A puzzle for theories of redundancy: exhaustification, incrementality, and the notion of local context

The present paper discusses novel data which are problematic for assertability con- ditions based on redundancy (Stalnaker 1979, Fox 2008, Schlenker 2009, Singh 2007, Chierchia 2009, Meyer 2013, Katzir & Singh 2014 among others). The problem comes from disjunctions like Either Mary isn’t pregnant or (she is and) it doesn’t show and in particular from the optional presence of she is (pregnant). These data are even more puzzling if compared to corresponding conditionals like If Mary is pregnant, (#she is and) it doesn’t show where the she is (pregnant) part is unacceptable as expected. In response to this puzzle, we present two solutions: the first is based on a notion of incrementality without local contexts as proposed by Fox (2008, 2013), building on Schlenker 2008, and a constraint on the interaction between redundancy and exhaustification proposed in Meyer 2013. The second solution is based on Schlenker’s (2009) incremental theory of local contexts. In this system, exhaustifying a sentence can modify the local contexts of its parts. As a consequence of this, she is (pregnant) is actually not redundant in the disjunctive sentence above, provided the latter is exhaustified. We also discuss how this solution is not readily reproducible in an approach where local contexts are computed com- positionally from the syntactic structure of the sentence in question, as traditionally in dynamic theories (Heim 1983, Beaver 2001; see also Chierchia 2009). Therefore, this second solution, if correct, is an argument for the incremental approach to local contexts. Finally, we briefly compare the two solutions and point to a potential advantage of local contexts-based solution in dealing with the different readings of the disjunctive sentence above. We also discuss other issues that the disjunctive case above raises in connection to embeddings, the calculation of alternatives, and presupposition projection