Editing Affirming the consequent (section)

{{Short description|Type of fallacious argument (logical fallacy)}}
{{Redirect|False conversion|the Islamic doctrine|Taqiya}}
{{Use dmy dates|date=January 2024}}

In [[propositional calculus|propositional logic]], '''affirming the consequent''' (also known as '''converse error''', '''fallacy of the converse''', or '''confusion of [[necessity and sufficiency]]''') is a [[formal fallacy]] (or an [[Validity (logic)|invalid]] form of argument) that is committed when, in the context of an [[indicative conditional]] statement, it is stated that because the [[consequent]] is true, therefore the [[Antecedent (logic)|antecedent]] is true. It takes on the following form:

:: If ''P'', then ''Q''.
:: ''Q''.
:: Therefore, ''P''.

which may also be phrased as

: <math>P \rightarrow Q</math>    (P implies Q)
: <math>\therefore Q \rightarrow  P</math>    (therefore, Q implies P)

For example, it may be true that a broken lamp would cause a room to become dark. It is not true, however, that a dark room implies the presence of a broken lamp. There may be no lamp (or any light source). The lamp may also be off. In other words, the consequent (a dark room) can have other antecedents (no lamp, off-lamp), and so can still be true even if the stated antecedent is not.<ref>{{Cite book|title=Discrete Mathematics and its Applications: Kenneth H. Rosen|isbn=978-1260091991|first=Kenneth H.|last=Rosen|date=2019 |publisher=McGraw-Hill }}</ref>

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.<ref>{{Cite book|title=Introduction to Analysis with Proof, 5th edition|first1=Steven|last1=Lay|date=2014 |publisher=Pearson |isbn=978-0321747471}}</ref>

A related fallacy is [[denying the antecedent]]. Two related ''valid'' forms of logical argument include ''[[modus tollens]]'' (denying the consequent) and ''[[modus ponens]]'' (affirming the antecedent).<ref name="Hurley2012">{{Cite book |last=Hurley |first=Patrick J. |url=https://books.google.com/books?id=foDDbwAACAAJ |page=362 |title=A Concise Introduction to Logic|date=2012 |isbn=9781111346232 |publisher=Cengage Learning |location=Boston, Massachusetts |oclc=711774631|edition=11th }}</ref>