Limits of Logic : Higher-Order Logic and the Lowenheim-Skolem Theorem

Limits of Logic : Higher-Order Logic and the Lowenheim-Skolem Theorem

by Stewart Shapiro
     
 

Product Details

ISBN-13:
9781855217317
Publisher:
Ashgate Publishing, Limited
Publication date:
10/01/1996
Series:
International Research Library of Philosophy
Pages:
525
Product dimensions:
6.80(w) x 9.70(h) x 1.70(d)

Meet the Author

Table of Contents

Acknowledgments
Series Preface
Introduction
1Beyond First-order Logic: The Historical Interplay between Mathematical Logic and Axiomatic Set Theory3
2Which Logic is the Right Logic?47
3On Second-Order Logic69
4Second-Order Languages and Mathematical Practice89
5What Are Logical Notions?119
6A Curious Inference131
7The Rationalist Conception of Logic143
8A Critical Appraisal of Second-Order Logic177
9Who's Afraid of Higher-Order Logic?197
10Ontological Reduction211
11Intended Models and the Lowenheim-Skolem Theorem225
12Categoricity241
13Skolem's Paradox and Constructivism263
14Second-Order Logic, Foundations, and Rules301
15To Be is To Be a Value of a Variable (Or To Be Some Values of Some Variables)331
16Nominalist Platonism351
17Second-Order Logic Still Wild369
18Kreisel, the Continuum Hypothesis and Second Order Set Theory385
19Skolem and the Lowenheim-Skolem Theorem: A Case Study of the Philosophical Significance of Mathematical Results403
20Skolem and the Skeptic419
21Skolem and the Skeptic451
22Predication Versus Membership in the Distinction Between Logic as Language and Logic as Calculus473
23Logicism, The Continuum and Anti-Realism509
Name Index523

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