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Mathematics -- Philosophy Books

Best books

Henri Poincaré

The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

"The Foundations of Science: Science and Hypothesis, The Value of Science" by Henri Poincaré is a philosophical work published in 1904. This French mathematician and physicist explores fundamental questions about how science works, examining the interplay between intuition and logic in mathematics, and the deep connections between mathematical theory and physical reality. Poincaré investigates how scientists choose theories, why mathematical language proves essential for physics, and confronts emerging crises challenging established principles like energy conservation and Newton's laws at the dawn of the twentieth century.

Bertrand Russell

Introduction to Mathematical Philosophy

Wikipedia page about this book: https://en.wikipedia.org/wiki/Introduction_to_Mathematical_Philosophy

Auguste Comte

The philosophy of mathematics

"The Philosophy of Mathematics" by Auguste Comte is a scientific publication written in the mid-19th century. The book delves into the fundamental aspects of mathematical science, analyzing its nature, scope, and methods. Through comprehensive examination, it aims to provide a deeper understanding of mathematics not merely as a collection of techniques but as a profound scientific discipline interconnected with various branches of knowledge. The opening of the book sets the stage for Comte's exploration of mathematical philosophy by discussing the historical context and necessity of clearly defining the scope and divisions of mathematics. Comte argues that while mathematics is the most ancient and perfected of sciences, its true nature is often misunderstood due to vague definitions. He emphasizes the importance of indirect measurement in mathematics and outlines the methodological evolution that has allowed mathematicians to derive quantities from one another using established relationships. He anticipates a systematic classification of mathematical inquiries, which further frames the discussion for the chapters that will follow. This introduction establishes a philosophical foundation that Comte will build upon as he navigates complex ideas related to both abstract and concrete mathematics.

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