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.
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.
César Frederico dos Santos obtained bachelors degrees in Information Systems (2004) and Philosophy (2010), and a masters 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.
