Numerical Cognition and the Epistemology of Arithmetic
Cambridge University Press (Verlag)
978-1-009-46888-6 (ISBN)
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.
Markus Pantsar is a Visiting Professor at the RWTH Aachen University, Germany, and Docent in theoretical philosophy at the University of Helsinki, Finland. He is the author of Truth, Proof, and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics (2009), and many journal articles on the cognitive foundations of arithmetical knowledge.
Preface; Introduction: a fractured landscape; Part I. Ontogeny: 1. Proto-arithmetical; 2. Acquisition of number concepts; 3. Enculturation; Part II. Phylogeny and History: 4. The phylogeny and cultural history of number concepts; 5. The Development of arithmetic; 6. Cumulative cultural evolution; Part III. Epistemology and Ontology: 7. Conventionalism and intersubjectivity; 8. The character of arithmetical knowledge; 9. Ontological considerations; Conclusion; Bibliography; Index.
| Erscheinungsdatum | 16.03.2024 |
|---|---|
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Gewicht | 527 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Naturwissenschaften | |
| ISBN-10 | 1-009-46888-X / 100946888X |
| ISBN-13 | 978-1-009-46888-6 / 9781009468886 |
| Zustand | Neuware |
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