Numbers as Cognitive Tools: An Empirically Informed Nominalistic Account of the Nature of Numbers

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César Frederico dos Santos

Numbers as Cognitive Tools

An Empirically Informed Nominalistic Account of the Nature of Numbers

César Frederico dos Santos

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English

Springer International Publishing AG
19 July 2025

Analytical philosophy & Logical Positivism; Child & developmental psychology; Cognition & cognitive psychology; Teaching of a specific subject; Philosophy of mathematics

Series: Synthese Library

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.

By: César Frederico dos Santos
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Volume: 510
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031984266
ISBN 10: 3031984269
Series: Synthese Library
Pages: 248
Publication Date: 19 July 2025
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

César Frederico dos Santos obtained bachelor’s degrees in Information Systems (2004) and Philosophy (2010), and a master’s degree in Philosophy (2012) at the Federal University of Santa Catarina, Brazil. In 2013, he got a permanent position at the Department of Philosophy of the Federal University of Maranhão, Brazil. He recently obtained a PhD in Philosophy at the Vrije Universiteit Amsterdam. His main interests lie in the ontological status of numbers and other abstract objects, the epistemology of formal sciences, and empirically informed approaches to traditional philosophical issues. He has published articles on the philosophy of mathematics and logic exploring the philosophical importance of findings from experimental psychology for these disciplines.