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From exemplars to discriminative contrasts

Let us now summarize the broader issues under consideration here. One conclusion that can be drawn from this discussion is that studies of economy effects from different perspectives lend support to the claims underlying principles like the PEP or NBP. The “tendency” that Carstairs (1983:127) discerns “towards keeping the total of paradigms for any word class close to the logical minimum” appears to be robustly attested in paradigmatic systems. Morover, from a classical WP perspective, this tendency derives from the implicational structure of inflectional systems. Within a modern WP model, this structure can be measured in information- theoretic terms. The correspondence between economy effects and paradigm entropy thus illustrates another dimension of a classical WP model that can be reconstructed in uncertainty-based terms. As with the selection of principal parts and the validation of analogies, a formal reconstruction of economy in terms of uncertainty carries no commitment to the kinds of pedagogical idealizations that usually accompany these notions.

More generally, a reconceptualization of economy effects in terms of uncertainty-reducing interdependencies conforms to the general uncertainty- sensitive perspective of a classical WP model. The importance attached to words in Section 71 can be seen tobe motivated by the contribution that their morphotactic and morphosyntactic stability makes to reducing uncertainty in the association between properties and forms. At the level of form, the word is a maximally discriminable “perceptual gestalt” (Hockett 1987:52). At the level of grammatical meaning, the word provides “a more stable and solid focus of grammatical relations than the component morpheme by itself” (Robins 1959:128). As discussed at greater length in Sections 7.2 and 7.3, the affiliation between words and paradigms also reduces uncertainty, by exploiting the information implicit in the interdependencies between cells in a paradigm.

The selection of words and paradigms in WP models thus serves the goal of minimizing grammatical uncertainty (rather than minimizing unit or inventory size). The core claims that underlie the exemplar-based structure of a classical WP model can be summarized as in (7.2).

(7.2) a. The uncertainty that arises in associating grammatical properties with word forms is less than (or equal to, in the case of simple forms) the sum of the uncertainty that arises in associating properties with the component morphs of those word forms. b. The uncertainty associated with the set of cells of a paradigm is less than (or equal to, in the case of single-cell paradigms) the sum of the uncertainty of each of the component cells.

The usefulness of information theory for quantifying the notions of ‘uncertainty’ and ‘uncertainty reduction’ is highly suggestive, particularly given that an entropy- based formalization appears to offer solutions to problems that have traditionally been regarded as recalcitrant for the WP model. A formal reconstruction of WP models in terms of uncertainty helps to clarify the fundamental questions raised by the descriptive success of this model. Foremost among these are the issues of how variation at the level of individual forms determines the implicational structure of systems, why inflectional systems exhibit the type of structure and the degree of economy that they do, and even why information theory is a useful tool for measuring this structure. These issues are taken up from a discriminative standpoint in the final chapter.

 
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