Marcin Wągiel – The form and meaning of numerals

Numerals are funny words. On the one hand, it seems that they share some core component that justifies grouping them together as if they formed a single category, a practice common in both descriptive and theoretic approaches to language. On the other hand, though, morphologically and syntactically they form a very heterogeneous class of expressions with different items often exhibiting distinct properties.
In this class, we will investigate a number of topics in numeral (morpho-)semantics. We will start by situating numerals as linguistic expressions in the more general context of the philosophy of numbers and the psychology of counting and we will look at various uses of basic numerals such as `five’ (1) (e.g., Bultinck 2005, Rothstein 2017, Bylinina & Nouwen 2020).
(1) a. Five cats meowed. b. My reasons for saying this are five. c. Five is a Fibonacci number. d. Player number five scored a hat-trick.
We will then discuss four semantic treatments of numerals: (i) as determiners in the Generalized Quantifier Theory (Barwise & Cooper 1981), (ii) as cardinal predicates (Landman 2003), (iii) as predicate modifiers equipped with measure functions (Krifka 1989) and (iv) as degree quantifiers (Kennedy 2015) and see how they compare with respect to capturing the variety of meanings in (1).
Next, we will examine cross-linguistic morphological marking patterns suggesting that numerals in fact lexicalize complex syntactic and semantic structures derived from a set of more primitive notions and consider a proposal of a unified morpho-semantic analysis based on combining compositional semantics with Nanosyntax (Wągiel & Caha 2020).
Finally, we will explore a diverse, yet still mostly uncharted, land of numerical expressions other than cardinals (with an emphasis on Slavic data), e.g., English multipliers such as `double’ and `two-time’, Polish collectivizers like `dwójka’ (`group of two’), Czech taxonomic numerals such as `dvojí’ (`of two kinds’), and check whether the proposed account can help us to develop a better understanding of their form and meaning.

References
Barwise, J. & R. Cooper. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy 4(2): 159–219.

Bultinck, B. (2005). Numerous meanings: The meaning of English cardinals and the legacy of Paul Grice. Amsterdam: Elsevier.

Bylinina, L. & R. Nouwen. (2020). Numeral semantics. Language and Linguistics Compass 14(8): e12390.

Kennedy, C. (2015). A `de-Fregean’ semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics & Pragmatics 8: 1–44.

Krifka, M. (1989). Nominal reference, temporal constitution and quantification in event semantics. In: R. Bartsch et al. (eds.), Semantics and contextual expression, 75–115. Dordrecht: Foris.

Landman, F. (2003). Predicate-argument mismatches and the adjectival theory of indefinites. In: M. Coene & Y. D’hulst (eds.), From NP to DP, Vol. 1: The syntax and semantics of noun phrases, 211–237. Amsterdam: John Benjamins.

Rothstein, S. (2017). Semantics for counting and measuring. Cambridge: Cambridge University Press.

Wągiel, M. & P. Caha. (2020). Universal semantic features and the typology of cardinal numerals. Catalan Journal of Linguistics 19: 199–229.