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Modus Ferio

A form of syllogism in which a new negative existential proposition is derived from a negative universal and an affirmative existential proposition.

No M is P.
Some S are M.
Therefore, some S are not P.

For example:

No square is a circle.
Some rectangles are squares.
Therefore, some rectangles are not circles.


The name “Ferio” is an artificial word describing the inference scheme: The “e” and “i” stand for a negative and positive universal quantifications, respectively, and the “o” for the negative existential quantification in the conclusion..

For more information on this naming scheme, and on syllogisms in general, see the article on syllogisms in the glossary.


The following forms are the variants of Modus Ferioand can all be transformed back to it:

See also

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