= Introduction

About mathematical logic, we mainly concern about three questions:
+ What does it mean for one sentance to "follow logically" from certain others? (What is *logically reasoning*?)
+ If a sentance does follow logically from certain others, what methods of proof might be necessary to establish this fact? (How to prove a sentance is *truly* follow logically from others?)
+ Is there a gap between what we can prove in an axiomatic system and what is true in the system.(Does _proved_ means _true_ in an axiomatic system?)

命题逻辑 (sentential logic) 过于简单，不兼容更广义的演绎；而一阶逻辑 (first-order logic) 则在数学上兼容演绎。

#v(3em)
See also:
- _A Mathmatical Introduction to Logic_, by <NAME>.
- _Analysis I_, by <NAME>. Chapter A Appendix: the basics of mathematical logic.
