Modeling Deductive Inference: A Historico-Philosophical Introduction to First-Order Logic

Abstract

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.https://huskiecommons.lib.niu.edu/allfacultyother-bookschapters/1025/thumbnail.jp