Constructing a concept of number (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.
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.
The relationship between language and conceptual thought is an unresolved problem in both philosophy and psychology. It remains unclear whether linguistic structure plays a role in our cognitive processes. This special issue brings together cognitive scientists and philosophers to focus on the role of language in numerical cognition: because of their universality and variability across languages, number words can serve as a fruitful test case to investigate claims of linguistic relativism.