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Modus Cesaro

Form of a syllogism based on the Modus Celarent, in which a negative existential proposition is inferred from positive and negative universal premisses.

No P is M.
All S are M.
[and there exists at least one S]*

Some S are not P.

For example:

No circle is a rectangle.
All squares are rectangles.
[and there exists at least one square]*

Some squares are not circles.

* Note: When an existential conclusion is inferred from universal premisses, this requires an (implicit or explicit) existential import, i.e. it must be proven that what the term refers to actually exists. In case of the Modus Cesaro it is sufficient to prove existence for the minor term (S), as this also implies existence of M, while the conclusion does not require existence for P.

Modus Cesaro is the weaker form of the Modus Cesare, which only infers an existential conclusion. Since every universal quantification that does not refer to an empty extension set always implies an existential quantification, this variation is possible, but this is of course also a weaker statement than the universal conclusion of the Modus Cesaro.

Name

The name “Cesaro” is a mnemonic term that helps to remember the most important characteristics of this mode: The “C” at the beginning indicates that it is related to the Modus Celarent, the “e” and “a” indicate the negative and affirmative universal statements in the premisses and the “o” indicates that the conclusion is a negative existential statement.

See also

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