====== Negative conclusion from affirmative premises ======

A [[logic:formal_fallacies:index|formal fallacy]], in particular in [[glossary:syllogism|syllogisms]], where a negative conclusion is (erroneously) inferred from affirmative premises.

For example<span no-print> [[app>#AA4O|Open in Syllogism-Finder App]]</span>:

> All <var>squares</var> are <var>rectangles</var>.
> All <var>rectangles</var> are <var>tetragons</var>.
> <span conclusio><s invalid "Negative conclusion from affirmative premises">Therefore, Some <var>tetragons</var> are not <var>squares</var>.</s></span>

===== Description =====

In principle, no negative conclusions can be drawn from exclusively affirmative (positive) premises. Therefore, a negative conclusion from exclusively affirmative premises is invalid.

===== When are such conclusions valid =====

In a certain cases, affirmative statements (especially all-propositions) can be //transformed// into negative statements (e.g. "all <var>A</var> are <var>B</var> " is equivalent to "no <var>A</var> is not-<var>B</var> "). However, this should be done before formulating the inference and not implicitly.

===== See also =====

  * [[glossary:syllogism|Syllogism]] – underlying form of inference.
  * [[logic:formal_fallacies:affirmative_conclusion_from_negative_premise|Affirmative conclusion from a negative premise]] – Similar form of fallacy.
  * [[logic:formal_fallacies:exclusive_premises|Fallacy of exclusive premises ]] – Reversal of this form of fallacy.

===== More information =====

  * [[wp>Negative conclusion from affirmative premises]] on //Wikipedia//
  * [[https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/133/Negative-Conclusion-from-Affirmative-Premises|Negative Conclusion from Affirmative Premises]] on //Logically Fallacious//
  * [[http://www.fallacyfiles.org/negfroma.html|Negative Conclusion from Affirmative Premisses]] on //Fallacy Files//