Quantity and Number

Humans and many other species have biologically endowed abilities for discriminating “quantities” to some degree (e.g., subitizing), but only humans, via the distinct capacity of “symbolic reference” exhibit “number” — i.e., exact symbolic quantification. To compare human and non-human animal data in some meaningful way, a crucial distinction between “quantical” (e.g., quantity discrimination) and “numerical” (exact, symbolic) cognition is needed: quantical cognition provides biologically evolved preconditions for numerical cognition but it does not scale up to “number” and “arithmetic”, which require conventionalized cultural mediation and (biological) enculturation. Indeed, human data from non-industrialized cultures show that “number”, although distinctively human and ubiquitous in the modern industrialized world, is not (and has not been) universal. “Number” — exact symbolic quantification — appears to be a cultural trait, not a (human) species-specific biologically determined trait, driven and materialized by cultural preoccupations and practices (e.g., management of stocks, precise measurements) that are supported by language and symbolic reference — crucial dimensions that lie largely outside natural selection. Language, with its symbolic properties although present in all human cultures, is a necessary condition for “number” but it is not a sufficient condition for it. The comparative analysis of “quantity” and “number” has implications for debates about the origins of other human special capacities such as geometry, music, and art.