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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: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262542234
Category : Mathematics
Languages : en
Pages : 350
Get Book Here
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.
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Author: Euclides
Publisher:
ISBN:
Category :
Languages : en
Pages : 434
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Author: Moffatt and Paige
Publisher:
ISBN:
Category :
Languages : en
Pages : 232
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Book Description
Author: Rossella Lupacchini
Publisher: Springer Science & Business Media
ISBN: 8847007844
Category : Philosophy
Languages : en
Pages : 285
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Book Description
This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G ̈ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.
Author: Arthur Lee Sparkes
Publisher:
ISBN:
Category :
Languages : en
Pages : 288
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Book Description
![The English language: its sources [&c., by T. Page]. PDF](https://books.google.com/books/content/images/frontcover/q5kDAAAAQAAJ?fife=w80-h100)
Author: Thomas Page (schoolmaster.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 144
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Author: George Collins (of the Borough road training coll.)
Publisher:
ISBN:
Category : School management and organization
Languages : en
Pages : 210
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Author: Euclides
Publisher:
ISBN:
Category :
Languages : en
Pages : 428
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Author: Robert Potts
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 446
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 300
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