In this thesis I explore the syntactic and semantic properties of movement and adjunction in natural language, and suggest that these two phenomena are related in a novel way. In a precise sense, the basic pieces of grammatical machinery that give rise to movement, also give rise to adjunction. In the system I propose, there is no atomic movement operation and no atomic adjunction operation; the terms "movement" and "adjunction" serve only as convenient labels for certain combinations of other, primitive operations. As a result the system makes non-trivial predictions about how movement and adjunction should interact, since we do not have the freedom to stipulate arbitrary properties of movement while leaving the properties of adjunction unchanged, or vice-versa. I focus first on the distinction between arguments and adjuncts, and propose that the differences between these two kinds of syntactic attachment can be thought of as a transparent reflection of the differing ways in which they contribute to neo-Davidsonian logical forms. The details of this proposal rely crucially on a distinctive treatment of movement, and from it I derive accurate predictions concerning the equivocal status of adjuncts as optionally included in or excluded from a maximal projection, and the possibility of counter-cyclic adjunction. The treatment of movement and adjunction as interrelated phenomena furthermore enables us to introduce a single constraint that subsumes two conditions on extraction, namely adjunct island effects and freezing effects. The novel conceptions of movement and semantic composition that underlie these results raise questions about the system's ability to handle semantic variable-binding. I give an unconventional but descriptively adequate account of basic quantificational phenomena, to demonstrate that this important empirical ground is not given up. More generally, this thesis constitutes a case study in (i) deriving explanations for syntactic patterns from a restrictive, independently motivated theory of compositional semantics, and (ii) using a computationally explicit framework to rigourously investigate the primitives and consequences of our theories. The emerging picture that is suggested is one where some central facts about the syntax and semantics of natural language hang together in a way that they otherwise would not.