Investigating the Social Foundations of Mathematics: Natural Number in Culturally Diverse Forms of Life

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Abstract
My contention is that `natural number' is a cultural construct, differently formulated in different societies. I argue that the categories adopted by mature language users become evident when one understands that predication leads language users to refer in particular ways and thus determines what kinds of objects their language defines as constituting the universe. I show that English and Yoruba (a West African language) predicate in different ways, and consequently postulate different kinds of objects. This, in turn, produces different constructions of number: how we count depends on how we conceive objects to exist. Yoruba numbers are verbal constructs, not adjectival, as in English; they hold the object to exist in a collective mode, with a particular numerosity. The numeral system begins with aggregates, and then, by a process of subtraction, breaks these down through the concurrent use of bases twenty, ten and five. The number system can thus be shown to be intimately related to the conceptual frame that the linguistic structure lays down.

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