Artículos relacionados a The Notion of Number and the Notion of Class (Classic...
Sinopsis
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.
"Sinopsis" puede pertenecer a otra edición de este libro.
Reseña del editor
Excerpt from The Notion of Number and the Notion of Class
We shall first be concerned with the notion of number as it appeared to Mill and the Kantians and shall attempt to Show that the various historical positions are liable to one or both of the following objections (a) subjective mental states have been introduced, (b) violence has been done to the facts. Frege's distinction here between a posteriori and a priori methods is important. He holds that a priori is deductive, a posteriori, inductive; synthetic means that which uses conceptions belong ing to a special science while an analytic proposition is derived from pure logic alone. Frege held that the concepts and laws of arithmetic are analytic a priori, that they are derived from the fundamental definitions and axioms of logic. We shall find Bertrand Russell espousing the same cause although inde pendently and from slightly different motives.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from The Notion of Number and the Notion of Class
Discussions about the nature of number may be readily divided into various types. It is one of the striking characteristics of the true mathematician that anything in the way of a vague statement causes him acute discomfort. He desires a change from the suggestive impressionistic expression of the subjectively self-evident to an objective explicit derivation. A striking example of this is Frege's rebellion against psychological theories of number. "States of mind have no place in mathematics," says the mathematician, and, so far from differing with him, we may well inquire whether, as such, they have any place in philosophy.
To the post-Kantian metaphysician no such ideal ever presented itself. For him the boasted Copemican revolution had indeed taken place, and like our pragmatists, he could think of no problem except in connection with some mind. Number depends upon the way we think of it and the logically simple is what we can think of most readily. The method used is introspection. Opposed to these is the empiricist who demands that all be reduced to physical terms. Crudities such as this represent J. S. Mill's rash intrusion into the philosophy of arithmetic.
Corresponding to these three classes of thinkers we find widely different conceptions of number and three variants of Aristotelian logic. The empiricist defines number as a physical property of external objects and emphasizes induction; the Kantian talks about thought-content, introducing all manner of the psychology of reasoning into his so-called logic. It remains for the formalistic mathematician to regard number as definable in terms of class and that bewildering maze of symbolic ramifications which has gained the title of logistic as the pinnacle of mathematical method.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
"Sobre este título" puede pertenecer a otra edición de este libro.
Resultados de la búsqueda para The Notion of Number and the Notion of Class (Classic...
Imagen del vendedor
The Notion of Number and the Notion of Class (Classic Reprint)
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Paperback. Condición: 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. Nº de ref. del artículo: 9781332061228_0
Comprar nuevo
EUR 16,00
Gastos de envío gratis
Se envía de Reino Unido a Estados Unidos de America
Se envía de Reino Unido a Estados Unidos de America
Cantidad disponible: Más de 20 disponibles
Imagen de archivo
The Notion of Number and the Notion of Class Classic Reprint
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332061228
Comprar nuevo
EUR 25,09
Gastos de envío gratis
Se envía dentro de Estados Unidos de America
Se envía dentro de Estados Unidos de America
Cantidad disponible: 15 disponibles
Imagen de archivo
The Notion of Number and the Notion of Class Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332061228
Comprar nuevo
EUR 25,01
Envío por EUR 3,83
Se envía de Reino Unido a Estados Unidos de America
Se envía de Reino Unido a Estados Unidos de America
Cantidad disponible: 15 disponibles