The co-evolution of number concepts and counting words

Abstract

Humans possess a number concept that differs from its predecessors in animal cognition in two crucial respects: (1) it is based on a numerical sequence whose elements are not confined to quantitative contexts, but can indicate cardinal/quantitative as well as ordinal and even nominal properties of empirical objects (e.g. 'five buses': cardinal; 'the fifth bus': ordinal; 'the #5 bus': nominal), and (2) it can involve recursion and, via recursion, discrete infinity. In contrast to that, the predecessors of numerical cognition that we find in animals and human infants rely on finite and iconic representations that are limited to cardinality and do not support a unified concept of number.In this paper, I argue that the way such a unified number concept could evolve in humans is via verbal sequences that are employed as numerical tools, that is, sequences of words whose elements are associated with empirical objects in number assignments. In particular, I show that a certain kind of number words, namely the counting sequences of natural languages, can be characterised as a central instance of verbal numerical tools.I describe a possible scenario for the emergence of such verbal numerical tools in human history that starts from iconic roots and that suggests that in a process of co-evolution, the gradual emergence of counting sequences and the development of an increasingly comprehensive number concept supported each other.On this account, it is language that opened the way for numerical cognition, suggesting that it is no accident that the same species that possesses the language faculty as a unique trait, should also be the one that developed a systematic concept of number.

The development of the SNARC effect: Evidence for early verbal coding

“…From birth on, we are immersed in a linguistic context that determines our cultural conventions and verbal concepts. When we grow older, there is a 14 co-development of number concepts and number words (Wiese, 2007). Hence, and in contrast to Berch et al (1999), linguistic influences do not override spatial associations with age.…”

Aquisição da linguagem e habilidades cognitivas superiores: o papel da língua no desenvolvimento da cognição numérica

“…Em que medida? Wiese (2007) defende a ideia de que o conceito de número, tal e como presente nos seres humanos, diferencia-se dos seus predecessores na cognição animal em dois aspectos cruciais. Em primeiro lugar, na nossa espécie esse conceito está baseado em uma sequência numérica cujos elementos não se restringem a contextos quantitativos, mas podem indicar cardinalidade/quantitatividade assim como ordinalidade e propriedades nominais dos objetos (três maçãs, o segundo colocado, o ônibus #150).…”

“…Já os precursores da cognição numérica encontrados em animais e em infantes humanos dependem de representações finitas e icônicas que estão limitadas à cardinalidade e não dão suporte para um conceito unificado de número. Segundo Wiese (2007), esse conceito unificado pode ter evoluído nos humanos a partir de sequências verbais empregadas como ferramentas numéricas, isto é, sequências de palavras cujos elementos são associados com objetos empíricos em vários tipos de tarefas. Em particular, certo tipo de palavras que fazem referência à quantidade (number words), como, por exemplo, as sequências de contagem, podem ser caracterizadas como as principais instâncias dessas ferramentas verbais numéricas.…”

The Mathematical Operations in Bàtɔ̀nū Numeral System

“…They are definite/specific words in a natural language that represent numbers (Von Mengden 2010). Many researches have been carried out on the numeral systems by experts in linguistics (Abraham 1958, Oduyoye 1969, Sanusi 1995, Blažek 1999, Atóyèbí 2006, Wiese 2007, Fabunmi 2010, Oyebade 2013 among others). As observed in Wiese (2007: 760-761), number assignments, across languages, fall into three categories.…”