Understanding Inductive and Deductive Reasoning

Sep 11, 2024

Lecture Notes: Inductive vs Deductive Reasoning

Introduction

  • Discussion of inductive and deductive reasoning.
  • Focus on the Law of Syllogism and the Law of Detachment.

Inductive Reasoning

  • Definition: Making predictions based on observed patterns or examples.
  • Characteristics:
    • Not definitive proof, only probable conclusions.
    • Patterns may not necessarily continue.
  • Examples:
    • Teacher drinks coffee every morning for the last five days; prediction she will drink again tomorrow.
    • Lana goes out for lunch for 30 days; prediction she will go out tomorrow.
    • First five popcorn kernels are caramel; prediction the rest are caramel too.

Deductive Reasoning

  • Definition: Uses laws of logic to reach verifiable conclusions.
  • Examples:
    • Living in San Francisco implies living in California.
    • Rachel lives in San Francisco, therefore she must live in California.

Law of Syllogism

  • Explanation: If "If P then Q" and "If Q then R" are true, then "If P then R" is also true.
  • Examples:
    • If staying up late then sleeping in; if sleeping in then late for school; thus, staying up late leads to being late for school.
    • Rectangle is a parallelogram; parallelogram area is base x height; therefore rectangle's area is base x height.
    • Studying leads to a high score; high score leads to $20; therefore studying earns $20.
    • 35-degree angle is acute; acute is not obtuse; therefore, 35-degree angle is not obtuse.

Law of Detachment

  • Explanation: If "If P then Q" is true and "P" is true, then "Q" is true.
  • Examples:
    • Living in Orlando implies living in Florida.
    • Alex works at a bar implies having a Smart Serve Certification.
    • Parallelogram is a quadrilateral; quadrilateral has four sides; therefore parallelogram has four sides.
  • Important Note: Conclusion truth does not imply hypothesis truth. For example, having a certification doesn't necessarily mean working at a bar.

Conclusion

  • Reviewed the differences between inductive and deductive reasoning.
  • Discussed the Law of Syllogism and the Law of Detachment.
  • Reinforced understanding with various examples.

These notes summarize the key points from the lecture on reasoning and logic laws. They are intended to aid in studying and understanding the concepts discussed.