Logical Reasoning: Formal Rules and Common Fallacies
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Fundamental Rules of Deduction
- Modus Ponens: A → B, A / B
- Modus Tollens: A → B, ¬B / ¬A
- Disjunctive Syllogism: A ∨ B; ¬A / B
- Hypothetical Syllogism: A → B, B → C / A → C
- Reductio ad Absurdum: A → (¬B ∧ B) / ¬A
Formal Fallacies in Reasoning
Formal methods of deduction can be misused. Reasoning incorrectly can lead to false conclusions even when starting from true premises.
- Affirming the Consequent: A → B, B / A
- Denying the Antecedent: A → B, ¬A / ¬B
Ambiguity
Deductions may be formally valid but contain misleading content due to ambiguous language. Example: "Only man is rational" (implying women are not).
Inductive Fallacies
- Inadequate Generalization: Inductions are weak when data is insufficient or biased.
- Mock Trial (Cherry Picking)