IFL2: Chapters on propositional natural deduction

Thanks to the kindness of strangers — not to mention some friends and relations (special thanks to The Daughter) — I have an improved version of the four chapters on propositional natural deduction for IFL2. Here they are. (Exercises to be added, which will fill some gaps, like noting the equivalence of DN and Classical Reductio, given the other rules, or dealing with biconditionals.)

One advantage about basing an intro logic book on trees (as in IFL1) is that people don’t get very exercised about how a tree system should be developed. By contrast, people get decidedly heated about the best form of natural deduction to adopt. So I’m probably not going to satisfy even half of those who urged me to go for natural deduction in the second edition. But there’s no pleasing everyone! What I propose is a standard enough Fitch-style system, with one deviation — the v-Elim rule is a Fitchian version of the liberalized rule recommended for Gentzen systems by Neil Tennant. That way we get disjunctive syllogism without relying on explosion. Which has always seemed more “natural” to me.

All comments (other than variants on “you have written the wrong book!”) and all corrections will of course be very gratefully received, as always.

 

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