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Series:   Elements in Philosophy and Logic

Classical First-Order Logic

Published online by Cambridge University Press:  26 April 2022

Stewart Shapiro  and
Teresa Kouri Kissel
Stewart Shapiro
Affiliation:
Ohio State University
Teresa Kouri Kissel
Affiliation:
Old Dominion University, Virginia

Summary

One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. The authors provide theorems about the system they developed, such as unique readability and the Lindenbaum lemma. They also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet.
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Keywords

classical logicfirst-order logicmodel theoryproof theorymeta-theory higher-order logicintuitionistic logicparaconsistent logic
Type
Element
Information
Series: Elements in Philosophy and Logic
Online ISBN: 9781108982009
Publisher: Cambridge University Press
Print publication: 19 May 2022

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