Scalar inferences have been shown to differ in strength. As an example, consider the contrast between the cardinal numerals “three” and the quantifier “some”: the scalar inference from “three” to “not four” is felt to be stronger than that from “some” to “not all” in some cases. Four diagnostics of strength corroborating this contrast are the following: 1) The stronger inference of the cardinal is more difficult to cancel, 2) easier to embed, 3) acquired earlier by children, and 4) accessed faster and more easily in online language processing. Several researchers have therefore claimed that cardinals like “three” must receive a fundamentally different analysis from other scalars. However, disjunction also exhibits a strength difference: “either A or B” is intuitively felt to more strongly exclude the truth of both A and B than a bare disjunction “A or B” does. Most proposals for cardinals cannot be extended to “either-or” As far as we know, there has been no general discussion of strength of scalar inferences within pragmatic theory despite numerous individual observations.
The goal of this project is to develop a theory of the strength of scalar inferences that extends beyond cardinals. Our empirical basis is a detailed investigation of the four diagnostic mentioned above for the pair of “or” and “either-or”. In addition to offline judgment tasks, we gather data from language acquisition and online language processing using self-paced reading, eye-tracking and mouse-tracking. Furthermore we engage language comparisons between German and Japanese since in several respects our experimental tests are easier to apply in Japanese. Within pragmatic theory, our goal is to develop a uniform theory of strength. In particular, we test the hypotheses that obligatory activation of alternatives within the grammatical analysis of implicatures underlies at least the two core cases of scalar inference strength.