Decomposing Logic: Modified Numerals, Polarity, and Exhaustification

Abstract

This dissertation investigates differences with respect to ignorance and anti-negativity in modified numerals, using as a starting point similar variation among various types of disjunction and indefinites, and their analysis under an alternative-based approach. In Ch. 1 I lay out the empirical patterns with respect to ignorance and anti-negativity for the English disjunction or and the English indefinite some NP SG, and show that with respect to ignorance CMNs are like some NP SG and SMNs like or, while with respect to anti-negativity CMNs are like or and SMNs are like some NP SG . Using insights from the existing literature, I show how these patterns can be derived for or and some NP SG . The overarching goal of the thesis is to extend this approach to CMNs and SMNs. The first step in extending the approach to CMNs and SMNs is to clarify their formal similarity to or and some NP SG . I do this in Ch. 3, where I offer a new way to decompose their truth conditions and derive from them their alternatives. A prediction is that CMNs and SMNs should give rise to scalar implicatures. This prediction goes against the received view. I defend it in Ch. 3. The solution to ignorance in CMNs and SMNs is given in Ch. 4. It is based on obligatory exhaustification relative to pre-exhaustified subdomain alternatives, and a subdomain alternative pruning parameter. I also discuss predictions and general fit to the existing experimental evidence. The solution to anti-negativity in CMNs and SMNs is given in Ch. 5. It is based on obligatory exhaustification relative to pre-exhaustified subdomain alternatives, and a proper strengthening parameter. New experimental evidence regarding anti-negativity patterns is also presented and discussed. Ch. 6 offers a global summary and directions for future research.