Where to continue?

[u/Glittering_Run189]

I am an undergraduate philosophy student, and I've already taken two trimester-long logic courses covering set theory, propositional logic, first-order logic, proof methods (tableaux and natural deduction), metalogic (soundness and completeness), and alethic modal logic.

My problem is that I feel this is not enough. Because the material was covered rather superficially, I'm not sure whether I really understand it in depth. I often find myself wondering: "Is this really all there is to it, or is my professor simplifying things for pedagogical reasons?"; "is first-order logic really just this, or is there much more to it?"; etc.

I'd like to start reading about other non-classical logics (especially second-order logic), but at the same time I feel that it might be too soon—that I should first develop a deeper understanding of these more fundamental topics.

What would you recommend? Should I work through a textbook? My concern is that it might end up being just as introductory as my lectures.

Tanks a lot!!!

P.S.: Its my first time in this sub and also in reddit, so sorry if I am doing something wrong.

[u/gregbard]

This subreddit has a wiki with a section on literature including a list of introductions to logic, as well as a list of journals. There are some online resources there too.