This dissertation began asking where do we see addition in natural language? This began by reframing comparatives, it extended to other types of addition, looking at list environments and opening up questions about the nature of the language that enables "adding to lists", which in turn effected a cross-categorical research project, building on work on degree semantics, event semantics, focus, and discourse structure.Work on comparatives is foundational in degree semantics and comparatives continue to be the source of ongoing research in the field (Cresswell, 1976; VonStechow, 1984; Kennedy & Levin, 2008; Schwarzschild, 2008). Here I work on an understudied ambiguity that can be analyzed as more creating an event summing reading instead of the typically studied reading. I contribute novel data showing a class of expressions participates in this ambiguity, supporting a compositional analysis. Event semantics typically analyzes adjectival constructions as stative constructions, in lieu of incorporating degrees (Davidson, 1967; Parsons, 1990). This research works in the interface between these two subfields, and provides an argument for studying their interactions, as well as a compositional account of one way we see degree constructions build to event constructions.From there, I follow morphological link to discover a class of data that impressionistically adds propositions to lists, including data with the focus sensitive particle also. Following Rooth (1992), I provide an analysis of this list effect via the semantics of focus and focus sensitivity. This requires assuming that propositions as a whole can be focused, which in turn requires precise assumptions about how the discourse context is framed formally. I follow both the Table theory from Farkas and Bruce (2010) and the conversational scoreboard model of Roberts (2004), showing that pieces of both models can function as contextual restrictions on the focus semantic value for focus sensitive expressions. Further investigation showed that other focus sensitive expressions can have similar restrictions, so major contributions of this include not only this revised notion of how to view "context", but also the ability to use focus sensitivity to investigate the nature of the discourse and what objects it contains.The final section of this dissertation focuses on data linking these two previous sections. The appearance of aspectual particles like still in comparatives has been noted in the literature (Ippolito 2007). This pretheoretically looks like an event related expression contributing to a degree construction, which is the opposite direction from the data analyzed earlier in this dissertation. However, following Ippolito's lead in analyzing still here as a focus sensitive particle, I implement the analysis of focus and contextual restrictions I laid out in the previous chapter. The result is that no evidence is found for treating this case as an event construction building to a degree construction, but also further evidence is given for my theory in which objects in the discourse are the contextual limitations on focus semantic values.The major contributions of this dissertation thus fall into two main categories or topics. On the subject of degrees and events, novel data solidified a previously observed link. Then the analysis I proposed supports a compositional and directional analysis where degree constructions can be built into event constructions. This highlights the importance of research on the interface between topics and theories within the same subfield, like degree and event semantics. On the subject of focus and the discourse, again I contribute novel data showing a class of expressions, which supports an analysis involving focusing whole propositions. This analysis gives evidence that objects in the discourse are the "context" that restricts the focus alternatives. These restrictions are lexical, showing that research in this area, looking at other focus sensitive expressions, gives us a new tool to investigate the structure of the discourse with.
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