Affirmative conclusion from a negative premise

{{logicnav}}{{hatnote|Not to be confused with [[negative proof]] or [[negative conclusion from affirmative premises]].}}
An '''affirmative conclusion from a negative premise''' (also '''illicit negative''') occurs when a categorical [[syllogism]] has a positive conclusion, but one or two negative premises.

It is a [[syllogistical fallacy]] and a [[formal fallacy]].

==Forms==
An affirmative conclusion from a negative premise can take three forms:

'''First form:''' (single "not", second premise)
{{syl
|2=Some A are B.
|4=Some B are not C.
|5=C|6=Some A are C.
}}

'''Second form:''' (single "not", first premise)
{{syl
|2=Some A are not B.
|4=Some B are C.
|5=C|6=Some A are C.
}}

'''Third form (called "exclusive premises"):''' (double "not")
{{syl
|2=Some A are not B.
|4=Some B are not C.
|5=C|6=Some A are C.
}}

===Legitimate use===
It is acceptable to have an affirmative premise and a negative premise ''as long as the conclusion is negative''. The only problem is when the conclusion is positive. Two examples make this clear:

'''Negative conclusion:'''<ref name=DL />
{{syl
|2=All farmers produce excess food.
|4=All city dwellers do not produce excess food.
|5=C|6=All city dwellers are not farmers.
}}

'''Positive conclusion:'''<ref name=DL>[https://web.archive.org/web/20160222141345/http://debatelogic.com/affirmative-conclusion-negative-premises/ Affirmative conclusion from negative premises] ''Debate Logic'' (archived from February 22, 2016).</ref>
{{syl
|2=Some city dwellers are not hungry.
|4=Some hungry people are farmers.
|5=C|6=Some city dwellers are farmers.
}}

==Problem==
The fallacy is invalid because any valid categorical syllogism with one (or more) negative premise(s) must have a negative conclusion.

==Examples==
{{syl
|2=No [[cats]] are marsupials.
|4=Some [[mammals]] are not cats.
|5=C|6=Some mammals are marsupials.<ref>http://www.fallacyfiles.org/afromneg.html</ref>
}}

{{syl
|2=No people under the age of 66 are senior citizens.
|4=No senior citizens are [[children]].
|5=C|6=All people under the age of 66 are children.<ref>http://www.logicallyfallacious.com/index.php/logical-fallacies/14-affirmative-conclusion-from-a-negative-premise</ref>
}}

{{syl
|2=All [[birds]] are [[reptiles]].
|4=[[Humans]] aren't birds.
|5=C|6=Therefore, humans are reptiles.
}}
::The exclusion of 'humans' from the 'birds' category gives no reason to include humans in the 'reptile' category. It is easily proven false by finding an example that disproves the conclusion, but doesn't invalidate the premises, such as finding a human that isn't a reptile.

{{syl
|2=[[Atheists]] are not good.
|4=[[Christians]] are not atheists.
|5=C|6=Thus, Christians are good.<ref name=IC>https://religions.wiki/index.php?title=Affirmative_conclusion_from_a_negative_premise</ref>
}}

{{syl
|2=[[Evolution]] is not true.
|4=[[Intelligent design]] is not evolution.
|5=C|6=Therefore, intelligent design is true.<ref name=IC />
}}

{{syl
|2=No [[fish]] are [[dog]]s.
|4=No dogs can fly.
|5=C|6=Therefore, all fish can fly.<ref name=WP>{{wpa|Affirmative conclusion from a negative premise}}</ref><ref name=FAD>http://fallacyaday.com/2011/08/affirmative-conclusion-from-a-negative-premise/</ref>
}}

{{syl
|2=We don't read that trash.
|4=[[No True Scotsman|People who read that trash don't appreciate real literature]].
|5=C|6=Therefore, we appreciate real [[literature]].<ref name=WP /><ref name=FAD />
}}

{{syl
|2=All mice are animals.
|4=Some animals are not dangerous.
|5=C|6=Therefore, some mice are dangerous.<ref name=One>http://onegoodmove.org/fallacy/dacnp.htm</ref>
}}

{{syl
|2=No honest people steal.
|4=All honest people pay [[taxes]].
|5=C|6=[[Non sequitur|Ergo, some people who steal pay taxes]].<ref name=One />
}}

==See also==
*[[Negative conclusion from affirmative premises]], in which a syllogism is invalid because the conclusion is negative yet the premises are affirmative

==External links==
*{{wpa|Affirmative conclusion from a negative premise}}
*{{wpa|Fallacy of exclusive premises}}
*[http://www.fallacyfiles.org/exclprem.html Fallacy of Exclusive Premises] — [[Fallacy Files]]
*[http://www.logicallyfallacious.com/index.php/logical-fallacies/82-exclusive-premises Exclusive Premises] — Logically Fallacious
*[http://philosophy.lander.edu/logic/conclusion_fall.html Syllogistic Fallacies: Affirmative Conclusions from a Negative Premiss], Philosophy.Lander.edu

==References==
{{reflist|2|80%}}

[[Category:Formal fallacies]]

Categories: Formal fallacies