Formal fuzzy logic has developed into an extensive, rigorous, and exciting discipline since it was first proposed by Joseph Goguen and Lotfi Zadeh in the midtwentieth century, and it is a wonderful topic for introducing students to the richness and fascination of formal logic and the philosophy thereof. This textbook grew out of an interdisciplinary course on fuzzy logic that I've taught at Smith College, a course that attracts philosophy, computer science, and mathematics majors. I taught the course for several years with only a course reader because the few existing texts devoted to fuzzy logic were too advanced for my undergraduate audience (and probably for some graduate audiences as well). Finally, after writing voluminous supplements for the course, I decided to write an accessible introductory textbook on many-valued and fuzzy logic. It is my hope that after working through this textbook, students will have the necessary background to tackle more advanced texts, such as Gottwald (2001), Hájek (1998b), and Novák, Perfilieva, and Močkoř (1999), along with the rest of the vast fuzzy literature.

This book opens with a discussion of the philosophical issues that give rise to fuzzy logic – problems and paradoxes arising from vague language – and returns to those issues as new logical systems are presented. There is a two-chapter review of classical logic to familiarize students and instructors with my terminology and notation, and to introduce formal logic to those who have no prior background.