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

The Limits of Logic
Higher-Order Logic and the Löwenheim-Skolem Theorem

Edited By

Stewart Shapiro

ISBN 9781855217317
Published October 31, 1996 by Routledge
552 Pages

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Book 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.

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.

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’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