Natural languages provide pairs of determiner phrases that are in some sense equivalent but that contrast in the ignorance inferences that they license. English provides ‘the’- and ‘whatever’-DPs – as in ‘the book she is holding’ vs. ‘whatever book she is holding’ – and ‘a’- and ‘some N or other’-DPs – as in ‘a book’ vs. ‘some book or other’. Similarly contrasting pairs are found in Spanish, German, Japanese, Hebrew, etc. This dissertation considers two hypotheses about the grammatical difference between the members of these pairs. The first is that the ignorance-implying members encode the concept of ‘unsettled’ or ‘unknown’, and the second is that they encode a disjunction of contextually-determined identifying properties, with the assumption that pragmatic principles are obeyed producing ignorance inferences. After examination of the meaning-contribution of these expressions in the scope of quantificational operators, the second hypothesis is found to be more empirically adequate. Various theories about the linguistically-privileged ways of knowing something or someone’s identity are reviewed and their applicability to the analysis of these determiner phrases is considered. Overall, this dissertation draws connections between previously distinct streams of empirical and theoretical work in the semantics of determiner phrases; it advances a new, unified account of both ignorance-implying, ‘epistemic’ indefinites – previously analyzed as encoding (something like) a disjunction of identifying properties – and ignorance-implying definites, such as ‘whatever’-DPs – previously regarded as encoding the concept of ‘unsettled’ or ‘unknown’.