Synopsis
Delve into how geometry finds its foundations across logic, psychology, and mathematics. This rigorous study traces the growth of metageometry and its impact on how we understand space, distance, and shape.
Bertrand A. W. Russell’s work blends history, philosophy, and technical insight. It surveys early questions about the nature of space, explores non‑Euclidean ideas, and analyzes how projective and metrical geometry interrelate. The text draws on lectures and scholarly correspondence to map a complex debate about what geometry can claim to prove and what it must assume.
- How metageometry emerged in three creative periods and what each period sought to show about parallels and space
- Connections between geometry, logic, and psychology, including Kant’s and Lotze’s views
- Critical examinations of notable theories and the role of axioms in geometric reasoning
- Arguments about space as subjective, objective, or something in between, and their implications for geometry
Ideal for readers of philosophy of mathematics, logic, and the foundations of geometry who want a careful, historically grounded analysis.
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About the Author
Bertrand Russell (1872-1970) was born in England and educated at Trinity College, Cambridge. His long career established him as one of the most influential philosophers, mathematicians, and social reformers of the twentieth century.
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Paperback. Condition: New. Print on Demand. This book delves into the fascinating realm of geometry, exploring its fundamental principles and challenging long-held assumptions. The author traces the historical evolution of non-Euclidean geometries, highlighting the groundbreaking contributions of mathematicians like Gauss, Lobatchewsky, and Riemann. By examining the concept of "curvature" and its application to spaces of multiple dimensions, the book sheds light on the limitations of traditional Euclidean geometry. Through a rigorous analysis of projective and metrical geometries, the author investigates the nature of space and its relationship to our understanding of the world. The book grapples with profound philosophical questions, such as the role of axioms in shaping our knowledge and the possibility of alternative spatial realities. By questioning the very foundations of geometry, this work ultimately reveals the intricate connections between mathematics, logic, and our perception of the universe. 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 # 9781330166345_0
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