Higher‐order Logic

Stewart Shapiro

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print March 2005 | ISBN: 9780195148770
Published online July 2005 | e-ISBN: 9780199835560 | DOI:

Series: Oxford Handbooks in Philosophy

Higher‐order Logic

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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

Chapter.  12758 words. 

Subjects: Philosophy of Mathematics and Logic

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