Predicates such as tall or to know Latin, which intuitively denote permanent properties, are called individual-level predicates. Many peculiar properties of this class of predicates have been noted in the literature. One such property is that we cannot say #John is sometimes tall. Here is a way to account for this property: this sentence sounds odd because it triggers the scalar implicature that the alternative John is always tall is false, which cannot be, given that, if John is sometimes tall, (...) then he always is. This intuition faces two challenges. First: this scalar implicature has a weird nature, since it must be surprisingly robust (otherwise, it could be cancelled and the sentence rescued) and furthermore blind to the common knowledge that tallness is a permanent property (since this piece of common knowledge makes the two alternatives equivalent). Second: it is not clear how this intuition could be extended to other, more complicated properties of individual-level predicates. The goal of this paper is to defend the idea of an implicature-based theory of individual-level predicates by facing these two challenges. In the first part of the paper, I try to make sense of the weird nature of these special mismatching implicatures within the recent grammatical framework for scalar implicatures of Chierchia (Structures and beyond, 2004) and Fox (2007). In the second part of the paper, I show how this implicature-based line of reasoning can be extended to more complicated properties of individual-level predicates, such as restrictions on the interpretation of their bare plural subjects, noted in Carlson (Reference to kinds in English. Doctoral dissertation, University of Massachusetts at Amherst, 1977), Milsark (Linguistic Analysis 3.1: 1–29, 1977), and Fox (Natural Language Semantics 3: 283–341, 1995); restrictions on German word order, noted in Diesing (Indefinites, 1992); and restrictions on Q-adverbs, noted in Kratzer (The Generic Book, ed. Carlson and Pelletier, 125–175, 1995). (shrink)

Boersma’s (1997, 1998) Gradual Learning Algorithm (GLA) performs a sequence of slight re-rankings of the constraint set triggered by mistakes on the incoming stream of data. Data consist of underlying forms paired with the corresponding winner forms. At each iteration, the algorithm needs to complete the current data pair with a corresponding loser form. Tesar and Smolensky (Linguist Inq 29:229–268, 1998) suggest that this current loser should be set equal to the winner predicted by the current ranking. This paper develops (...) a new argument for Tesar and Smolensky’s proposal, based on the GLA’s factorizability. The underlying typology often encodes non-interacting phonological processes, so that it factorizes into smaller typologies that encode a single process each. The GLA should be able to take advantage of this factorizability, in the sense that a run of the algorithm on the original typology should factorize into independent runs on the factor typologies. Factorizability of the GLA is guaranteed provided the current loser is set equal to the current prediction, providing new support for Tesar and Smolensky’s proposal. (shrink)

Idempotency requires any phonotactically licit forms to be faithfully realized. Output-drivenness requires any discrepancies between underlying and output forms to be driven exclusively by phonotactics. These formal notions are relevant for phonological theory and play a crucial role in learnability. Tesar and Magri provide tight guarantees for OT output-drivenness and idempotency through conditions on the faithfulness constraints. This paper derives analogous faithfulness conditions for HG idempotency and output-drivenness and develops an intuitive interpretation of the various OT and HG faithfulness conditions (...) thus obtained. The intuition is that faithfulness constraints measure the phonological distance between underlying and output forms. They should thus comply with a crucial axiom of the definition of distance, namely that any side of a triangle is shorter than the sum of the other two sides. This intuition leads to a faithfulness triangle inequality which is shown to be equivalent to the faithfulness conditions for idempotency and output-drivenness. These equivalences hold under various assumptions, crucially including McCarthy’s :75–138, 2003b) generalization that constraints are all categorical. (shrink)