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The Advanced Reasoning Forum publishes research volumes and textbooks in logic, mathematics, philosophy, linguistics, and related fields. ARF also publishes volumes of the Bulletin of Advanced Reasoning and Knowledge. Click on any of the links below for more information about that title.

Critical Thinking

Critical Thinking, Fifth Edition

Critical Thinking, Fifth Edition

Richard L. Epstein with Michael Rooney

Epstein's CRITICAL THINKING sets new standards of clarity for teaching how to reason well in daily life and how to write well. With over one thousand everyday examples and exercises, the text engages and challenges the student. A comprehensive instructor's manual, and many free supplements on the ARF website, make teaching the course a pleasure for instructor and student alike. Now with chapters on reasoning in the sciences.

The Semantic Foundations of Logic

Classical Mathematical Logic

Classical Mathematical Logic

Richard L. Epstein

This develops classical mathematical logic, viewing it as motivated by attempts to formalize mathematics. The scope and limitations of the formal system are explored: formalizations of theories of linear orders, arithmetic, groups, rings, fields, one- and two-dimensional Euclidean geometry, and second-order logic are all presented. It is the only place to see axiomatic geometry formulated in first-order logic where the syntax and semantics are clearly separated.

Logic, Language, and the World

Logic as the Art of Reasoning Well

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