Numerical origins: The critical questions (original) (raw)
Related papers
The materiality of numbers: Emergence and elaboration from prehistory to present
Cambridge University Press, 2023
This is a book about numbers—what they are as concepts and how and why they originate—as viewed through the material devices used to represent and manipulate them. Fingers, tallies, tokens, and written notations, invented in both ancestral and contemporary societies, explain what numbers are, why they are the way they are, and how we get them. Cognitive archaeologist Karenleigh A. Overmann is the first to explore how material devices contribute to numerical thinking, initially by helping us to visualize and manipulate the perceptual experience of quantity that we share with other species. She explores how and why numbers are conceptualized and then elaborated, as well as the central role that material objects play in both processes. Overmann's volume thus offers a view of numerical cognition that is based on an alternative set of assumptions about numbers, their material component, and the nature of the human mind and thinking.
From the history of mathematics, it is clear that some numerical concepts are far more pervasive than others. In a densely multimodular mind, evolved cognitive abilities lie at the basis of human culture and cognition. One possible way to explain the differential spread and survival of cultural concepts based on this assumption is the epidemiology of culture. This approach explains the relative success of cultural concepts as a function of their fit with intuitions provided by conceptual modules. A wealth of recent evidence from animal, infant, and neuroimaging studies suggests that human numerical competence is rooted in an evolved number module. In this study, I adopted an epidemiological perspective to examine the cultural transmission of numerical concepts in the history of mathematics. Drawing on historical and anthropological data on number concepts, I will demonstrate that positive integers, zero, and negative numbers have divergent cultural evolutionary histories owing to a distinct relationship with the number module. These case studies provide evidence for the claim that science can be explained in terms of evolved cognitive abilities that are universal in Homo sapiens.
Enculturation and the historical origins of number words and concepts
Synthese, 2021
In the literature on enculturation--the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture--numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical.
Numbers as Cognitive Tools (PhD dissertation)
Vrije Universiteit Amsterdam, 2021
Do numbers exist? Most of the answers to this question presented in the literature of the last decades have relied on a priori methods of investigation, where scientific data and theories about the human experience of numbers are irrelevant. These a priori approaches, however, have been inconclusive. In this dissertation, I adopt an empirically informed approach in which scientific descriptions of the human experience of numbers—as provided by cognitive sciences, linguistics, developmental psychology, and mathematics education—provide valuable information on the existence and status of what we call “numbers.” These scientific descriptions allow for the conclusion that numbers, conceived of as independent, non-spatiotemporal objects, do not exist. What exist are certain human-made techniques which engender in us the idea that a special class of objects called numbers exists. I show that, just as counting procedures and other arithmetical operations are cognitive tools that allow us to go beyond the limits of our genetically endowed cognitive skills, the very idea that numbers exist as independent objects is a cognitive tool that facilitates calculation—in other words, a useful reification. The ontological hypothesis suggested by the scientific description of the human experience of numbers is that operations such as counting and calculating procedures are the objective subject matter underlying arithmetic, rather than a putative class of non-spatiotemporal objects. Thus, the claim is that applied and pure arithmetical statements are true of the counting procedure and other arithmetical operations, rather than true of non-spatiotemporal numbers. In contrast to other attempted answers to the question of the ontological status of numbers, the hypothesis defended in this dissertation is accountable towards empirical data, and can thus be improved or refuted on an empirical basis.