Chapter 8: The marginal detraction hypothesis

In this chapter, we distinguish between central and marginal ICs. The more members an IC has, the more central it is in a language's inflectional morphology; the fewer members an IC has, the more marginal it is. This distinction relates purely to type frequency (the proportion of a language's lexemes in each of its ICs) and not at all to token frequency (the incidence of each lexeme or IC in a corpus). This definition should not be taken to suggest that we regard measures of token frequency as irrelevant to IC phenomena, but only that measures of type frequency reveal significant properties of IC systems. There is, of course, no logical necessity that central and marginal ICs should differ in their characteristics; indeed, the null hypothesis is that there is no systematic difference between the properties of central ICs and those of marginal ICs. Empirical evidence to the contrary is therefore significant. We provide evidence for the following hypothesis: Marginal ICs tend to detract most strongly from the IC predictability of other ICs. Intuitively, IC predictability is the fraction of subsets of a paradigm's cells that suffice as predictors of all of its other cells (given a particular universe of contrasting ICs) ­ ― the fraction of subsets of a paradigm's cells that constitute adequate (though not necessarily optimal) dynamic principal-part sets for that paradigm. We begin our discussion by explaining the notion of detraction from an IC's predictability, then investigate this notion in the context of Icelandic verb inflection. After a brief survey of Icelandic conjugation classes, we present a plat for their analysis, including various contrasting sub-plats, which we use to show that in Icelandic, marginal conjugations detract from the IC predictability of central conjugations more than central conjugations detract from the IC predictability of marginal conjugations. We propose a partial explanation for this observation, namely the fact that in Icelandic, marginal conjugations require more distillations than central conjugations. We discuss the significance of this fact and propose a deeper explanation for the observed asymmetry in detractiveness among marginal and central conjugations. We reëxamine our French data, demonstrating that it provides further confirmation for the Marginal Detraction Hypothesis.