Numbers as Cognitive Tools

An Empirically Informed Nominalistic Account of the Nature of Numbers

César Frederico dos Santos (Autor)

Buch | Hardcover

IX, 248 Seiten

2025
Springer International Publishing (Verlag)
978-3-031-98426-6 (ISBN)

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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.

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.

1 Introduction.- 2 Methodological shortcoming in the philosophy of arithmetic.- 3. A methodological alternative.- 4 Quantical cognition.- 5 Numerical cognition.- 6 The historical origins of number concepts.- 7 The reification of number concepts.- 8 Back to the philosophy of arithmetic.- 9 Concluding remarks.- Glossary.

Erscheinungsdatum	13.06.2025
Reihe/Serie	Synthese Library
Zusatzinfo	IX, 248 p. 19 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Geisteswissenschaften ► Philosophie
Schlagworte	anti-platonism • Numerical cognition • ontology of arithmetic • philosophy of mathematics • Quantical cognition
ISBN-10	3-031-98426-9 / 3031984269
ISBN-13	978-3-031-98426-6 / 9783031984266
Zustand	Neuware