by Brian Rivera
On this paper, Nuñez introduces a debate about the nature of mathematics. On one side there is the biological nativist view that argues that ‘mathematical objects’ along with the intuitions of space, time, and quantity are the result of millions of years of evolution. On the other side is the cultural view, which states that number capacities are based on biologically evolved preconditions (BEPs) which are scaffolded by culture to create number and arithmetic (thus them not being biologically inherited but culturally developed).
The main analogy running through the paper is that of snowboarding. Both snowboarding and arithmetic have biologically evolved preconditions: motor-balance for snowboarding and subitizing for arithmetic. These BEP are evolved or were selected for at one point of evolution. However, Nuñez goes on to make the point that although snowboarding’s BEPs have evolved they are not precursors of it. Similarly with number and mathematical abilities, their BEPs have evolved but are not necessarily precursors for them.
One reason Nuñez sees as contributing to the embrace of the nativist view of mathematics is that studies have downplayed data from non-industrialized cultures. Languages from some hunter-gatherer cultures show there can be a complete absence of exact quantifiers. This questions the conclusion that individual humans manifest a specific capacity for number. An additional reason to doubt the nativist view of mathematics according to Nuñez is due to the overextension of conclusions derived from animal studies. These studies hardly resemble the conditions any animal would encounter in its natural habitat and seem ill fitted to drive conclusions about biological capacities.
Furthermore, Nuñez goes on to say that numerical cognition has collapsed the concepts of number, numeral, numerousness, and numerosity. Nuñez proposes making a distinction between quantical and numerical abilities to distinguish the biologically endowed abilities of the former from the learned-cultural ones of the latter.
A criticism that seems relevant is the degree to which snowboarding is a fair analogy to criticize teleological arguments. The way in which some mathematical facts seem transcendental of human notions (i.e. infinity), discovered rather than created, and retrospectively useful have led many to make those claims of numbers being God-given or existing in Plato’s heaven. Although some people might feel this way about snowboarding, it is far from being known as the zenith of human sensory-motor coordination and it is but an example of this capacity. Snowboarding is too concrete of a case to talk about the evolved capacities for balance and motor-coordination. This contrast with mathematics being a widely adapted (possibly universal), unique, and successful abstraction system, it is not just a different type of writing. To have made the analogy to “sports” would have sustained the points about the cultural properties of snowboarding while giving justice to the fact that mathematics is not just a happenstance abstraction system.
Nuñez brings a critical view on the attempts to describe numerical abilities in terms of evolution. Additionally, Nuñez treats the interaction between culture and biology very seriously. I think this article is a good example of the dynamical view necessary to make sense of the complex history of a modern cognitive skill such as arithmetic.