Landman (1989) introduced contemporary linguistics to the as-phrase. An as-phrase is a qualifier, introduced in English by "as." "John is corrupt as a judge," for instance, contains the as-phrase "as a judge." Philosophical discourse is full of examples of as-phrase sentences. Their presence can make it difficult to distinguish valid from invalid arguments, a perennial concern for philosophers. Landman proposed the first formal semantic theory of as-phrases, based on a set of seven intuitively-valid patterns of inference involving as-phrases. Szabó (2003), Jaeger (2003), Asher (2011) each attempt to improve upon Landman's theory. Chapter 1 reviews and criticizes a temporal account of as-phrase semantics, while tracing some precedents and motivations for my approach. Chapters 2-3 criticize Szabó's and Asher's theories. Szabó's theory shows problems handling the future tense and intensional contexts. Asher's complex theory solves these problems, but resorts to the obscure notions of relative identity and bare particulars. Chapter 4 argues that neither Szabó's nor Asher's theory is clearly superior, because implicitly, they focus on different classes of sentences, which I call "Type A" and "Type B." From John Bowers' syntactic research, I argue that the element common to Type A and Type B is Pr, a predication head pronounced "as" in some contexts. Chapter 5 develops a formal semantic theory tailored to Type A sentences that solves the problems of Szabó's theory while avoiding Asher's assumptions. On my approach, the semantic properties of Type A sentences resolve into an interaction among generic quantifiers, determiner-phrase interpretation, and one core quantifier based on a principal ultrafilter. It is the interaction-effects of these elements that give rise to the many unusual readings we find in these as-phrase sentences. This result supports my motivating view that linguistic research helps to solve semantic problems of philosophical interest.