Editing Affirming the consequent (section)

==Formal description==
Affirming the consequent is the action of taking a true statement <math>P \to Q</math> and invalidly concluding its converse <math>Q \to P</math>. The name ''affirming the [[consequent]]'' derives from using the consequent, ''Q'', of <math>P \to Q</math>, to conclude the antecedent ''P''. This fallacy can be summarized formally as <math>(P \to Q, Q)\to P</math> or, alternatively, <math>\frac{P \to Q, Q}{\therefore P}</math>.<ref>Hurley, Patrick J. (2010), ''A Concise Introduction to Logic'' (11th edition). Wadsworth Cengage Learning, pp. 362–63.</ref>
The root cause of such a logical error is sometimes failure to realize that just because ''P'' is a ''possible'' condition for ''Q'', ''P'' may not be the ''only'' condition for ''Q'', i.e. ''Q'' may follow from another condition as well.<ref>{{cite web|url=http://www.fallacyfiles.org/afthecon.html|title=Affirming the Consequent|website=Fallacy Files|access-date=9 May 2013}}</ref><ref>{{cite book|title=Attacking Faulty Reasoning|last=Damer|first=T. Edward|publisher=Wadsworth|year=2001|edition=4th|page=150|chapter=Confusion of a Necessary with a Sufficient Condition |isbn=0-534-60516-8}}</ref>

Affirming the consequent can also result from overgeneralizing the experience of many statements ''having'' true converses. If ''P'' and ''Q'' are "equivalent" statements, i.e. <math>P \leftrightarrow Q</math>, it ''is'' possible to infer ''P'' under the condition ''Q''. For example, the statements "It is August 13, so it is my birthday" <math>P \to Q</math> and "It is my birthday, so it is August 13" <math>Q \to P</math> are equivalent and both true consequences of the statement "August 13 is my birthday" (an abbreviated form of <math>P \leftrightarrow Q</math>).

Of the possible forms of "mixed [[hypothetical syllogism]]s," two are valid and two are invalid. Affirming the antecedent ([[modus ponens]]) and denying the consequent ([[modus tollens]]) are valid. Affirming the consequent and [[denying the antecedent]] are invalid.<ref>Kelley, David (1998), ''The Art of Reasoning'' (3rd edition). Norton, pp. 290–94.</ref>