The Foundations of Mathematics: A Contribution to the Philosophy of Geometry

(7 User reviews)   4287
By Charlotte Girard Posted on Nov 15, 2025
In Category - Philosophy
Carus, Paul, 1852-1919 Carus, Paul, 1852-1919
English
Ever wondered why 2+2=4 feels so certain, but the rules of geometry seem to shift? If you've ever stared at a triangle and thought, 'What makes this true?', this book is for you. Paul Carus tackles the big question: Are the rules of math something we discover in the universe, or are they a brilliant invention of the human mind? It's not a dry textbook—it's a lively, century-old conversation about the very ground we stand on when we say something is 'true.' Perfect for anyone who loves a good brain puzzle.
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consulted widely on caring in nursing. Currently, she and Dr. Schoenhofer are engaged in a two-year funded demonstration project. The purpose of this project is to demonstrate the value of a model for health care delivery in an acute care setting that is intentionally grounded in Nursing as Caring. Savina O. Schoenhofer, Ph.D, is Professor of Graduate Nursing at Alcorn State University in Natchez, Mississippi. Dr. Schoenhofer is co-founder of the nursing aesthetics publication, Nightingale Songs. Her research and publications are in the areas of everyday caring, outcomes of caring in nursing, nursing values, nursing home management, and affectional touch. [Illustration: Button] FOREWORD Marilyn E. Parker, PhD, RN, Professor of Nursing Florida Atlantic University, Boca Raton, Florida Caring may be one of the most often used words in the English language. Indeed, the word is commonly used as much in talking about our everyday lives and relationships as it is in the marketplace. At the same time, nurses thinking about, doing, and describing nursing know that caring has unique and particular meaning to them. Caring is one of the first synonyms for nursing offered by nursing students and is surely the most frequent word used by the public in talking about nursing. Caring is an essential value in the personal and professional lives of nurses. The formal recognition of caring in nursing as an area of study and as a necessary guide for the various avenues of nursing practice, however, is relatively new. Anne Boykin and Savina Schoenhofer have received many requests from academic peers and students to articulate the nursing theory they have been working to develop. This book is a response to the call for a theory of nursing as caring. The progression of nursing theory development often has been led by nurse theorists who stepped into other disciplines for ways to think about and study nursing and for structures and concepts to describe nursing practice. The opportunity to use language and methods of familiar, relatively established bodies of knowledge that could be communicated and widely understood took shape as many nursing scholars received graduate education in disciplines outside of nursing. Conceptions and methods of knowledge development often came then from disciplines in the biological and social sciences and were brought into ways of thinking about and doing nursing scholarship. Evolution of new worldviews opened the way for nurses to develop theories reflecting ideas of energy fields, wholeness, processes, and patterns. Working from outside the discipline of nursing, along with shifts in worldviews, has been essential to opening the way for nurses to explore nursing as a unique practice and body of knowledge from inside the discipline, and to know nursing in unprecedented ways. Nursing as Caring: A Model for Transforming Practice sets forth a different order of nursing theory. This nursing theory is personal, not abstract. In order to express nursing as caring there is a clear need to know self as caring person. The focus of the Nursing as Caring theory, then, is not toward an end product such as health or wellness. It is about a unique way of living caring in the world. It is about nurses and nursed living life and nurturing growing humanly through participation in life together. Nursing as caring sets forth nursing as a unique way of living caring in the world. This theory provides a view that can be lived in all nursing situations and can be practiced alone or in combination with other theories. The domain of nursing is nurturing caring. The integrity, the wholeness, and the connectedness of the person simply and assuredly is central. As such,...

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Paul Carus's book isn't about solving equations. It's about asking the one question that comes before all the math: What are we even talking about? He focuses on geometry—the study of shapes and space—and asks where its fundamental rules come from. Is a straight line a real thing out in the world, or just a perfect idea in our heads?

The Story

There's no plot with characters, but there is a fascinating intellectual journey. Carus walks you through the history of geometry, from the ancient Greeks to the thinkers of his own time. He shows how our understanding of space and measurement has changed, and he argues passionately for a specific view: that mathematical truths are a special kind of human creation, built from logic and experience together. The 'conflict' is between seeing math as a physical fact versus a mental framework.

Why You Should Read It

I loved how this book makes you question your assumptions. We take so much for granted. Carus pulls the rug out gently and makes you look at the floorboards. His writing is clear and surprisingly personal for a philosophy book. You get the sense he's genuinely excited to share these ideas with you, not just lecture. It turns an abstract topic into a relatable human quest for certainty.

Final Verdict

This is for the curious non-expert. If you enjoyed books like 'Gödel, Escher, Bach' or just like pondering big questions over coffee, you'll find a lot here. It's not for someone looking for a quick read or practical math tips. Think of it as a deep, rewarding conversation with a very thoughtful friend from 1908 about the nature of truth itself.



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Betty Lewis
4 months ago

Text is crisp, making it easy to focus.

Donald Lee
1 year ago

Comprehensive and well-researched.

5
5 out of 5 (7 User reviews )

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