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Linking - how semantic arguments map to the syntax - is one of the challenges for theories of the syntax-semantics interface. In this new approach, Janet Randall explores the hypothesis that the positions of syntactic arguments are strictly determined by lexical argument geometry. Yielding novel - if sometimes surprising - conclusions, her Isomorphic Linking Hypothesis establishes the linking patterns of a wide range of verbs and, with those results, shows how to reason "backwards" from how a given verb's arguments link to what its lexical representation must be. Along the way, the investigation takes on thorny lexical issues - reformulating the Theta Criterion, revisiting the multiple lexical-entry debate, eliminating "indirect" arguments and redefining unaccusativity. It offers new insights into how arguments are represented, assembles a host of argument/adjunct diagnostics, and re-examines the relation between arguments and predicates. The result of this incisive study is a simple and consistent account of linking, integrated with a radical rethinking of the nature of arguments and argument structure.