A non-Boolean analysis of conjunction in additive numerals: A mereotopological approach

Abstract

In this paper, I investigate the underlying meaning of additive numerals such as two hundred and three. Cross-linguistically, additive numerals often involve a conjunction marker (e.g., Hurford, 1975; Ionin and Matushansky, 2018), which indicates a deep relationship between the expression of arithmetical addition and mereological sum formation. Inspired by the classical results in ontology of numbers showing that numbers are not primitives, but rather complex derived objects, and the ideas concerning the spatial metaphor for numbers by Nouwen (2016) and Matushansky and Zwarts (2017), I propose a mereotopological approach (Grimm 2012 et seq.) to the part-whole structure of additive numerals. I argue that in language numbers are conceptualized as vertically-oriented 1-dimensional maximally self-connected entities (type e) of a given height that can be fused by mereological sum formation. Given the nature of space they occupy and the adopted mereotopological framework, the result is a new greater maximally self-connected object that can be mapped onto its higher point. By utilizing ontological assumptions that were developed independently, the proposed systems allows to capture conjunction in additive numerals as non-Boolean ‘and’.