The Notion of Number and the Notion of Class (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 18.06
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book's main focus is on the origins of mathematics, specifically how we perceive numbers. The author begins with a discussion of different philosophical theories on the origins of numbers, including theories from people like John Stuart Mill and Immanuel Kant. The author argues that these theories are based on introspection, which can vary significantly from person to person. Instead, the author argues that we should look at how people actually behave when dealing with numbers and use that to determine how we perceive numbers. The second part of the book examines the implications of anthropology and psychology on the origins of the number concept. The author argues that number perception is not a specifically human trait and can be seen in animals as well. The author also argues that number perception is not something that is learned through language or education but is instead a natural ability that humans have. Finally, the author discusses the development of number systems and how they have changed over time. The author argues that the development of number systems is not a linear progression but instead a complex process that has been influenced by many different factors, including culture, language, and technology. The author concludes by arguing that the study of the origins of the number concept can give us valuable insights into the nature of human cognition. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781332061228_0
- Title
- The Notion of Number and the Notion of Class (Classic Reprint)
- Author
- Richard A. Arms
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332061222
- ISBN 13
- 9781332061228
- Seller catalogs
- Logic
The book surveys how thinkers from Mill to Frege and Russell have understood number and class. It frames these notions through practical questions about how we experience quantity, and whether number can be explained by time, space, or pure logic. The discussion weighs empirical and Kantian views against analytic and formal theories, testing assumptions about why arithmetic should be thought of as a matter of observation, language, or abstract reasoning.
Readers will trace debates over extension versus intension, the role of abstraction, and the paradoxes that arise when counting infinite collections. The work also examines how ranges and functions contribute to defining numbers and classes, and it presents postulates proposed to ground the existence of these abstract entities. The tone is analytic but accessible, inviting verification by observable facts and careful argument.
- Learn how different historical views connect number to time, space, or logic.
- Explore the shift from purely extensional ideas of a class to more nuanced notions like ranges and abstraction.
- See how famous paradoxes, such as Russell's, challenge simple definitions of classes and numbers.
- Understand the motivations for introducing new logical postulates to ground these concepts.
Ideal for readers with an interest in the philosophy of mathematics, logic, and the foundations of arithmetic.
"Synopsis" may belong to another edition of this title.
Forgotten Books
London, United Kingdom
AbeBooks seller since June 2, 2021
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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FB &c Ltd
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