Numbers As Cognitive Tools
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Numbers As Cognitive Tools
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Author : César Frederico dos Santos
language : en
Publisher: Springer Nature
Release Date : 2025-08-19
Numbers As Cognitive Tools written by César Frederico dos Santos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-19 with Mathematics categories.
This books offers a novel account of the nature of numbers firmly grounded in results from numerical cognition and the philosophy of mathematics. Drawing on empirical data on the human experience of what we call “numbers,” the author shows that numbers do not exist as abstract objects, but that the idea that they do is a useful cognitive tool. Contrary to the platonist view, according to which arithmetic is true of a realm of abstract entities, the nominalistic account presented in this book shows arithmetic to be true of descriptions of structural properties of techniques such as counting and calculating procedures. This book is of interest to both philosophers and cognitive scientists who want to have a deeper understanding of what numbers are.
Numbers As Cognitive Tools
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Author :
language : en
Publisher:
Release Date : 2021
Numbers As Cognitive Tools written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
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.
Computers As Cognitive Tools
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Author : Susanne P. Lajoie
language : en
Publisher: Routledge
Release Date : 1993
Computers As Cognitive Tools written by Susanne P. Lajoie and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Computers categories.
First Published in 1993. Routledge is an imprint of Taylor & Francis, an informa company.
Numbers As Cognitive Tools
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Author : César Frederico dos Santos
language : en
Publisher: Springer
Release Date : 2025-09-13
Numbers As Cognitive Tools written by César Frederico dos Santos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-09-13 with Mathematics categories.
This books offers a novel account of the nature of numbers firmly grounded in results from numerical cognition and the philosophy of mathematics. Drawing on empirical data on the human experience of what we call “numbers,” the author shows that numbers do not exist as abstract objects, but that the idea that they do is a useful cognitive tool. Contrary to the platonist view, according to which arithmetic is true of a realm of abstract entities, the nominalistic account presented in this book shows arithmetic to be true of descriptions of structural properties of techniques such as counting and calculating procedures. This book is of interest to both philosophers and cognitive scientists who want to have a deeper understanding of what numbers are.
Numbers And Numeracy In The Greek Polis
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Author :
language : en
Publisher: BRILL
Release Date : 2021-12-20
Numbers And Numeracy In The Greek Polis written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-20 with History categories.
We tend to think of numbers as inherently objective and precise. Yet the diverse ways in which ancient Greeks used numbers illustrates that counting is actually shaped by context-specific and culturally-dependent choices: what should be counted and how, who should count, and how should the results be shared? This volume is the first to focus on the generation and use of numbers in the polis to quantify, communicate and persuade. Its papers demonstrate the rich insights that can be gained into ancient Greek societies by reappraising seemingly straightforward examples of quantification as reflections of daily life and cultural understandings.
The Oxford Handbook Of Numerical Cognition
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Author : Roi Cohen Kadosh
language : en
Publisher: Oxford Library of Psychology
Release Date : 2015
The Oxford Handbook Of Numerical Cognition written by Roi Cohen Kadosh and has been published by Oxford Library of Psychology this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. This handbook brings together the different research areas that make up the vibrant field of numerical cognition in one comprehensive and authoritative volume.
Numbers And The Making Of Us
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Author : Caleb Everett
language : en
Publisher: Harvard University Press
Release Date : 2017-03-13
Numbers And The Making Of Us written by Caleb Everett and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-13 with Social Science categories.
Number concepts are a human invention developed and refined over millennia. They allow us to grasp quantities precisely: recent research shows that most specific quantities are not perceived in the absence of a number system. Numbers are not innate or universal; yet without them, the world as we know it would not exist.
Numbers Language And The Human Mind
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Author : Heike Wiese
language : en
Publisher: Cambridge University Press
Release Date : 2003-12-11
Numbers Language And The Human Mind written by Heike Wiese and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-11 with Language Arts & Disciplines categories.
What constitutes our number concept? What makes it possible for us to employ numbers the way we do; which mental faculties contribute to our grasp of numbers? What do we share with other species, and what is specific to humans? How does our language faculty come into the picture? This 2003 book addresses these questions and discusses the relationship between numerical thinking and the human language faculty, providing psychological, linguistic and philosophical perspectives on number, its evolution and its development in children. Heike Wiese argues that language as a human faculty plays a crucial role in the emergence of systematic numerical thinking. She characterises number sequences as powerful and highly flexible mental tools that are unique to humans and shows that it is language that enables us to go beyond the perception of numerosity and to develop such mental tools.
Numerical Cognition And The Epistemology Of Arithmetic
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Author : Markus Pantsar
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-28
Numerical Cognition And The Epistemology Of Arithmetic written by Markus Pantsar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-28 with Science categories.
Arithmetic is one of the foundations of our educational systems, but what exactly is it? Numbers are everywhere in our modern societies, but what is our knowledge of numbers really about? This book provides a philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition. It explains how humans have developed arithmetic from humble origins to its modern status as an almost universally possessed knowledge and skill. Central to the account is the realisation that, while arithmetic is a human creation, the development of arithmetic is constrained by our evolutionarily developed cognitive architecture. Arithmetic is a sophisticated cultural development, but it is ultimately based on abilities with numerosities that we already possess as infants and share with many non-human animals. Therefore, arithmetic is not purely conventional, an arbitrary game akin to chess. Instead, arithmetic is deeply connected to our basic cognitive capacities.
Abstract Mathematical Cognition
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Author : Wolfgang Grodd
language : en
Publisher: Frontiers Media SA
Release Date : 2016-08-09
Abstract Mathematical Cognition written by Wolfgang Grodd and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-09 with Mathematics categories.
Despite the importance of mathematics in our educational systems little is known about how abstract mathematical thinking emerges. Under the uniting thread of mathematical development, we hope to connect researchers from various backgrounds to provide an integrated view of abstract mathematical cognition. Much progress has been made in the last 20 years on how numeracy is acquired. Experimental psychology has brought to light the fact that numerical cognition stems from spatial cognition. The findings from neuroimaging and single cell recording experiments converge to show that numerical representations take place in the intraparietal sulcus. Further research has demonstrated that supplementary neural networks might be recruited to carry out subtasks; for example, the retrieval of arithmetic facts is done by the angular gyrus. Now that the neural networks in charge of basic mathematical cognition are identified, we can move onto the stage where we seek to understand how these basics skills are used to support the acquisition and use of abstract mathematical concepts.