Synopsis
How did we come to number and class? A historical, critical look at the idea behind counting.
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.
Other Popular Editions of the Same Title
Search results for The Notion of Number and the Notion of Class (Classic...
Seller Image
The Notion of Number and the Notion of Class (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: New. 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. print-on-demand item. Seller Inventory # 9781332061228_0
Buy New
£ 13.87
Free Shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: Over 20 available
Stock Image
The Notion of Number and the Notion of Class Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
Seller rating 5 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332061228
Stock Image
The Notion of Number and the Notion of Class Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 4 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332061228
Buy New
£ 17.82
£ 3.29 shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: 15 available