Lecture on Deduction and Induction

Introduction to Deductive Reasoning

• Key Concept: Deduction
• Sherlock Holmes Reference: Uses deductive reasoning frequently.
• Types of Reasoning: Deduction vs. Induction

Logic and Contradiction

• Tautology: Always true
  • Example: It will rain tomorrow or it will not
• Contradiction: Always false
  • Example: It is raining and it is not raining at the same time
• Deductive Validity: Avoid contradictions; aim for consistent logic

Example of Deductive Reasoning

• Sherlock Holmes Story: Evidence-based deduction
  • Premises: Went to bed in tent, woke up seeing the sky
  • Conclusion: Tent must have been stolen
  • Challenge: Identifying flawed premises can lead to improper conclusions

Inductive Reasoning

• Nature: Deals with probability rather than certainty
• Example: Accusation of murder based on collected evidence
  • Evidence: DNA at scene, blood on clothes, footprints, testimony, video
  • Conclusion: Probabilistic, not absolute certainty like deduction

Evaluating Arguments

• Deductive Argument: Intends conclusion to be necessarily true based on premises
• Inductive Argument: Intends conclusion to be probably true based on premises

Common Forms of Deductive Arguments

• Categorical Syllogism
  • Example: All men are mortal; Socrates is a man; Socrates is mortal
• Hypothetical Syllogism: If-then reasoning
  • Modus Ponens: Affirming the antecedent
    • If P then Q; P; Therefore, Q
  • Modus Tollens: Denying the consequent
    • If P then Q; Not Q; Therefore, not P

Pure Hypothetical Syllogism

• Chain Argument: All premises and conclusions are conditionals
  • If P then Q; If Q then R; Therefore, if P then R

Disjunctive Syllogism

• Either-Or Statements
  • Example: Either P or Q; Not P; Therefore, Q
  • Inclusive vs. Exclusive Disjuncts

Arguments from Definition

• Uses Defined Terms to Draw Conclusions
  • Example: God is defined as an all-perfect being; therefore, God must exist

Reductio ad Absurdum

• Method: Assume the opposite to show it leads to absurdity or contradiction
  • Example: Assume God does not exist; leads to logical contradictions

Historical Context

• Aristotle: Pioneer of deductive logic
• Francis Bacon: Criticized Aristotle, contributed to philosophy of science

Reading and Assignments

• Recommended Reading: Herrick, Paul Carrick on deductive and inductive indicators
• Next Class: Methods of evaluating deduction; focus on validity and soundness