The Principles of Mathematics (Classic Reprint) - Couverture souple

Bertrand Russell

Couverture souple

ISBN 10 : 133087143X ISBN 13 : 9781330871430

Editeur : Forgotten Books, 2018

Synopsis

Explore the foundations of mathematics and logic in this concise, landmark study. The Principles of Mathematics, Vol. 1 offers a clear introduction to Bertrand Russell’s rigorous approach to logic, numbers, space, motion, and the nature of mathematical reasoning. It frames how pure mathematics uses abstract concepts to model ideas independent of physical objects.

The book is written for both philosophers and mathematicians, and it sketches the connections between symbolic logic and mathematical theory. It discusses how definitions, predicates, and logical constants underlie much of mathematics, and it surveys topics such as real numbers, complete and incomplete series, and the correlation of infinite classes. The author also outlines the role of dynamics, geometry, and the philosophy of space, with emphasis on careful analysis rather than empirical details.

What you’ll experience
- An overview of the logical foundations that support arithmetic, geometry, and analysis
- Concepts like complete vs. incomplete series and how functions relate infinite classes
- A discussion of real numbers as a way to understand number through rational classes
- The relationship between philosophy and mathematics, and guidance for readers new to symbolic logic

Ideal for readers of philosophy and mathematics who want a rigorous, practitioner-friendly view of foundational ideas and their implications.

A propos du livre

Présentation de l'éditeur

Principles of Mathematics was published in 1903, and most of JL it was written in 1900, In the subsequent years the subjects of which it treats have been widely discussed, and the technique of mathematical logic has been greatly improved ;while some new problems have arisen, some old ones have been solved, and others, though they remain in a controversial condition, have taken on completely new forms. In these circumstances, it seemed useless to attempt to amend this or that, in the book, which no longer expresses my present views. Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject. I have therefore altered nothing, but shall endeavour, in this I ntroduction, to say in what respects I adhere to the opinions which it expresses, and in what other respects subsequent research seems to me to have shown them to be erroneous. The fundamental thesis of the following pages, that mathematics and logic are identical, is one which I have never since seen any reason to modify. This thesis was, at first, unpopular, because logic is traditionally associated with philosophy and A ristotle, so that mathematicians felt it to be none of their business, and those who considered themselves logicians resented being asked to master a new and rather difficult mathematical technique. But such feelings would have had no lasting influence if they had been unable to find support in more serious reasons for doubt. These reasons are, broadly speaking, of two opposite kinds :first, that there are certain unsolved difficulties in mathematical logic, which make it appear less certain than mathematics is believed to be ;and secondly that, if the logical basis of mathematics is accepted, it justifies, or tends to justify, much work, such as that of Georg Cantor, which is viewed with suspicion by
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Présentation de l'éditeur

The Principles of Mathematics: Vol. 1 is a terrific introduction to the fundamental concepts of mathematics. Although the book's title involves mathematics, it is not a textbook packed with equations and theorems. Instead philosopher Bertrand Russell uses mathematics to explore the structure of logic. Russell's ultimate point is that mathematics is logic and logic itself is truth.

The book is substantial and covers all subjects of mathematics. It is divided into seven sections: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. Russell covers all the major developments of mathematics and the contributions of important figures to the field. His sharp mind is evident throughout The Principles of Mathematics, as he challenges established rules and teachers readers how to think through difficult problems using logic.

Russell was one of the great minds of the 20th Century. In this book he discusses how his ideas were influenced by the logician Peano. He also debates other philosophers and mathematicians, and even anticipates the Theory of Relativity, which had not yet been published by Einstein.

One does not need to love mathematics to gain insights from The Principles of Mathematics: Vol. 1. Those who are interested in logic, intellectualism, philosophy or history will find significant insights into logical principles. Readers who desire an intellectual challenge will truly enjoy The Principles of Mathematics: Vol. 1.

About the Publisher

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Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 133087143X
• ISBN 13: 9781330871430
• Reliure: Broché
• Nombre de pages: 573
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