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Variation as uncertainty

Although informativeness remains implicit in the classical WP model, this ultimately reflects the purposes for which the model was initially developed. An explicit formalization of the classical WP model can be founded on two basic assumptions. The first is that variation within a system corresponds to uncertainty. The second is that implicational structure within the system corresponds to uncertainty reduction. The various notions of ‘informativeness’ mentioned above likewise represent different types of uncertainty reduction. The role of uncertainty is also reflected in the selection of units and structures. As discussed in Chapters 3 and 4, neither words nor paradigms have a privileged status a priori in a classical WP model. The abstraction of word-sized units and their assignment to larger paradigmatic structures is justified by the reduction in uncertainty that this achieves in a grammatical analysis.

There is an obvious trade-off between the determinacy and the generalizability of a unit. At the level of utterances, many of the ambiguities that arise at lower levels are resolved, as Bloomfield (1914) remarks. Yet a grammatical analysis that merely classifies utterances is universally regarded as too coarse-grained, obscuring regular associations between smaller recurrent units of form and meaning. An analysis into phonemes suffers from the opposite problem, disrupting associations between larger units and properties. Differing assessments of the trade-off between determinacy and generalizability lead approaches to select different units between utterances and phonemes.

As discussed in Chapter 4.1, the choice of segmentally minimal units within initial models of morphemic analysis is motivated by the goal of maximizing “scientific compactness”. In contrast, the selection of word-sized units in the classical WP tradition reflects a conception of economy based on the minimization of indeterminacy and the efficient characterization of patterns, rather than on the avoidance of redundancy. A central claim of classical WP models is that words exhibit a morphosyntactic and morphotactic stability that contributes to maximally general descriptions of regularities within a system.

Robins (1959) provides a traditional statement of this position on p. 6 above when he claims that “the word is a more stable and solid focus of grammatical relations than the component morpheme by itself”. In uncertainty-based terms, the uncertainty that arises in associating grammatical properties with a word is on average less than the cumulative uncertainty that arises in assigning properties to its parts. The association between words and paradigm cells (or other property sets) ‘anchors’ a form within a grammatical system, facilitating implicational deductions that further constrain uncertainty within the system.1 The conception of a morphological system as a structured network of individually stable units determines a notion of economy which corresponds to the characterization of “morphological simplicity” in Bochner (1993:2) “as conformity with patterns of the grammar, rather than as brevity”.

In sum, the status of words in implicational models ultimately reflects the claim that word-sized units minimize uncertainty along both dimensions of a grammatical analysis. Along the syntagmatic axis, words are minimal in the sense that any disassembly into smaller units creates greater uncertainty. Along the paradigmatic axis, words are the minimal units that participate in uncertainty- reducing implicational relations. These dimensions of uncertainty are elaborated in Sections 7.1.1 and 7.1.2 and formalized in Section 7.2.

 
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