Featural variables

Abstract

A long line of research takes some sign language loci to be the overt realization of variables. But as argued in Kuhn (2015), this analysis fails in ASL in two cases. (i) First, loci sometimes appear to be inherited through agreement rather than directly interpreted, in particular in those environments in which phi-features are known to remain uninterpreted (= ‘Kuhn’s Generalization’). (ii) Second, there are cases in which one and the same locus can refer to different individuals, in contradiction with the predictions of the standard theory. Kuhn concludes that sign language loci are an open class of features rather than of variables; and he provides a variable-free treatment of them, although without accounting for their deictic uses. While granting the correctness of Kuhn’s Generalization, we offer an alternative in which ASL loci are both features and variables: some loci (in particular deictic ones) obtain their value from an assignment function, and introduce presuppositions on the value of other (covert) variables; but loci are also subject to the same rules of agreement as phi-features, and they can thus remain uninterpreted in some other environments. We discuss their behavior both from the perspective of morpho-syntactic and of semantic theories of (apparent) feature agreement. Finally, we argue that in the tense domain spoken languages also have expressions that are featural while containing a variable element.

Appendix:  Complement set anaphora and loci as variables

Part of this discussion borrows from Schlenker et al. (2013) and Schlenker (2015a, 2015b).

We briefly discuss below an interpretive property of plural loci that can be analyzed within a variable-full system, but might not be trivial to handle in a pure agreement-based analysis. Plural loci are realized in ASL (and LSF) as semi-circular areas, which closely correspond to plural variables. Now in some cases one plural locus a can be embedded within a larger plural locus ab, with the result that a ‘complement locus’ b suddenly pops into existence, and denotes the complement of the denotation of a within the denotation of ab. An ‘iconic’ analysis was offered for this phenomenon in Schlenker et al. (2013), but it hinged rather crucially on a treatment of plural loci as variables that have a denotation.

To introduce the issue, we start with the English sentence Most students came to class. Recent research has argued that it makes available two discourse referents for further anaphoric uptake: one corresponding to the maximal set of students, as illustrated in (41b) (‘maximal set anaphora’); and one for the entire set of students, as illustrated in (41c) (‘restrictor set anaphora’).

• (41)

  

By contrast, no discourse referent is made available for the set of students that didn’t come to class (‘complement set anaphora’, as this is the complement of the maximal set within the restrictor set); this is what explains the deviance of (41a) (see Nouwen 2003 and Schlenker et al. 2013 for further discussion of apparent counterexamples).

On the basis of ASL and LSF data, Schlenker et al. (2013) made two main observations.

Observation 1

When a default plural locus is used in ASL, data similar to (41) can be replicated—e.g. complement set anaphora with most is quite degraded.

Observation 2

When embedded loci are used, the effect is circumvented: one large locus (written as ab, but signed as a single circular locus) denotes the set of all students; a sub-locus (=a) denotes the set of students who came; and a complement locus (=b) thereby becomes available, denoting the set of students who didn’t come, as illustrated in (42) and (43).

• (42) 7 poss-1 student ix-arc-ab most ix-arc-a a-came class. ix-arc-a a-ask-1 good question.

  ‘Most of my students came to class. They asked me good questions.’ (ASL; 8, 196)

• (43)

Schlenker et al. (2013) account for Observation 1 and Observation 2 by assuming that (i) Nouwen is right that in English, as well as ASL and LSF, the grammar fails to make available a discourse referent for the complement set, i.e. the set of students who didn’t come; but (ii) the mapping between plural loci and mereological sums preserves relations of inclusion and complementation, which in (42a) makes available the locus b.

The main assumptions are that (A1) the set of loci is closed with respect to relative complementation: if a is a sublocus of b, then (b-a) is a locus as well; and (A2) assignment functions are constrained to respect inclusion and relative complementation: if a is a sublocus of b, the denotation of a is a subpart of the denotation of b, and (b-a) denotes the expected complement set. In (42a), where embedded loci are used, we can make the following reasoning:

• Since a is a proper sublocus of a large locus ab, we can infer (by assumption A1) that (ab-a) (i.e. b) is a locus as well.

• By assumption A2, we can also infer that s(a) ⊂ s(ab) and that s(b) = s(ab)-s(a).

In this way, complement set anaphora becomes available because ASL and LSF can rely on an iconic property which is inapplicable in English. For present purposes, what matters is that the locus b in (42a) and (43) is not inherited by way of agreement, since it is not introduced by anything. From a variable-full perspective, the existence of this locus is inferred by a closure condition on the set of loci, and its denotation is inferred by an iconic rule. But the latter makes crucial reference to the fact that loci have denotations. It is not trivial to see how this result could be replicated in a variable-free analysis in which loci don’t have a denotation to begin with. One possibility is that the complement set locus should be treated as being deictic (which is the one case in which the variable-free analysis has an analogue of variable denotations). This might force a view in which complement set loci are handled in a diagrammatic-like fashion, with co-speech gestures/diagrams incorporated into signs—something that would require a more detailed investigation.