Lecture Notes on Reasoning

Introduction to Reasoning

Reasoning is the action of thinking or expressing something logically.
It serves as a defense mechanism to justify actions and statements.
Important in various fields: philosophy, science, language, mathematics, and art.
Distinguishing ability of humans.

Conclusion drawn from general ideas (premises).
Visualized as a funnel: narrowing general ideas into specific conclusions.
Uses recognized rules, laws, theories, and accepted truths to prove conclusions.
Syllogism:
- Example:
  - All men are mortal.
  - Ram is a man.
  - Therefore, Ram is mortal.
- Symbolically: If A implies B, B implies C, then A implies C.
- Similar to the transitive property of equality.
More Examples:
- All even numbers are divisible by 2.
  - 22 is even.
  - Therefore, 22 is divisible by 2.
- Iron Man is a Marvel Comics character.
  - Therefore, Iron Man is fictional.
- Citrus fruits are rich in vitamin C.
  - Orange is a citrus fruit.
  - Therefore, an orange is rich in vitamin C.
Invalid Deductive Reasoning Example:
- All musical instruments make sounds.
- Jeepneys make sounds.
- Therefore, jeepneys are musical instruments.
- Explanation: True premises do not justify false conclusions.

General conclusion reached by examining specific observations.
Starts from narrow premises and expands to broader conclusions.
No standard format; conclusions are probable based on patterns.
Example:
- Yesterday, Isa jogged.
- Today, Isa jogged again.
- Therefore, Isa will probably jog tomorrow morning.

Inductive arguments can be weak or strong.
Example of Weak Inductive Argument:
- Knowing what's funny for friends doesn’t guarantee what's funny for others.
Example of Strong Inductive Argument:
- Identifying patterns in multiples of 3.
- Next term after 15 is 18.

Inductive Reasoning:
- Teacher used Google Classroom in past classes.
- Likely to use it tomorrow, but not definite.
Deductive Reasoning:
- All licensed drivers are 17+.
- Marcus has a driver's license.
- Therefore, Marcus is at least 17.
Deductive Reasoning:
- All spiders have eight legs.
- Black widows are spiders.
- Thus, black widows have eight legs.
Inductive Reasoning:
- Father and brother have black hair.
- Conclusion about related individuals having black hair is probable.
Inductive Reasoning:
- Game of Thrones was a success.
- Sequel likely to be successful.