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.

Types of Reasoning

1. Deductive Reasoning

• 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.

2. Inductive Reasoning

• 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.

Comparing Inductive Arguments

• 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.

Identifying Reasoning Types

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

Conclusion

• Importance of understanding reasoning types in various contexts.
• Encouragement to check out more video lessons and subscribe.