Between “cost” and “default” of Scalar Implicature

The ongoing theoretical debate Scalar Implicatures (SIs) are pragmatic inferences that are normally derived in conversational exchanges when a scalar term is used. Different theoretical accounts have been proposed to explain how and when implicatures are derived. We will focus here on one particular aspect of this debate, namely, the question of the “cost” of implicature computation, which has been the centre of the most recent debate between supporters of Relevance Theory on the one hand (cf., a.o., Sperber and Wilson, 1986) and of Default approaches on the other (cf., a.o., Levinson, 2000). Under the latter view, implicature computation constitutes a default process, i.e. something that our computational/processing system performs automatically, thus it is by definition virtually costless. On the Relevance Theoretical view, instead, every operation imposed to our processing system must be evaluated in terms of “costs and benefits”, ultimately in terms of “relevance” to contextual assumptions: SIs are only computed if they are relevant enough to be worth a processing effort. Between these two approaches, there is a third proposal, very recently delineated by Chierchia (2006), whose intent is that to provide a unified account of the phenomenon of SI and negative polarity. In Chierchia’s new proposal, a binary feature σ is introduced as regulating the activation of scalar alternatives associated to scalar and negative polarity items. This feature can be assigned two values: [± σ]. Selecting [+σ] results in the activation of the scalar alternatives (ALTs henceforth); selecting [-σ] results in the selection of the plain meaning in which ALTs are not active. The crucial point is that, whenever the feature [+σ] is selected, then the constraint on strengthening applies and an exhaustivization operator O (which has a meaning akin to that of only) must be used. Very informally, the operator O applied to a sentence containing a scalar expression of the form “A or B” in which the ALTs are active will result in the derivation of the scalar implicature associated to or: O (singing or[+σ] dancing) = only (singing or dancing) = only (singing or dancing) and not (singing and dancing). For our purposes, it suffices saying that the result of this mandatory operation always leads us to select the strongest (i.e. most informative) interpretation of a sentence containing a scalar item. Crucially, adding an implicature in Downward Entailing (DE) contexts leads to a weakening of the overall assertion (given that informativity is “reversed”), while it leads to a strengthening in case the scalar term appears in a NON-DE context. With respect to sentences (1), representing a DE context, and (2), representing a NON-DE context, we can derive the distributional generalizations listed below (if ALTs are active as the result of a subjective choice):