Classical First-Order Logic

First-order classical logic is a commonly proposed system for logical reasoning. It develops a language, proof theory, and model theory, and provides theorems about the system, such as unique readability and the Lindenbaum lemma. It also compares it to other systems, such as classical higher order logic, intuitionistic logic, and paraconsistent logics.

Format: Paperback / softback
Length: 75 pages
Publication date: 19 May 2022
Publisher: Cambridge University Press

When one engages in logical reasoning, it is commonly acknowledged that they are employing sound reasoning. Numerous proposals have been made to define logical reasoning, yet one widely accepted system is first-order classical logic. This Element will delve into the fundamentals of first-order classical logic and explore various philosophical implications surrounding it.

The first half of the Element establishes a framework for the system, encompassing a language, proof theory, and model theory. The authors present theorems that they have developed, such as the unique readability theorem and the Lindenbaum lemma. They also discuss the meta-theory of the system, presenting several results, including proving soundness and completeness theorems.

In the second half of the Element, first-order classical logic is compared to other systems: classical higher-order logic, intuitionistic logic, and several paraconsistent logics that deviate from the law of ex falso quodlibet. The authors analyze the strengths and weaknesses of each system and discuss their respective applications and implications.

By examining the basics of first-order classical logic and exploring its philosophical implications, this Element aims to provide a comprehensive understanding of this important branch of logic and its role in shaping our understanding of the world.

Weight: 136g
Dimension: 152 x 228 x 9 (mm)
ISBN-13: 9781108987004