We present an argument for revising the theory of alternatives for Scalar Implicatures and for Association with Focus. We argue that in both cases the alternatives are determined in the same way, as a contextual restriction of the focus value of the sentence, which, in turn, is defined in structure-sensitive terms. We provide evidence that contextual restriction is subject to a constraint that prevents it from discriminating between alternatives when they stand in a particular logical relationship with the assertion or (...) the prejacent, a relationship that we refer to as symmetry. Due to this constraint on contextual restriction, discriminating between alternatives in cases of symmetry becomes the task of focus values. This conclusion is incompatible with standard type-theoretic definitions of focus values, motivating our structure-sensitive definition instead. (shrink)

Scalar implicatures depend on alternatives in order to avoid the symmetry problem. I argue for a structure-sensitive characterization of these alternatives: the alternatives for a structure are all those structures that are at most as complex as the original one. There have been claims in the literature that complexity is irrelevant for implicatures and that the relevant condition is the semantic notion of monotonicity. I provide new data that pose a challenge to the use of monotonicity and that support the (...) structure-sensitive definition. I show that what appeared to be a problem for the complexity approach is overcome once an appropriate notion of complexity is adopted, and that upon closer inspection, the argument in favor of monotonicity turns out to be an argument against it and in favor of the complexity approach. (shrink)

We revisit a typological puzzle due to Horn (Doctoral Dissertation, UCLA, 1972) regarding the lexicalization of logical operators: in instantiations of the traditional square of opposition across categories and languages, the O corner, corresponding to ‘nand’ (= not and), ‘nevery’ (= not every), etc., is never lexicalized. We discuss Horn’s proposal, which involves the interaction of two economy conditions, one that relies on scalar implicatures and one that relies on markedness. We observe that in order to express markedness and to (...) account for a bigger typological puzzle, namely the absence of lexicalizations of ‘XOR’ (= exclusive or), ‘all-or-none’, and many other imaginable logical operators, one must restrict the basic lexicalizable elements to a small set of primitives. We suggest that an ordering based perspective, following Keenan and Faltz (Boolean semantics for natural language, 1985), makes the stipulated primitives that we arrive at more natural. We also propose a modification to Horn’s proposal, based on recent work on implicatures, in which only the implicature condition is operative and in which markedness is part of the definition of the alternatives for scalar implicatures rather than an independent condition. (shrink)

The semantics of association with focus and the pragmatic conditions governing the appropriateness of focus in discourse are usually taken to depend on focus alternatives. According to a common view, these alternatives are generated by a permissive process. This permissive view has been challenged by Michael Wagner, who has noted that certain alternatives are systematically excluded from consideration. Wagner describes a more restrictive view, on which only contrastive alternatives are relevant for association with focus and for the appropriateness of focus (...) in discourse. I use recent work on the role of contradiction to show that the standard, permissive view derives the same results as the contrast-based view for the basic cases. These basic cases involve a contradiction that prevents us from using them to distinguish the two approaches. I show that when this contradiction is eliminated, evidence of non-contrastive alternatives emerges, supporting the permissive standard view over the restrictive contrast-based one. (shrink)

The sensitivity of focus to context has often been analyzed in terms of focus-based anaphoric relations between sentences and surrounding discourse. The literature, however, has also noted empirical difficulties for the anaphoric approach, and my goal in the present paper is to investigate what happens if we abandon the anaphoric view altogether. Instead of anaphoric felicity conditions, I propose that focus leads to infelicity only indirectly, when the semantic processes that it feeds—in particular, exhaustification and question formation—make an inappropriate contribution (...) to discourse. I outline such an account, in line with Roberts (In Papers in semantics, Vol. 49 of Working papers in linguistics, 91–136, The Ohio State University, 1996 ) and incorporating recent insights from Büring (In Questions in discourse, Vol. 36 of Current research in the semantics/pragmatics interface, 6–44, Leiden: Brill, 2019 ) and Fox (In Proceedings of Sinn und Bedeutung 22, 403–434, 2019 ). This account, which I motivate on conceptual grounds, has no anaphoric conditions on focus placement and has only an economy condition as a potential felicity condition on focus. However, there are cases where the fine control offered by anaphoricity seems needed, either to block deaccenting that would be licensed by a question or to allow local deaccenting that is not warranted by a question. Such cases challenge non-anaphoric accounts such as the present one and appear to support recent anaphoric proposals such as Schwarzschild (In Making worlds accessible. Essays in honor of Angelika Kratzer, 167–192, 2020 ), Wagner (In The Wiley Blackwell companion to semantics, Oxford: Wiley-Blackwell, 2020 ), and Goodhue (Journal of Semantics 39: 117–158, 2022 ). I argue that this potential motivation for anaphoricity is only apparent and that to the extent that anaphoric conditions on focus from the literature are not inert, they are in fact harmful. (shrink)