The Limits of Logic: Higher-Order Logic and the Löwenheim-Skolem Theorem, 1st Edition (Hardback) book cover

The Limits of Logic

Higher-Order Logic and the Löwenheim-Skolem Theorem, 1st Edition

Edited by Stewart Shapiro

Routledge

552 pages

Purchasing Options:$ = USD
Hardback: 9781855217317
pub: 1996-10-31
$375.00
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eBook (VitalSource) : 9781315238647
pub: 2016-12-05
from $182.50


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Description

The International research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the library deals with a field of enquiry which has received significant attention in philosophy in the last 25 years and is edited by a philosopher noted in that field.

Reviews

’Almost every significant paper on second-order logic and the philosophical importance of the Löwenheim-Skolem theorems is here in this collection…a useful addition to the library of anyone interested in the nature of logic in general and in the function of second-order methods in particular.’ Studia Logica

Table of 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 Jané; Who's afraid of higher-order logic?, Peter Simons. Ontological Reduction, Intended Interpretations and the Löwenheim-Skolem Theorems: Ontological reduction, Leslie H. Tharp; Intended models and the Löwenheim-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 Löwenheim-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.

About the Series

The International Research Library of Philosophy

The International Research Library of Philosophy
The International Research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the Library deals with a field of inquiry which has received significant attention in philosophy in the last 25 years, and is edited by a philosopher noted in that field. No particular philosophical method or approach is favoured or excluded. The Library will constitute a representative sampling of the best work in contemporary English-language philosophy, providing researchers and scholars throughout the world with comprehensive coverage of currently important topics and approaches. The Library is divided into four series of volumes which reflect the broad divisions of contemporary philosophical inquiry: Metaphysics and Epistemology The Philosophy of Mathematics and Science The Philosophy of Logic, Language and Mind The Philosophy of Value

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Subject Categories

BISAC Subject Codes/Headings:
PHI000000
PHILOSOPHY / General