In seminal work, Potts (2005) claimed that the behavior of “supplements”—appositive relative clauses (ARCs) and nominals—offers a powerful argument in favor of a multidimensional semantics, one in which certain expressions fail to interact scopally with various operators because their meaning is located in a new semantic dimension. Focusing on ARCs, with data from English, French, and German (Poschmann 2018), I explore an alternative to Potts’s bidimensional account in which (a) appositives may be syntactically attached with matrix scope, despite their appearance in embedded positions, as in McCawley 1981; (b) contra McCawley, they may also be syntactically attached within the scope of other operators, in which case they semantically interact with them; (c) they are semantically conjoined with the rest of the sentence, but (d) they give rise to nontrivial projection facts when they do not have matrix scope. In effect, the proposed analysis accounts for most of the complexity of these data by positing a more articulated syntax and pragmatics, while eschewing the use of a new dimension of meaning.

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