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Scott Grimm, University of Rochester, USA

Beyond the Mass/Count Dichotomy: Examining Variation in Grammatical Forms and Semantic Formalisms of Countability

The vast majority of work on countability is concerned with a binary distinction between countable words (‘dog’/‘dogs’) and non-countable words (‘water’); yet, there is much richer variation in how countability may be manifested in language than a binary distinction would suggest.  This course will examine this variation both in terms of within-language variation, e.g. lexical classes within English, and across languages, e.g. examining various languages with richer grammatical number systems. The second half of the course relates this larger set of data to semantic theories, both lexical and formal, identifying challenges and exploring ways to enrich our formal tools to account for the richer data encountered: Topics covered include:

A. Re-examining the Diagnostics of Countability

B. Lexical Classes of Countability: Form-based and Meaning-based Approaches

C. Typological Views on Countability

D. Foundational Work: Mereological Approaches and Lexical Semantic Approaches to Countability

E. Collectives and Mereotopology

F. Artifact Nouns and Event Semantics

Daniel Hyde, University of Illinois, USA

Non-verbal numerical cognition and its relation to the emergence of verbal numerical abilities

A working hypothesis is that conceptions of number are rooted, at least in part, in two non-verbal numerical systems.  These cognitive systems are present from early infancy, continuous across the human lifespan, and shared with many non-human animals.  These lectures will describe the nature of and evidence for these systems, their neural basis, and current theories, as well as emerging evidence, on their relationship to verbal/symbolic numerical abilities. Topics covered include

A. Two non-verbal systems of numerical cognition:  Brain and behavioral signatures

  • Brief Overview of Two Non-Verbal Systems of Number
  • Parallel Individuation
  • Approximate Number System
  • One System or Two:  Distinctness in behavior and the brain

B.  Relationship between non-verbal numerical cognition and early conceptual development in numeracy/counting

  • Developmental trajectory of early numeracy
  • Theories of the relationship of non-verbal systems to early numeracy/counting
  • Emerging empirical brain and behavioral evidence

Fred Landman, Tel Aviv University/Tübingen University, Israel/Germany

Iceberg semantics for Count nouns and Mass nouns

Semantic analyses of plurality (and recent theories of mass nouns) following Link 1983 have been solidly based on Boolean notions of semantic atoms and atomicity (for singularity, counting, distributivity, collectivity etc.)  Iceberg semantics does without atomicity as a semantic notion.  In Iceberg semantics the standard mereological interpretations of noun phrases are replaced by slightly richer interpretations: pairs consisting of such a set and a set of generators for that set. In these lectures we will explore the fruitfulness of Iceberg semantics as a framework for analyzing count predicates (some interesting new perspectives on old plurality debates), and in particular for studying the semantics of different types of mass predicates. Topics covered include:

A. Boolean models, replacing, in counting, sets of atoms by disjoint sets, and generalizing this to Iceberg semantics.  Basic Iceberg semantics for NPs and DPs (including: how, without atoms, to distribute from a sum of cyclists to the individual cyclists, and how the DP the furniture denotes a mass object.)

B. Iceberg semantics for modifiers, including plural adjectives and numericals. Extension of the theory to classifiers and measures.  The role of the head of the construction in determining the mass/count nature of complex Iceberg interpretations.

C. Iceberg semantics for mass nouns: semantic definition of mess mass nouns (like mud) and neat mass nouns (like kitchenware) and showing how the semantics derives their different properties.

Suzi Lima, Federal University of Rio de Janeiro, Brazil

Acquisition of the count-mass distinction

Much literature on the count-mass distinction explores the syntactic and semantic properties of the distribution of count and mass nouns across languages. Currently, we know that there are at least three types of languages: number-marking languages, classifier languages and number-neutral languages (cf. Chierchia  2010). This course discusses proposals that account for the acquisition of count and mass nouns across these different types of languages. Topics include the following issues.

A. Is the path of acquisition of count and mass nouns affected by the type of language one speaks?

B.  Does the acquisition of count and mass nouns affect our perception of construal of objects?

C.  What do studies on the acquisition of count and mass nouns contribute to the formal literature on those topics?

D.  How much does the acquisition of count/mass nouns in one’s L1 language affect its acquisition in L2?

E.  Finally, how does the acquisition of count nouns impact the acquisition of count and mass quantifiers (or ambiguous quantifiers in languages that do not have these two different classes of quantifiers) and container phrases?

Susan Rothstein, Bar-Ilan University/Tübingen University, Israel/Germany

Counting and Measuring Crosslinguistically.

This course will review the evidence that counting and measuring are two different semantic operations associated crosslinguistically with two different types of semantic and syntactic structures. We will consider different ways of encoding countability crosslinguistically, and evaluate the evidence that the lexical count/mass distinction is (only) one way of encoding countability. Topics include:

A. The semantics of numericals

B. A semantics for counting and measuring

C. Counting and measuring crosslinguistically

D. Object mass nouns

E. Quantity judgements crosslinguistically.

F. Expressing countability crosslinguistically