Starting to really appreciete the beauty of the type of thinking involved in symbolic logic, and finding myself at ease with theorem proving exercises that can be commonly found in introductory books on propositional calculus, I have a question that kind of boggles me:
What Is the most efficient way (if there exist such a way) to progress in learning logic? Next thing I would like to learn is predicate calculus, but after that?
I find my self sort of confused, given that, for istance, books on model theory seem hard to grasp for me (of course you say, is where you get your hands dirty): I comprehend the main ideas but I find, say, proving theorems by mathematical induction very difficult.
What would you suggest me?
Thanks for your attention and for the great community.
Before doing model theory I would do some proof theory, i.e. look into notions of soundness and completeness of proof systems. And yes, those proofs will involve mathematical induction ... but one thing you can do is just doing more and more proofs, so you really start thinking about the proof system rather than within the proof system.
Also, try applying some proofs at some actual content you can sink your teeth into, i.e. not the small textbook exercise problem that usually can be proved with 5 to 30 lines, but some mathematical theorem (set theory, arithmetic) where proofs become a hundred lines or more. Again, that is good background for going into the meta-logical topics.