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

Ashgate Publishing, Limited
Publication date:
International Research Library of Philosophy
Product dimensions:
6.80(w) x 9.70(h) x 1.70(d)

Meet the Author

Table of Contents

Series Preface
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
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

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network


Most Helpful Customer Reviews

See all customer reviews >