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Foundations Without Foundationalism: A Case for Second-Order Logic
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PublishedOn
2000-05-18
Title
Foundations without Foundationalism: A Case for Second-order Log
ISBN
9780198250296
Subject Area
Social Science, Philosophy
Publication Name
Foundations Without Foundationalism : a Case for Second-Order Logic
Item Length
9.3 in
Publisher
Oxford University Press, Incorporated
Subject
Philanthropy & Charity, Logic
Publication Year
2000
Type
Textbook
Format
Uk-Trade Paper
Language
English
Item Height
0.7 in
Author
Stewart Shapiro
Item Width
6.1 in
Item Weight
15.6 Oz
Number of Pages
300 Pages

Über dieses Produkt

Product Information

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.

Product Identifiers

Publisher
Oxford University Press, Incorporated
ISBN-10
0198250290
ISBN-13
9780198250296
eBay Product ID (ePID)
66354

Product Key Features

Author
Stewart Shapiro
Publication Name
Foundations Without Foundationalism : a Case for Second-Order Logic
Format
Uk-Trade Paper
Language
English
Subject
Philanthropy & Charity, Logic
Publication Year
2000
Type
Textbook
Subject Area
Social Science, Philosophy
Number of Pages
300 Pages

Dimensions

Item Length
9.3 in
Item Height
0.7 in
Item Width
6.1 in
Item Weight
15.6 Oz

Additional Product Features

Intended Audience
College Audience
Reviews
"Contains more on second-order logic than is readily available in any other textbook or survey. Philosophically, the book also contains many words of wisdom." --Journal of Symbolic Logic"The most comprehensive all-round account and defense of second-order logic as a vehicle for mathematics known to the reviewer. It is also very comprehensively documented with a large bibliography and a wealth of interesting material in the numerous footnotes." --Mathematical Reviews"An excellent book, covering all of the main results in second-order logic and its applications to mathematical theories. There is a great wealth of material about second-order logic in this book. . . . it is really an excellent book, and . . . the author is to be commended for a job well done." --Notre Dame Journal of Formal Logic, 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; References; Index, "Contains more on second-order logic than is readily available in any other textbook or survey. Philosophically, the book also contains many words of wisdom." -- Journal of Symbolic Logic "The most comprehensive all-round account and defense of second-order logic as a vehicle for mathematics known to the reviewer. It is also very comprehensively documented with a large bibliography and a wealth of interesting material in the numerous footnotes." -- Mathematical Reviews "An excellent book, covering all of the main results in second-order logic and its applications to mathematical theories. There is a great wealth of material about second-order logic in this book. . . . it is really an excellent book, and . . . the author is to be commended for a job well done." -- Notre Dame Journal of Formal Logic, "Contains more on second-order logic than is readily available in any other textbook or survey. Philosophically, the book also contains many words of wisdom." --Journal of Symbolic Logic "The most comprehensive all-round account and defense of second-order logic as a vehicle for mathematics known to the reviewer. It is also very comprehensively documented with a large bibliography and a wealth of interesting material in the numerous footnotes." --Mathematical Reviews "An excellent book, covering all of the main results in second-order logic and its applications to mathematical theories. There is a great wealth of material about second-order logic in this book. . . . it is really an excellent book, and . . . the author is to be commended for a job well done." --Notre Dame Journal of Formal Logic
Table of Content
PART I: Orientation1. Terms and Questions2. Foundationalism and Foundations of MathematicsPART II: Logic and Mathematics3. Theory4. Metatheory5. Second-Order Logic and Mathematics6. Advanced MetatheoryPART III: History and Philosophy7. The Historical Triumph of First-Order Languages8. Second-Order Logic and Rule-Following9. The Competition
Copyright Date
1999
Dewey Decimal
511.3
Dewey Edition
21
Illustrated
Yes

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