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.

Presents a unified account of the nature of numbers Offers a hypothesis about the nature of numbers that is accountable towards empirical data, and thus refutable on an empirical basis Does justice to empirical findings in numerical cognition and the long tradition of philosophical reflection on the ontological status of numbers

Autorentext

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.

Inhalt

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.