How far do you recommend taking students in a semester of formal logic (say, for non-majors)? And what order do you each topics in?
The book I use (Gensler) recommended teaching modal logic before quantificational (I try to get to both in an intro semester, though I've been rethinking this as we're all pretty exhausted by the end!). Although I was hesitant at first, I've come to really like that approach, for two reasons: it lends itself to interesting philosophical arguments, and it's symbolically easy to learn.
#1 is obvious: there's always a handful of students that are interested in phil religion questions like the problem of evil and free will / omniscience and enjoy using modal logic to deal with those.
#2- I realized in the middle of class one day that the modal operators are syntactically just like the negation sign: anywhere it's legal to put ~, it's legal to put a box or diamond (and vice versa), and anywhere it's illegal to put ~, it's illegal to put a box or diamond (and vice versa). So there's no new syntax to learn, just new meaning and new inference rules. I always have students who really struggle figuring out where to put the modal operators and they tend to find this tip very helpful.
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Jacob Joseph Andrews
Upper School Latin Teacher and IT Administrator – Covenant Classical School
PhD Candidate, Philosophy – Loyola University Chicago
https://jacobjandrews.wordpress.com/
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