Formal logic

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

1. All men are mortal; and,
2. Socrates is a man;

we can deduce (and prove) that

1. Socrates is mortal.

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

1. Lucifer is immortal (i.e., not mortal)
2. Whoever is not mortal, is not a man.
3. 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

Modus Ponens:

1. If A, then B.
2. A
3. Therefore, B.

Modus Tollens:

1. If A, then B.
2. Not B
3. Therefore, not A.

Disjunctive Syllogism:

1. A or B
2. Not A
3. Therefore, B

Hypothetical Syllogism (or Chain Argument):

1. If A, then B
2. If B, then C
3. Therefore, if A, then C