Philosophical and Mathematical Logic

More about the book

This book serves as an introduction to logic, emphasizing its connections with philosophy, mathematics, language, and theoretical computer science. Readers will explore classical logic alongside philosophical variants such as modal, epistemic, deontic, and temporal logic, as well as intuitionistic logic. The initial chapter offers a non-technical overview, while subsequent chapters delve into topics like Propositional Logic, Sets, Predicate Logic, Arithmetic, Gödel’s Incompleteness Theorems, Modal Logic, and the Philosophy of Language. Applications in Prolog, Relational Databases, SQL, and Social Choice Theory, particularly Majority Judgment, are also discussed. Historical developments in logic, including Stoic and Aristotelian traditions, logic in the Middle Ages, and the contributions of Frege, Boole, and De Morgan, are highlighted. The book places significant emphasis on conditionals—material, strict, and relevant implication, entailment, counterfactuals, and conversational implicature—providing ample references for further reading. Each chapter concludes with exercise answers. This recent work (2018) combines rigor, depth, and clarity, making it a valuable resource that transcends a mere introductory text. It invites readers to engage deeply with the diverse themes of logic, blending philosophy and mathematics seamlessly.