Classical First-Order Logic
Classical First-Order Logic by Stewart Shapiro, published by Cambridge University Press on May 19, 2022, is a concise exploration of first-order classical logic and its philosophical implications. This new edition, comprising 75 pages, delves into the foundational aspects of logical reasoning, presenting a structured language for the system alongside its proof and model theories.
Readers will find a thorough examination of theorems related to first-order classical logic, including unique readability and the Lindenbaum lemma. The text also addresses the meta-theory of the system, offering insights into soundness and completeness theorems. Additionally, the book compares first-order classical logic with other logical systems, such as classical higher-order logic, intuitionistic logic, and various paraconsistent logics, providing a comprehensive overview of the subject matter within the realms of philosophy and logic.
Official synopsis Publisher
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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