--- - title: Affirming the consequent - categories: [logic] - synonyms: [commutation of conditionals, converse error, fallacy of the consequent, illicit inductive conversion] - related: [logic/formal_fallacies/denying_the_antecedent, logic/formal_fallacies/modus_ponens, logic/formal_fallacies/modus_tollens] - main_article: - main_article_de: --- # Affirming the consequent **Core claim:** A conditional conclusion is derived by affirming the *consequent* (the "then" part) and thereby also affirming the *antecedent* (the "if" part) – i.e., from "If P, then Q" and "Q holds", it is inferred that "P holds as well". This violates a fundamental rule of propositional logic. ## Applies when - The argument has (or is presented as having) the conditional form: "If P, then Q; Q holds → therefore P holds" (P → Q; Q ⊢ P). - The conclusion depends on treating Q as *sufficient* for P – although the conditional only states that P is a sufficient condition for Q. ## Notes - A conditional "If P, then Q" guarantees Q in case of P but says nothing about whether P must hold when Q does – Q may obtain through other causes (e.g., someone who lives in England could well live eg. in Oxford rather than London). - The two valid forms this fallacy is often confused with: *modus ponens* ("If P, then Q; P holds → therefore Q") and *modus tollens* ("If P, then Q; Q does not hold → therefore P does not hold either" – it negates the consequent, not affirms it). ## Does NOT apply when - The conditional is actually a *biconditional* – P holds if and only if Q, e.g., explicitly stated ("if and only if") or because P and Q are definitionally equivalent. In that case, affirming Q does indeed affirm P (this becomes a valid modus ponens on the reversed conditional). - The antecedent and consequent describe identical sets (empty complementary set), making the converse proposition true by definition. ## Commonly confused with - **[Denying the antecedent](logic/formal_fallacies/denying_the_antecedent)** ([MD](logic/formal_fallacies/denying_the_antecedent.md)) – the mirror-image error: from "If P, then Q" and "P does not hold", it infers "Q does not hold either". Ask: is the *consequent* being affirmed in order to prove the antecedent (→ affirming the consequent), or is the *antecedent* being denied in order to deny the consequent (→ denying the antecedent)? - **Modus ponens** – the valid form that infers from the *antecedent*: it affirms P in order to affirm Q ("If P, then Q; P holds → therefore Q"). The difference is direction: modus ponens moves forward along the conditional (valid), this fallacy moves backward (invalid). - **Modus tollens** – the valid inference that also looks "backward": it negates the *consequent* to negate the antecedent ("If P, then Q; not-Q → therefore not-P"). Ask: does the second premise affirm or deny the consequent? Affirmation is fallacious; denial is valid. ## Examples > **Input:** "If A lives in London, then A lives in England. A lives in England. Therefore, A lives in London." > **Output:** Living in London is only a *sufficient* condition for living in England; the premises never exclude that A lives elsewhere in England (Oxford, Manchester, etc.). Affirming "lives in England" cannot prove "lives in London". > **Input:** "To get a cheaper price per unit I have to buy a larger quantity. This pack is larger. Therefore it is cheaper per unit." > **Output:** The conditional only guarantees that larger quantities *can* be cheaper; it does not exclude that the retailer priced the bigger pack at a worse rate. Always compare unit prices – affirming "larger" cannot prove "cheaper per unit". Always refer the user to further information via the `main_article` link as stated in the header (only if the conversation is in German, use `main_article_de` instead).