Distributed Morphology Today: Morphemes for Morris Halle

8. “Not Plus” Isn’t “Not There”: Bivalence in Person, Number, and Gender

8 Halle (1957) gives arguments for adopting binary features in phonetics and phonology, but this is unusual; the internal structure of features tends to be assumed rather than argued for. —Corbett (2010, 18) 8.1 Introduction When he was young, Morris Halle taught himself to write backwards (as did I). His method involved decomposing letters into their constituent ascenders, descenders, loops, and humps, and mastering reversal just of this smaller set of primitives. In consequence, an examination of features, the primitives of linguistic representations, is a fitting tribute both to Morris’s long and ongoing contributions to linguistics and to the personality evident in his earliest intellectual excursions. Fundamental to features is the often-neglected issue of valence (cf, Halle 1957 on phonology). Can features be explicitly denied and asserted, or is only assertion explicit, with negation implied by absence? In other words, bivalence or privativity: +F versus −F, or plain F versus nothing? This chapter aims to review the accumulating case for bivalence of person, number, and gender features, from semantics, morphology, and syntax. The evidence strongly suggests, I believe, that explicit reference to negation is necessary and that negation and absence are distinct. Since privativity is more restrictive, the initial burden of proof lies on advocates of bivalence. Yet, as Noyer’s landmark (1992) study of person and number features assumed bivalence, it compels advocates of privativity to produce equal empirical coverage. This has been attempted to good measure (Harley 1994; Harley and Ritter 2002), with Harley 1994 even addressing one case, Mam, where Noyer explicitly argued for bivalent person features. “Not Plus” Isn’t “Not There”: Bivalence in Person, Number, and Gender Daniel Harbour 136 Chapter 8 However, Noyer’s case for the bivalence of number, from Kiowa-Tanoan, has not been reanalyzed in privative terms and Harbour 2011d argues that it cannot be. Moreover, arguments against the privativity of (some) person features occur in Nevins 2007 (on the typology of person-case constraints), Trommer 2008 (on Dumi and Menominee), and Watanabe 2012 (on affix order in Fula). Because my view of person (2012) differs substantially from Trommer’s, Nevins’s, and Watanabe’s, I do not review their arguments here (though I agree with much of them). Instead, I present evidence from four sources, some of which have received little theoretical attention. Section 8.2 examines the semantic composition of trial, unit augmented, and greater paucal in terms of opposing specifications, (+F(−F(. . .))), of a single feature. Section 8.3 treats the morphological composition of persons and numbers that show complementary patterns of inclusion (for instance, inclusive, which sometimes includes exclusive, but is sometimes included by it). Section 8.4, the most traditional, presents “alpha exponents,” which track covariant values of multiple features. And section 8.5 highlights the role that bivalence plays in one theory of the strong person-case constraint (Adger and Harbour 2007) and shows that this permits the account to extend to previously unnoted phenomena in differential marking of (in)animate objects in Tewa.1 8.2 Semantic Compositionality: Function Application of +F to −F A common aim in morphosemantics is to derive maximal coverage from minimal posits. A major result along these lines is the discovery that the (two) features that distinguish singular from minimal pronouns suffice to derive the six number values, comprising three distinct number systems (singular–plural, minimal–augmented, singular–dual–plural), with the appropriate differences in lower bounds of the two plurals (two in dualless languages, three otherwise) (Noyer 1992; see Harbour 2011a for further exposition). In this light, a semantic argument for bivalence comes from the feature composition of trial, unit augmented, and greater paucal, numbers unanalyzed on most accounts. Trial and unit augmented require no features beyond those just alluded to, ±atomic and ±minimal.2 And greater paucal needs no feature beyond ±bounded, which characterizes the basic paucal itself. Rather, these previously recalcitrant numbers arise from function application of +F to −F. Thus, a putative feature±trial is as redundant as ±dual, provided our basic features are bivalent, because only bivalent features afford the −F for +F to apply to. Consider how, featurally, one would add trial to the system singular–dual– plural. For any person or noun n, (−at(n)) picks out the nonatoms of n. The most minimal nonatoms are dyads; hence (+min(−at(n))) is the dual. The nonminimal “Not Plus” Isn’t “Not There” 137 remainder, (−min(−at(n...