In this dissertation, I address two outstanding questions regarding how linguistic and extra-linguistic information are brought together in the interpretation of language situated within a discourse. The first part of this dissertation experimentally addresses how alternatives invoked by sentences containing the focus-sensitive operator 'only' are generated and constrained during online interpretation. The latter part of the dissertation addresses an ongoing debate in linguistics surrounding the meaning of number words in language. Drawing on research in early conceptual development and language acquisition, I present a formal characterization of the properties of the natural number system, according to which natural number concepts like THREE and SEVEN simultaneously convey cardinal and ordinal meanings. I then present a linguistic proposal that systematically relates this multidimensional conceptual meaning to the range of interpretations observed to arise in sentences containing numerically quantified noun phrases like 'three children' and 'seven books'. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]