Logical Reasoning: Formal Rules and Common Fallacies

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): Hiding unfavorable data and presenting only favorable evidence.
• False Cause: Inferring causation without sufficient basis, often due to coincidental timing (accidental correlation) or sequence (post hoc ergo propter hoc).

Fallacies of Relevance

• Ad Hominem: Attacking or discrediting the person defending a thesis rather than addressing the premises. Example: X says P, X is not credible, therefore P is false.
• Ad Baculum: Basing a conclusion on threats or fear rather than pertinent premises.
• Ad Verecundiam: Appealing to an authority that is not an expert in the specific field.
• Ad Populum: Using emotional appeals to the audience instead of providing logical reasons.
• Ad Ignorantiam: Supporting a conclusion simply because it has not been proven false. Example: We have no evidence that P is false, therefore P is true.