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Synopsis
Explore how mathematics builds on logic, symbols, and precise definitions you can trust.
This concise guide shows why ordinary language can mislead when dealing with numbers, functions, and proof, and how mastering symbolic methods leads to clear, exact thinking.
Through topics like limits and continuity, Cantorian and Dedekindian notions of continuity, and the role of tautology in logic and mathematics, the book frames how rigorous foundations support mathematical reasoning. It contrasts familiar ideas with their formal counterparts and explains why a symbolic approach matters for mastering the subject. The discussion situates these ideas within a broader view of philosophy, aiming to clarify what can be known a priori and what depends on empirical facts.
- How continuity and limits are defined and why they matter for functions
- Different notions of continuity in mathematics and their implications
- The role of symbols, definitions, and logical structure in rigorous proof
- Connections between mathematics, logic, and philosophical questions about existence
Ideal for readers of mathematical philosophy and anyone seeking a clear account of how logic underpins the structure of mathematics.
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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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Introduction to Mathematical Philosophy (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book delves into the foundations of mathematics, exploring the fundamental concepts that underpin this seemingly complex field. By carefully analyzing familiar notions like numbers and counting, the author reveals a surprising truth: the essence of mathematics can be found in the realm of logic. This journey into the heart of mathematics begins with the seemingly simple series of natural numbers. However, even these familiar building blocks hold hidden depths, and their true nature has often eluded even the most astute thinkers. Through a process of meticulous analysis, the author unveils the logical principles that govern these numbers, demonstrating how they can be defined and understood in terms of pure logic. This groundbreaking approach not only illuminates the inner workings of mathematics but also sheds light on its historical development. Concepts like infinity and continuity, once considered the domain of philosophy, are now shown to be firmly rooted in the logical framework of mathematics. Ultimately, this book offers a profound revelation: the intricate and powerful world of mathematics is built upon a foundation of logic, revealing a deep and unexpected connection between these two seemingly disparate disciplines. 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 # 9781330323038_0
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