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Foundations without Foundationalism
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Foundations without Foundationalism: A Case for Second-Order Logic

Stewart Shapiro

Abstract

A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal development of second‐ and higher‐order logic and an extended argument that higher‐order systems have an important role to play in the philosophy and foundations of mathematics. The development includes the languages, deductive systems, and model‐theoretic semantics for higher‐order languages, and the basic and advanced results in its meta‐theory: completeness, compactness, and the Löwenheim–Skole ... More

Keywords: completeness, foundationalism, foundations, logic, mathematics, model theory, philosophical logic, philosophy of logic, Quine, second‐order logic, set, Löwenheim–Skolem, Stewart Shapiro, Wittgenstein

Bibliographic Information

Print publication date: 2000 Print ISBN-13: 9780198250296
Published to Oxford Scholarship Online: November 2003 DOI:10.1093/0198250290.001.0001

Authors

Affiliations are at time of print publication.

Stewart Shapiro, author
The Ohio State University at Newark, Ohio
Author Webpage