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Modus Darii

A form of syllogism in which a new affirmative existential statement is derived from general and existential statements.

All M are P.
Some S are M.
Therefore, some S are P.

For example:

All squares are rectangles.
Some rhombuses are squares.
Therefore, some rhombuses are rectangles.


The name “Darii” is a mnemonic term, in which the vowels (a-i-i) indicate that the first premise is an affirmative universal quantification (type “a”), and that the second premise as well as the conclusion are both affirmative existential quantifications (type “i”).

Although there is an existential statement inferred from a universal proposition in this form, no further proof of existence is needed, as the minor statement already implies existence at the intersection of S and M.

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 Darii and can all be transformed back into it:

See also

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