# Difference between revisions of "Formal logic"

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− | '''Formal logic''' (or '''symbolic logic''') is the Western Civilization's system of reasoning. It is used in law, religion, science, and mathematics. | + | '''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 | Logic is used in proofs. For example, given that | ||

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==Rules of inference== | ==Rules of inference== | ||

− | + | [[Modus ponens]]: | |

#If A, then B. | #If A, then B. | ||

#A | #A | ||

#Therefore, B. | #Therefore, B. | ||

− | #If | + | [[Modus tollens]]: |

+ | #If A, then B. | ||

#Not B | #Not B | ||

#Therefore, not A. | #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 | ||

+ | [[Category:Logic]] |

## Latest revision as of 08:04, 13 July 2016

**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