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An Introduction to Non-Classical Logic is a 2001 textbook by philosopher and logician Graham Priest, published by Cambridge University Press. The book provides a systematic introduction to non-classical propositional logics, which are logical systems that differ from standard classical propositional logic. It covers a wide range of topics including modal logic, intuitionistic logic, many-valued logic, relevant logic, and fuzzy logic.

Two editions

The first edition is from 2001 and is titled just An Introduction to Non-Classical Logic, while the second edition, from 2008, is titled An Introduction to Non-Classical Logic: From If to Is (being a greatly improved and expanded version of the first edition). Both are published by Cambridge University Press.

Topics

1st edition

It covers many different propositional logics, including classical logic.

2nd edition

The subtitle From If to Is was added because the 2nd edition also deals with predicate calculi. The book is divided into two parts: Part 1 covers the first edition content with improvements, and Part 2 is the totally new content of the book. The 2nd edition covers all topics from the first, and many more topics. The table of contents include: modal logic, intuitionist logic, fuzzy logics, and more.

Reception

Intended audience

An Introduction to Non-Classical Logic was designed for multiple audiences. According to American professor of philosophy Stewart Shapiro, the book is accessible to readers with a first or second undergraduate course in symbolic logic, though its optional metatheory sections require graduate-level knowledge. Czech professor of mathematics and philosophy Petr Hájek noted that while Priest included a brief "mathematical prolegomenon" covering set-theoretic notation and proof by induction, advanced material on metatheory would still require graduate-level coursework.

Critical reception

The book received positive reviews from academic philosophers. In The Review of Metaphysics: A Philosophical Quarterly, Shapiro praised it as "a very good" introduction, noting that it filled an important gap given the "extensive interest in nonclassical logics" and the typical focus on classical logic in university courses. He commended Priest's "lively and entertaining style when presenting technical material" and the book's balance between overview and technical detail, concluding that it well-served both "casual and diligent" readers.

In The Bulletin of Symbolic Logic, Hájek described it as "a very valuable source in many directions" despite some criticisms of its treatment of fuzzy logic. He noted that Priest acknowledged the book's limitations, quoting the author's preface: "If one waited for perfection one would wait forever." Following discussion with Hájek, Priest indicated plans to revise the fuzzy logic chapter in a future edition.

According to J. Mackenzie, the first edition of the book "deserves to become the standard textbook in its field", which he reiterated for the second edition.

Reviewers particularly noted the book's utility as either a supplement to standard logic textbooks or as a primary text for courses on non-classical logic. However, some limitations were identified, including its restriction to propositional logic and relatively brief treatment of some philosophical issues underlying different logical systems. Shapiro encouraged Priest to write a companion volume covering quantification in non-classical logics.

References

1. Hájek, Petr (2008). "Graham Priest. An introduction to non-classical logic: From If to Is. Second Edition. Cambridge University Press, Cambridge, United Kingdom, 2008, xxxii + 613 pp". Bulletin of Symbolic Logic. 14 (4): 544–545. doi:10.1017/S1079898600001505. ISSN 1079-8986.
2. Hájek, Petr (2006). "Review of An Introduction to Non-Classical Logic". The Bulletin of Symbolic Logic. 12 (2): 294–295. ISSN 1079-8986.
3. Shapiro, Stewart (2003). "Review of An Introduction to Non-Classical Logic". The Review of Metaphysics. 56 (3): 670–672. ISSN 0034-6632.
4. Yaqub, Aladdin M. (2010). "An Introduction to Non-Classical Logic: From If to Is ". Teaching Philosophy. 33 (4): 432–436. doi:10.5840/teachphil201033453. ISSN 0145-5788.
5. Hájek, Petr (2008). "Review of An Introduction to Non-Classical Logic: From If to Is". The Bulletin of Symbolic Logic. 14 (4): 544–545. ISSN 1079-8986.
6. ^ "Document Zbl 0981.03002 - zbMATH Open". zbmath.org. Retrieved 2025-01-07.
7. ^ "Document Zbl 1148.03002 - zbMATH Open". zbmath.org. Retrieved 2025-01-07.
8. "Document Zbl 1152.03001 - zbMATH Open". zbmath.org. Retrieved 2025-01-07.
9. ^ Shapiro, Stewart (2003). "Review: An Introduction to Non-Classical Logic". The Review of Metaphysics. 56 (3): 670–672. JSTOR 20131881.
10. ^ Hájek, Petr (2006). "Review: An Introduction to Non-Classical Logic by Graham Priest". The Bulletin of Symbolic Logic. 12 (2): 294–295. JSTOR 4617265.

Further reading

• Roy, Tony (2006-03-20). "Natural Derivations for Priest, An Introduction to Non-Classical Logic". The Australasian Journal of Logic. 4. doi:10.26686/ajl.v4i0.1779. ISSN 1448-5052. Retrieved 2025-01-06.

External links

• An Introduction to Non-Classical Logic: From If to Is at Google Books: https://books.google.com/books?id=rMXVbmAw3YwC (with limited preview).
• Errata: https://www.cambridge.org/files/5214/5570/7670/Corrections_12.pdf

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