An essay on the foundations of geometry

Name: An essay on the foundations of geometry
Author: Bertrand Russell

By Bertrand Russell

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About This Book

The work investigates the logical and epistemological basis of geometric knowledge, asking which geometric principles must be presupposed for experience. It surveys the historical emergence of non‑Euclidean systems and Riemann's notions of manifolds and curvature, then compares metrical and projective approaches developed by Cayley, Klein, Beltrami and others. It examines Kantian claims about space, treats axioms as conditions of measurement rather than empirical facts, and argues that many geometric propositions owe their necessity to conceptual choices and the logical structure of the methods used.

About the Author

Bertrand Russell

Bertrand Russell (1872-1970) was a British philosopher, logician, and social critic, renowned for his contributions to a variety of fields including mathematics, philosophy, and education. He is best known for his work in analytic philosophy and for co-authoring the monumental 'Principia Mathematica' with Alfred North Whitehead. Russell's writings often explore the intersection of philosophy and social issues, as seen in his influential essays such as 'Free Thought and Official Propaganda' and 'Political Ideals.' His advocacy for rational thought and skepticism has left a lasting impact on modern philosophical discourse.