To round out suggestions for studying logic, I recommend the following.<p>Mathematical Logic, Set Theory and its Logic, Methods of Logic. All three of these are by Willard van Orman Quine. If you know anything about modern logic, then that is a name that you should recognize.<p>A more accessible textbook is Sweet Reason by Tymoczko & Henle. They're a philosopher & mathematician pair and I like their approach. I'm currently halfway through the first edition. The errors are a bit annoying and I wish that I had waited for the second edition.<p>We're all nerds, here, so I understand the emphasis on mathematical logic, but you owe it to yourself to be familiar with traditional Aristotelian logic, as well. Noting the difference in mindset between traditional and modern logic is enlightening.<p>Being Logical, by D.Q. McInerny is a quick introduction to traditional logic. Socratic Logic by Peter Kreeft is much more involved. Be warned; Kreeft takes a strong stand against modern logic. He has some good points, but he's a bit unfair.