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Foundations without Foundationalism: A Case for Second-Order Logic
 

Foundations without Foundationalism: A Case for Second-Order Logic (Hardback)

By Shapiro, Stewart

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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 it...s 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.
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ISBN 9780198533917
Released NZ 19 Sep 1991
Publisher Oxford University Press (S1)
Format Hardback
Alternate Format(s) View All (1 other possible title(s) available)
Series Oxford Logic Guides (part: 17)
Availability
Back Order Indent title (sourced internationally), Allow 8-12 weeks due to Covid 19 freight delays

Full details for this title

ISBN-13 9780198533917
Stock Available
Status Back Order Indent title (sourced internationally), Allow 8-12 weeks due to Covid 19 freight delays
Publisher Oxford University Press (S1)
Imprint Clarendon Press
Released 19 Sep 1991
Publication Country United Kingdom United Kingdom
Format Hardback
 › 1 other possible formats available
Author(s) By Shapiro, Stewart
Series Oxford Logic Guides (part: 17)
Category Logic
Philosophy Of Mathematics
Mathematical Logic
Number of Pages 300
Dimensions Width: 161mm
Height: 242mm
Spine: 24mm
Dewey Code 511.3
Weight 659g
Interest Age General Audience
Reading Age General Audience
Library of Congress Logic, Symbolic and mathematical
NBS Text Mathematics
ONIX Text Professional and scholarly

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