Formal and Informal Fallacies

A fallacy is an argument that seems persuasive but fails — either because its logical structure is broken (a formal fallacy) or because it relies on irrelevant, misleading, or psychologically manipulative content rather than legitimate evidence (an informal fallacy). Fallacies are not merely mistakes; many are rhetorical weapons, deployed deliberately to win arguments by means other than logic. Cataloging them precisely makes you harder to fool.

Formal Fallacies: Structural Invalidity

A formal fallacy is an argument whose form is invalid — it would be invalid regardless of the content of its premises. We already met two in Lesson 2: Affirming the Consequent: If P then Q; Q; therefore P. Example: 'If it snows, the roads are slippery. The roads are slippery; therefore it snowed.' The roads could be slippery from ice, oil, or rain. The conclusion does not follow. Denying the Antecedent: If P then Q; not-P; therefore not-Q. Example: 'If you study hard, you pass. You did not study hard; therefore you will not pass.' Passing without studying hard is perfectly possible. Undistributed Middle: All A are B; all C are B; therefore all A are C. Example: 'All terrorists are people who own knives. John owns a knife; therefore John is a terrorist.' Both groups share a property (knife ownership) without that making them the same group. This fallacy underlies a great deal of prejudiced reasoning. The formal fallacies can always be exposed by truth tables or counterexamples — just find a way to make the premises true and the conclusion false.

Informal Fallacies: Content-Level Errors

Informal fallacies are errors in the content, relevance, or framing of an argument rather than its logical structure. They are divided into several families. Fallacies of Relevance: The premises are simply irrelevant to the conclusion. - Ad hominem (attacking the person): 'You cannot trust her climate research — she drives an SUV.' The researcher's personal choices are irrelevant to the validity of her data and methods. - Appeal to authority (in improper form): 'This diet must work — a celebrity endorses it.' Celebrity status confers no nutritional expertise. - Appeal to the masses (ad populum): 'Millions of people believe it, so it must be true.' Popularity is not evidence of truth. - Red herring: Introducing an irrelevant distraction to derail the argument. Fallacies of Presumption: The argument assumes something it has not established. - Straw man: Misrepresenting an opponent's view in a weaker, easier-to-attack form. 'My opponent wants to reduce defense spending — she wants to leave the country defenseless.' - Begging the question (circular reasoning): The conclusion is already hidden in the premises. 'This book is reliable because it says so, and the book is reliable.' - False dichotomy: Presenting only two options when others exist. 'Either you support this policy completely, or you want chaos.' - Slippery slope (unsupported): 'If we allow X, then Y, then Z, and eventually catastrophe' — without showing that each step follows. Fallacies of Ambiguity: Exploiting unclear language. - Equivocation: Using the same word in two different senses. 'The law punishes criminals. Poverty is a crime. Therefore the law should punish poverty.' - Amphiboly: Exploiting grammatically ambiguous sentences.