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In Praise of Graham Priest's *Intro to Non-Classical Logic*

This summer, I am directing an independent study on non-classical logics. In part because of Ole's glowing recommendation, the primary text has been Graham Priest's

*Introduction to Non-Classical Logic*. The book has been fantastic; I can recommend it without qualification. It is pitched at just the right level for a philosophy student with maybe one logic course under their belt -- neither too slow nor too quick. The end-of-chapter exercises are also just right: neither too difficult nor too easy. And each chapter closes with a couple of pages dealing with how the technical material presented there connects up with overtly philosophical questions, keeping up motivation for people whose primary interest is not in the formal/ mathematical side of things.

Another aspect of the book that appealed to me was that (partial) soundness and completeness proofs were given at the end of each chapter, separated from the main course of discussion as optional material. Such proofs are of course incredibly important to practicing logicians, but I sometimes think that the amount of time and effort needed for them is better spent elsewhere given the limitations of a classroom, and the fact that most philosophy students in logic classes won't go on to be practicing logicians. The nice thing about Priest's presentation is that if you think soundness and completeness proofs are essential, you can cover them, or if (like me) you'd rather spend that time covering a wider array of logics, you can easily skip over them without loss or inconvenience.

Last but not least, I certainly have learned a thing or two (or ten), even though it is labeled as an introductory textbook. I will definitely use this book again in future classes.

## 3 Comments:

Have you got the new version, with all the material on quantifiers? I just have the first edition, but the second is rumored to be twice the size. I'm thinking of upgrading next year...

I did get the massive 2nd edition; it is certainly a weighty tome. However, I cannot comment on the material on quantifiers: we didn't even come close to getting through the propositional stuff in the directed study. Given the book's current size, I think it would be difficult to get through even given an an entire school year's worth of class time.

I need to buy a copy of the new version, but I can say that I've read much of the material on quantifiers that appears in the new chapters and it is equally as good as the first half. The discussion of free logics and the connections drawn out with many-valued quantification theory is very well done.

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