Do numbers, sets, and so forth exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing these questions that have attracted lively debate in recent years, Stewart Shapiro argues that standard realist and antirealist accounts of mathematics are both problematic. To resolve this dilemma, he articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers, existing independently, but simply a natural structure, the pattern common to any system that follows the general laws of addition. Shapiro concludes by showing how his approach can be applied to wider philosophical questions such as the nature of an object. Clear, compelling, and tautly argued it will be of deep interest to both philosophers and mathematicians.
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"This book is an important contribution...presenting an original, structuralist philosophy and axiomatic framework in comprehensive detail, placing it in broad philosophical and historical perspective, and comparing it systematically with other approaches seen as leading structuralist alternatives to the one set forth by Shapiro himself....this is an interesting, important, and thought-provoking book."--Journal of Symbolic Logic
About the Author
Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and the University of St. Andrews, Scotland.
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This review is from: Philosophy of Mathematics: Structure and Ontology (Paperback)
"Philosophy of Mathematics: Structure and Ontology", es una de las obras fundamentales de uno de los más importantes filósofos de las matemáticas del siglo XXI. Shapiro con una prosa soberbia, por ratos árida, nos presenta y fundamenta, desde el estructuralismo al que pertenece, una visión de las matemáticas. Su libro comienza repasando aspectos generales sobre la filosofía de las matemáticas para que, posteriormente, en el capítulo segundo, nos muestre su propuesta entrando a analizar en detalle su aspecto ontológico y epistemológico. Shapiro finaliza su tratado proponiendo extender el estructuralismo a otras ramas de las matemáticas, la ciencia y el lenguaje natural. Como acertadamente afirma: " Es un trabajo de interés tanto para filósofos como matemáticos"
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First Sentence:
For a long time, many philosophers and some mathematics believed that philosophical matters, such as metaphysics and ontology, determine the proper practice of mathematics. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Julius Caesar, Euclid's Elements, Ozzie Smith, Third Man, Arthur Fine, Frege's Caesar, Hilbert's Grundlagen New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
For a long time, many philosophers and some mathematics believed that philosophical matters, such as metaphysics and ontology, determine the proper practice of mathematics. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Julius Caesar, Euclid's Elements, Ozzie Smith, Third Man, Arthur Fine, Frege's Caesar, Hilbert's Grundlagen New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 7
books:
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20
books
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- Philosophy of logic (Harper essays in philosophy) by Hilary Putnam in Back Matter
- Symbolic Logic by Clarence Irving Lewis in Back Matter
- University of Pittsburgh by Tim Williams in Back Matter
- Collected Works, Vol. 3: Unpublished Essays and Lectures by Kurt Godel in Back Matter
- Muirhead Library of Philosophy (95 volumes): Philosophy in America by Black Max in Back Matter
See all 7 books this book cites
- Identity and Modality (Mind Association Occasional Series) by Fraser MacBride on 6 pages
- Kant, Science, and Human Nature by Robert Hanna on page 329, and Back Matter
- The Law of Non-Contradiction by Graham Priest in Front Matter
- Liars and Heaps: New Essays on Paradox by JC Beall in Front Matter
- The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics by Bob Hale in Back Matter
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