====== Modus Bocardo ======

Form of a [[glossary:syllogism|syllogism]] based on the [[logic:inferences:modus_barbara:index|Modus Barbara]], in which a negative [[glossary:existential_quantification|existential]] proposition is inferred from another negative existential and a positive [[glossary:universal_quantification|universal]] proposition.

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<h3>Modus Bocardo</h3>
{{modus_bocardo.svg?nolink|Modus Bocardo}}
<figcaption>Type ''OAO'', Figure ''3'' <span noprint>[[app>#OA3O|Modus Bocardo]]</span> \\ Parent: [[logic:inferences:modus_barbara:index|Barbara]]</figcaption>
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> Some <abbr "middle term">M</abbr> are not <abbr "major term">P</abbr>.
> All <abbr "middle term">M</abbr> are <abbr "minor term">S</abbr>.
> <span conclusio>Therefore, some <abbr "minor term">S</abbr> are not <abbr "major term">P</abbr>.</span>

For example:

> Some <var>rectangles</var> are not <var>squares</var>.
> All <var>squares</var> are <var>polygons</var>.
> <span conclusio>Therefore, some <var>polygons</var> are not <var>squares</var>.</span>

The //Modus Bocardo// and the [[logic:inferences:modus_barbara:modus_baroco|Modus Baroco]] are the only two modes that require an indirect proof of validity in order to be reducible to their general form (the [[logic:inferences:modus_barbara:index|Modus Barbara]]). In fact, these two modes are identical, except that the premises are in reverse order.

===== Name =====

The name "Bocardo" is a [[wp>Mnemonic|mnemonic]] term that helps to remember the most important characteristics of this mode: The "B" at the beginning indicates that it is related to the [[logic:inferences:modus_barbara:index|Modus Barbara]], the two "o" stand for negative [[glossary:existential_quantification|existential]] and the "a" for an affirmative [[glossary:universal_quantification|universal]] statement. The "c" in the name indicates that the transformation to the basic form requires further proof of validity.

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

  * [[logic:inferences:modus_barbara:index|Modus Barbara]]
  * [[logic:inferences:modus_barbara:modus_baroco|Modus Baroco]]
  * [[glossary:syllogism|Syllogism]]

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