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2000, ISBN: 9780198250296

ID: 1001004001379917

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows ho..., The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.Taal: Engels; Afmetingen: 19x234x156 mm; Gewicht: 441,00 gram; Verschijningsdatum: maart 2000; ISBN10: 0198250290; ISBN13: 9780198250296; , Engelstalig | Paperback | 2000, Mens & Maatschappij, Filosofie, Exacte wetenschappen, Wiskunde & Statistiek, Oxford University Press

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ISBN: 9780198250296

ID: 9780198250296

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. Books, [PU: Oxford University Press]

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Foundations without Foundationalism: A Case for Second-order Logic (Oxford Logic Guides)

*- Paperback*

2000, ISBN: 0198250290

ID: 14096214100

[EAN: 9780198250296], Neubuch, [PU: Oxford University Press], Philosophy|Logic, Social Science|Philanthropy & Charity, Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: PART I: Orientation 1. Terms and Questions 2. Foundationalism and Foundations of Mathematics PART II: Logic and Mathematics 3. Theory 4. Metatheory 5. Second-Order Logic and Mathematics 6. Advanced Metatheory PART III: History and Philosophy 7. The Historical Triumph of First-Order Languages 8. Second-Order Logic and Rule-Following 9. The Competition

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2000, ISBN: 0198250290

ID: 16919891579

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** Details of the book - Foundations Without Foundationalism: A Case for Second-Order Logic**

EAN (ISBN-13): 9780198250296

ISBN (ISBN-10): 0198250290

Paperback

Publishing year: 2000

Publisher: OXFORD UNIV PR

304 Pages

Weight: 0,422 kg

Language: eng/Englisch

Book in our database since 12.06.2007 12:52:52

Book found last time on 13.09.2017 21:04:08

ISBN/EAN: 0198250290

ISBN - alternate spelling:

0-19-825029-0, 978-0-19-825029-6

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