Language and the core knowledge system of number
Knowledge and culture subproject 2: "Language and number" of Leiden University Centre for Linguistics
The project focuses on the interaction between the faculty of language and cognitive systems of number. Recent research shows that the core knowledge system of number consists of two subsystems -- the Approximative Number System (ANS) and the Object Tracking System (OTS). An impressive amount of observations on the functioning, aquisition and the limits of these subsystems has been accumulated in the last several years. One of the most important questions concerning ANS and OTS is what kind of mechanism forms the basis for the combination of these two systems, manifested, for example, in symbolic mathematics. Spelke (2011) hypothesises that language plays a crucial role in this integration of ANS and OTS. However, the linguistic properties of number-related expressions in languages of the world are still waiting for a systematic study. A wide-range exploration of the linguistics of numbers would provide crucial input for research in the field of the core knowledge systems. The project aims at building precisely this kind of input and has two main directions: 1) looking for limits of cross-linguistic variation in the domain of numbers, and 2) exploring the linguistic meaning of number-related expressions.
The main result of the study of cross-linguistic variation in the domain of numeric expressions will be a typological database on numerals in the wold's languages. A considerable amount of typological information of this sort appears in various existing databases (the World Atlas of Language Structures is one prominent example; see Dryer & Haspelmath 2011, Comrie 2011; ). The database that is being built as part of the current project makes a more systematic and explicit connection between the morphosyntactic properties of different kinds of numerals and the core knowledge paradigm. The information in the database is organised along two axes: 1) numeral constructions (cardinal construction, ordinal construction, constructions with vague numerals, etc.), and 2) the number line (i.e. whether a particular construction is limited to a certain sub-range of the number line or has certain special properties within a certain area). This design would allow the current and future researchers of language and number to make generalisations on the special linguistic status of different numerosities across languages and constructions, such as low numbers (1-4), or 'round numbers' (10, 100, etc.), or 1 as opposed the rest of the number line, etc. This information can be used to answer the question of whether and in what way the ANS vs. OTS distinction is represented in natural language. The database in currently in the data collection stage.
The second direction of this project -- an in-depth study of meanings of various number-related expressions -- necessarily involves less languages than the typological database due to the fine-grainedness of judgments and distinctions that constitute the data in such studies. At the same time, the importance of the semantic study of numerals showing how natural language packages the concepts of quantity in the linguistic structure can't be overestimated for cognitive studies. One result of the work in this direction a comparison between superlative ('the tallest man to play in our team') and ordinal ('the first woman to win the Nobel prize') constructions, showing the deep semantic and structural differences between the two, contrary to what has been assumed in the literature (Bylinina, Ivlieva, Podobryaev & Sudo 2014 "A non-superlative semantics for ordinals and the syntax of comparison classes", to be presented at NELS45 @MIT).