Affirming the consequent

Affirming the consequent is the invalid inference from “if P then Q” and Q to P. It mistakes a consequence of P for proof that P occurred.

Conditional statement: A statement asserting that one proposition holds whenever another proposition holds. The fallacy misuses the conditional by reversing its direction of support.
Denying the antecedent: The invalid inference from “if P then Q” and not P to not Q. It is the other common fallacy that mishandles a conditional’s direction.
Fallacy: A pattern of reasoning that fails to support its conclusion despite appearing persuasive. Affirming the consequent is a formal fallacy: its invalidity follows from its structure.
Proposition: A declarative statement that can be assigned a truth value, true or false. P and Q stand for propositions whose truth values determine whether the inference is valid.
Modus ponens: A valid inference form: from “if P then Q” and P, infer Q. It preserves the conditional’s direction, unlike affirming the consequent.
Affirming a disjunct: An invalid inference that concludes one disjunct is false from a true disjunction and the other disjunct’s truth. Like affirming the consequent, it confuses a relationship among propositions with stronger support than it provides.
Confirmation bias: The tendency to favor information that supports existing beliefs over information that challenges them. Treating confirming evidence as proof of a favored cause can encourage this inference.
Logical consequence: A relation in which premises guarantee a conclusion’s truth under every permitted interpretation. The premises of affirming the consequent do not logically entail its conclusion.
Modus tollens: A valid inference form: from “if P then Q” and not Q, infer not P. It uses the same conditional without mistaking Q for evidence sufficient to establish P.
Disjunctive syllogism: A valid inference that concludes one disjunct is true when the other is false and their disjunction is true. It shows a valid way to infer from a connective and information about one component.

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