Why Formalize?

This post orginally appeared on the Faculty of Language blog (February 10, 2014). http://facultyoflanguage.blogspot.com/2014/02/where-norbert-posts-chriss-revised-post.html

Why Formalize?

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. Lastly, the issues that I discuss below have come up in my joint work with Edward Stabler on formalizing minimalism, to which I refer the reader for more details.

I take it that the goal of linguistic theory is to understand human language faculty by formulating UG, a theory of the human language faculty. Formalization is a tool toward that goal. 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.

Frege in the Begriffsschrift (pg. 6 of the Begriffschrift in the book Frege and Godel) 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 should 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 for the same level of formalization that Frege aimed for.

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 Noam 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 advance, allowing one insight into UG. Ultimately, this paper led to the Move-Alpha framework, which then led to Merge (the simplest and most general operation yet).

 “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.

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 NLLT contribution on formalization. The semi-formal nature of syntactic theory, also found in such classics as “Infinite Syntax” by Haj Ross and “On Raising” by Paul Postal, has led to a huge explosion of knowledge that people outside of linguistics/syntax do not really appreciate (hence all the uninformed and uninteresting discussion out there on the internet and Facebook about what the accomplishments of generative grammar have been), in part because syntacticians are generally not very good popularizers.

Theoretical work, according to Chametzky 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 Juan Uriagereka’s original work on multi-spell-out qualifies and so does Sam 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. One 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, the Extension Condition and Inclusiveness should really be thought of as theorems proved on the basis of assumptions about UG.  If they were theorems, they could be eliminated from UG. One could ask if this program could be extended to the full range of what syntacticians normally think of 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 (Strong Minimalist Thesis) 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 (assumptions about the interfaces and computational efficiency) 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 compare competing proposals. One of the biggest such areas nowadays is whether syntactic dependencies make use of chains, multi-dominance structures or something else entirely. 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 between these theories?  Are either of them really necessary? The SMT makes it clear that one should not go beyond Merge, the lexicon, and the structures produced by Merge. So any additional assumptions needed to implement multi-dominance or chains are suspect. But what are those additional assumptions? I am afraid that without formalization it will be impossible to answer these questions.

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 (other than the initial attempt in Collins and Stabler 2013). 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. Giving explicit and perhaps formalized statements of TransferPF and TransferLF should in turn lead to new empirical work exploring the predictions of the algorithms used to define these functions.

A last reason for formalization is that it may bring out complications in what appear to be innocuous concepts (e.g., “workspaces”, “occurrences”, “chains”).  It will also help one to understand what alternative theories without these concepts would have to accomplish. In accordance with the SMT, we would like to formulate UG without reference to such concepts, unless they are really needed.

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., the notion of copy), 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 the conceptual and the empirical properties of the various proposals, and compare and evaluate them.

My expectation is that selective formalization in syntax will lead to an explosion of interesting research issues, both of an empirical and conceptual natural (in Chametzky’s terms, both analytical and theoretical). One can only look at a set of empirical problems against the backdrop of a particular set of theoretical assumptions about UG and I-language. The more that these assumptions are articulated; the more one will be able to ask interesting questions about UG.