- Bare grammar: Lectures on linguistic invariants
Linguistic structure occurs at different scales. At one level, where we model the relation of language to consciously observable physical events (e.g. speech, writing, signing), the postulation of linguistic structure plays an essential role in explaining why we can judge one and the same physical entity in more than one way and why we can judge distinct physical entities to be linguistically [End Page 652] equivalent. For example, a single acoustic event can represent both John Seams is sleeping and John seems is sleeping. If we regard the first of these as grammatical and the second as ungrammatical, then it is clear that these contradictory judgments cannot be consistently supported by the single postulated physical event alone. We need more. In this particular case, we gain partial insight into the difference between these distinct abstract analyses from the orthographic distinctions between Seams and seems and the consequences of this distinction (whatever these may be). We lack complete intuitive access to the nature of this structure (just as we lack intuitive access to structural properties of experience in other cognitive domains, such as vision), but we have an arsenal of tests, techniques, and assumptions that we use to resolve, temporarily at least, the structural questions that face us.
At other levels, the question of structure may be even less intuitive. We can describe the structure of a language as a whole by appealing to the properties of a grammar of it—essentially falling back on the structural properties and relations we use to model linguistic entities—or by using the comparison of a set of languages with one another to reveal the important structures we attribute to each. In Bare grammar, and in courses and lectures in many venues, two creative, linguistically knowledgeable, and mathematically talented scholars, Edward Keenan and Edward Stabler, explore a different approach.
Informally, one can think of their program as starting with an investigation of the intuitive relation 'has-the-same-structure-as', as this applies to pairs of expressions from a given language. The interest of this relation was anticipated by Jespersen (1965:19):
even without any special grammatical training we feel that the two sentences
John gave Mary the apple,
My uncle lent the joiner five shillings,
are analogous, that is, they are made after the same pattern. In both we have the same type. The words that make up the sentences are variable, but the type is fixed.
But K&S are the first to study this relation with the sophisticated tools that contemporary mathematics provides, yielding a diverse set of structural conclusions. Their investigation draws on the rich tradition that goes back to the Erlangen Program of Felix Klein (1872),1 who introduced a perspective in which different geometries (e.g. projective, affine, Euclidean) correspond to different algebraic groups of transformations: a group is appropriate for a geometry if the automorphisms of the group preserve exactly the essential properties of the geometry. How can this deep and valuable perspective be applied to grammars, rather than geometries?
K&S ground their investigation of linguistic invariants in a simple and powerful formal framework— the 'bare grammar' of their title. They introduce this framework in the first chapter, along with some basic definitions and a quick survey of some of the highlights to come. Ch. 2 consists of a number of small case studies (three and a half by K&S's count): toy grammars that are simple enough to present in a page or two, yet rich enough to illustrate and support significant claims. Ch. 3 provides an interesting comparison of a broad spectrum of competing frameworks, including context-free grammars, classical categorial grammars, combinatory categorial grammars, pre-group grammars, multiple component context-free grammars, and some constraint-based grammars (first-order model-theoretic grammars, monadic second-order model-theoretic grammars, and versions of optimality-theoretic grammars). The conclusion of Ch. 3 contains a table listing a number of interesting properties of formal...