Mixture distribution: Difference between revisions

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The [[formal fallacy]] of '''affirming a disjunct''' also known as '''the fallacy of the alternative disjunct''' or a '''false exclusionary disjunct''' occurs when a [[deductive logic|deductive]] argument takes the following [[logical form]]:
 
:A or B
:A
:Therefore, it is not the case that B
 
Or in [[logical operators]]:
 
:<math> p \vee q</math>
:<math> p </math>
:<math>{} \vdash {}</math> ¬ <math>q</math>
 
Where <math>{} \vdash {}</math> denotes a [[logical assertion]].  
 
==Explanation==
 
The fallacy lies in concluding that one [[disjunction|disjunct]] must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively. It is a fallacy of [[equivocation]] between the operations [[Logical_disjunction|OR]] and [[Exclusive_or|XOR]].
 
Affirming the disjunct should not be confused with the valid argument known as the [[disjunctive syllogism]].
 
==Example==
 
The following argument indicates the invalidity of affirming a disjunct:
 
:Max is a cat or Max is a mammal.
:Max is a cat.
:Therefore, Max is not a mammal.
 
This [[inference]] is invalid. If Max is a cat then Max is also a mammal. (Remember "or" is defined in an inclusive sense not an exclusive sense.)
 
:The car is red or the car is large.
:The car is red.
:Therefore, the car is not large.
 
The above example of an argument also demonstrates the fallacy.
 
==See also==
* [[Exclusive disjunction]]
* [[Logical disjunction]]
* [[Syllogistic fallacy]]
 
==External links==
 
* [http://www.fallacyfiles.org/afonedis.html Fallacy files: affirming a disjunct]
 
{{Formal fallacy}}
 
[[Category:Propositional fallacies]]
[[Category:Syllogistic fallacies]]

Revision as of 19:22, 24 February 2014

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