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Description
This book is a companion text for lectures on first-order logic and its elementary metatheory (used in Intermediate Logic at Northern Illinois University). It covers the basic concepts of set theory necessary for a mathematical development of first-order logic; develops a formal language of first-order logic; presents a classical Tarskian semantics for the language and the “semantic” conception of logical consequence; presents a Gentzenian proof system and the “syntactic” conception of logical consequence; develops a partial decision procedure for logical consequence in the language; demonstrates applications of the formal system to modeling deductive inference expressed in natural language; and extends the system to include identity. Unlike a typical logic textbook, however, these topics are embedded within an overarching historico-philosophical narrative that illuminates (some of) the interaction of rational argument and historical context that led to their development and exhibits their engagement with broader philosophical issues.
Publication Date
2025
Department
Department of Philosophy
Publisher
Northern Illinois University
City
DeKalb
Keywords
logic, elementary logic, mathematical logic, first-order logic, philosophy of logic, philosophical logic, history of logic
Disciplines
Logic and Foundations | Logic and Foundations of Mathematics | Philosophy
Rights Statement
© 2025 David J. Buller
Rights Statement 2
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Modeling Deductive Inference: A Historico-Philosophical Introduction to First-Order Logic © 2025 by David J. Buller is licensed under CC BY-NC-ND 4.0. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-nd/4.0/
DOI
10.58933/MKVM5892
Original Citation
David J. Buller, Modeling Deductive Inference: A Historico-Philosophical Introduction to First-Order Logic. Northern Illinois University, 2025. doi:10.58933/MKVM5892
