Lieb, Hans-Heinrich. 2005. "Notions of paradigm in grammar"
Lieb, Hans-Heinrich. 2005. "Notions of paradigm in grammar".

In: D. Alan Cruse, Franz Hundsnurscher, Michael Job, and Peter Lutzeier (eds). Lexikologie / Lexicology: Ein internationales Handbuch zur Natur und Struktur von Wörtern und Wortschätzen / An international handbook on the nature and structure of words and vocabularies. Vol. 2. Berlin etc.: de Gruyter. (= Handbücher zur Sprach- und Kommunikationswissenschaft 21.2). 1613–1646.


A. Table of contents

  1. Paradigm conceptions: History and current state
    1.1 Introduction
    1.2 The Greek and Latin tradition
    1.3 Theodosius Alexandrinus: the Kanones
    1.4 Evaluation
    1.5 Analytic forms: a modern problem
    1.6 Paradigms: the second half of the 20th century
    1.7 Are word paradigms morphological?
    1.8 The ontology of paradigms
    1.9 "Paradigm": towards a formal explication
  2. Orientation: Categories and forms
    2.1 Forms of words: example
    2.2 Relational category labels and category terms: example
    2.3 Functional categories: syntactic and morphological
    2.4 Form categories for simple forms
    2.5 Form categories for analytic forms
    2.6 Definition of terms vs. identification of categories
  3. The concept of word paradigm: Outline of an explication
    3.1 Syntactic paradigm bases: the first six components
    3.2 Syntactic paradigm bases: the seventh and eighth components
    3.3 Syntactic paradigm bases: the ninth component
    3.4 Syntactic paradigm bases: a detailed account
    3.5 Proper and improper paradigms
    3.6 "Word paradigm", "improper paradigm", "proper paradigm": definitions
    3.7 Defining "lexical word"
    3.8 Towards a general concept of paradigm
  4. Exemplification: English noun paradigms
    4.1 English nouns with analytic forms: a sample paradigm
    4.2 The functional Nf system
    4.3 Sets permitted by the functional system
    4.4 The structural Nf system: simple forms
    4.5 The structural Nf system: analytic forms
    4.6 The system link
    4.7 The notion of going-with: example
    4.8 The sample paradigm as a word paradigm
  5. Literature (a selection)

