The classical factorization of inflectional systems into principal parts and exemplary paradigms embodies a strong hypothesis about the interdependency of forms in a paradigm. A language whose paradigms consisted entirely of mutually independent forms could not be broken down in this way, since no set of forms smaller than a full paradigm would identify the class of an item. Matthews’ observation that predictive relations prevent alternations from becoming too ‘numerous’ on p. 80 is a traditional formulation of what have come to be known as ‘paradigm economy’ effects. A ‘principal parts and exemplary paradigms’ description of a language with weakly interdependent forms would likewise achieve negligible economy and indeed obscure the patterns in the language within a large and unilluminating collection of paradigms that ‘multiplied out’ the unconstrained cooccurrence possibilities. Hence patterns of mutual implication in a system must be fairly tight in order for classical factorizations to simplify rather than complicate the description of the system. Implicational relations between the forms of a lexeme play a similar role in constraining the size of the principal part inventories required to describe conjugational systems comprising multiple paradigms and series.
At the same time, it is important to recognize that the interpretation of familiar notions such as ‘paradigm’ and ‘principal part’ taken over from pedagogical and reference grammars is strongly coloured by the uses to which the notions have been put in descriptive sources. It is usually assumed that inflectional systems can be factored into a discrete number of inflection classes, each represented by the full paradigm of some exemplary member of the class. Principal part inventories are likewise taken to be ‘static’ in the sense of Finkel and Stump (2007), in that each non-exemplary item of a given class is represented by the same forms or sets of forms, e.g., the nominative singular or first person singular indicative active. The deduction of new forms from exemplary paradigms and principal parts is in turn attributed to the operation of symbolic processes of the kind typically expressed by proportional analogies.
Insofar as these assumptions contribute to the “scientific compactness” so prized by Bloomfield (1933: 238), they play a well-defined role within standard pedagogical and descriptive grammars. But, as with Bloomfieldian notions of ‘compactness’ and ‘concision’, these assumptions contribute to the economy and uniformity of a classical WP model when it is interpreted as a template for (usually written) grammatical descriptions. There is no justification for maintaining these kinds of idealizations when, following Robins (1959), classical WP accounts are interpreted as models of the acquisition and use of language by speakers. The contrast between pedagogical and psychological interpretations of WP models is, again, clearly drawn by Hockett (1967):
There would remain this difference: the situation for the student is artificially simplified. He is enabled to operate, in his analogizing, in terms of a neat minimal set of reference paradigms and a fixed point-of-departure set of principal parts. The native user of the language, of course, does not do this. He operates in terms of all sorts of internally stored paradigms, many of them doubtless only partial; and he may first encounter a new basic verb in any of its inflected forms. For the native user, the forms that we have for convenience selected to be our ‘principal parts’ have no such favored position. They are as likely to be created analogically, as needed, as are any of the other forms. (Hockett 1967:221)
Unsurprisingly, each of the familiar pedgagogical idealizations creates problems for classical WP accounts when these accounts are interpreted as general morphological models. The practice of identifying a single exemplary paradigm for each inflection class of a language, if taken literally, gives rise to the pseudo-problem of selecting ‘the’ exemplary paradigm for each class. It is of course possible to specify selectional criteria. One could, for example, select the lexeme whose forms had the the highest summed frequency. However, as Hockett (1967) observes in the passage on p. 93 above, the real problem lies in the idealization that speakers must impose a rigid separation of exemplary paradigm and principal part and then find themselves compelled to pick one item as exemplary. Any psychologically plausible WP model would represent classes by families of paradigms that reinforce a pattern. As Hockett once again stresses, there is no reason to assume that the patterns need be represented by full paradigms for each item. Given the suggestive connection between frequency and storage established by Stemberger and MacWhinney (1986) and Bybee (1999, 2010), among others, the split between exemplary and analogized forms is likely to come down to frequency. Exemplary patterns will then be emergent generalizations over partial paradigms, themselves composed of forms that occur above the frequency threshold for storage.
Questions about the number and composition of inflection classes raise analogous issues. Within a pedagogical tradition, there may be broad agreement concerning the approximate number of classes in a language. However, as in the case of agreement regarding the choice of exemplary items, this consensus usually reflects established practices or shared pedagogical goals. Attempts to enumerate the classes of a language confront essentially the same kind of analytic indeterminacy at the paradigm level as attempts to identify ‘correct’ segmentations at the word level. Just as descriptions of Romance verbs explore the possible space of segmentations into roots, theme vowels and inflections, estimates of the number of declension classes in a language like Estonian vary enormously between sources. At one extreme, Saagpakk (2000) recognizes over 400 types, organized into six classes and Murk (1997) distributes 260-odd types over eight classes. More conservative estimates are offered by Erelt (2006:18ff.), who identifies 38 basic ‘word types’, Viks (1992:43ff.), who distinguishes 26 nominal ‘types’, and Erelt et al. (1995:333), who give twelve basic ‘exemplary declensional paradigms’. Karlsson (2006:476) reports similar variation in descriptions of Finnish.
