The Notion of Number and the Notion of Class (Classic Reprint) - Hardcover

Richard A. Arms

Hardcover

ISBN 10: 0656830646 ISBN 13: 9780656830640

Publisher: Forgotten Books, 2018

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.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0656830646
• ISBN 13: 9780656830640
• Binding: Hardcover
• Number of pages: 86