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The Oxford Handbook of Philosophy of Mathematics and Logic$
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Stewart Shapiro

Print publication date: 2005

Print ISBN-13: 9780195148770

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0195148770.001.0001

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Higher‐order Logic

Higher‐order Logic

Chapter:
(p.751) Higher‐order Logic
Source:
The Oxford Handbook of Philosophy of Mathematics and Logic
Author(s):

Stewart Shapiro (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0195148770.003.0025

This chapter provides an overview of second-order logic and higher-order logic generally. It provides the basic formal languages, deductive systems, and model-theoretic semantics, including a brief account of George Boolos’s interpretation of second-order languages in terms of the plural construction. It then goes into some of the arguments in favor of second-order logic.

Keywords:   logic, second-order logic, higher-order logic, language, deductive system, model theory, semantics, Boolos, plural

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