Scalar operators

Why should polarity items be sensitive to scalar inferencing? In some cases the answer is simple. Just like the quantificational superlatives, many NPIs literally designate a scalar endpoint. Some are themselves superlatives indicating minimal degrees: the foggiest notion, the least bit, in the slightest. Others, like sleep a wink, lift a finger, and a shred of evidence, feature a stereotypical minimal unit on some scale. These minimizer NPIs are like superlatives which only allow a quantificational reading: they have no inherent referential value, and so they cannot refer to a specific minimal unit, but they can be used emphatically, as a way of triggering reference to the ordered set of elements on a conceptual scale. And of course this is only possible in scale-reversing contexts, where pragmatic inferences are licensed from lower to higher scalar values.

So, at least for the minimizer NPIs, the sensitivity to scalar inferencing seems intuitively well motivated. But how should this sensitivity be represented in the lexicon? And more importantly, will this sort of intuitive explanation extend to other polarity items with similar sensitivities but with very different scalar semantic properties? This chapter seeks answers to these questions by exploring the hypothesis that polarity items in general constitute a broad but well-defined class of scalar operators.