In chapter 3, we continue to look for ways to determine the validity of the argument. Before moving on let me remind myself again on the role of logic: “Logic does NOT answer the question of are the premises of the argument true? All logic can say is whether the inference of the conclusion from the premise is valid. Logic can never tell us if our arguments are sound.” And let me remind that whether the premise is true or not can be assumed by observation in case of science. In mathematics, however, which is called the logic fully developed, we just assume axioms and postulates to go on to prove theorem. And also remember that you cannot prove anything without accepting something. https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

I can only write down summary in words. For clarification, please refer to diagrams and illustrations on the textbook! (It’s much more helpful)

- Proof method in general
- A way of reaching conclusion by adding lines of premises according to rules of inference
- You keep adding new lines until you reach a conclusion statement
- You must add new lines according to rules of inference
- Proof is finished when you reach a conclusion

- Rules of inference
- Modus Ponens (MP, “method for providing”)
- If there is a line of conditional and an another line of antecedent of that conditional, you can add the consequent of the conditional

- Two Important remarks before moving on
- Justification
- You need to write down what rules you apply to what number of premises next to the new line you add
- In other word, you have to justify the new line you add!

- Rules of inference apply to the whole line (not component of a line)

- Justification
- Modus Tollens (MT, “method for removing”)
- Disjunctive Syllogism
- Simplification
- Conjunction
- Disjunction Introduction (DI)

- Modus Ponens (MP, “method for providing”)