[Fair notice: This one’s almost all theory, and may be entirely stultifying, albeit in a potentially amusingly pompous way]
Bruce, Craig, et al.:
I think it’s important to remember in this kind of discussion that by “formal model,” what linguists typically mean as “model within a model-theoretic framework.” Model-theoretic frameworks attempt to describe things in terms of two explicit components (I know this is repeating what you already know, but I have to lay it out on the table before doing something else with it):
· A set of object (“symbols,” “primitives”)
· A set of rules for manipulating the objects
Either implicitly or explicitly, theorists also use a simplicity metric for resolving disputes about competing ways of modeling the same thing in the same system.
There are three points about traditional model-theoretic systems that are problematic when discussing language:
(1) They assume that there are objects to be manipulated.
(2) Traditionally, the operation of the system is fully determinate
(3) Traditionally (again), the simplicity metric is expressed only in terms of number of objects and number of rules.
Point (1) is problematic because, from a philosophical position, one does not have to posit objects, and, from a biological position, the neural network that language “runs on” seems to be all connections, with no objects. That is, while a “rule” might be formulated that describes the operation of the network, there are no observable objects in there being manipulated. The objects may be adduced as theoretical constructs, but the theorist then has to be very, very careful to avoid circular reasoning. Otherwise, you can end up saying that the objects must be there because that’s the only way your model can work, when in fact you started by choosing a kind of model that requires objects to begin with. That kind of argument is based on the initial assumption that your model is correct to start with.
Point (2) makes traditional model-theoretic systems have trouble approaching inherently indeterminate phenomena – the kind of thing that sociolinguists sometimes try to deal with via “variable rules.” In a traditional model-theoretic system, “variable rule” is an oxymoron. The standard way of dealing with the problem is to say either (a) that anything indeterminate is outside language and therefore doesn’t need to be modeled, or (b) there is more than one determinate system, and the speaker is switching among systems. The second option strikes me as being a bit more responsible, but still lets the analyst avoid questioning the initial assumption that the system has to be determinate.
Point (3) leads to simplicity being computed relative to the model as a static whole, not relative to the operation of the model. A version that uses two objects and three rules is automatically simpler than a version that uses five objects and nine rules, even if the “simpler” version requires eighty steps to model a given phenomenon instead of the twenty the second version does.
Generative grammar deals with (2) and (3) via the competence/performance dichotomy – if we accept the dichotomy, then variability is a performance issue (and hence irrelevant) and the operation of the model when performing a given task is, again, performance – and hence irrelevant. It’s an internally consistent position.
Here’s the problem I have with it: People don’t question it enough. It’s one of many, many ways one might model language, but “formalizing” an account usually means having to make it conform to this type of system – objects and rules, full determinism, and atemporal simplicity metrics. The problem is not the framework itself, but rather its hegemonic status. The metrics that would establish this framework as better than others are internal to the framework itself, and while that criticism would hold as well of any comparable framework, not consciously acknowledging it leads to thinking that a statement about the model , by virtue of the fact that it’s expressed in terms of the model, thereby automatically becomes a statement about language. We lose sight of the fact that, while models can reflect (or metaphorically represent) explanations, the act of modeling something – in and of itself – does not constitute explanation. A valid explanation remains valid even if it’s not formalized in a particular framework, and a potentially infinite number of wildly wrong explanations can be easily formalized.
Bill Spruiell
Dept. of English
Central Michigan University