How should someone who hasn't studied any math at a university level start studying mathematical logic? (There are already questions like this but they mostly focus on book recommendation for people with already some university background)
I think I should begin with set theory (I know the basics of set theory), before actually trying to study mathematical logic. What books or other sources (preferably books) would be good for self studying set theory? Enderton's Elements of Set Theory seems like a good one.
After getting familiar with set theory, what should I study next (assuming that it's wise to begin with set theory)? A book, again by Enderton, A Mathematical Introduction to Logic, seems like a good intro to the subject.
If one wants to master mathematical logic, should one also study formal logic from philosophy's point of view?
All kinds of recommendation are welcome.
Raymond Smullyan's A Beginner's Guide To Mathematical Logic is a gentle but useful introduction to the topic, and you don't need any background for it. You might find it useful.
I also recommend Godel, Escher, Bach, which is not at all a logic textbook. But it incorporates many of the most important ideas of mathematical logic and the cornerstones of computational theory, and it's a really engaging and interesting book.