There is no principled basis for adjudicating between these kinds of divergent estimates because they are merely descriptions at different levels of generality, designed to serve different needs. Again like segmentations, classifications of word forms are not ‘more or less correct’ in some absolute sense but ‘more or less useful’ for a particular purpose. The classes are part of a description imposed on a language, not discovered ‘in’ the language, so that estimates of the number and type of classes can only be evaluated against the intended purposes of the classes. In a grammatical description, prepared for reference or pedagogical purposes, it is clearly useful to adopt a fixed classification scheme. However, this is not a constraint that has any counterpart when classical WP approaches are construed as general morphological models. Native speakers are under no pressure to reach a decision about the precise number of classes in a language, any more than they are constrained to identify exemplary items. Instead, they are free to analogize over classes and patterns at different levels of specificity in the production or interpretation of novel forms.
The difficulty of motivating the choice of principal parts (or ‘leading forms’) is the third and most familiar of this group of recalcitrant problems:
One objection to the Priscianic model... was that the choice of leading form was inherently arbitrary: the theory creates a problem which it is then unable, or only partly able, to resolve. (Matthews 1972:74)
The origin of this problem is transparent. For pedagogical purposes, it is clearly useful to draw the most informative cells of a paradigm to the attention of language learners. It is particularly useful to emphasize diagnostic cells that unambiguously identify class. Some theoretical accounts integrate this pedagogical desideratum into a general model of paradigm organization or a morphological acquisition strategy. A consequence of the Paradigm Economy Principle of Carstairs (1983) (discussed in Chapter 7.3) is that every inflection class system will have some maximally allomorphic cell that predicts the variation in the other cells. The Single Base Hypothesis of Albright (2002) likewise constrains the bases available to learners in the course of paradigm acquisition:
The first [hypothesis JPB] is that learners are limited to selecting a single form as the base, and that the base must be a surface form from somewhere within the paradigm. Furthermore, the choice of base is global, meaning that the same slot must serve as the base for all lexical items. (Albright 2002: ix)
However, there is no reason to assume that a single form will always identify the inflectional pattern of an item. And even in systems that contain such a form, there is no guarantee that a speaker will encounter that form first. As Hockett (1967) remarks above “[t]he native user of the language ... may first encounter a new basic verb in any of its inflected forms”. The binary split between principal parts (or cells or bases) and the forms that are deduced from these privileged elements provides a misleadingly idealized description of inflectional systems. Although individual forms vary in informativeness, they vary as a matter of degree, and there are almost always multiple combinations of partially informative forms that identify the other forms of an item.
All of the standard assumptions discussed above are reasonably well motivated in the pedagogical or descriptive contexts in which they arose. The assumptions only become problematic when classical WP accounts are reinterpreted as general morphological models. Those assumptions with natural counterparts in a general model will be susceptible to explicit analysis. In particular, the problem of principal part selection can be subsumed under the more general problem of measuring relative informativeness. This problem can be approached using information-theoretic notions of uncertainty and uncertainty reduction to model the interdependence of paradigm cells, as discussed in Chapter 7. Familiar principal parts will correspond to cells that eliminate all (or nearly all) uncertainty, but they just represent limiting cases. The same formal measures identify cells that reduce uncertainty about a subset of other cells, as well as sets of cells that are collectively diagnostic.
Moreover, just as the classical WP model is defined primarily by implica- tional relations, and only secondarily by specific units of analysis (‘words’ and ‘paradigms’), the structure of an inflectional system will be modelled by networks of implications, expressed in terms of uncertainty reduction. One type of implication holds between cells and patterns of exponence. A second type holds between pairs (or clusters) of cells. An inflection class in the broad sense is defined by any mutually consistent set of inflectional implications. Standard classes will again be definable as limiting cases, corresponding to maximally specific sets of implications. Reconstructing notions like ‘principal part’ and ‘inflection class’ in terms of implicational relations thus preserves the central role of these notions. However, this interpretation jettisons the pedagogical baggage that these notions had acquired and highlights the fact that they are part of a classification scheme and not elements in a language.
Extracting pedagogical idealizations from notions like ‘paradigm’ and ‘inflection class’ addresses some reservations about the relevance of these notions to a general model of morphology. Within the Post-Bloomfieldian tradition, there are also avowedly ‘atomistic’ approaches that entirely reject the classical notion of morphological ‘units’ consisting of collections of forms. In much the same way that classical models lack counterparts of morphemes, these approaches tend to regard paradigms as ‘descriptive artifacts’ or ‘epihenomena’. Yet this assessment of paradigms is itself largely an artifact of a method of analysis. By reducing words to inventories of stems, exponents and combinatory rules, radically constructivist models disrupt any morphological relations that hold across larger networks of words. To the extent that those relations are preserved at all, they are encapsulated in the system of rules and constraints employed to construct words from smaller parts. Relations between these ‘outputs’ can only be expressed in terms of relations between their parts or between the derivations that combined them. The claim that paradigms have no “theoretical significance” thus makes a virtue of necessity.
The descriptive cost of this theoretical virtue is described in a preliminary way in this chapter and elaborated in more detail in those that follow.
-  Paradigm and lexeme economy effects are discussed in more detail in Chapter 7.3.
-  Finnish declensional patterns and their relevance for measures of inflectional economy arediscussed at more length in Chapter 7.3.
-  These relations are most familiar as ‘rules’ that define the formal ‘spell-out’ of features in therealizational models in Chapter 6. However, as discussed in Chapter 7 the same relations can also beinterpreted as constraints that are satisfied (or not, as the case may be) by pairs consisting of paradigmcells and full word forms.
-  From the perspective adopted by Muller (2002:113), “the notion of paradigm emerges as anepiphenomenon without theoretical significance”.