Author: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262542234
Category : Mathematics
Languages : en
Pages : 350
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Book Description
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Author: Peter van Inwagen
Publisher: Taylor & Francis
ISBN: 1000938298
Category : Philosophy
Languages : en
Pages : 299
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Book Description
In Do Numbers Exist? Peter van Inwagen and William Lane Craig take opposite sides on whether there are abstract objects, such as numbers and properties. Craig argues that there are no abstract objects, whereas Van Inwagen argues that there are. Their exchange explores various arguments about the existence and nature of abstract objects. They focus especially on whether our ordinary and scientific thought and talk commit us to abstract objects, surveying the options available to us and the objections each faces. The debate covers central problems and methods in metaphysics, and also delves into theological questions raised by abstract objects. Key Features: Showcases the presentation and defense of two points of view on the existence of abstract objects, from two of the world’s leading philosophers Presents definitions in an easily accessible form Provides frequent summaries of previously covered material Includes a glossary of all specialized vocabulary
Author: Jim Holt
Publisher: W. W. Norton & Company
ISBN: 0871404095
Category : Philosophy
Languages : en
Pages : 321
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Book Description
In this astonishing and profound work, an irreverent sleuth traces the riddleof existence from the ancient world to modern times.
Author: Stewart Shapiro
Publisher: OUP Oxford
ISBN: 0192893068
Category : Philosophy
Languages : en
Pages : 323
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Book Description
Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.
Author: Geoffrey Hellman
Publisher: Cambridge University Press
ISBN: 110863074X
Category : Science
Languages : en
Pages : 167
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Book Description
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.
Author: Geoffrey Hellman
Publisher: Clarendon Press
ISBN: 019152011X
Category : Philosophy
Languages : en
Pages : 172
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Book Description
Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.
Author: George Lakoff
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 520
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Book Description
A study of the cognitive science of mathematical ideas.
Author: Øystein Linnebo
Publisher: Princeton University Press
ISBN: 069120229X
Category : Mathematics
Languages : en
Pages : 214
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Book Description
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
Author: Devon Price
Publisher: Simon and Schuster
ISBN: 1982140135
Category : Self-Help
Languages : en
Pages : 256
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Book Description
From social psychologist Dr. Devon Price, a conversational, stirring call to “a better, more human way to live” (Cal Newport, New York Times bestselling author) that examines the “laziness lie”—which falsely tells us we are not working or learning hard enough. Extra-curricular activities. Honors classes. 60-hour work weeks. Side hustles. Like many Americans, Dr. Devon Price believed that productivity was the best way to measure self-worth. Price was an overachiever from the start, graduating from both college and graduate school early, but that success came at a cost. After Price was diagnosed with a severe case of anemia and heart complications from overexertion, they were forced to examine the darker side of all this productivity. Laziness Does Not Exist explores the psychological underpinnings of the “laziness lie,” including its origins from the Puritans and how it has continued to proliferate as digital work tools have blurred the boundaries between work and life. Using in-depth research, Price explains that people today do far more work than nearly any other humans in history yet most of us often still feel we are not doing enough. Filled with practical and accessible advice for overcoming society’s pressure to do more, and featuring interviews with researchers, consultants, and experiences from real people drowning in too much work, Laziness Does Not Exist “is the book we all need right now” (Caroline Dooner, author of The F*ck It Diet).
Author: Lulu Miller
Publisher: Simon and Schuster
ISBN: 1501160346
Category : Biography & Autobiography
Languages : en
Pages : 256
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Book Description
Nineteenth-century scientist David Starr Jordan built one of the most important fish specimen collections ever seen, until the 1906 San Francisco earthquake shattered his life's work.
