Classical First-Order Logic

Introduces classical logic, and its alternatives. Other books of its type usually do one or the other, but not both.

Stewart Shapiro (Author), Teresa Kouri Kissel (Author)

9781108987004, Cambridge University Press

Paperback / softback, published 19 May 2022

75 pages
23 x 15.1 x 0.6 cm, 0.14 kg

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.

1. Introduction
2. Formal System
3. Language
4. Deduction
5. Model-Theoretic Semantics
6. Meta-theory
7. Classical Higher-Order Logic
8. Intuitionism
9. Paraconsistency: demurring from ex falso quodlibet
10. Conclusion.

Subject Areas: Philosophy: logic [HPL], Philosophy [HP]