**Formal logic** (or **symbolic logic**) is the Western Civilization's system of reasoning. It is used in law, religion, science, and mathematics.

Logic is used in proofs. For example, given that

- All men are mortal; and,
- Socrates is a man;

we can deduce (and *prove*) that

- Socrates is mortal.

Using one of the same premises, we can prove that Lucifer is not a man:

- Lucifer is immortal (i.e., not mortal)
- Whoever is not mortal, is not a man.
- Hence, Lucifer is not a man.

The key element here is the inference from *All men are mortal* to *whoever is not mortal is not a man* (see Syllogisms)

## Rules of inference

- If A, then B.
- A
- Therefore, B.

- If A, then B.
- Not B
- Therefore, not A.

Disjunctive Syllogism:

- A or B
- Not A
- Therefore, B

Hypothetical Syllogism (or Chain Argument):

- If A, then B
- If B, then C
- Therefore, if A, then C