The symmetry problem: current theories and prospects

The structural approach to alternatives (Katzir, 2007, Fox and Katzir, 2011, Katzir, 2014) is the most developed attempt at solving the symmetry problem of scalar implicatures in the literature. Problematic data with indirect and particularised scalar implicatures have however been raised (Romoli, 2013, Trinh and Haida, 2015). In an attempt to address these problems, Trinh and Haida (2015) recently proposed to augment the theory with the Atomicity Constraint. In this paper, we show that Trinh and Haida’s Atomicity Constraint falls short of explaining minimal variants of the original problems, and moreover that it runs into trouble with the inferences of sentences involving gradable adjectives like full and empty. We furthermore discuss how the structural approach suffers from the problem of ‘too many lexical alternatives’ pointed out by Swanson (2010) and the opposite problem of ‘too few lexical alternatives.’ These three problems epitomise the challenge of constructing just enough alternatives under the structural approach to solve the symmetry problem in full generality. Finally, we also sketch another recent attempt at solving the symmetry problem, which is the approach based on relative informativity and complexity by Bergen et al. (2016), and we argue that they also do not provide a general solution to the symmetry problem, by pointing to some of the open problematic cases for this approach as well. We conclude that while important progress has been made in the theory of alternatives for scalar implicatures in the last few years, a full solution to the symmetry problem remains an important open challenge for such theories.