## Introduction to Logic

Using a formal reasoning structure is a great way to make sure you are following a chain of logic.

## Deductive Reasoning

**Law of Detachment**: Use one relationship to prove a more specific case.

- If A then B
- A
- Therefore, B

__Example__

- If an object is dropped on Earth then gravity will cause it to fall. <-- if this is true
- A ball is dropped on Earth. <-- and this is true
- Therefore, the ball will fall. <-- then this is definitely true

**Law of Syllogism**: Use two relationships to prove a third relationship.

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

__Example__

- If a student is in 7th grade, then they do science during class.
- If a student does science during class, then they are a scientist.
- Therefore, all the students in 7th grade are scientists.

**Law of Contrapositive**: Use general rules to prove a negative

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

__Example__

- If it is raining, then there are clouds in the sky
- There are no clouds in the sky
- Therefore, it is not raining.

## Inductive Reasoning

0 |
1 |
2 |
3 |
4 |

Not Possible |
Possible |
Plausible |
Probable |
Almost Certain |

**Predictions**: Apply observed facts to make future predictions.

- A
- Therefore, B

__Example__

- All biological life forms that we know of depend on liquid water to exist. <-- if this is true
- Therefore, if we discover a new biological life form it will probably

**Argument from Analogy**: Assume that similar systems have similar parts.

- A is similar to B
- A has property x
- So, B probably has property x

__Example__

- Jenny has similar musical tastes to Martha.
- Jenny likes Beyoncé.
- So, Martha will probably like Beyoncé.

**Generalizations**: Make a claim about a larger group based on observations from a similar small group. You can replace "all" with "most", "some", or a percent or fraction.

- All observed A are B
- Therefore, all A are B

__Example__

- All the houses I've seen on Market street are large.
- Therefore, all the houses on Market street are probably large.

- Jenny lives on Market street.
- Jenny's house is probably large.