Modus Calemos

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

All P are M.
No M is S.
[and there exists at least one S]*
Therefore, some S are not P.

For example:

All squares are rectangles.
No rectangle is a circle.
[and there exists at least one circle]*
Therefore, some circles are not squares.

The Modus Calemos is a weaker form of the Modus Calemes, in which the conclusion is an existential rather than a universal statement. This is possible since every universal quantification that does not refer to an empty extension set always implies an existential quantification, but this is of course also a weaker statement than the universal conclusion of the Modus Calemes.

The name “Calemos” 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 “a” and “e” indicates the affirmative and negative universal premisses, and the “o” that there is a negative existential conclusion.

• Modus Calemop

• Existential import
• Existential quantification
• Modus Celarent
• Syllogism
• Universal quantification