else entirely (perhaps nothing else) is needed to model human language syntax will require a concomitant formalization of TransferPF and TransferLF, since these are the functions that make use of the structures formed by Merge.
Minimalist syntax calls for formalization in a way that previous syntactic theories did not. First, the nature of the basic operations is simple enough (e.g., Merge) to make formalization a real possibility. The baroque and varied nature of “transformations” in the “On Wh-Movement” framework and preceding work made the prospect for a full formalization more daunting.
Second, the nature of the concepts involved in minimalism, because of their simplicity and generality (e.g., copies, occurrences), are just too fundamental and subtle and abstract to resolve by talking through them in an informal or semi-formal way. With formalization we can hope to state things in such a way to make clear conceptual and empirical properties of the various proposals, and compare and evaluate them. In fact, I have recently being doing a lot of this with my colleagues, because only recently (by helping to write Collins and Stabler 2012) have I seen what the issues are.
So, in the spirit of Frege, formalization should be a tool for ordinary working syntacticians to clarify their ideas and examine them empirically and conceptually.