In this post, I don't mean any word by its somewhat "mathematical or logical" meaning but just "literally".
It's been three years since I started "formal" mathematics, and now I'm familiar with set theory and formal proof.
In the meantime, I have never studied "logic" before (it's nonsense to me), so now i think it's the time to start with it.
I have asked a similar question before, and people recommended me some texts. Almost all of them started with introducing "proposition logic". I guess authors intended to introduce a rather easier example at first. I don't think it's a good way to study logic rigorously. I felt like I'm not studying mathematics when I was reading those books, but I felt like I'm reading an philosophy article, which I felt extremely uncomfortable.
Frankly, to me, it's really hard to know what people mean by logic. I have searched wikipedia, but there are so many types of logics such as propositional logic, intuition logic(?), classical logic and etc. I even found some "logics" are subcategory of other! What is logic exactly?
I don't want to start logic with 'handy and easy' examples. I want to study logic from its core so I could answer questions like: What is "proof"? What is "truth"?
Please... please recommend me a good precise logic textbook. I'm eager to learn logic precisely... Thank you in advance ! :)