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The limits of logic : higher-order logic and the Löwenheim-Skolem theorem

Author: Stewart Shapiro
Publisher: Aldershot ; Brookfield, USA : Dartmouth, ©1996.
Series: International research library of philosophy, 18.; International research library of philosophy., Philosophy of logic, language, and mind.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

The articles in this volume represent a part of the philosophical literature on higher-order logic and the Skolem paradox. They ask the question "what is second-order logic?" and examine various  Read more...

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Document Type: Book
All Authors / Contributors: Stewart Shapiro
ISBN: 1855217317 9781855217317
OCLC Number: 34077442
Description: xxii, 525 pages ; 25 cm.
Contents: Contents: Is Second-Order Logic Logic?: Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory, Gregory H. Moore; Which logic is the right logic?, Leslie H. Tharp; On second-order logic, George S. Boolos; Second-order languages and mathematical practice, Stewart Shapiro; What are logical notions?, Alfred Tarski; A curious inference, George Boolos; The rationalist conception of logic, Steven J. Wagner; A critical appraisal of second-order logic, Ignacio Jane; Who's afraid of higher-order logic?, Peter Simons. Ontological Reduction, Intended Interpretations and the LA wenheim-Skolem Theorems: Ontological reduction, Leslie H. Tharp; Intended models and the LA wenheim-Skolem theorem, Virginia Klenk; Categoricity, John Corcoran; Skolem's paradox and constructivism, Charles McCarty and Neil Tennant; Second-order logic, foundations and rules, Stewart Shapiro. Plural Quantification: To be is to be a value of a variable (or to be some values of some variables), George Boolos; Nominalist Platonism, George Boolos; Second-order logic still wild, Michael D. Resnick. Philosophy of Set Theory: Kreisel, the continuum hypothesis, and second-order set theory, Thomas Weston; Skolem and the LA wenheim-Skolem theorem: a case study of the philosophical significance of mathematical results, Alexander George; Skolem and the skeptic, Paul Benacerraf; Skolem and the skeptic, Crispin Wright; Predication versus membership in the distinction between logic as language and logic as calculus, Nino B. Cocchiarella; Logicism, the continuum and anti-realism, Peter Clark; Name index.
Series Title: International research library of philosophy, 18.; International research library of philosophy., Philosophy of logic, language, and mind.
Responsibility: edited by Stewart Shapiro.
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'Almost every significant paper on second-order logic and the philosophical importance of the Lowenheim-Skolem theorems is here in this collection...a useful addition to the library of anyone Read more...

 
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