Affirming the consequent

In propositional logic, affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "if the lamp were broken, then the room would be dark") under certain assumptions (there are no other lights in the room, it is nighttime and the windows are closed), and invalidly inferring its converse ("the room is dark, so the lamp must be broken"), even though that statement may not be true under the same assumptions. This arises when the consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room").^[1]

Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes.^[2]

The opposite statement, denying the consequent, is called modus tollens and is a valid form of argument.^[3]

^ Rosen, Kenneth H. "Discrete Mathematics and its Applications: Kenneth H. Rosen". ISBN 978-1260091991.
^ Lay, Steven. Introduction to Analysis with Proof, 5th edition. ISBN 978-0321747471.
^ Hurley, Patrick J. (2012). A Concise Introduction to Logic (11th ed.). Boston, Massachusetts: Cengage Learning. p. 362. ISBN 9781111346232. OCLC 711774631.

[1] Rosen, Kenneth H. "Discrete Mathematics and its Applications: Kenneth H. Rosen". ISBN 978-1260091991.

[2] Lay, Steven. Introduction to Analysis with Proof, 5th edition. ISBN 978-0321747471.

[Hurley2012-3] Hurley, Patrick J. (2012). A Concise Introduction to Logic (11th ed.). Boston, Massachusetts: Cengage Learning. p. 362. ISBN 9781111346232. OCLC 711774631.

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