B. Abstract

This handbook article begins by characterizing paradigm conceptions as found in the history of linguistics (Section 1), with an emphasis on Greek and Latin Antiquity on the one hand and, on the other, the second half of the twentieth century up to the present. The main part of the article is devoted to a detailed reconstruction of traditional and modern conceptions of word paradigms, with some suggestions made for morphological (stem and affix) paradigms (Sections 2 and 3); the proposed framework for paradigms is then exemplified (Section 4) by applying it to nouns in Modern English, whose paradigms are construed so as to include analytic (Art + N) forms. The main text is followed by a bibliography of roughly one hundred entries.
Section 1 characterizes, in particular, the detailed paradigm lists formulated for the Greek verb by Theodosius Alexandrinus (4th century AD), who naturally included analytic forms in his verb paradigms, forms that tend to create problems for modern paradigm notions. All through antiquity right into the Middle Ages, the forms of any word paradigm were characterized in non-morphological terms since no notion of stem was available: formally, all forms of a paradigm are 'derived' from a few basic forms by referring to differences between forms regarding their sound (or letter) structure, or their syllable structure; at the same time, any form of a paradigm is characterized in terms of grammatical meaning by being associated with a set of functional categories, such as Person categories or Tense categories. Section 1 of the article goes on to outline the fate of this 'word and paradigm' (WP) model in twentieth-century linguistics, concentrating on its increasing popularity in recent morphology. Various problems, especially finding an adequate treatment for analytic forms, are pointed out.
In Sections 2 and 3, a concept of word paradigm is developed that retains essential properties of notions of paradigm implicit in the linguistic tradition up to and including recent adaptations of the WP model but avoids the shortcomings of such notions. In particular, analytic forms, assigned to syntax, are analysed as consisting of a main part and a non-empty auxiliary part, and the main part as consisting of a centre (the centre of the form) and a periphery, which may be empty. This conception is generalized to simple forms, with an empty auxiliary part. A simple form with an empty periphery is synthetic, i.e. is the unit sequence of a phonological word (in a sense where a phonological word may but need not be identifiable by phonological means alone). Any form, be it analytic or simple, is a sequence of phonological words. Forms with a non-empty periphery are forms of idioms; such forms are sequences whose length is at least 2. Any paradigm form, including synthetic forms, is a syntactic unit that occurs in a sentence as a primitive constituent: none of its proper parts (main part etc.) is again a constituent, is again associated with a constituent category.
A word paradigm is a relation between syntactic units (the forms of the paradigm) and sets of functional syntactic categories (such as 3P, Sg, Ind, Pres, etc., in the case of English verbs); put differently, a word paradigm is a set of pairs that each consist of a syntactic unit and a set of categories (a categorization of the unit). The nature of these categories is clarified: each is a set of syntactic units that is characterized by means of a general sentence-semantic definition in the theory of language (a definition for a term such as "Present") but is identified in the grammar of the given language in purely formal terms (allowing for reference to lexical meaning), i.e. the grammar contains theorems that permit to identify each category on the basis of the form (and possibly, the lexical meaning) of syntactic units.
In a form/categorization pair  f, J , the form f is an element of each category in the categorization J. For a given paradigm there must be a concept b such that it is true of each pair  f, J  in the paradigm that the concept is a meaning of f given J. Concept b then is also a meaning of the paradigm itself.
All lexical meanings are construed as concepts in a specific sense that also allows for an 'empty concept' bo to account for syntactic units in cases where normally no conceptual meaning would be assumed. Relaxing certain requirements on categorizations, the notion of 'improper paradigm' is introduced, which allows us to spread the paradigmatic approach beyond its traditional application (to 'proper paradigms', such as verb paradigms in English): extend it to include paradigms, 'improper' ones, also in the case of lexical words such as the English negation particle not.
Word paradigms are relations between syntactic units and sets of syntactic categories that are sets of syntactic units. Word paradigms therefore belong to syntax not morphology, differently from stem paradigms and, if admitted, affix paradigms, which do belong to morphology. The nature of morphological paradigms is briefly considered but not discussed in any detail.
The notion of word paradigm is defined independently of the notion of lexical word; thus, "lexical word" can be defined using "word paradigm". Such a definition is proposed.
For any approach using concepts of word paradigm it is paramount to answer the question of how word paradigms are given in (the idiolects of) a language. It is suggested that word paradigms of a given type, such as noun paradigms, result from a 'syntactic paradigm base'. This is a nine-tuple consisting of:
  1. a basic set M, which is a proper or improper subset of one of the basic constituent categories Noun form, Verb form, and Particle form;
  2. a function R1 — the main part function — that assigns to each form in the basic set its main part;
  3. a function R2 — the centre function — that assigns to each form in the basic set its centre;
  4. a classification system O1 on the basic set — the structural system — that supplies syntactic form categories, such as, for English, 'simple verb form with s-suffix' (O1 may be empty);
  5. a second classification system — the functional system — on the basic set that supplies functional syntactic categories, such as, for English, 3P or Pres (O2 may be empty);
  6. a two-place relation R3 — the system link — that relates sets of form categories to sets of functional categories;
  7. the stem-assignment base N and
  8. the stem assignment R4: two components needed to collect the right form/categorization pairs  f, J  as elements of a single paradigm; and
  9. a relation R5 — the meaning relation — that relates concepts b to forms f and their categorizations J, a relation used to satisfy the 'same-meaning requirement' for the pairs  f, J  in a paradigm.
Section 4 exemplifies this conception by applying it to the English noun, in particular, the English substantive. Substantival paradigms in Modern English are assumed to contain both simple forms, which may be synthetic: the unit sequences of door and doors — and analytic forms: a door, the door, the doors, some door, some doors, any door, any doors, no door, no doors (where the phonological words a, the, some, any, and no that provide the auxiliary parts all inherently lack word accent). Since no proper part of an analytic form is a constituent, the problem of NP vs. DP no longer arises for a form like the doors, assigned, in its entirety, to Noun form: neither the the-part nor the doors-part is a head of the doors; rather, the doors, an analytic form, is a head of itself.
The proposed conception of word paradigms is exemplified in Section 4 by characterizing the paradigm base for English nouns and using this base for constructing a sample substantival paradigm.